New Wave Maths - Teachers Guides: Level B - Ages 6-7 by Teacher Superstore

RIC–1085 11.2/587

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New Wave Maths Teachers Guide – B Published by R.I.C Publications® PO Box 332, Greenwood Western Australia 6924

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Robert Dayman 2003

RIC-1085 ISBN 978-1-86311-706-7 Copyright Notice No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system without written permission from the publisher.

Foreword The New Wave Maths Teachers Guide has been written to both supplement and support the New Wave Maths Workbook series based on the Western Australian Mathematics Student Outcome Statements.The New Wave Maths Teachers Guide provides a summary of three documents that are at the forefront of mathematical teaching and learning:

• Curriculum Frameworks;

• Student Outcome Statements; and

• National Outcome Statements.

Between the New Wave Maths Teachers Guide and the New Wave Maths Workbook, there is a comprehensive coverage of activities to assist the development of the students' mathematical concepts. However, student progress is very much in the hands of the teacher, his or her style of teaching and the provision made for each individual to ensure complete mastery of concepts is gained.

r o e t s Bo r e p ok u S This series caters for:

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Assessment followed in this series is consistent with the approach outlined within the appropriate section in the Curriculum Framework document.

• sharing ideas through discussion;

• school–home partnerships through parent information sheets;

• mixed ability groups through the use of challenge activities; and

• the use of concrete materials where required by teachers and students.

R.I.C. Publications has a recommended range of blackline masters that, together with New Wave Maths, will ensure a thorough coverage of the mathematics outcomes and further develop the students' mathematical competency at this level.

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The author and publisher wish to acknowledge the Education Department of Western Australia for its permission to reproduce selected information contained within this document.

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References Learning Mathematics Handbook: Pre-primary to Stage Seven Mathematics Syllabus, Curriculum Programs Branch, Ministry of Education, Perth, WA – 1989 Learning Mathematics Pre-Primary to Stage Seven, Curriculum Programs Branch, Ministry of Education, Perth, WA – 1989 Curriculum Framework, Curriculum Council of Western Australia, Perth, WA – 1998 A National Statement in Mathematics for Australian Schools, The Australian Education Council and Curriculum Corporation, Australian Education Council, Carlton, Vic. – 1991 Mathematics – Student Outcome Statements, Education Department of Western Australia, 1998

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New Wave Maths Book B – Teachers Guide • i •

Contents Introduction..........................................................................................................................................................1 Appreciating Mathematics............................................................................................................................2 Learning Environment.....................................................................................................................................3 Language and Mathematics..........................................................................................................................4 Mixed Abilities.....................................................................................................................................................4 General Content Outline................................................................................................................. 5 – 10 Technology......................................................................................................................................................... 11 Assessment........................................................................................................................................................ 12 Cross-curriculum Linkages........................................................................................................................ 13 How to Use the Teachers Notes.......................................................................................................... 16 Materials List...................................................................................................................................................... 17 Overview of Activities Term One—Units 1 – 10..................................................................................................................... 18 Term Two—Units 11 – 20................................................................................................................... 19 Term Three—Units 21 – 30................................................................................................................ 20 Term Four—Units 31 – 40.................................................................................................................. 21 Lesson Notes, Consolidation and Answers Term One—Units 1 – 10..........................................................................................................22 – 61 Term Two—Units 11 – 20.....................................................................................................62 – 101 Term Three—Units 21 – 30...............................................................................................102 – 141 Term Four—Units 31 – 40.................................................................................................142 – 181

r o e t s Bo r e p ok u S Additional Activities

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Teachers Notes and Answers

Space Activities...............................................................................................................................184 – 185 Measurement Activities..............................................................................................................186 – 187 Number Activities....................................................................................................................................... 188

Assessment

Grid Paper.........................................................................................................................................198 – 201 Number Cards, Lines and Charts........................................................................................202 – 209 Place Value Charts....................................................................................................................................... 210 Spinners .............................................................................................................................................211 – 212 Calendar – Any year..................................................................................................................................... 213 Clocks................................................................................................................................................................. 214 Money................................................................................................................................................................ 215 Bingo Cards.......................................................................................................................................216 – 219 Classification Chart.................................................................................................................................... 220 Sorting Circles............................................................................................................................................... 221 Capacity Labels............................................................................................................................................. 222 Venn Diagram – Blank............................................................................................................................... 223 Carroll Diagram – Blank..................................................................................................................................................224 Line or Bar Graph – Blank............................................................................................................................................225 Graph and Table – Blank........................................................................................................................... 226 2-D Shapes........................................................................................................................................227 – 228 3-D Shapes...................................................................................................................................................... 229 Tangrams........................................................................................................................................................... 230 Map...................................................................................................................................................................... 231

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Reference to Student Outcomes....................................................................................................... 190 Record Sheets – Blank.................................................................................................................191 – 195 Proforma – Blank.......................................................................................................................................... 196

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Expectations of Knowledge of Basic Facts.................................................................................... 234 Primary School Mathematics..................................................................................................235 – 236 Problem-solving Strategies..................................................................................................................... 237 Concrete to Mental................................................................................................................................... 238 Mathematical Learning Areas................................................................................................................ 239 Homework Policy........................................................................................................................................ 240 • ii • New Wave Maths Book B – Teachers Guide

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Introduction Mathematics provides methods of representing patterns, relationships and logic and developing mathematical knowledge. Students should be encouraged to speculate, observe and investigate, to explore and solve problems in mathematics in real-life situations. Mathematics is important to people in providing tools which can be used at the personal, civic and vocational level. A National Statement on Mathematics for Australian Schools, 1990 (pages 11 – 14) lists the following goals for school mathematics: 1. Students should develop confidence and competence in dealing with commonly occurring situations. 2. Students should develop positive attitudes towards their involvement in mathematics.

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3. Students should develop their capacity to use mathematics in solving problems individually and collaboratively. 4. Students should learn to communicate mathematically. 6. Students should exercise the processes through which mathematics develops. A National Statement in Mathematics for Australian Schools, 1990 (page 15) continues in goal identification by determining, that as a result of learning mathematics in school, all students should:

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5. Students should learn techniques and tools which reflect modern mathematics.

1. realise that mathematics is relevant to them personally and to their community; 2. gain pleasure from mathematics and appreciate its fascination and power; 3. realise that mathematics is an activity requiring the observation, representation and application of patterns; 4. acquire the mathematical knowledge, ways of thinking and confidence to use mathematics to:

(a) conduct everyday affairs such as money exchanges, planning and organising events, and measuring;

(b) make individual and collaborative decisions at the personal, civic and vocational levels; and

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5. develop skills in presenting and interpreting mathematical arguments; 6. possess sufficient command of mathematical expressions, representations and technology to:

(a) interpret information (for example, from a court case or media report) in which mathematics is used;

(b) continue to learn mathematics independently and collaboratively; and

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(a) that mathematics is a dynamic field with its roots in many cultures; and

(b) its relationship to social and technological changes.

New Wave Maths Book B – Teachers Guide • 1 •

Appreciating Mathematics The following attitudes are seen as fundamental to the acquisition of processes and content and should be the focus of mathematical development.The attitudes are listed in Learning Mathematics Pre-Primary to Stage Seven Mathematics Syllabus Handbook (pages 6 – 7) as: 1. an awareness of the relevance of mathematics to life; 2. an ability to enjoy mathematical games and pursuits; 3. having pride in their skills and abilities; 4. being confident of their ability to experiment and solve problems; and 5. a willingness to express ideas and hypotheses. These are summarised as part of the Appreciating Mathematics substrand found in The Curriculum Framework 1998 (page 180):

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The development of positive attitudes towards mathematics is an important goal. This may be done by:

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1. Show a disposition to use mathematics to assist with understanding new situations, solving problems and making decisions, showing initiative, flexibility and persistence when working mathematically and a positive attitude to their own continued involvement in learning and doing mathematics.

1. providing mathematical experiences relevant to the students' world;

2. providing students with mathematical opportunities to gain personal enjoyment and satisfaction; 3. providing activities which construct conceptual understanding through manipulation of materials and time to reflect on the activities; 4. allowing free discussion of mathematical experiences;

5. providing mathematical activities which are appropriate to the students' levels of development; 6. recognising that students require differing amounts of time to complete tasks as they explore problems and ideas in a variety of ways; 7. assessment that reflects the teaching methods used; and

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8. modelling positive attitudes towards mathematics.

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• 2 • New Wave Maths Book B – Teachers Guide

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Learning Environment Much has been learnt about how students learn mathematics and the classroom conditions required to support that learning. The teaching of mathematics requires a suppor tive, stimulating, varied and rich mathematical learning environment that reflects the diversity of Australian society.There should be a wide range of resources that includes collected and commercial products.The classroom learning environment should encourage practical activity, the use of appropriate technology and discussion. Mathematics lessons should extend beyond a ‘chalk and talk’ or ‘textbook, pencil and paper’ subject. The Curriculum Framework, 1998 (pages 206 – 209) highlights the following perspectives on learning mathematics:

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• Opportunity to learn

Learning experiences should enable students to engage with, observe and practise the actual ideas, processes, products and values which are expected of them. • Connection and challenge

Learning experiences should connect with students’ existing knowledge, skills and values while extending and challenging their current ways of thinking and acting.

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• Action and reflection

Learning experiences should be meaningful and encourage both action and reflection on the part of the learner.

• Motivation and purpose

Learning experiences should be motivating and their purpose clear to the student.

• Inclusivity and difference

Learning experiences should respect and accommodate differences between learners.

• Independence and collaboration

Learning experiences should encourage students to learn both from, and with, others as well as independently.

• Supportive environment

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The school and classroom setting should be safe and conducive to effective learning. These perspectives have several implications for teaching. They are listed as:

• a supportive environment for learning;

• appropriate mathematical challenge is provided; and

• fostering processes which enhance learning.

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The teaching of mathematics is not definitive in approach or style but rather is influenced by the mathematical concept being taught, and the abilities, experiences and attitudes of the students. Enhanced mathematical learning is likely to occur when activities are provided which build upon and respect students’ experiences, and which the learner regards as purposeful and interesting. Feedback is critical to enhanced learning. Students need to believe that mathematics makes sense; therefore, clear and logical feedback on errors or inconsistencies is required. Students should be encouraged to take risks in a challenging environment to extend their knowledge. Challenges need to be achievable as success is critical in building positive attitudes towards mathematics. Success on easy or rote tasks does not enhance mathematical learning.

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New Wave Maths Book B – Teachers Guide • 3 •

Language and Mathematics Developing appropriate language is important to the growth of a student’s conceptual understanding. Teachers need to be aware of the natural language used by students and respond appropriately to it. To assist in developing an understanding of mathematical ideas, students need to represent their knowledge in spoken and written words, with concrete materials and with pictures; diagrams and graphs; and symbols. The use and development of appropriate language should also enhance mathematical learning. The use of appropriate language helps in working through and clarifying ideas.

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Mathematical ideas are more likely to be developed when they are clearly labelled when discussed by students. Regular, clear and explicit use of mathematical expressions by the teacher is essential. Students should be encouraged to develop their knowledge and understanding of mathematical expressions by being encouraged to describe orally or in writing the situations in which they are involved.

Mixed Abilities© R. I . C.Publ i cat i ons

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Teachers need to be aware of the individual differences of all students and provide learning experiences which develop a level of success and independence for each student. To do this, teachers plan lessons that build on current knowledge and allow progress and success at the students’ own rate. New concepts should be introduced in simple form leading to the complex by using concrete materials and relevant examples.Where possible, use group work to allow for content language and ability differences. Keep parents well informed of their child’s progress and work with them to aid students in reaching their potential. Above all, provide a positive, receptive learning environment, acknowledging various differences. Students with special needs can be catered for by ensuring that fundamental concepts are understood before proceeding with dependent concepts. The identification of the initial point of difficulty must be made and the concept then developed from this stage. Instructions need to be given slowly, simply and clearly and then checked for understanding.

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New Wave Maths allows individuals to achieve at their own rate by providing a number of similar activities.The series may also be used at differing stages of students’ development so the workbook chosen is level-appropriate rather than Year-level specific, because each book is sequentially developmental with both the previous and following book. By allowing students to work to their capacity on activities, teachers are also able to provide the learning opportunities for individual students to perform at their optimum level.

• 4 • New Wave Maths Book B – Teachers Guide

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General Content Outline Goals and Guidelines Once Year 1 has been completed and is understood, students may then proceed to Year 2. Students learn at different rates and in different ways and bring to school a diverse range of attitudes and experiences from living within different cultural and geographic settings. Because of this, we require uncommon curriculums to achieve common outcomes. Young students develop strong mathematical values if activities recognise the mathematics inherent in home activities. Activities should use a wide variety of materials and be presented in a problem-solving format that has meaning to the child.

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Students now begin to think beyond visual perception and start to think operationally, but they still need concrete experiences to aid learning. During this stage they are able to conserve both number and length.

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Mathematical thinking will reflect, in most instances, the student's family as this is the centre of his/her personal world. Many cultural beliefs will reinforce the values shown by students at this age. Strengths in spatial knowledge and number should be utilised as starting points for the development of mathematical ideas.

In all activities the development of mathematical language should be a key focus. Students should be encouraged to question mathematically aspects of their world and seek to answer such questions themselves, or in collaboration with their peers. Students should be encouraged to persist with problems and ask questions. They are also more able to think of concepts as mathematical objects in their own right. With teaching emphasising the investigation of mathematical ideas and relationships, students should also be learning to make speculations and test them.

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The teaching of processes is necessary to develop independent problem-solvers.Therefore, for students to acquire concepts, skills and factual knowledge, opportunities need to be provided in settings that foster positive attitudes to mathematics.The Curriculum Programs Branch, Ministry of Education, 1989, publication Learning Mathematics: Pre-Primary to Stage Seven Mathematics Syllabus Handbook (page 4) lists the following processes as part of the learning of mathematics. These processes are not tied to one particular aspect of content but are used across a range of areas: 1. comprehension of mathematical information given in oral and/or written forms; 2. selection of appropriate strategies; 3. purposeful use of materials;

4. selection of appropriate operations to solve problems;

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6. expression of mathematical ideas in words, pictures and symbols; 7. construction of lists, tables and graphs;

8. estimation of number and measurement activities; 9. identification of patterns and relationships; 10. classification, ordering and comparing;

11. analysis and interpretation of information; 12. formulation of hypotheses; and 13. justification of conclusions and inferences. Understanding, skills and knowledge relationships make up the content that builds up conceptual structures.

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New Wave Maths Book B – Teachers Guide • 5 •

In the New Wave Maths series the following areas of mathematical content are included:

1. Working Mathematically – develops mathematical thinking processes through conceptualising, investigating, applying and verifying and reasoning mathematically.

2. Space – describes and analyses the features of objects, environments and movements through location, shape, transformations and geometric reasoning.

3. Measurement – using direct and indirect measurement and estimation skills in length, area, mass, volume and capacity and time.

4. Chance and Data – using knowledge of chance and data processes to collect and organise data, summarise and represent data, interpret data and understand chance.

5. Number – using operations, number concepts and relationships in the number system to calculate, reason about number patterns and understand numbers and operations.

r o e t s Bo r e p ok u S Appreciating Mathematics

Students appreciate mathematics through using it to assist with understanding new situations, solving problems and decision making, and show a positive attitude in learning and doing mathematics. They should also recognise mathematical origins from a range of cultures, its significance in reflecting social and historical contents and understand its significance in explaining and influencing aspects of our lives.

Working Mathematically

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The Curriculum Framework, 1998 (pages 183 – 193) identifies seven clusters of outcomes, some of these being:

Activities should be focused on the students’ world with simple activities that may be represented pictorially or with objects. Through constant exposure and manipulation of objects, students become familiar with patterns which they are able to copy and continue; follow provided rules; create their own mathematical patterns; and describe the rules which produce them. While success is important, students should also be challenged and encouraged to experiment with new ideas and to persist with difficult tasks.

Problem-solving

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The development of mental strategies for use in problem-solving is important as is the development of a range of learning activities using physical materials, pictures, learning activities using physical materials, pictures, calculators and some informal paper and pencil strategies.

The classroom teacher has an important role in the development of processes used in problem-solving.Through guidance, discussion and experimentation, students are able to adopt different strategies to solve problems and appreciate that there is more than one approach to a solution. The following broad strategies may be of assistance in helping students solve non-routine problems:

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1. Understand the problem – rewording, breaking into smaller parts may assist. 2. Prepare a plan to solve the problem – working from the known to the unknown, draw diagrams, tables, charts to assist. 3. Carry out the plan – using different strategies as appropriate. 4. Review final solution to check and discuss its reliability and validity.

• 6 • New Wave Maths Book B – Teachers Guide

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By asking questions of the student, providing hints (without providing answers), having students suggest strategies, guiding discussion and comparison of strategies used and providing extension to the original problem, the teacher helps the students develop processes which allow generalisation to a variety of other situations. It is the teacher’s responsibility to provide experiences which contribute to the construction of each student’s mathematical understanding. Each student is an individual with different experiences and knowledge.The teacher should recognise that because of this the student may interpret the teaching in a different way.

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Students move through a number of phases as they develop understanding. Students manipulate the materials and work through activities guided by open-ended questioning and discussion. The activities are explored by the students using the processes as listed in Learning Mathematics Pre-Primary to Stage Seven Mathematics Syllabus Handbook, 1989 (pages 16 – 18):

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In accepting the individuality of each student, teachers should also accept that students will interpret teaching in different ways and need new content to be presented by easily understood, believable methods and for that content to be seen as more useful than knowledge already held. Knowledge that students already hold is important to later learning and should be used as the basis for subsequent teaching through learning activities which are relevant to the students’ environment. Encouragement of discussion within the class allows for reflection on experiences and understanding. Where students lack the skills required to complete a task satisfactorily, more effective alternative methods that nurture their understanding need to be used.

1. observing and identifying; 2. comparing, ordering and classifying; 3. making patterns and arrangements;

5. estimating and measuring; 6. recording and calculating;

7. inferring, predicting and hypothesising; and 8. discussing what they are doing.

Following this the students express, represent and interpret their workings by:

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2. identifying patterns and relationships; 3. using symbols and words; 4. drawing pictures, diagrams and graphs; 5. constructing models;

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1. discussing findings and interpretations;

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9. interpreting results; and

10. communicating findings.

Then follows a period of consolidation of understanding through further activities that embody the mathematical idea. Students should apply and extend their understanding through work in familiar, and then more novel, contexts.

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New Wave Maths Book B – Teachers Guide • 7 •

Number Students should be able to count in one-to-one correspondence situations, develop cardinal and ordinal concepts to ten as well as be able to combine and separate small sets of objects in informal settings. The New Wave Maths series focuses heavily on these activities and on developing the use of number sequence to determine the number of items in the set. There are also extensive activities requiring the combination and partitioning of numbers to assist the development of the value of a number as a composition of other numbers. Students at this stage need a lot of varied experiences using concrete materials, involving estimating, counting, ordering, classifying, sorting and comparing.

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During Year 2, students should have experienced, through discovery, all the basic facts of addition and subtraction. Book B in the New Wave Maths series provides this experience in both practical and symbolic form. An initial introduction to grouping and sharing activities is also provided.

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Students continue to be introduced to experiences with larger numbers through grouping and trading activities. Multi-base Arithmetic Blocks (MAB) should be used to represent numbers. To further develop understanding of symbolic representation, the calculator is a valuable tool.The calculator also aids in the recognition of decimal numbers in symbolic format.

Recommended Progression for Algorithms Year 1

• Use concrete materials to manipulate and arrange objects with either oral or written answer in addition and subtraction.

• Sharing objects in practical situations.

• Using basic facts to 9 + 9 = 18 and adding three numbers each less than 6. It is recommended that concrete materials are used.

• Symbol ‘x’ is introduced to assist with grouping. Use of language to support activities – ‘lots of ’, ‘sets of ’ or ‘groups of ’ to 20 or 30.

• Division experience is through sorting, sharing and grouping activities using concrete materials.

• Introduction to open number sentences. For example:

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4–1=

3 lots of 4 =

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Year 3

• Activities without regrouping may be done without concrete materials; for example: 4 +5

17 +2

372 + 416

54 – 22

469 – 217

• Addition and subtraction requiring regrouping should be done with the assistance of concrete materials, particularly Base 10 MAB; for example:

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18 + 19 =

21 + 14 + 37 =

256 + 48 =

329 + 257 =

76 – 25 =

100 – 60 =

700 – 300 =

638 – 73 =

• Use Base 10 MAB and other concrete materials for multiplication; for example:

40 x 2 =

42 =

34 x 2 =

200 =

6 x 100 =

30 x

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21 23 + 14

• All subtraction working out must start with top line number; for example, 9 take 7 equals 2. 36 – 3

43 + 24

x 21

x 40

= 90

• Division is set out as shown in the examples below. 6 4 24

24 ÷ 4 = 6

Measurement © R. I . C .Publ i cat i ons •f orr evi ew pur posesonl y•

Initially, students will make judgments of more or less, bigger or smaller and equal to or not equal to when applying measurement of objects. Students will need to be guided to an awareness of the attributes of length, area, mass, capacity and time in order to make appropriate comparisons. A wide and continuous range of activities is an integral component of the program.

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Development of the language of mathematics will take time but is an essential part of the learning process. Language is developed as part of the direct comparison of objects. Encouragement in estimation and checking will assist in developing students’ preparedness to make educated guesses and develop the habit of checking for accuracy. Students begin to conserve length and are therefore able to progress from the direct comparison of objects to measuring length using arbitrary units and, eventually, to standard units. Students should also be able to use standard units of measurement to measure time.

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Students should undertake activities in measuring capacity by using arbitrary units both for estimation and for practical measuring.

New Wave Maths Book B – Teachers Guide • 9 •

Chance and Data Students are able to use and understand the language of chance and from this make a statement about the likelihood an event will occur. Students are to be able to plan and undertake data collection and then to organise, summarise and represent data for effective and valid interpretation and communication. Students are able to locate data that has been published, interpret, analyse and draw conclusions from this data taking into account data collection techniques and chance processes involved. In the New Wave Maths series, students are directed to make sensible judgments about the quality of the data and then to make a decision and draw inferences from the data. Chance and data work should focus on collecting, representing and interpreting data. Data collection activities should lead to classification, organisation, summarising and displaying in a variety of ways.

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Classification skills are developed through a variety of activities. Where practical, students are asked to record and represent data. Students are directed to construct graphs or represent data in a format that is logical and easy to read.

Space

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In the New Wave Maths series, students are introduced to activities that include an element of unpredictability and refine their use of some of the everyday language of chance.

Students are to recognise shapes as well as visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them. Using their knowledge of shapes, transformations and arrangements, students are able to solve problems and justify solutions. Space activities should emphasise the investigation of the features of objects in the environment, including their shape and the effect on them of changes in shape, size and position, and include symmetry and tessellations.

The features of objects should be emphasised in space activities. Relationships between three-dimensional shapes and two-dimensional shapes are represented by nets, diagrams and scale models. Sorting and classifying of shapes continues.

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The New Wave Maths series develops space exploration of the students’ own environment and objects within it. By manipulating materials in a variety of ways students learn to observe and describe them in everyday language.

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• 10 • New Wave Maths Book B – Teachers Guide

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Technology Calculators are an important technological resource in the teaching and learning of mathematics. The calculator should be used as both an instructional aid and as a computational tool. With the advent of cheaper and more sophisticated calculators there comes a natural deemphasis on written calculations.There is, as a consequence, a reduction in the complexity of written computation work but a clear emphasis on the use of concrete material to improve understanding of concepts to be developed through the New Wave Maths series. Greater emphasis is placed on quick and accurate mental computation. Students' expected level of written computational skill is to a two-digit by two-digit multiplication, addition or subtraction sum, and a single divisor into a two-digit number for division.

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Mental calculations and calculator use need to be developed as these form the basis of most computational needs of adults in real-life situations. It is strongly recommended that all students use calculators at all Year levels (K–12). The Learning Mathematics Handbook Pre-Primary to Stage Seven Mathematics Syllabus, 1989 (pages 30 – 31) details where calculators can be used as an instructional aid to:

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An emphasis on knowledge of basic addition and multiplication facts and relationships, place value understanding, estimation, checking of results and confidence in applying appropriate calculations is essential.

• assist in the development of mathematical content and processes; for example, place value, multiplication as repeated addition and the learning of basic facts;

• provide immediate feedback on a student’s own calculation so errors and misunderstandings can be remedied; and

• improve attitudes towards mathematics through its effective use.

• enable attention to focus on mathematical processes by allowing calculations to be done swiftly and accurately by all children; for example, in problem-solving or investigative activities;

• enable rules or patterns to be discovered and investigated, by generating many examples in a short time;

• encourage students to employ a wider range of strategies to solve problems; and

• allow students to use data drawn from real life, rather than artificial numbers chosen to make the computation easier; for example, in exploring distances or costs of shopping.

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As a computational aid, the calculator can:

Computers also have their place in the mathematical learning environment and should be accorded appropriate time. Computers may be used for ‘number crunching’ and data analysis; as a simulation device; for graphics and symbol manipulation; and for running spreadsheets.

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Teachers need to select software which is sufficiently flexible and open-ended to allow children to develop their own ideas and use their initiative. The computer can be used in problem-solving, investigations, modelling, strategy games, refining ideas, concept development, skill development and gaining factual knowledge.

There is still a place for textbooks in the teaching and learning of mathematics. However, emphasis must be placed on the need to use a variety of print materials. No single text is likely to cater for the interests of all students or cover the mathematics curriculum in full. The New Wave Maths series provides a solid foundation and allows teachers the opportunity to add their own ideas and activities to suit their individual class and students.

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New Wave Maths Book B – Teachers Guide • 11 •

Assessment Assessment is a critical component of the teaching program and is outlined in The Curriculum Framework, 1998 (pages 210 – 212) by these points:

• Valid

Assessment should provide valid information on the actual ideas, processes, products and values which are expected of students.

• Educative

Assessment should make a positive contribution to students' learning.

• Explicit

Assessment criteria should be explicit so that the basis for judgments is clear and public.

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• Fair

Assessment should be demonstrably fair to all students and not discriminate on grounds that are irrelevant to the achievement of the outcome. • Comprehensive

Judgments on student progress should be based on multiple kinds and sources of evidence.

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Assessment is a crucial aspect of the mathematics learning process. Assessment provides feedback on individual development to the student, teachers and parents. It provides the information for future teaching. All the outcomes of the school mathematics curriculum should be reflected in the assessment process. All assessments should be demonstrably fair, valid and reliable. The fairness of mathematical testing is brought into question by the practice of using one form of test only. Individual students respond to different environments in different ways; therefore the use of a single assessment tool, such as a pencil and paper test, may be valid and reliable but not fair, as the individual may respond better to short-answer questions, extended response questions or other forms of assessment. Hence, using nonrepresentative sampling of the mathematics curriculum outcomes or narrow sampling methods of assessment may be unfair to many students.

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It is clearly understood now that conventional forms of tests (pencil and paper) cannot address all areas of the mathematics curriculum; therefore, additional, not alternative, methods of assessment must be developed. Such methods include: teacher observation and questioning; structured interviews with students; paper and pencil tests; oral tests; practical skill tests; work- or project-based assessment; collected samples of students’ independent work; individual homework assignments; group reports; anecdotal records; self-assessment; and peer assessment.

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It is recommended that students’ mathematics be assessed using the Student Outcome Statements. Commercially prepared assessment packages are available from R.I.C. Publications® as follows: Maths Assessment Level 1 (RIC-0028) Maths Assessment Level 2 (RIC-0029) Maths Assessment Level 3 (RIC-0030) Maths Assessment Level 4 (RIC-0087)

Where possible, links to these pages have been included in the teachers notes, pages 22 – 181. New Wave Maths is not a stand-alone assessment document. Activities may be assessed based on Student Outcome Statements. Teachers will need to be familiar with these to make the appropriate assessments. All activities may be assessed in this way. It is suggested that a random sample of activities only is assessed using Student Outcome Statements to determine progress. • 12 • New Wave Maths Book B – Teachers Guide

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Cross-curriculum Linkages The learning and application of mathematics occurs across all curriculum areas. Literacy skills are developed in the English learning area where language foundations are provided that are essential for the learning of mathematics. Mathematics also provides for the development of language skills.Together, English and mathematics provide the information skills used in activities such as reading the newspaper, information text such as a telephone directory, and preparing and presenting reports. Spatial and measurement tasks are interwoven in many art activities which may in themselves provide alternative stimulus for the learning of mathematical skills. Data collection and interpretation skills as well as measuring activities are a part of both The Society and Environment and Health and Physical Education areas.

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Science provides for a variety of measurement activities with particular emphasis on the measurement component.

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Design activities and spatial knowledge development are a practical component of the Technology and Enterprise learning area. Activities in this learning area provide a wider diversity of learning opportunities than those provided from the basic mathematics syllabus.

The cultural significance of mathematics, its origins and different developments may be explored in the Languages Other than English and Society and Environment learning areas.

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New Wave Maths Book B – Teachers Guide • 13 •

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• 14 • New Wave Maths Book B – Teachers Guide

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Teachers Notes and Answers

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Contents

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How to Use the Teachers Notes.......................................................................................................... 16 Materials List...................................................................................................................................................... 17 Overview of Activities

Term One—Units 1 – 10.......................................................................................................................... 18 Term Two—Units 11 – 20......................................................................................................................... 19 Term Three—Units 21 – 30..................................................................................................................... 20 Term Four—Units 31 – 40....................................................................................................................... 21

Lesson Notes, Consolidation and Answers Term One—Units 1 – 10...............................................................................................................22 – 61 Term Two—Units 11 – 20...........................................................................................................62 – 101 Term Three—Units 21 – 30....................................................................................................102 – 141 Term Four—Units 31 – 40......................................................................................................142 – 181 R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 15 •

How to Use the Teachers Notes Language terms relevant to the workbook page have been listed here. It is preferred these words be introduced before beginning the activity to ensure students have a clear understanding of the terminology used in the activities.

Indicators from the Student Outcome Statements have been included as a quick guide. Resources have These are directly related to been listed to aid organisation before the main activity only.

Unit and student page shown here as a quick reference to the equivalent page in the student workbook.

the lesson.

Outcomes relevant to all activities on the student workbook page have been listed as a ready reference.

Unit 6–1

Student page 16

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N2.3, N2.4

Skills

• recognising patterns • describing patterns • recognising odd and even numbers

Skills relevant to the main activity have been listed.

A space for you to record notes relevant to the lesson has been provided. This space could be used for any purpose. Some suggestions: • record any improvements you made to the lesson; • record any problems you or your students experienced during the lesson; • record individual student's progress or development; • add any ideas for extension or remediation of the lesson; or • include any interesting facts or ideas you came across which were relevant to the lesson.

Indicators

The student is able to: • decide whether handfuls of tiles can be arranged into rectangles two units wide, use the results to classify numbers into odd and even, and explain why every second whole number from 2 must be even, and the numbers in between must be odd.

Resources

• • • •

Base 10 MAB counters pencil 1-cm or 2-cm cubes or tiles

Language

• • • • • • •

add cubes grid odd even number left over

The student workbook page is broken into distinct sections. These are each discussed in detail in this section of the teachers notes. The section is stated, followed by the relevant outcome in brackets. Then bullet points are used to guide you through the activity.

• The focus for this unit is basic facts of addition.

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Notes

Number (N2.3)

Main Activity (N2.4) Warm up

• Distribute counters to groups of students and allow time for free play. • Ask students to make patterns with the counters.

What to do • Ask students to select 8 cubes/tiles and make a pattern. Select 7 cubes/tiles and make a different pattern. Select 11 cubes/tiles and make a pattern. Discuss each pattern. • Continue with several different patterns. • Ask students to select 10 cubes/tiles and make a pattern of pairs. Keep this pattern. • Select 5 cubes/tiles. Make a pattern with pairs. What happened? Is the pattern the same as the one using 10 cubes/tiles? What is different? • What can you say about the two rows in the pattern with 10 cubes/tiles? (They are even or the same.) Ten is called an even number. Because five can not make even pairs it is called an odd number. • Use your cubes/tiles to find the other odd and even numbers. • Use the workbook to make a written record of odd and even numbers.

The great thing is that once this information is recorded, when you come to teach the lesson again, these notes will refresh your memory and enhance the smooth running of the lesson.

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Unit 6—Answers

Answers have been provided to assist teachers in marking students' work. Some answers do require a teacher check as they are dependent on the classroom environment and the students in your class. Where possible, all answers are given.

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This section is a guide only and you are more than welcome to take from it what you choose, modify it or add your own touches.

Where possible, links to a relevant assessment activity in the R.I.C. Publications® Maths Assessment Level 2 document have been provided. Note: Page numbers will vary according to the edition.

Student pages 16 – 18

Unit 6–1 1. (a) 9 (b) 16 2. (a) odd (b) Teacher check 3. (a) odd (b) Teacher check 4. (a) Yes (b) Teacher check

1. 2. 3. 4.

(d) 17

1. (a) 13 (b) 17 2. Teacher check 3. Teacher check

Unit 6–2

(d) 14

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Suggested activities for consolidation of the main activity on the workbook page have been provided as a guide only. Feel free to use, modify, extend or disregard these as you feel necessary. • 16 • New Wave Maths Book B – Teachers Guide

(a) 18 (a) 3 (a) 3 (a) 8 (b) 16 (c) 8 (d) 9 (e) 7

(b) 11 (b) 2 (b) 2 (f) 6 (g) 7 (h) 12 (i) 12 (j) 7

(d) 17

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Consolidation 6–1 • Ask a certain number of students to stand up and arrange themselves in pairs, to verify whether their number is odd or even.

Consolidation 6–2 • Repeat the activity using different features and changing the variety of concrete materials.

Consolidation 6–3 • Use concrete materials if necessary to add three, four, or ﬁve numbers together with a total of 20 or less.

New Wave Maths Book B – Teachers Guide • 45 •

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Materials List The following list of suggested materials is a guide only. It is not suggested that they must be purchased or are the only items that may be used. If compiling a set of materials that will both supplement and compliment the teaching program, the following items will assist. Some items are required to complete the workbook activities. These are listed in more detail on the relevant page in the teachers notes. • Denotes items produced in New Wave Maths Teachers Guide as a blackline master which are available on pages 198 to 231. Teachers may photocopy and use them with their class(es). aerosol lids

egg cartons

rice

attribute blocks

eggtimer

ropes

balance scales

elastic bands

rulers

erasers

sand

fraction cake

school map • page 231

fraction chart • page 295

seesaw balances

geoboards

sharpener

hoops

shells

interconnecting cubes

shoe boxes

blocks

jars

sorting trays

books

jigsaw puzzles

spinners • pages 211 – 212

bottle and jar tops

kitchen scales

spoons

bottles

leaves

stapler

boxes

lids

sticks

buckets

magazines

straws and joiners

building blocks

marbles

streamers

buttons

matchboxes

string

matchsticks

tape

calendars • page 213

metal pieces

tie-string bags

canteen and restaurant menu

metre stick

tiles

cards for games

miras

timers

cartons – all sizes

mirrors

tins

cereal boxes

modelling clay

toothpicks

class diary

money frames

toys

clocks • page 214

nails

washers

coins • page 215

number cards • page 202

wire

number charts • pages 206 – 209

wooden solids

number lines • pages 203 – 205

wool

paints

1-cm dot grid • page 198

paper

1-cm grid • page 199

pattern blocks

1-cm triangle grid • page 201

peas, beans, grain

2-cm grid • page 200

cotton wool

pegboard and pegs

2-D shapes • pages 227 – 228

counters

pencils

3–D shapes • page 229

crayons

percussion instruments

cubes • 1- and 2-cm

pipe-cleaners

cups

plastic money

dice • 6- and 10-sided

playdough

dominoes

popsticks

dusters

ribbons

balloons Base 10 MAB bathroom scales beads biscuit cutters

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coloured pencils coloured rods

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concrete materials construction kits containers cotton reels

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calculator

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beanbags

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New Wave Maths Book B – Teachers Guide • 17 •

Term One Week Unit Outcomes

Page

1 1 S2.1—Follow guidelines to draw and colour scribble patterns.

N2.1a—Identify the ordinal number of objects.

M2.1, M2.2, M2.3—Compare the area of his/her hand and foot and classmates’ hands and feet.

2 N2.1a, N2.4—Identify ordinal numbers. Identify and describe number patterns.

C&D2.4—Analyse and represent data in a pictograph.

S2.3, WM2.2—Create patterns using given numbers of shapes.

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3 S2.1—Draw a plan for a specific purpose.

N2.1a, N2.2, N2.4—Skip count. Identify and describe number patterns.

M2.2—Compare the length of sets of cubes.

9 10

C&D2.1—Distinguish possible and impossible events.

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4 N2.4—Identify, create and describe number patterns.

N2.2, N2.4—Group sets using diagrams. Use the constant function on a calculator to skip count. 5

5 S2.2, S2.4—Identify spatial features of 3-D shapes.

S2.3, WM2.2—Identify and continue patterns using shapes.

M2.2—Use informal units to measure area. 6

6 N2.4—Distinguish between odd and even numbers.

C&D2.2, C&D2.3—Collect, tally and analyse data.

17 18

7 7 S2.2, WM2.2—Construct copies of 3-D shapes and count the number of sets of cubes needed to make each structure.

N2.1b—Mark and share diagrams in equal parts.

M2.2, C&D2.4—Use informal units to measure capacity. Record and analyse data.

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8 N2.1a, N2.2—Count, combine and compare collections.

C&D2.2, C&D2.3, C&D2.4—Record data in a Carroll diagram.

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N2.1a—Count and make amounts of money in different ways.

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N2.3—Count and combine collections of objects and numerals.

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22 23 24

9 M2.1, M2.3—Sort objects by size, considering length and mass.

N2.3—Add two-, three- and four-digit number combinations to a total of 20.

M2.2—Measure, order and compare the mass of equal amounts of different materials.

10 WM2.2, WM2.3, S2.4—Distinguish and describe shapes and patterns on objects in the environment. 28

M2.2—Use informal units to measure the length of objects.

N2.1a, N2.2—Combine and separate collections.

• 18 • New Wave Maths Book B – Teachers Guide

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Term Two Week Unit

Outcomes

Page

11 S2.2, S2.4—Construct 3-D shapes and discuss spatial features.

N2.2, N2.3—Combine and separate collections of objects and numerals.

M2.3, M2.2, WM2.3—Estimate and measure mass. Order activities by days of the week.

12 N2.2, N2.3—Count collections according to attributes.

C&D2.2, C&D2.3, C&D2.4—Collect, tally and analyse data.

N2.2, N2.3—Use count on strategies to solve addition problems.

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13 S2.4, M2.2—Sort objects according to spatial criteria. Order objects according to length.

37 38

M2.2—Order objects by mass using hefting and a seesaw balance. Order objects by length.

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N2.2—Group collections of objects.

14 N2.2—Separate collections of objects.

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C&D2.3, C&D2.4—Analyse and represent data on a pictograph.

N2.2—Separate and group collections of objects. Solve subtraction number sentences. 5

15 S2.2—Copy 2-D shapes onto dotted grid paper.

N2.2—Identify the difference in number between collections of objects. M2.2, WM2.1—Recognise 12-hour time on analog clocks. 6

16 WM2.1, WM2.2, WM2.3, M2.1, M2.2—Work mathematically to determine the heavier of two objects.

40 41 42 43 44 45

C&D2.1, C&D2.2, C&D2.4—Collect, record and analyse data.

N2.2, N2.3—Solve addition and subtraction number sentences.

17 S2.3—Complete mirror images on grid paper.

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M2.2, WM2.1—Read a calendar to complete questions.

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18 N2.2, N2.3—Combine collections. Solve number sentences.

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C&D2.3, C&D2.4—Analyse data in graphs.

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N2.2, N2.3—Count in multiples. Identify and describe number patterns. 9

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N2.2, N2.3—Solve addition and subtraction number sentences.

19 S2.2—Draw specific 2-D shapes on dotted grid paper.

52 53 54 55

N2.2—Group and share collections of objects.

M2.2, C&D2.4—Use informal units to measure length. Record data.

20 N2.2, N2.3—Group and count collections. Count in multiples.

C&D2.3, C&D2.4—Record data in Venn and Carroll diagrams.

N2.2, N2.3—Group and count collections. Count in multiples.

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New Wave Maths Book B – Teachers Guide • 19 •

Term Three Week Unit Outcomes

Page

1 21 N2.1a, S2.2—Count in order. Identify objects that involve 2-D shapes.

N2.2, N2.3—Group and count collections. Combine collections.

M2.2, M2.3—Estimate then measure the length of objects using informal units.

2 22 N2.1a, N2.2—Group and count collections. Count coins in multiples.

WM2.1, WM2.2—Identify and describe ways numbers are used for particular purposes in real-life situations.

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3 23 S2.3, WM2.4—Complete a mirror image on grid paper. Verify correctness of image by checking each stage of working.

N2.2, N2.3, N2.1a—Group and count collections. Count coins in multiples.

M2.2, N2.4—Interpret a calendar to identify number patterns.

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N2.2, N2.3—Group and count collections.

4 24 N2.2, N2.3—Group and count collections.

M2.2, C&D2.4—Use informal units to measure and compare the length of objects. Collect and analyse data.

N2.2, N2.3, N2.1b—Group and count collections. Show halves and fourths on pictures of objects.

5 25 S2.3—Recognise symmetry in diagrams. Repeat a pictorial pattern of 2-D shapes.

N2.2, N2.3—Group and count collections.

6 26 N2.2, N2.3—Group and count collections with remainders.

C&D2.3, C&D2.4—Record and analyse data in a Carroll diagram.

N2.2—Group and count collections.

7 27 S2.2—Construct 3-D shapes according to set criteria.

N2.4—Exchange sets of cubes into Base 10 MAB.

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M2.2, C&D2.4—Measure and compare the length of objects using informal units. Record and analyse data.

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8 28 N2.4—Exchange sets of cubes into Base 10 MAB.

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M2.2, M2.3—Estimate, measure and compare the length of objects using informal units.

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C&D2.2, C&D2.3—Classify, tally and record data.

81 82 83

N2.1a—Solve addition and subtraction number sentences with money.

9 29 S2.1—Find and describe a path on a given map.

N2.4—Copy, continue and describe pictorial repeating patterns.

M2.2, M2.3—Estimate, measure and compare the area of objects using informal units.

10 30 N2.1a—Calculate the amount of change needed for given amounts.

N2.4, S2.3—Identify, copy, continue and describe repeating pictorial patterns.

N2.1a—Calculate amounts of money.

• 20 • New Wave Maths Book B – Teachers Guide

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Term Four Week Unit

Outcomes

Page

1 31 WM2.2, WM2.3, M2.1, M2.2—Work mathematically to determine which container has the greatest capacity.

N2.1a, N2.2—Use a number grid to identify number patterns.

M2.2—Interpret a calendar to answer questions.

2 32 N2.1a—Calculate the amount of change needed for given amounts.

C&D2.2, C&D2.4—Record data in a Venn diagram. Collect and record data in a table.

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3 33 M2.2—Draw shapes on a grid with given perimeters.

N2.1a—Identify the number of coins needed to make given values.

M2.2—Measure and compare the length of objects using a ruler. Use informal units to compare the perimeter and area of given 2-D shapes.

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N2.1a—Exchange amounts of money into given values.

4 34 N2.1a—Exchange amounts of money for a single coin. Share amounts of money equally.

100

C&D2.3, C&D2.4, C&D2.1—Collect, record and analyse data.

101

N2.1a—Calculate amounts of money.

102

5 35 S2.3, N2.4—Identify, copy, continue and describe repeating pictorial patterns. N2.1b, N2.2—Identify equal shares in pictures of objects. Count in multiples.

103 104

M2.2—Use informal units to measure and compare the capacity and area of different containers. Measure and order the lengths of similar objects in centimetres.

105

6 36 N2.1a—Calculate amounts of money, counting in multiples.

106

C&D2.2, C&D2.3, C&D2.4—Classify, record and analyse data.

107

N2.4, WM2.2—Create a pictorial number pattern using given guidelines.

108

7 37 S2.1—Find and describe paths on a given map.

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WM2.2, N2.3—Apply mathematical reasoning to solve a problem. M2.2, WM2.1—Identify and describe activities at different times of the day.

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8 38 WM2.2, N2.3—Apply mathematical reasoning to solve a problem.

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110 111 112

C&D2.2, C&D2.4—Classify and record data in a Venn diagram and tree diagram.

113

WM2.2, WM2.4—Apply mathematical reasoning to verify the correct answer to a problem.

114

9 39 S2.1—Draw a plan for a specific purpose.

115

WM2.2, N2.3—Solve number problems using the correct operation.

116

M2.1, M2.2—Use informal units to measure the area of given shapes, then explain which one was the more effective unit.

117

10 40 WM2.2, N2.3—Apply mathematical reasoning to solve a problem.

118

C&D2.3, C&D2.4—Collect, record and analyse data.

119

WM2.4—Identify errors in repeating pictorial number patterns.

120

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New Wave Maths Book B – Teachers Guide • 21 •

Unit 1–1

Student page 1

Indicators

Outcomes

The student is able to: • describe the location of an object as ‘between’ two other locations.

N2.3, S2.1

Skills • drawing patterns • recognising boundaries • logical thought

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Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language

• add • space • pattern • regions • same • boundary • different

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• The focus for this unit is basic facts of addition.

Warm up

• Demonstrate on the blackboard/whiteboard how to draw a scribble pattern with large shapes. Explain the colouring process so that regions sharing a boundary are not coloured the same.

What to do

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Main Activity (S2.1)

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• Ask students to complete a scribble pattern in the top space in their workbook. Colour the regions so that no two regions sharing a boundary are coloured the same. • When completing the second scribble pattern, suggest that students might like to choose a theme—sea, desert, forest etc. and make the shapes into creatures that might be found in the scene, then colour their work. • Alternatively, students might like to see what is the least number of colours they are able use without having the same colour in regions sharing the same boundary.

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• 22 • New Wave Maths Book B – Teachers Guide

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Unit 1–2

Student page 2

Indicators

Outcomes

The student is able to: • read, write and say the numbers in order to beyond 100 and count on or back from any number to 100.

N2.3, N2.1a

Skills • recognising ordinal number value • counting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • interconnecting cubes • concrete materials • coloured pencils/ crayons

Language

• add • left • right • tenth • sixth • nineteenth • first

• third • twelfth • grid • fifteenth • twentieth • sixteenth • fifth

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Main Activity (N2.1a) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Ask students to make a line of 20 items. At your direction ask the students to move the second, ninth, fifth, fourteenth and seventeenth items to a space below the line. Check with students by counting, using ordinal numbers (first, second, etc.) to see that the correct items were moved. • Repeat this type of activity a number of times. Questions may take the form of ‘What object is in the third place?’ • Written records of these activities may be made in the workbook. Work with students to assist them.

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• The focus for this unit is basic facts of addition.

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New Wave Maths Book B – Teachers Guide • 23 •

Unit 1–3

Student page 3

Indicators

Outcomes

The student is able to: • recognise that the same things can be ordered by different attributes. • compare the area of two regions directly by superimposing one over the other. • attend to the right attribute when judging which of two things is bigger.

N2.3, M2.1, M2.2, M2.3

Skills

• measuring • comparing

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials (including 2-D shapes)

Language

• add • trace • space • bigger • compare • biggest

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Main Activity (M2.1, M2.2, M2.3) Warm up

• Distribute concrete materials among groups of students. Allow time for free play. • Direct students to cover objects of their own choosing with the concrete materials. Discuss whether they are able to cover the object adequately. How many items did it take to cover an object? Compare sizes of objects.

What to do

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• The focus for this unit is basic facts of addition.

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• Ask students to trace around their hand in the space provided in the workbook. • Now trace around a foot in the space provided. Students may superimpose or overlap drawings. • Ask students which is the bigger. How can they be sure? Can they check? Are there other means of checking? Have they changed their mind? • Compare hand and foot size with classmates, following the same line of questioning.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 74 – 75. • 24 • New Wave Maths Book B – Teachers Guide

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Unit 1—Answers

Student pages 1 – 3

Unit 1–1 1. (a) 9 (b) 5 (c) 4 (d) 8 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check

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1. (a) 2 (b) 3 (c) 4 (d) 5 2. Teacher check

Unit 1–2

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• Students can repeat the activity, improving on their original scribble patterns to use fewer colours than before.

Consolidation 1–2

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1. (a) 10 (b) 6 (c) 7 (d) 3 2. (a) Teacher check (b) Teacher check (c) Teacher check

• Arrange students in rows. Give all students except one an ordinal number according to their position. Call out ordinal numbers at random to the student without a number, who must find the correct student. Swap positions after a few turns.

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Consolidation 1–3

• Make a display of tracings of students’ hands and feet in order of size.

New Wave Maths Book B – Teachers Guide • 25 •

Unit 2–1

Student page 4

Indicators

Outcomes

N2.3, N2.1a, N2.4

The student is able to: • read, write and say the numbers in order to beyond 100 and count on or back from any number to 100. • describe a rule which could have been used to generate an adding or subtracting sequence and test.

Skills • recognising ordinal numbers • describing number patterns • counting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • interconnecting cubes • concrete materials

Language

• add • third • left • square • pattern • fifth • fourth

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Main Activity (N2.1a, N2.4) Warm up

• Distribute concrete materials to groups of students. Allow time for free play. • Ask students to make a line of 20 items. At your direction ask the students to move the second, ninth, fifth, fourteenth and seventeenth items to a space below the line. Check with students by counting, using ordinal numbers (first, second, etc.) to see that the correct items were moved. • Repeat this type of activity a number of times. Questions may take the form of ‘What object is in the third place?’

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• Written records of these activities may be made in the workbook. Work with students to assist them. • Use interconnecting cubes, or similar, to make a pattern. Ask students to describe their patterns.Where a regular fixture occurs, focus on the number of items between recurrence, colour of regular items (third, fifth, etc.).

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• 26 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 2–2

Student page 5

Indicators

Outcomes

The student is able to: • read and compare frequencies from lists and simple one-way tables. • interpret block graphs produced by others. • comment on information in displays of data produced by himself/herself and peers.

N2.3, C&D2.4

Skills • reading graphs • creating graphs

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils

Language

• add, • graph • most • least • how many

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.4) Warm up

• Construct a picture graph on the blackboard/whiteboard using students’ pets as criteria. Ask students to stand if they have a dog as a pet—draw dots for dogs to represent the number. Repeat for other pets chosen. • Discuss the graph with the class. Shows totals, makes it easy to compare totals, each dot represents one pet, the dots are drawn above the pet type.

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• Use the graph in the workbook to answer the questions. Work this activity as a whole class. Assist students to complete answers. • Ask students what fruit is their favourite of those listed. Students stand when their choice is named. Class counts standing students and writes total above fruit name on top of the graph. • After all fruits have been named, draw a picture of a piece of fruit or a dot above the fruit name until the total showing student choice is reached. Complete the graph. (Fruits/dots will need to be drawn as close to the same size as possible.)

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 110 – 111. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 27 •

Unit 2–3

Student page 6

Indicators

Outcomes

The student is able to: • repeat multiple copies of two or three figures in a recognisable pattern for decorative purposes. • represent a problem with concrete materials and manipulate the materials to find a solution.

N2.3, S2.3, WM2.2

Skills

• pattern making • describing patterns

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials • coloured pencils/ crayons

Language

• add • pattern • different • shapes • two • four • three • fifth

r o e t s Bo Notes r e p ok u S

Main Activity (S2.3, WM2.2) Warm up

• Distribute concrete materials among groups of students. Allow time for free play. • Direct students to make patterns using the materials. Describe the pattern to the group. Share some patterns with the whole class. • Repeat, making different patterns.

• Direct students to their workbook. The first activity requires a pattern to be made using two shapes. Students may choose concrete materials to trace around or draw shapes freehand. • Share patterns within the group. Select some to share with the class. Students describe their patterns. • Repeat pattern making, using four different shapes then three different shapes. • Share patterns each time.

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 24 – 25. • 28 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 2—Answers

Student pages 4 – 6

Unit 2–1 1. (a) 10 (b) 6 (c) 8 (d) 9 2. (a) carrot (b) corn (c) 5 (d) 4 3. Teacher check

r o e t s Bo r e p ok u S

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1. (a) 4 (b) 11 (c) 5 (d) 7 2. (a) 2 (b) Teacher check (Most students will say counting in threes.) 3. Teacher check (Most students will say counting in fives.) 4. (a) Tim (b) Bob 5. Teacher check

Unit 2–2

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• Write a direction about a pattern for a classmate to complete and describe, using a number line or strip.

Consolidation 2–2

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1. (a) 8 (b) 5 (c) 6 (d) 7 2. Teacher check 3. Teacher check 4. Teacher check

• Make a graph as in Exercise 3, using a selection of vegetables.

Consolidation 2–3

• Provide further opportunities for students to create and describe patterns with a variety of concrete materials.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 29 •

Unit 3–1

Student page 7

Indicators

Outcomes

The student is able to: • place important things in the environment in order on the map. • describe the location of an object as ‘between’ two other locations.

N2.3, S2.1

Skills • drawing plans

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • ruler • coloured pencils/ crayons • 1-cm grid transparency (see page 199)

Language

• add • plan

r o e t s Bo Notes r e p ok u S

Main Activity (S2.1) Warm up

• Draw the outline of a grid on the blackboard/whiteboard or use an overhead transparency of the grid from the workbook. • Work with the students to develop a plan of the classroom showing the location of the door(s), windows, teachers desk, cupboards and, if space and time permit, student desks. • When locating items on the plan, discuss with students the accuracy of the location. Perfect location is not required; approximation of location and size is sufficient. Ask what will happen if the location is not close to its actual position.

What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• Direct students to draw a plan of their own bedroom showing the door, bed, window and cupboard/wardrobe. Remind students that size and location are important. • Display and discuss finished plans in the groups or some selected ones with the class.

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• 30 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 3–2

Student page 8

Indicators

Outcomes

The student is able to: • recognise counting as a measure of set size. • use materials and diagrams to represent multiplication stories which can be thought of as repeated addition. • describe a rule which could have been used to generate an adding or subtracting sequence and test.

N2.3, N2.1a, N2.2, N2.4

Skills • recognising patterns • describing patterns • following instructions • skip counting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials • number line (see page 204)

Language

• add • lots of • pattern

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a, N2.2, N2.4) Warm up

• Distribute concrete materials to groups of students. Allow time for free play. • Direct students to make patterns using the materials. Discuss the patterns within the groups. • Repeat, making several different patterns. • Direct the pattern making so that patterns are made using specified lots of materials; e.g. lots of two, or lots of three, or lots of four. Students explain their patterns. Students will begin to see that they can count using the number of items in a group; e.g. 2, 4, 6, …; 3, 6, 9 ….

What to do

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• The focus for this unit is basic facts of addition.

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• Students can complete the activity in the workbook, working with the teacher’s guidance as required. • The early patterns are a basic introduction to multiplication.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 31 •

Unit 3–3

Student page 9

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • realise that if he/she knows how many of the same unit fit end to end along each of two lengths, he/she can say which is bigger without directly comparing.

N2.3, M2.2

Skills

• measuring • comparing

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • interconnecting cubes or 2-cm cubes

Language

• add • arrow • long • same • length • difference between • tallest • shortest

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Distribute interconnecting cubes or 2-cm cubes to groups of students. Allow time for free play.

What to do

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Teac he r

• The focus for this unit is basic facts of subtraction.

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• Make a length using the cubes. Make another the same length. • Compare the lengths of structures made within the group. Whose is longest, shortest or tallest, shortest? Are there any the same length? Make structures of the same length. • Arrange structures in order from shortest to longest. • Use the workbook page to make a written record of these activities.

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• 32 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 3—Answers

Student pages 8 – 9

Unit 3–1 (d) 10

1. (a) 12 (b) 10 (c) 8 (d) 11 2. counting by fours 3. counting by threes 4. counting; adding one more each time

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 9 (b) 11 (c) 12 2. Teacher check

Unit 3–2

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• Draw a plan of another room in their house.

Consolidation 3–2 • Use number lines to show counting in ones, twos, threes etc. to develop the connection that multiplication is repeated addition.

Consolidation 3–3

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1. (a) 9 (b) 6 (c) 13 (d) 7 2. The number 7 comes in between 6 and 8 (or similar). 3. Sets with five cubes are the same length (green and red). Difference in length between the tallest and the shortest set is 10 – 3 = 7.

• With a partner, make different length sets of interconnecting cubes or 2-cm cubes. Discuss which are longer than a selected set, which is longest, which is shortest etc.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 33 •

Unit 4–1

Student page 10

Indicators

Outcomes

The student is able to: • describe a rule which could have been used to generate an adding or subtracting sequence and test.

N2.3, N2.4

Skills • recognising patterns • describing patterns

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language

• add • pattern • squares • fourth • number • third • grid

r o e t s Bo Notes r e p ok u S

Main Activity (N2.4) Warm up

• Direct students to find patterns in objects around the classroom; e.g. wallpaper, book covers, table or bench cloths or mats, curtains, school uniform material.

What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• Use the grid to make a pattern by colouring the squares. Explain to the students that the pattern is of their choice but they must be able to describe it when it is finished. • Allow students time to colour their pattern. • Ask selected students to describe their pattern or organise students into groups and allow time for each student to discuss his/her pattern. • Work with the whole class and direct them to draw a star on every fourth number. Which number will the first star be drawn on? The second? and so on. • Repeat, drawing a dot on every third number. • Ask students to circle the number that have both a dot and a star. • Ask students to describe the pattern orally then write an explanation. • The pattern shows multiples of 3 and 4 and the common multiple of 12. Students do not need to know this terminology.

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• 34 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 4–2

Student page 11

Indicators

Outcomes

The student is able to: • respond appropriately to, and use, ‘possible’ and ‘impossible’ for describing familiar events/actions. • distinguish impossible from unlikely events. • describe familiar events as being more or less likely to happen.

N2.3, C&D2.1

Skills • estimating probability

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language

• add • chance • likely • certain • possible

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.1) Warm up

• Explain to students what chance is. Some may be able to provide an explanation. Focus on the use of language such as ‘possible’, ‘certain’ or ‘likely’ for events or activities to happen.

What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• Work with students as a class to find the answer to the questions posed. • Discuss each question with the class before a decision is made, then ask students to colour yes or no.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 102 – 103. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 35 •

Unit 4–3

Student page 12

Indicators

Outcomes

The student is able to: • use materials and diagrams to represent multiplication stories which can be thought of as repeated addition. • use the inbuilt constant function of a calculator to generate ‘facts’ based on patterns.

N2.3, N2.2, N2.4

Skills

• grouping • using a calculator

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • calculator • concrete materials

Language

• add • how many • calculator • results • equal • shape

• lots of • altogether • press • share • groups

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.4) Warm up

• Distribute materials among groups of students and ask them to have their calculator ready. Ask them what is the largest number they can key into a calculator. Discuss answers briefly.

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• Direct students to take out a given number of items and then share them equally into a set number of groups; e.g. 10 items shared into 5 groups. How many items? How many groups? How many in each group? • Repeat this many times. • Use the calculator and press 3. Press +. What happens? (Nothing) Press =. What happens? (Nothing) Press =. What happens? (6 appears) How do you explain this? (Three is being added when the equal sign is pressed after the first pressing of the equal sign.) Press = again. What happens? (9 appears) What number would you expect to appear if you pressed = again? (12) Continue pressing = and note the number that appears. How could describe the sequence of numbers that are appearing? (Counting by threes) Note: different keystrokes might be required for different models of calculator. • Try this with other numbers. Does the result come up as you expected? • Use the workbook to make written records of these activities. • Exercise 6 requires students to use logical thinking. The answer would appear to be ‘No’, as all other shapes have four sides. However some students may answer ‘Yes’, as all shapes have straight sides.

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• 36 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 4—Answers

Student pages 10 – 12

Unit 4–1 (d) 7

1. (a) 9 (b) 11 (c) 8 2. Teacher check

(d) 13

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 10 (b) 12 (c) 14 2. Teacher check 3. (a) 4, 8, 12, 16 (b) 3, 6, 9, 12, 15 (c) 12 pattern – teacher check

Unit 4–2

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• Provide further opportunities to make patterns on 1- or 2-cm grid paper and describe to other students.

Consolidation 4–2

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1. (a) 14 (b) 8 (c) 11 (d) 15 2. 4 3. 12 4. Teacher check 5. 4 6. Answers may vary.The answer would appear to be ‘No’ as other shapes have four sides. Some students will answer ‘Yes’ as all shapes have straight sides.

• Brainstorm further questions as a class that ask, ‘Is it likely?’, ‘Is it possible?’, ‘Is it certain?’ Discuss answers.

Consolidation 4–3

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R.I.C. Publications® www.ricpublications.com.au

• Repeat the calculator activity and discussion after a period of a few days, to consolidate the concept with the students.

New Wave Maths Book B – Teachers Guide • 37 •

Unit 5–1

Student page 13

Indicators

Outcomes N2.3, S2.2, S2.4

The student is able to: • draw figures which show the essential spatial features of named geometric shapes. • respond to ‘Tell me about the shape of this (object, place or mathematical model)’ using language such as ‘flat’, ‘curved’, ‘corner’, ‘side’, ‘round’, ‘square’, ‘edge’. • sort things according to simple spatial criteria.

Skills • modelling • identifying spacial features

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencils • 3-D shapes • plasticine or modelling clay • straws and joiners

Language • add • 3-D • pentagonal • triangular • rectangular • cube • surfaces • edges • length

• models • shape • prism • pyramid • square • most • corners • same • least

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition.

Warm up

• Distribute 3-D models and materials that can be used to construct copies of the models. Allow time for free play. • Direct students to try to construct models similar to the 3-D shapes they have. • Display models made or attempted.

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• Using the 3-D shapes provided and the workbook, ask students to identify each of the shapes drawn in the workbook with actual models (if available). • Examine each shape and count surfaces and record the number. Count edges and record the number. Count the corners and record the number. (Note: The correct name for a corner is a vertice, which is the point where all edges meet.) • Use the models and the recordings of corners, edges and surfaces to answer the questions in the workbook. Where differences in answers occur, discuss reasons for the difference.

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What to do

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Main Activity (S2.2, S2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 14 – 15. • 38 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 5–2

Student page 14

Indicators

Resources

• Base 10 MAB • counters • pencil • pattern blocks • variety of concrete materials

Outcomes N2.3, S2.3, WM2.2

Skills • recognising patterns • describing patterns • copying patterns

Teac he r

Number (N2.3)

Language • add • pattern • blocks • layer • continue

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition.

Warm up

• Distribute pattern blocks and/or concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to make patterns. • Ask another member of your group to continue your pattern. Discuss your pattern with your group. • Repeat this several times. • Ask students to examine the patterns in their workbook. Copies of the patterns may be made if it helps students complete the activities. • Check students’ work, discuss the patterns as they are developing. Share student descriptions with the class. There may be different views or combination of patterns; if these are valid, accept them.

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Main Activity (S2.3, WM2.2)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 24 – 25. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 39 •

Unit 5–3

Student page 15

Indicators

Outcomes N2.3, M2.2

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure area.

Skills • measuring

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 1-cm or 2-cm cubes

Language • add • cubes • cover • area • how many

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Distribute cubes among groups of students. Allow them time for directed play. Ask students to use the cubes to cover items of their choice. (The same sized cube must be used.) • Discuss with the whole class the activities that each group has been involved in.

What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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• Ask students to use cubes to cover the first shape in their workbook. How many did they use? Why did different people use different numbers of counters? Does it matter about the spaces left or the overlap of counters outside the boundary? Allow students to determine their own stance. • Repeat for the other shapes. Which shape required the most counters to cover it? Discuss the findings.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80 – 81. • 40 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 5—Answers

Student pages 13 – 15 Unit 5–1 1. (a) 9 (b) 15 (c) 13 2. Teacher check 3. Teacher check

(d) 10

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 12 (b) 9 (c) 13 (d) 7 2. (a) pentagonal prism (b) pentagonal prism (c) cube (d) triangular pyramid

Unit 5–2

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(d) 14

• Construct a table showing the number of surfaces, edges and corners each 3-D shape has.

Consolidation 5–2

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• Provide further opportunities for students to examine patterns made by others in a group.

Consolidation 5–3

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R.I.C. Publications® www.ricpublications.com.au

• Ask students to repeat the exercise using different shapes, or materials such as counters, to cover the areas.

New Wave Maths Book B – Teachers Guide • 41 •

Unit 6–1

Student page 16

Indicators

Outcomes

N2.3, N2.4

Skills • recognising patterns • describing patterns • recognising odd and even numbers

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 1-cm or 2-cm cubes or tiles

Language • add • cubes • grid • odd • even • number • left over

r o e t s Bo Notes r e p ok u S

Main Activity (N2.4) Warm up

• Distribute counters to groups of students and allow time for free play. • Ask students to make patterns with the counters.

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• Ask students to select 8 cubes/tiles and make a pattern. Select 7 cubes/tiles and make a different pattern. Select 11 cubes/tiles and make a pattern. Discuss each pattern. • Continue with several different patterns. • Ask students to select 10 cubes/tiles and make a pattern of pairs. Keep this pattern. • Select 5 cubes/tiles. Make a pattern with pairs. What happened? Is the pattern the same as the one using 10 cubes/tiles? What is different? • What can you say about the two rows in the pattern with 10 cubes/tiles? (They are even or the same.) Ten is called an even number. Because five can not make even pairs it is called an odd number. • Use your cubes/tiles to find the other odd and even numbers. • Use the workbook to make a written record of odd and even numbers.

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 42 – 43. • 42 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 6–2

Student page 17

Indicators

Resources

The student is able to: • offer suggestions about how to classify objects or information. • organise data by classifying items in categories they have created. • suggest ways of efficiently counting how many there are in each of several categories.

• Base 10 MAB • counters • pencil • variety of concrete materials • bag or box

Outcomes N2.3, C&D2.2, C&D2.3

Skills • sorting objects • tallying

Number (N2.3)

Language • add • features • tally • total • most • common • least

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.3) Warm up

• Collect a variety of objects from the classroom. Place the objects into the bag or box. Ask one student to take a double handful of objects from the bag or box without looking. • With all the class sitting on the mat, discuss the features of the objects then agree on which of these features the objects will be sorted.

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• List the features on the blackboard/whiteboard. Features may include construction materials, shape, size, colour etc. Choose no more than five features. • Sort the materials into the groups. • Count and keep a tally on the board of the items as they are counted. Introduce the tally system of I I I I to show sets of five. • Count the tally marks to find the total in each group. • Students copy the record into the space in their workbook and answer the questions. • Repeat the activity and record again on the board for students to copy. • Is the record the same?

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What to do

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Teac he r

• The focus for this unit is basic facts of addition.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 104 – 105. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 43 •

Unit 6–3

Student page 18

Indicators

Outcomes

The student is able to: • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number. • remember many basic addition facts and work out the others.

N2.3

Skills • grouping • adding

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • add • how many • altogether

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition.

Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

• Direct students to select a given number of items—4. Select another 5 items. How many items in the first group? How many items in the second group? How many altogether? 4 and 5 equal 9. • Repeat this many times with a variety of numbers to a total of 20. Three or four sets of items may be selected instead of just the two. • Written records of this activity may be made in the workbook. Use concrete materials to assist where required.

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Main Activity (N2.3)

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• 44 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 6—Answers

Student pages 16 – 18

Unit 6–1 (d) 17

1. (a) 13 (b) 17 (c) 12 2. Teacher check 3. Teacher check

(d) 14

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 9 (b) 16 (c) 11 2. (a) odd (b) Teacher check 3. (a) odd (b) Teacher check 4. (a) Yes (b) Teacher check

Unit 6–2

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• Ask a certain number of students to stand up and arrange themselves in pairs, to verify whether their number is odd or even.

Consolidation 6–2

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1. (a) 18 (b) 11 (c) 13 (d) 17 2 (c) 7 2. (a) 3 (b) 3. (a) 3 (b) 2 (c) 5 4. (a) 8 (f) 6 (b) 16 (g) 7 (c) 8 (h) 12 (d) 9 (i) 12 (e) 7 (j) 7

• Repeat the activity using different features and changing the variety of concrete materials.

Consolidation 6–3

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R.I.C. Publications® www.ricpublications.com.au

• Use concrete materials if necessary to add three, four, or five numbers together with a total of 20 or less.

New Wave Maths Book B – Teachers Guide • 45 •

Unit 7–1

Student page 19

Indicators

Outcomes

The student is able to: • copy pictures composed of simple geometric figures so that the main components are recognisable in shape, position and orientation. • represent a problem with concrete materials and manipulate the materials to find a solution.

N2.3, S2.2, WM2.2

Skills • modelling

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • interconnecting cubes

Language • add • cubes • how many • sets • structure

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition.

Warm up

• Distribute the cubes among groups of students. Allow time for free play. • Direct students to make the cubes into sets of three and four. • Ask students to make patterns or structures using just the sets of three and four cubes. • Partners should either copy the structure or count the number of sets used. • Allow time for different structures to be made and explored.

What to do

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Main Activity (S2.2, WM2.2)

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• Direct students to their workbook to complete written activities similar to those already attempted. Students may need to make physical copies of the structures to find the answers.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4 – 5. • 46 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 7–2

Student page 20

Indicators

Outcomes

The student is able to: • link the action of sharing into two equal portions with the language of ‘half ’. • see the need to check that the ‘halves’ are the same size. • understand that constructing a number of fair shares from a whole requires splitting all of the whole into equal parts. • use halving based on symmetry.

N2.3, N2.1b

Skills • recognising fractions • constructing fair shares

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • counters • fraction cake • concrete materials

Language • cut • four • equal parts • three • how many • equal shares • thirds • fourths (quarters)

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute concrete materials to groups of students. Allow time for free play. • Use a fraction cake to demonstrate halves, fourths (quarters) and thirds. Discuss these in terms of equal parts/shares and fair share. • Direct students to select four items. Share these into fourths (4 equal shares). How many in each share? • Repeat for halves, thirds and fourths using 4, 8, 6, 10 for halves; 3, 6, 9 for thirds; and 4, 8, 12 for fourths.

What to do

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Main Activity (N2.1b)

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• Students may make written records of their activities in their workbook. Assistance may be required from the teacher to ensure activities are understood and completed correctly.

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New Wave Maths Book B – Teachers Guide • 47 •

Unit 7–3

Student page 21

Indicators

Outcomes N2.3, M2.2, C&D2.4

The student is able to: • use repetitions of a uniform unit to measure capacity. • read and compare frequencies from lists and simple one-way tables. • describe how his/her graph shows the results of the data collection. • comment on information in displays of data produced by himself/herself and peers.

Skills • measuring • comparing • counting • investigating capacity

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • aerosol can lid • tin • jar • coffee cup (or similar) • sand

Language • aerosol • cup • tin • fill • how many • arrange • largest

• plastic • cap • jar • graph • more • smallest • order

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, C&D2.4) Warm up

• Organise the class into groups. Each group is to collect an aerosol lid or small plastic cup, a tin, a jar and a coffee cup. • Take class to the sand pit and allow time for free play.

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• Direct students to use the aerosol can lid to fill the tin. A record of the number of lids can be made on scrap paper to be later entered into the workbook. • Repeat to fill and record filling the jar. • Repeat to fill and record filling the coffee cup. • Students can now draw on the graph the amount of lids used to fill each container. • Work with the class explaining how to read the graph to answer each of the questions on the page. Note: Explain to students that the lids need to be drawn the same size in the grid for ease of counting and comparing.

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What to do

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• The focus for this unit is adding on.

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• 48 • New Wave Maths Book B – Teachers Guide

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Unit 7—Answers

Student pages 19 – 21 Unit 7–1

(d) 12

1. (a) 1 (b) 3 (c) 1 (d) 3 2. Teacher check 3. Teacher check 4. 3 5. 6 6. 3

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1. (a) 16 (b) 14 (c) 15 2. (a) 3 16 (b) (c) 12 (d) 12

Unit 7–2

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• Use sets of five or six interconnecting cubes to complete similar activities.

Consolidation 7–2

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1. (a) 1 (b) 4 (c) 2 (d) 2 2. Teacher check 3. Teacher check

• Provide opportunities for similar activities.

Consolidation 7–3

• Repeat the activity using three larger containers to fill, such as an ice-cream container, or use the same measuring containers but fill with rice. Compare and discuss results.

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New Wave Maths Book B – Teachers Guide • 49 •

Unit 8–1

Student page 22

Indicators

Resources

The student is able to: • understand he/she can tell from the numbers alone which collection has more. • select addition to deal with situations which involve combining collections.

• Base 10 MAB • counters • pencil • coloured pencils/ crayons • concrete materials • 1-cm or 2-cm grid paper (see pages 199 and 200)

Outcomes N2.3, N2.1a, N2.2

Skills • grouping • adding • counting

Number (N2.3)

Language • how many • altogether • same • length • longest • shortest

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a, N2.2) Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to select 5 items. Select another 4 items. How many items do you have altogether? Five and four equal nine. • Repeat this with many different combinations to a total of 20. • Ask each student in the group to select a number of items of his/her own choice less than ten. Check with other group members to see who has the same number, the most and the least. • Repeat several times. • Ask students in the group to look at their name. The letters of each student’s name could be written on grid paper so the length will become more obvious and counting easier. Count the letters in each name. Who in the group has the longest name? (the one with most letters); the shortest?; and the same length? • Written records of these activities may be made in the workbook. Guidance may be required for students to complete the activities.

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• The focus for this unit is adding on.

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• 50 • New Wave Maths Book B – Teachers Guide

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Unit 8–2

Student page 23

Outcomes

Indicators

Resources

N2.3, C&D2.2, C&D2.3, C&D2.4

The student is able to: • offer suggestions about how to classify objects or information. • make graphs and plots using oneto-one correspondence between ‘real’ data and a representation. • comment on information in displays of data produced by himself/herself and peers.

• Base 10 MAB • counters • pencil • plastic coins • concrete materials

Skills • sorting objects • tallying • classifying

Number (N2.3)

Language • sort • groups • Carroll diagram • how many

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.3, C&D2.4) Warm up

• Distribute coins and concrete materials to groups of students and allow time for free play. • Direct students to sort coins into groups. Describe how they have sorted the coins. Can the coins be sorted in another way? Try. • Different sortings should be encouraged. • Ask students to collect a handful of items and sort them into two groups. Sort each group into another group so that there are now four groups. Place the second sorting below the first. • Repeat this a number of times.

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• The focus for this unit is adding on.

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• The workbook shows a Carroll diagram. Explain to the students that this is a means of recording sortings of items. • The first sorting is of coins. Ask students to sort coins into gold and silver. Sort the silver coins into those less than $1.50 and those more than $1.50. Write the value of the coins in the correct space on the Carroll diagram. Help students to locate the correct box. • Sort the gold coins into those less than $1.50 and those more than $1.50. Write these coin values in the correct boxes. Assist students as required. • Ask the boys in the class to stand in one group and the girls in another. • Ask the left-handed boys to stand together and the right-handed boys to stand together. Repeat for the girls. • Count the members of each group. Record these numbers in the correct boxes in the second Carroll diagram.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 51 •

Unit 8–3

Student page 24

Indicators

Resources

The student is able to: • count coins, including in multiples of 5c, 10c, 20c, 50c, $1 and $2, and record total amounts. • read amounts of money and make up the amount with coins in different ways.

• Base 10 MAB • counters • pencil • plastic coins • photocopies of coins on page 215 (optional)

Outcomes N2.3, N2.1a

Skills • recognising value • counting money

Teac he r

Number (N2.3)

Language • smallest • coins • different

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute coins to groups of students. Allow time for free play.

What to do

• Direct students to select a 10c coin. How many different ways are there of making 10c? (2—Two 5c coins or one 10c coin.) • Repeat for 20c, 50c, $1. Discuss the combinations. • Without using the actual coin itself, what is the least number of coins you require to make 10c, 20c, 50c, $1, $2? • Written records of these activities may be made in the workbook. Students may need to redo the activities from above to complete the answers. (Photocopies of coins could also be glued in the workbook instead of drawing the coins. If drawn, the number value only needs to be drawn in the coin shape and not the picture.)

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Main Activity (N2.1a)

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• 52 • New Wave Maths Book B – Teachers Guide

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Unit 8—Answers

Student pages 22 – 24 Unit 8–1 1. (a) 5 (b) 6 (c) 5 (d) 1 2. 50c

Less than $1.50

10c 5c

Gold

Silver

Less than $1.50

20c

r o e t s Bo r e p ok u S

3. Teacher check

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1. (a) 4 (b) 3 (c) 7 (d) 2 2. (a) 4 stars, 3 planets 7 (b) 3. (a) 6 pencils, 3 erasers (b) 9 4. Wagga Wagga, Kalgoorlie, Townsville, Launceston 5. (a) Melbourne (b) Perth (c) Sydney, Hobart and Darwin – six letters Brisbane, Canberra and Adelaide – eight letters

Unit 8–2

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Consolidation 7–2

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1. (a) 7 (b) 4 (c) 6 (d) 3 2. 20c, 20c, 10c 3. 10c, 10c 10c, 5c, 5c 5c, 5c, 5c, 5c 4. Teacher check. Answers will include: 20c, 20c, 10c 20c, 10c, 10c, 10c 10c, 10c, 10c, 10c, 10c 10c, 10c, 10c, 10c, 5c, 5c 20c, 5c, 5c, 5c, 5c, 10c There are several other combinations. 5. 50c, 20c, 10c, 10c, 10c 50c, 50c 50c, 20c, 20c, 10c 50c, 20c, 20, 5c, 5c

• Brainstorm other data to organise in a Carroll diagram such as the number of boys and girls who can or can not ride a bike or skateboard, or perform a handstand.

Consolidation 7–3

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• Show how many different ways there are to make $1.00 using six, seven or eight coins or more.

New Wave Maths Book B – Teachers Guide • 53 •

Unit 9–1

Student page 25

Indicators

Outcomes

N2.3, M2.1, M2.3

Skills • sorting • estimating size

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language

• sort • groups • large • small

r o e t s Bo Notes r e p ok u S

Main Activity (M2.1, M2.3) Warm up

• Distribute concrete materials to groups of students. Allow time for free play. • Direct students to select a number of items. Sort these into large and small. • Select a different set of items. Sort these into materials (e.g. plastic, non plastic). • Repeat, choosing different criteria for sorting. Students may select their own criteria to sort the items into two groups. Discuss the criteria for sorting.

What to do

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• The focus for this unit is adding on.

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• Complete the activity in the workbook, colouring the items as directed. Discuss with the students what they consider to be large and small objects. • Make a list of the large, red coloured objects and small, blue coloured objects.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 74 – 75. • 54 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 9–2 N2.3

Student page 26

Indicators

Outcomes

Skills • addition

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• add • how many • total

r o e t s Bo Notes r e p ok u S

Main Activity (N2.3) Warm up

• Distribute concrete materials, including counters to groups of students. Allow time for free play.

What to do

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Teac he r

• The focus for this unit is adding on.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 55 •

Unit 9–3

Student page 27

Indicators

Outcomes

N2.3, M2.2

The student is able to: • say which is heavier of two objects of apparently similar size by hefting or using a balance beam.

Skills • measuring • comparing

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • cup • rice • sand • washers • nails • cotton wool • balance scales

Language

• measure • amounts • equal • compare • order • mass • list • heaviest • lightest • how many • balance scales

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Organise the class into groups and have a group member collect items—cup, rice, sand, washers, nails, cotton wool and balance scales. Allow groups time to familiarise themselves with items. • Explain how a balance scale works. Heavier items tilt down, lighter items rise. If items weigh the same, the scales are level. Allow groups to experiment to find items that balance and those that are heavier and lighter.

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• Use the cup to collect equal amounts of rice, sand, washers, nails and cotton wool. • Use the balance scales to arrange them in order from heaviest to lightest. List the order in the workbook. • Use the items to answer the questions. Fill the one cup first and place contents on one balance scale pan. Add cups carefully to the other pan of the second material until the scale balances. • Record their findings.

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What to do

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• The focus for this unit is adding on.

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• 56 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 9—Answers

Student pages 25 – 27 Unit 9–1 1. (a) 5 (b) 3 (c) 6 (d) 8 (j) 7 (s) 9 2. (a) 13 (b) 12 (k) 11 (t) 16 (c) 15 (l) 8 (u) 7 (d) 8 (m) 14 (v) 9 (e) 12 (n) 12 (w) 16 (f) 13 (o) 12 (x) 14 (g) 10 (p) 11 (h) 15 (q) 15 (i) 7 (r) 11 3. (a) 12 4. (a) 12

r o e t s Bo r e p ok u S

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1. (a) 9 (b) 2 (c) 4 (d) 5 2. Answers may vary according to students considerations as to which objects are large or small.

Unit 9–2

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• Sort objects in the classroom into large and small. Discuss the ‘medium-sized’ objects. Should they be in the large or small section?

Consolidation 9–2

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1. (a) 3 (b) 7 (c) 2 (d) 8 4. Teacher check 5. Teacher check

• Provide flashcards with addition sums to 12 with two, three or four addends. Students solve the number sentences mentally or use counters etc. to assist.

Consolidation 9–3

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• Brainstorm other items to measure in cupfuls and compare their mass, such as counters, water or pebbles.

New Wave Maths Book B – Teachers Guide • 57 •

Unit 10–1

Student page 28

Indicators

Outcomes

WM2.2, WM2.3, S2.4

The student is able to: • ask questions about collected objects or pictures following the modelling of questions by the teacher. • make conjectures (often guesses) about shapes and measurements. • respond to ‘Tell me about the shape of this (object, place or mathematical model)’ using language such as ‘flat’, ‘curved’, ‘corner’, ‘side’, ‘round’, ‘square’, ‘edge’.

Skills • identifying shapes • identifying patterns • problem-solving • working mathematically • discussing

Resources

• pencil

Language

• shape • spots • bands • five • symmetry • circular • round

• pattern • stripes • sea star • points • colour • cylindrical

r o e t s Bo Notes r e p ok u S

Main Activity (WM2.2, WM2.3, S2.4)

• The aim of the activity is for students to identify and describe shapes and patterns in the animals pictured. • The activity can be completed as a whole-class discussion or in small groups after initial teacher direction. If the latter approach is taken, groups can report their findings to the class before each student describes the shapes and patterns in his/her workbook. • Findings from whole-class discussion or small-group reports can be recorded on the blackboard/whiteboard for students to refer to when writing in their workbooks. • Stimulus questions to ask students or ideas to think about could include: Sea star (formerly known as a starfish) – What is the name of this creature? – What shape is it? – What patterns can you see? (Shape and colour) – How many ‘arms’ does it have? (Could lead to counting by 5s) – Discuss the symmetry seen. Where is/are the line(s) of symmetry? – Is it truly symmetrical? Snake (Pilbara Death Adder) – What is the name of this creature? – What shape is it? (When curled up and when stretched out) – What patterns can you see? (Shape and colour) – How could you count the bands or stripes? (Could lead to counting by 2s) – Discuss the symmetry seen. Where is/are the line(s) of symmetry? – Is it truly symmetrical? Frog – What is the name of this creature? – What shape is it? – What patterns can you see? (Shape and colour) – How many eyes does it have? (Could lead to counting by 2s) – How many legs does it have? (Could lead to counting by 4s) – How many toes on each foot? (Could lead to counting by 3s) – Discuss the symmetry seen. Where is/are the line(s) of symmetry? – Is it truly symmetrical? • Word problems could also be created for each animal. For example – ‘Five sea stars were lying on the coral. How many arms altogether?’ ‘One frog has three webbed toes on each foot. How many altogether on three frogs?’

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What to do

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• 58 • New Wave Maths Book B – Teachers Guide

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Unit 10–2

Student page 29

Indicators

Outcomes

N2.3, M2.2

Skills • measuring • tallying • comparing

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • longs • rulers • disk • blackboard • play area

Language

• longs • rulers • tally • how many • measured • smallest

• add • measuring • total • longest • bigger • record

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Provide longs and or rulers to groups of students. • Explain to the students they are to record the length of six items of their own choosing. Each item must be at least as long as their desk. Items may be found and measured outside.

• The items will be measured using either the longs or a ruler. Each item is to be measured with the same measuring item. • Ask for a demonstration of how the measuring item will be used. Ensure each measure starts level with the edge of the item being measured and the next unit commenced at the end of the previous—no gap, no overlap. • Write the name of the item being measured. Keep a tally of how many units in length the item is, then record the total number of units required to measure the length of the item. • Use the findings to answer the questions.

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What to do

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 78 – 79. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 59 •

Unit 10–3

Student page 30

Indicators

Outcomes

N2.3, N2.1a, N2.2

The student is able to: • understand he/she can tell from the numbers alone which collection has more. • select addition to deal with situations which involve combining collections. • see the connection between comparison and take away situations.

Skills • adding • subtracting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• solve • left • how many • take

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a, N2.2) Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

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Teac he r

• The focus for this unit is adding on.

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• 60 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 10—Answers

Student pages 28 – 30

Unit 10–1 1. (a) 3 (b) 5 (c) 4 (d) 9 3. Teacher check 4. Teacher check

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1. Teacher check

Unit 10–2

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• Students find photographs in magazines or bring photos from home of animals with shapes and patterns to identify and describe.

Consolidation 10–2

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1. (a) 7 (b) 5 (c) 8 (d) 6 2. (a) 7 (b) 5 (c) 8 (d) 5 3. (a) 3 (b) 8 (c) 3

• Measure other items with a uniform unit, tally and total how many were used.

Consolidation 10–3

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• Make up ‘take away’ word problems and draw pictures and diagrams to solve as in Exercise 3.

New Wave Maths Book B – Teachers Guide • 61 •

Unit 11–1

Student page 31

Indicators

Outcomes N2.3, S2.2, S2.4

Skills • modelling • identifying spatial features

Number (N2.3)

The student is able to: • select materials and methods to achieve the ends he/she has in mind. • respond to ‘Tell me about the shape of this (object, place or mathematical model)’ using language such as ‘flat’, ‘curved’, ‘corner’, ‘side’, ‘round’, ‘square’. • distinguish between a 3-D object and its face.

Resources • Base 10 MAB • counters • pencil • playdough • cartons • blocks • straws • toothpicks • 3-D shapes

Language • model • similar • drawings • second • bigger • same • shape

r o e t s Bo Notes r e p ok u S

Main Activity (S2.2, S2.4) Warm up

• Distribute materials and 3-D shapes to groups of students. Allow time for free exploration.

What to do

• Direct students to the 3-D shapes and ask them to find 3-D shapes that match the drawings in their workbook. • Use the drawings and the 3-D models to construct models of their own using materials of their own choice from those available. Each student makes one model which can then be examined by others. Ensure all models will be made. • Direct students to examine edges, corners and faces. Look at their size—are they the same, different? Are corners square or angled? Are surfaces flat or curved? Are edges straight or curved?

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4 – 5. • 62 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 11–2

Student page 32

Indicators

Resources

The student is able to: • select addition to deal with situations which involve combining collections. • see the connection between comparison and take away situations. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • adding • subtracting

Teac he r

Number (N2.3)

Language • how many • solve • circle • square • triangle

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to select 5 items. Select another 4 items. How many items do you have altogether? Five and four equal nine. • Repeat this with many different combinations to a total of 20. • Ask each student in the group to select a number of items of their own choice less than 10. Check with other group members to see who has the same number, the most and the least. • Repeat several times. • Select more items. Remove four. How many are left? (Five) Nine take four equals five. • Repeat this, asking students to verbalise their actions, many times, using up to 20 items and removing up to 10 at a time. • Select seven items. I have two left. How many do I need to take away? (Five) Seven take five equals 2. • Repeat this many times using different numbers. • Written records of these activities may be made in the workbook. Guidance may be required for students to complete the activities.

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Main Activity (N2.2, N2.3)

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New Wave Maths Book B – Teachers Guide • 63 •

Unit 11–3

Student page 33

Indicators

Outcomes N2.3, M2.3, M2.2, WM2.3

The student is able to: • estimate by ‘looking’ which objects are heavier or lighter. • locate in time and order regular activities. • make conjectures (often guesses) about shapes and measurements.

Skills • measuring • comparing • recognising progression of time

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • bathroom scales

Language • estimate • heaviest • lightest • bathroom • scales • record • results • mass • measure • Sunday • Monday • Tuesday • Wednesday • Thursday • Friday • Saturday

r o e t s Bo Notes r e p ok u S

Main Activity (M2.3, M2.2, WM2.3) Warm up

• Organise the class into groups of five.

What to do

• Ask students to make an estimate of how heavy each member of the group is in kilograms. • Students write the name of each group member in their workbook. Next to the names, write the order of mass from heaviest to lightest. Use 1 for heaviest through to 5 for lightest. • Use the bathroom scales to find the mass of each group member. • In the space provided, record the measured mass in the order, using 1 for heaviest through to 5 for lightest. • Discuss any differences from your estimate. Tall people tend to be heavier. • Discuss the activities that students do through the week. • Ask students to write, next to the days of the week, the things they did/do or would like to do. Note: Some teacher sensitivity may be required for this activity.

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 86 – 87. • 64 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 11—Answers

Student pages 31 – 33

Unit 11–1 1. (a) 7 (b) 8 (c) 6 (d) 5 2. (a) 4 (b) 2 3. (a) 3 (c) 6 (e) 7 (b) 4 (d) 6 (f) 2 4. (a) 6 (b) 10 (c) 8 (d) 8

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1. (a) 6 (b) 8 (c) 9 (d) 5 2. Teacher check

Unit 11–2

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• Construct a different model from the one chosen in Exercise 2. Complete a table showing the number of faces, edges and corners of each model pictured.

Consolidation 11–2

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1. (a) 8 (b) 5 (c) 6 (d) 7 2. Teacher check 3. Teacher check

• Complete similar activities with numbers of objects up to 20.

Consolidation 11–3

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• Estimate which objects in the classroom are heavier or lighter and test using scales.

New Wave Maths Book B – Teachers Guide • 65 •

Unit 12–1

Student page 34

Indicators

Resources

The student is able to: • use materials and diagrams to represent situations involving comparison of two groups. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • grouping • adding • counting

Number (N2.3)

Language • circles • how many • large • triangles • small • squares • tiny • count • sides

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.3) Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to select a handful of items. • Sort the items into two groups. Discuss with other group members why you sorted the items as you did. • Tell your group how many items you selected altogether. Tell the group how many items there are in one of the two groups. Repeat many times. • Written records of these type of activities may be made in the workbook. • The workbook activity also asks for the total number of sides in a group of shapes. If students need to, suggest that they write the number of sides inside each shape as they are counted. • Ask students how they might find the total number of sides. (Add sides from each shape; count on from each shape.) • Complete the activities.

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• The focus for this unit is adding on.

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• 66 • New Wave Maths Book B – Teachers Guide

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Unit 12–2

Student page 35

Outcomes

Indicators

N2.3, C&D2.2, C&D2.3, C&D2.4

The student is able to: • pose questions suggested by collected data. • organise data by classifying items in categories. • suggest ways of efficiently counting how many there are in each of several categories. • read and compare frequencies from lists and simple one-way tables.

Skills • sorting objects • tallying • classifying

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 2-D shapes

Language • tally • how many • shape • square • triangle • oval

• total • choose • different • rectangle • circle

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.3, C&D2.4) Warm up

• Distribute 2-D shapes among groups of students. Allow time for free exploration. • Discuss the construction of a tally with the class. Record items using a stroke and for every fifth item use a diagonal line across the previous four; i.e. 1111.

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• Open the workbook and look at the five foods shown. Students decide which is their favourite of the five. • When the name of the food is mentioned, students stand up if it is their favourite of these five. • Class keeps a tally of the students who stand and writes the total in space provided. • Continue until all foods have been covered. • Answer questions. • Look at the 2-D shapes. Ask students if they can see any of these shapes in the classroom. Blackboard, door, desk, cupboard, book (all rectangles). • Make a tally for each different item showing one of the shapes named. Count each different item once only. • Complete the total and answer the question. • Students can work outside as well or instead.

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What to do

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 67 •

Unit 12–3

Student page 36

Indicators

Resources

The student is able to: • see the connection between comparison and take away situations and select subtraction for ‘take away’, ‘complementary addition’ and ‘difference’ situations. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • counting on • taking away

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Number (N2.3)

Language • how many more • to make • have • need • solve

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to select three items. How many more items do I need to make seven? How will I find out? Count on. Take away (7 – 3 = 4). • Choose different numbers to repeat this activity many times. Students should verbalise their actions at all times. • Periodically ask a student to explain to the class what he/she has done. • Written records of this activity may be made in the workbook.

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Main Activity (N2.2, N2.3)

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• 68 • New Wave Maths Book B – Teachers Guide

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Unit 12—Answers

Student pages 34 – 36

Unit 12–1 1. (a) 9 (b) 7 (c) 9 (d) 8 2. (a) Teacher check (b) Teacher check 3. (a) Teacher check (b) Teacher check

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1. (a) 9 (b) 6 (c) 8 (d) 9 2. 10 circles, 4 large circles 3. 8 squares, 1 tiny square 4. 11 sides 5. 11 triangles, 8 small triangles 6. 7 sides 7. 21 sides

Unit 12–2

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• Use attribute blocks with a partner and make up number stories about shapes and colours similar to those on page 34.

Consolidation 12–2

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1. (a) 2 (b) 3 (c) 2 (d) 1 2. (a) 6 (b) 3 (c) 5 (d) 9 (e) 3 (f) 7 (g) 3 2. (a) 5c (b) 5c

• Choose five different foods and make a tally to show the order of favourites.

Consolidation 12–3

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• Make written or pictorial records of activities outlined in the ‘What to do’ section.

New Wave Maths Book B – Teachers Guide • 69 •

Unit 13–1

Student page 37

Indicators

Outcomes

The student is able to: • respond to ‘Tell me about the shape of this (object, place or mathematical model)’ using language such as ‘flat’, ‘curved’, ‘corner’, ‘side’, ‘round’, ‘square’. • sort things according to simple spatial criteria. • use repetitions of a uniform unit consistently and carefully to measure length.

N2.3, S2.4, M2.2

Skills • recognising shape attributes • comparing • classifying • measuring

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons • ruler • measuring unit

Language • colour • curved • shapes • red • green • number • order • longest • shortest

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Ask students to examine the shapes drawn in their workbook. Describe the shapes.

What to do

• Sort the shapes into two groups—those with curves and those without curves. • Discuss which shapes have been selected. • Colour the curved shapes red. • Colour all other shapes green. • Look at the rockets. Which is the longest? Which is the shortest? Which is the second longest? How can you be sure? • Use a ruler or a measuring unit (e.g. Base 10 MAB long) to compare the lengths of each of the rockets. • If using a ruler, explain to students that the mark beside the 0 on the ruler is the point to start measuring from. Read the measurement to the nearest centimetre. • Record the order of the rocket lengths using 1 for the longest and 6 for the shortest.

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Main Activity (S2.4, M2.2)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 78 – 79. • 70 • New Wave Maths Book B – Teachers Guide

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Unit 13–2

Student page 38

Indicators

Outcomes

The student is able to: • use materials and diagrams to represent multiplication stories which can be thought of a repeated addition.

N2.3, N2.2

Skills • following patterns • grouping

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Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • add • continue • pattern • groups • lots of • divide • equal groups • sets of

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

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Main Activity (N2.2)

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• Direct students to select six items. Put the items into lots of two. How many items in each lot? (Two) How many lots? (Three) Six is equal to three lots of two. • Repeat this many times with multiples to 20 for lots of 2, 3, 4, or 5 with equal amounts in each lot. Encourage students to verbalise their actions. • Select 10 items. Divide the items into two equal groups. How many in each group? (5) How many groups? (Two) Ten divided by two equals five. • Repeat this many times with multiples to 20 for groups of 2, 3, 4 or 5 with equal distribution. Students verbalise their actions. • Written records of these activities may be made in the workbook.

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New Wave Maths Book B – Teachers Guide • 71 •

Unit 13–3

Student page 39

Indicators

Resources

The student is able to: • say which is heavier of two objects of apparently similar size by hefting or using a balance beam. • realise that if he/she knows how many of the same unit fit end to end along each of two lengths, he/she can say which is bigger without directly comparing.

• Base 10 MAB • counters • variety of objects made from the same materials • ruler • 2-cm cubes • seesaw balance – made from a cardboard tube cut in half lengthwise with a ruler to balance on top.

Outcomes N2.3, M2.2

Skills • measuring • comparing • ordering

Number (N2.3)

Language • add • heaviest • same • seesaw balance • shortest

• order • lightest • material • arrange • longest

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Distribute a variety of materials to groups of students. Allow them to heft pairs of objects.

What to do

• Ask students to examine the pictures of the four items shown in their workbook. Order these items from heaviest to lightest. If required students, may collect a duster, pencil, eraser and sharpener and use hefting to help order items. • Select four objects made from the same material—plastic, wood, etc. Place them on your desks in order from lightest to heaviest. Write the items in their order in the workbook. Explain why the items were chosen in this order. • Show students how to make a seesaw balance. • Students make their own seesaw balance and practise balancing 2-cm cubes. • Talk about what happens and what they discover. • Select three objects from in the classroom. Arrange the objects from shortest to longest. • Explain how they determined which item was shortest and which was longest. • Write the names of the objects in order in the space provided.

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• The focus for this unit is adding on.

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• 72 • New Wave Maths Book B – Teachers Guide

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Unit 13—Answers

Student pages 37 – 39

Unit 13–1 1. (a) 1 (b) 1 (c) 1 (d) 2 2. Teacher check 3.

5 4

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1. (a) 6 (b) 5 (c) 1 (d) 3 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check

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Unit 13–2

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• Sort attribute blocks into those with curved and straight sides. • Arrange their coloured pencils in order from longest to shortest.

Consolidation 13–2

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1. (a) 2 (b) 4 (c) 2 (d) 3 2. Answers may vary according to size of objects chosen. 3. Teacher check 4. Teacher check 5. Teacher check

• Provide further opportunities to group sets of objects.

Consolidation 13–3

• Order items in their schoolbag from heaviest to lightest and longest to shortest.

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New Wave Maths Book B – Teachers Guide • 73 •

Unit 14–1

Student page 40

Indicators

Resources

The student is able to: • use materials and diagrams to represent situations that involve starting with one group and removing some; that is, ‘take away’.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • subtracting • counting

Number (N2.3)

Language • how many • left

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2) Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

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• The focus for this unit is adding on.

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• 74 • New Wave Maths Book B – Teachers Guide

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Unit 14–2

Student page 41

Indicators

Outcomes

The student is able to: • suggest ways of efficiently counting how many there are in each of several categories. • make block graphs using ‘real’ data. • interpret block graphs produced by others. • comment on information in displays of data produced by himself/herself and peers.

N2.3, C&D2.3, C&D2.4

Skills • tallying • reading a graph • constructing a graph

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils

Language • graph • how many • more • altogether

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.3, C&D2.4) Warm up

• Students examine the graph of hair colour shown in their workbook.

What to do

• Work through the questions with the whole class. Record answers in the space provided. • Ask all students with blonde hair to stand. Count these students. Record the number on the blackboard/whiteboard. • Ask all students with black hair to stand. Count and record. • Repeat for brown, red and any other hair colour as one separate group. • Ask students how they might show this information as a graph. Use a head for each student or a dot for each student. • Assist students to construct the graph.

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• The focus for this unit is adding on.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 108 – 109. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 75 •

Unit 14–3

Student page 42

Indicators

Resources

The student is able to: • use materials and diagrams to represent situations that involve starting with one group and removing some; that is, ‘take away’. • use materials and diagrams to represent division stories which can be thought of either as repeated subtraction or ‘sharing out’.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • subtracting • grouping • counting

Teac he r

Number (N2.3)

Language • solve • take • equals • share • evenly • groups

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

• Direct students to select nine items. Remove three items. How many items are left? (Six) • Students verbalise their actions as this process is repeated many times using different combinations of numbers. I have nine items, I take away three. I have six left. 9 take 3 equals 6. • Written records of this activity may be made in the workbook. • Direct students to select six items. Put the items into lots of two. How many items in each lot? (Two) How many lots? (Three) Six is equal to three lots of two. • Repeat this many times with multiples to 20 for lots of 2, 3, 4, or 5 with equal amounts in each lot. Encourage students to verbalise their actions. • Select 10 items. Divide the items into two equal groups. How many in each group? (5) How many groups? (Two) Ten divided by two equals five. • Repeat this many times with multiples to 20 for groups of 2, 3, 4 or 5 with equal distribution. Students verbalise their action. • Written records of these activities may be made in the workbook.

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Main Activity (N2.2)

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• 76 • New Wave Maths Book B – Teachers Guide

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Unit 14—Answers

Student pages 40 – 42

Unit 14–1 1. (a) 9 (b) 4 (c) 5 (d) 7 2. (a) 6 (b) 4 (c) 2 (d) 11 3. Teacher check

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1. (a) 7 (b) 6 (c) 6 (d) 7 2. 5 3. 5 4. 4 5. 6 6. 6 7. 3

Unit 14–2

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• Students could draw their own pictures of various numbers of animals and use the pictures to solve subtraction problems.

Consolidation 14–2

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1. (a) 8 (b) 9 (c) 8 (d) 9 2. (a) 4 (b) 5 (c) 6 3. (a) 5 (b) 3

• Create a pictograph of types or colour of footwear worn or schoolbags used by students.

Consolidation 14–3

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• Provide further opportunities for students to take away and share sets of objects or pictures.

New Wave Maths Book B – Teachers Guide • 77 •

Unit 15–1

Student page 43

Indicators

Outcomes

The student is able to: • copy pictures composed of simple geometric figures so that the main components are recognisable in shape, position and orientation.

N2.3, S2.2

Skills • recognising shape attributes • modelling

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • ruler • 1-cm dot grid paper (see page 198) • elastic bands • geoboards • coloured pencils/ crayons

Language • copy • shapes • grid

r o e t s Bo Notes r e p ok u S

• The focus for this unit is adding on.

Warm up

• Distribute elastic bands and geoboards among groups of students. Allow students time to explore using the boards. Stress safety issues when using elastic bands.

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• Direct students to make given shapes using the geoboards—a square, a rectangle, a triangle, shapes of their own choosing. Describe the shapes within the group.Talk about size, edges, number of pins inside. Ask students if they can make the same shape with more or fewer pins inside. • If geoboards are not available, the same activity may be undertaken using dotted grid paper. • Students may be directed to copy shapes that other group members have made on their geoboards. • The workbook provides an opportunity for students to copy shapes on to the grid paper. A ruler will be required to measure the lengths of the sides of the shapes to see how many dots in length each side is. Use the ruler to draw straight lines. Note: The length along the diagonal will be longer than horizontal or vertical lines. • Suggest that each shape is drawn using a different colour.

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What to do

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Main Activity (S2.2)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 2 – 3. • 78 • New Wave Maths Book B – Teachers Guide

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Unit 15–2

Student page 44

Indicators

Resources

The student is able to: • use materials and diagrams to represent situations that involve starting with one group and removing some; that is, ‘take away’. • use materials and diagrams to represent situations involving comparison of two groups. • see the connection between comparison and take away situations.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills • subtracting • comparing

Teac he r

Number (N2.3)

Language • take • difference • between • sets • how many • more

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute concrete materials to groups of students. Allow time for free play.

What to do

• Direct students to select eight items. Arrange these items in a row. Select another three items and arrange in a row below the first set of items. How many are there more in the first set? or, what is the difference between the two sets? • Show students how this is recorded—8 – 3 = 5. • Repeat comparison of sets a number of times using different combinations of basic facts. • Students are to describe what they are doing each time. ‘I have a set of eight items. I have a set of three items. The difference between the two sets is five.’ Or, ‘I have a set of eight and a set of three. There are five more items in the set of eight’. • Written records of this activity are available in the workbook. Students should use concrete materials if they require assistance.

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Main Activity (N2.2)

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New Wave Maths Book B – Teachers Guide • 79 •

Unit 15–3

Student page 45

Indicators

Outcomes

The student is able to: • recognise ‘key times’ on an analog clock and tell the time of day on digital clocks in hours and minutes. • know that the numbers, position and movement of the hands on clocks reflect the passage of time.

N2.3, M2.2, WM2.1

Skills • measuring • telling time

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • large-faced clock with readily movable hands

Language

• take • twelve-hour time • clock face

r o e t s Bo Notes r e p ok u S

Main Activity (WM2.1) Warm up

• Use a large-faced analog clock to display given times for students to read. • Explain to the class that the long hand is the minute hand. The minute hand tells us how many minutes past the hour or until the next hour. How many minutes in an hour? (60) • The little hand is the hour hand. It points to the hour. As the minute hand moves around the clock face the hour hand moves on to the next number—the next hour. When the hour hand is between two numbers it shows the hour as the number that it has just left; e.g. between 4 and 5, the hour is still 4 o’clock plus the number of minutes. • Display many hour times for students to read. Where is the minute hand on the hour? (Always at 12) Where is the hour hand on the hour? (Always at the number showing the hour)

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• The focus for this unit is basic facts of subtraction.

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• Complete activities in the workbook to provide written records.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 98 – 99. • 80 • New Wave Maths Book B – Teachers Guide

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Unit 15—Answers

Student pages 43 – 45

Unit 15–1 1. (a) 7 (b) 2 (c) 5 (d) 8 2. 2 3. 11 4. 4 5. 3 6. 8 7. 4

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1. (a) 6 (b) 9 (c) 7 (d) 7 2. Teacher check

Unit 15–2

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• Make a shape on a geoboard or dotted grid paper and ask a classmate to copy it.

Consolidation 15–2

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1. (a) 2 (b) 6 (c) 1 (d) 3 2. (a) 6 o’clock (b) 3 o’clock (c) 9 o’clock (d) 10 o’clock (e) 5 o’clock (f) 1 o’clock (g) 2 o’clock (h) 7 o’clock (i) 4 o’clock

• Provide opportunities for similar activities using concrete materials.

Consolidation 15–3

• Direct students to look at the classroom clock and study the time passing. Introduce half past or 30 past etc.

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New Wave Maths Book B – Teachers Guide • 81 •

Unit 16–1

Student page 46

Indicators

Outcomes WM2.1, WM2.2, WM2.3, M2.1, M2.2

Skills • problem-solving • working mathematically • measuring • hefting • estimating mass

The student is able to: • provide examples of his/her family measuring things for a purpose. • ask questions about collected objects or pictures following the modelling of questions by the teacher. • make conjectures (often guesses) about shapes and measurements. • attend to the right attribute when directly comparing things. • say which is heavier of two objects by hefting.

Resources • pencil • orange • banana • basketball • shoe • 1 kg breadcrumbs

Language • weigh • heft • shape • smaller • lighter • kilogram

• measure • size • larger • heavier • level

r o e t s Bo Notes r e p ok u S

What to do

• The aim of the activity is for students to determine the heavier of two objects by viewing a photograph of a student hefting them. • The activity can be completed as a whole-class discussion; or in small groups or individually after initial teacher direction. If either of the latter approaches is taken, groups can report findings to the class before each student writes his/her explanation in the workbook. • Findings from whole-class discussions etc. can be recorded on the blackboard/whiteboard for students to refer to when writing in their workbooks. • Stimulus questions to ask students or ideas to think about could include: Top photograph – Are the objects the same size? Describe them. – Are the objects the same shape? Describe them. – How level is the boy holding the objects? – Are the objects hollow or solid inside? Middle photograph – Are the objects the same shape? Describe them. – Are the objects the same size? Describe them. – How level is the boy holding the objects? – Are the objects hollow or solid inside? – Does a larger object mean it is always heavier? Bottom photograph – Are the objects the same shape? Describe them. – Are the objects the same size? Describe them. – How level is the boy holding the objects? – What measure is marked on the breadcrumb packet? – Could the shoe weigh less or more than 1 kg? How could you find out? • After students have decided which object they think is heavier in each photograph, the corresponding box is ticked and an explanation is written. • Compare answers and explanations among the class members. • Students could heft both objects to verify answers. However, these could differ according to the size and mass of the orange, banana and basketball and also the type of shoe. Note: In this activity, the student estimated which was heavier before hefting. Results: Estimate Heavier object orange orange basketball basketball breadcrumbs breadcrumbs

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Main Activity (WM2.1, WM2.2, WM2.3, M2.1, M2.2)

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• 82 • New Wave Maths Book B – Teachers Guide

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Unit 16–2

Student page 47

Outcomes

Indicators

N2.3, C&D2.1, C&D2.2, C&D2.4

The student is able to: • identify possible results of an action or event by collecting data. • with guidance, organise outcomes from simple experiments consistently. • comment on information in displays of data produced by himself/herself and peers.

Skills • graphing • analysing data

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 6-sided die • coloured pencils/ crayons

Language • take • six-sided die • colour • graph • total • biggest • bigger

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.1, C&D2.2, C&D2.4) Warm up

• Organise the class into small groups and provide each group with a 6-sided die to explore freely.

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• Direct each group to throw the die once. Ask what number is shown.Throw the die again. What number is shown? Repeat several times. • Throw the die twice and add the two numbers that show. Who has the biggest total? Who has the smallest? Do any group members have the same total? Ask students to explain why totals may be different. • Use the workbook graph activity to record the total of three throws of the die. When graphing a different colour may be used for each throw. • Repeat graphing for another ‘three throw total’. • Record the total of two throws of the die. • Repeat with a second graphing of two throws. • Which graph has the biggest total? Ask for explanations from students. If students have used different colours for each throw they may see that the ‘three throw’ numbers were small and the ‘two throw’ numbers big. This will assist them in finding an explanation. • Explanations of why totals may not be expected may introduce chance and the randomness of adding numbers from dice throws.

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What to do

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Teac he r

• The focus for this unit is basic facts of subtraction.

o c . che e r o t r s super

For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 83 •

Unit 16–3

Student page 48

Indicators

Outcomes

The student is able to: • use a range of different everyday expressions for the addition and subtraction operations. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number. • remember many basic addition facts and work out the others. • use his/her understanding of the relationship between addition and subtraction to work out subtractions.

N2.3, N2.2

Skills • adding • subtracting • counting • adding on

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • counters

Language

• take • how many • number sentence • add

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute counters to groups of students, allow them to explore addition, subtraction, adding on etc. within their groups.

What to do

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Main Activity (N2.2, N2.3)

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• Direct students to their workbook. Tell them they may complete the sums by just writing the answers if they are able to. If students require concrete materials, use counters to represent the numbers, then add, subtract, add on as required. • Provide assistance where needed. • If groups of students are having difficulties work with the group collectively.

o c . che e r o t r s super

For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46 – 47. • 84 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 16—Answers

Student pages 46 – 48

Unit 16–1 1. (a) 4 (b) 1 (c) 5 (d) 2 2. Teacher check 3. Teacher check 4. Teacher check

r o e t s Bo r e p ok u S

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Teac he r

1. Teacher check

Unit 16–2

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(d) 2

• Collect a variety of objects to estimate which is the heavier between two and verify by hefting.

Consolidation 16–2

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1. (a) 7 (b) 4 (c) 8 2. (a) 6 (f) 7 (k) 5 (b) 8 (g) 11 (l) 15 (c) 8 (h) 6 (m) 2 (d) 3 (i) 5 (n) 7 (e) 2 (j) 3 (o) 5 3. (a) 8 (j) 6 (b) 3 (k) 2 (c) 11 (l) 7 (d) 7 (m) 3 (e) 4 (n) 6 (f) 16 (o) 7 (g) 4 (h) 7 (i) 8

• Throw a six-sided die four times and compare results with those in this activity.

Consolidation 16–3

o c . che e r o t r s super

R.I.C. Publications® www.ricpublications.com.au

• Provide further opportunities to add, subtract and add on numbers in written form.

New Wave Maths Book B – Teachers Guide • 85 •

Unit 17–1

Student page 49

Indicators

Outcomes

N2.3, S2.3

The student is able to: • make symmetrical pictures using a variety of means which include cut-out figures and flipping and drawing around templates.

Skills • measuring • telling time

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • ruler • mirror/mira

Language

• take • copy • pattern • mirror • image • above

r o e t s Bo Notes r e p ok u S

Main Activity (S2.3) Warm up

• If mirrors/miras are available distribute these to groups of students. Allow time for students to explore using the mirrors/miras. Encourage students to explain what they can see when looking into the mirror/mira.

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• Direct students to their workbook. Place a mirror/mira on the dotted line—look into it to see the mirror image. Draw the image. • Explanation of the drawing may be required. If so, start at the top of the drawing, draw a line two squares long along the top line to the right of the dotted line. Use a ruler to draw the straight line. Where does the next line go? Down the page for two squares. Draw the line. • Continue to ask the class where the next line is to be drawn and how long it will be before they draw the line. If the drawing is accurate they will finish on the bottom line at the dotted line. • Repeat the process with mirrors/miras and/or verbal explanations for the remaining four drawings.

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What to do

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Teac he r

• The focus for this unit is basic facts of subtraction.

o c . che e r o t r s super

For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26 – 27. • 86 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 17–2

Student page 50

Indicators

Outcomes

N2.3, N2.2

Skills • subtracting • adding • adding on • problem-solving • counting

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • counters

Language

• take • add • solve • number sentences

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute counters to groups of students, allow them to explore addition, subtraction, adding on, etc. within their groups.

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• Direct students to their workbook.Tell them they may complete the sums by just writing the answers if they are able. If students require concrete materials, use counters to represent the numbers, then add, subtract, add on as required. • Provide assistance where needed. • If groups of students are having difficulties work with the group collectively. • Set the challenge for students to explore and find out why 3 + 3 + 3 and 3 lots of 3 are the same. Encourage discussion and debate. Students will realise that they are the same if encouraged to use counters to represent both sums. • Students record their findings and explanation.

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What to do

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Main Activity (N2.2, N2.3)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46 – 47. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 87 •

Unit 17–3

Student page 51

Indicators

Outcomes

The student is able to: • locate in time and order regular activities. • connect mathematical ways of ordering times of day and year to the ways we order time by natural events (the ground becomes clear, first light, sunrise, the Wet) … or by ‘cultural’ events (New Year, school starts, Naidoc Week).

N2.3, M2.2, WM2.1

Skills

• reading a calendar

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language • take • January • March • May • July • September • November • month

• calendar • February • April • June • August • October • December

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, WM2.1) Warm up

• Open workbook to activity page. • Look at the calendar - How many months are there? Name the months.

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• Point to the month your birthday is in. • Point to the month of the year we are in. • Which month is Christmas in? • How many months have 30 days? Which are they? • Name the months with 31 days. • Which month does not have either 30 or 31 days? • How many days does February have? Always? Explain about leap years. • Work with the whole class to complete the questions relating to the calendar.

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What to do

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Teac he r

• The focus for this unit is basic facts of subtraction.

o c . che e r o t r s super

• 88 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 17—Answers

Student pages 49 – 51

Unit 17–1 1. (a) 9 (b) 2 (c) 6 2. (a) 11 (m) 18 (b) 11 (n) 10 (c) 4 (o) 9 (d) 9 (p) 7 (e) 9 (q) 7 (f) 6 (r) 5 (s) 9 (g) 2 (h) 1 (t) 8 (i) 6 (u) 11 (j) 14 (v) 4 (k) 9 (w) 9 (l) 11 (x) 4 3. Both equal 9. Explanation – teacher check

(d) 8

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 3 (b) 6 (c) 5 (d) 1 2. Teacher check 3. Teacher check

Unit 17–2

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• Students could attempt to create their own shapes on grid paper on one side of a line and then complete the mirror image. (Hint: Use straight lines only.)

Consolidation 17–2

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1. (a) 3 (b) 7 (c) 1 (d) 4 2. (a) June (b) Teacher check (20 Jan – 26 Jan) (c) March (d) October (e) September (f) Teacher check (g) Teacher check (h) August

• After a few days, present a similar challenge to the students as in Exercise 3. Change the numbers to 5 + 5 + 5 + 5 and 4 lots of 5.

o c . che e r o t r s super

R.I.C. Publications® www.ricpublications.com.au

Consolidation 17–3

• Ask further questions based on the calendar for students to find the answers.

New Wave Maths Book B – Teachers Guide • 89 •

Unit 18–1

Student page 52

Indicators

Outcomes

The student is able to: • use materials and diagrams to represent situations involving comparison of two groups. • use a range of different everyday expressions for the addition and subtraction operations. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

N2.3, N2.2

Skills • problem-solving • adding • counting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• take • solve • problems

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.3) Warm up

• Distribute concrete materials among groups of students and allow time for free play.

What to do

• Direct students to select twelve items. Select another seven items. How many items altogether? Students verbalise their actions: 12 + 7 = 19. • Repeat this many times with totals extending beyond 20. • Direct students to select eighteen items. ‘You need to have a total of twenty-five. How many more do you need?’ Students will verbalise this activity as: 18 and 7 more to make (equal) 25. • Repeat this activity many times with totals extending beyond 20. • Written records of these activities may be found in the workbook.

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Teac he r

• The focus for this unit is basic facts of subtraction.

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• 90 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 18–2

Student page 53

Indicators

Outcomes

The student is able to: • compare heights (or lengths) of the columns in a block graph to place categories in order. • read and compare frequencies from lists and simple one-way tables. • interpret block graphs produced by others.

N2.3, C&D2.3, C&D2.4

Skills • graphing • analysing data

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil

Language

• take • graph • how many • more than • total • most common • least

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Direct students to their workbook. • Discuss the two different ways the data are represented on the page—pictures for the first graph and dots for the second. Also discuss how each picture or dot is the same size on the graph.

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• Look at the graph of the animals.What animals and birds are shown on the graph? (Peacock, reindeer, flamingos, camel.) • How many of each animal or bird is there? Write the total of each on the graph. • Either by comparison or by using the totals, answer the questions about the graph. Work with the class to guide them. • Repeat the process for the second graph, starting with the means of getting to school, working through the totals, and finally answering the questions.

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What to do

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Main Activity (C&D2.3, C&D2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 91 •

Unit 18–3

Student page 54

Indicators

Outcomes

The student is able to: • use materials and diagrams to represent multiplication stories which can be thought of as repeated addition. • use multiples (i.e. equivalent groups) to count and compare collections.

N2.3, N2.2

Skills

• following instructions • recognising patterns • skip counting

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language • take • count • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute counters to groups of students. Ask them to arrange them in two rows. Practise counting by twos. • Repeat, arranging the counters in three and four rows.

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• Direct students to their workbook. • Count the first five dots in row 1. Colour these five dots red. Repeat for rows 2 and 3. • Count all the dots you coloured in rows 1, 2, and 3 by threes. What is the best way to do this? (Make lots of 3 by using the first column in each row as one set, the second column as another set of 3 and so on.) • How many red dots? Could this total be said in a different way? (5 lots of 3 = 15.) • Colour the dots in rows 6 and 7 green. Count these by fours. ‘What is a way of making lots of four?’ (Circle the first two rows of two – two dots from row 6 and two from row 7.) How many green dots? How might this be written? (5 lots of 4 = 20.) • Colour the dots in rows 9 and 10 blue. Count these by two. The best way to make pairs is to use the columns in rows 9 and 10. How many blue dots? (20) This might be written as …? (10 lots of 2 = 20) • Complete the last two activities. Draw explanations from students leading to counting by 10 and 5.

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What to do

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Main Activity (N2.2, N2.3)

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• 92 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 18—Answers

Student pages 52 – 54

Unit 18–1 1. (a) 3 (b) 5 (c) 6 (d) 2 2. (a) 2 (b) 1 (c) 6 3. (a) 3 (b) 5 (c) 6

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 9 (b) 8 (c) 7 (d) 4 (e) 13 2. (a) 19 (b) 21 (f) 30 (c) 26 (g) 3 (d) 7 (h) 16

Unit 18–2

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• Provide further opportunities to solve number sentences using concrete materials with totals extending beyond 20.

Consolidation 18–2

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• Create a pictograph or dot graph of how students in their class get to school.

Consolidation 18–3

o c . che e r o t r s super

R.I.C. Publications® www.ricpublications.com.au

• Complete the same activity using a 1–100 grid.

New Wave Maths Book B – Teachers Guide • 93 •

Unit 19–1

Student page 55

Indicators

Outcomes

N2.3, S2.2

The student is able to: • draw figures which show the essential spatial features of named geometric shapes. • copy pictures composed of simple geometric figures so that the main components are recognisable in shape, position and orientation.

Skills • modelling • exploring 2-D shapes

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • ruler • coloured pencils/ crayons • geoboard • elastic bands

Language

• take • dotted grid • shape • different • sides

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute geoboards and elastic bands to groups of students and allow time to explore. Stress safety rules with use of elastic bands.

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• Direct students to make a three-sided figure on the geoboard. What shape is it? How many sides does it have? Are all sides the same length? Can you make a triangle with all sides the same length? Can you make a triangle with two sides the same length? Can you make a triangle with three sides of different lengths? • Copy one of your triangles into your workbook. • Make a four-sided figure on the geoboard. Are all sides the same length? Can you make one with all sides the same length? Can you make a four-sided figure with different length sides? • Draw one of your four-sided figures in your workbook. Use a colour different from the triangle you drew. • Repeat this for the five- and six-sided shapes. • Students may be told names of shapes but do not need to remember them.

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What to do

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Main Activity (S2.2)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 2 – 3. • 94 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 19–2

Student page 56

Indicators

Outcomes

N2.3, N2.2

The student is able to: • use materials and diagrams to represent division stories which can be thought of either as repeated subtraction or ‘sharing out’.

Skills • grouping • dividing

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• take • division • lots of • how many • group • share

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to select six items. Put the items into lots of two. How many items in each lot? (Two) How many lots? (Three) Six is equal to three lots of two. • Repeat this many times with multiples to 20 for lots of 2, 3, 4, or 5 with equal amounts in each lot. Students to verbalise their actions. • Select 10 items. Divide the items into two equal groups. How many in each group? (5) How many groups? (Two) Ten divided by two equals five. • Repeat this many times with multiples to 20 for groups of 2, 3, 4 or 5 with equal distribution. Students verbalise their actions. • Written records of these two activities may be made in the workbook.

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Main Activity (N2.2)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46 – 47. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 95 •

Unit 19–3

Student page 57

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • describe how his/her graph shows the results of the data collection.

N2.3, M2.2, C&D2.4

Skills

• recognising months

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 1-cm cubes • thumb • duster • sharpener • stapler • eraser

Language • take • cubes • measure • length • graph

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Have available items to be measured—pencil, duster, sharpener, stapler and rubber, along with 1-cm cubes—so that groups of students are able to collect the materials. • Allow students to experiment with measuring lengths of the items without any specific direction from the teacher.

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• Ask students how they could measure the length of one of the items using 1-cm cubes. Use one cube and mark off the number of times it fits the item; or, place a number of cubes in a line alongside the item then count how many cubes were used. • Measure the pencil using 1-cm cubes. • Use the graph in the workbook to record the number of cubes used by colouring one box in the pencil column for each cube used. • Repeat this for the other five items. • Discuss the results of the measuring with students, particularly any variance in measures. Find out why this may have happened.

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What to do

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Main Activity (M2.2, C&D2.4)

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• 96 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 19—Answers

Student pages 55 – 57

Unit 19–1 1. (a) 6 (b) 4 (c) 9 2. (a) Teacher check (b) Teacher check (c) Teacher check (d) Teacher check (e) Teacher check (f) Teacher check 3. (a) 2 (b) 4

(d) 8

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 4 (b) 3 (c) 1 (d) 6 2. Teacher check

Unit 19–2

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(d) 2

• Compare the shapes drawn on his/her workbook with a classmate and discuss.

Consolidation 19–2

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• Students could draw their own pictures to circle or colour in specified ‘lots of ’.

Consolidation 19–3

o c . che e r o t r s super

R.I.C. Publications® www.ricpublications.com.au

• Find other items in their desks or around the classroom to measure using 1-cm cubes.

New Wave Maths Book B – Teachers Guide • 97 •

Unit 20–1

Student page 58

Indicators

Outcomes

The student is able to: • use materials and diagrams to represent multiplication stories. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number. • use multiples (i.e. equivalent groups) to count and compare collections.

N2.3, N2.2, N2.3

Skills • skip counting • grouping • adding on

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• take • sets • objects • how many • lots of • altogether • count

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute concrete materials among groups of students and allow time for free play.

What to do

• Direct students to make three sets of five items. How many sets are there? (3) How many items in each set? (3) How many items altogether? (15) • Repeat this activity many times using up to ten sets of 2, 3, 4, or 5 items. Focus on smaller sets and numbers of items. • Students are to verbalise their actions—I have three sets (or lots of) five. I have 15 altogether. • Written form may be shown as: 3 lots of 5 = 15 or 3 x 5 = 15. • Written records of this activity may be made using the workbook. Encourage students to use concrete materials if they are having difficulties using the diagrams.

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Main Activity (N2.2, N2.3)

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• 98 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 20–2

Student page 59

Indicators

Outcomes

N2.3, C&D2.3, C&D2.4

The student is able to: • suggest ways of efficiently counting how many there are in each of several categories. • comment on information in displays of data produced by himself/herself and peers.

Skills • sorting objects • recording data

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • attribute block • hoops

Language

• take • attribute • blocks • Venn diagram • Carroll diagram • total • thick • thin • round

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute attribute blocks to groups of students. Allow time for free exploration.

What to do

• Direct students to sort the blocks into two groups. Ask groups to explain how they sorted their blocks. • Allow time to make a second sorting using two criteria. Explain how the blocks were sorted. • Repeat using three criteria for sorting the blocks. • Repeat using four criteria for sorting the blocks. • Introduce a Venn diagram as a means of sorting.Two hoops overlapping as in the workbook may assist. • Ask students to select all the large shapes and all the yellow shapes from their attribute blocks. • Place all the large shapes in one hoop. Place all the yellow shapes in one hoop. • Ask students if there are any shapes that belong in both groups. The answer is yes. Ask where these items might be placed. The correct place is in the overlap of the two hoops. This shows the items belong to both groups. • Count the items in each of the three groups and record the totals in the Venn diagram in the workbook. • Using all the attribute blocks, sort them into thick and thin piles. • Using just the thick blocks, sort these again into two groups—one for round and another for not round. • Sort the thin blocks into round and not round groups. • There are now four piles of blocks. These sortings can be recorded on a Carroll diagram as in the workbook. Count the round, thick blocks and write the total in the top left box. Count the round, thin blocks and record the total in the top right box. Count the thick, not round blocks and record in the bottom left box. Finally count the thin, not round blocks and record in the bottom right box. • The Carroll diagram is now complete, showing the total of each of the four collections of blocks.

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Main Activity (C&D2.3, C&D2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 108 – 109. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 99 •

Unit 20–3

Student page 60

Indicators

Resources

The student is able to: • use materials and diagrams to represent multiplication stories. • use counting strategies such as combining collections and counting the lot counting on form the first number, counting on from the largest number. • use multiples (i.e. equivalent groups) to count and compare collections.

• Base 10 MAB • counters • pencil • concrete materials

Outcomes N2.3, N2.2

Skills

• counting on • skip counting

Teac he r

Number (N2.3)

Language • take • how many • lots of • altogether

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Distribute concrete materials among groups of students and allow time for free play.

What to do

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Main Activity (N2.2)

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• 100 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 20—Answers

Student pages 58 – 60

Unit 20–1 1. (a) 4 (b) 5 (c) 8 (d) 7 2. Teacher check

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 2 (b) 6 (c) 4 (d) 3 (b) 15 2. (a) 5 3. (a) 12 15 (b) (c) 18 (d) 22

Unit 20–2

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• Count the number of sides on attribute blocks. Instruct students to use the same type of shape to practise skip counting and then use shapes selected at random.

Consolidation 20–2

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1. (a) 9 (b) 2 (c) 8 (d) 3 2. (a) 4 lots of two. 8 altogether (b) 5 lots of three. 15 altogether (c) 8 lots of four. 32 altogether (d) 3 lots of five. 15 altogether

• Repeat the Venn diagram using all large shapes and all red shapes. • Repeat the Carroll diagram changing, ‘Not Round/Round’ to ‘Not Square/Square’.

o c . che e r o t r s super

R.I.C. Publications® www.ricpublications.com.au

Consolidation 20–3

• Practise counting in twos, threes, fours etc. using counters.

New Wave Maths Book B – Teachers Guide • 101 •

Unit 21–1

Student page 61

Indicators

Outcomes N2.3, N2.1a, S2.2

The student is able to: • read, write and say the numbers in order to beyond 100 and count on or back from any number to 100. • identify mathematical shapes such as cones or rectangles on which familiar things are based.

Skills • counting • following instructions

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil

Language • take • join • dots • number order

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of subtraction.

Warm up

• Undertake a series of counting activities with the class—by ones, twos etc. Vary the total to a maximum of 40.

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• Ask students to open their workbook. • The activities require a series of dots to be joined in the correct order, starting from the number 1. • Ask students to place their pencil on the number 1. Hold the pencil there and point to the number 2. Draw a line between 1 and 2. • Keep the pencil at 3 and point to the number 3. Draw a line between 2 and 3. • Continue like this until the shape is drawn. • Ask students to name the shape. • Students who are able to may complete the other two drawings by themselves. For those who are having difficulties, continue with the step-by-step process as for the star.

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Main Activity (N2.1a, S2.2)

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• 102 • New Wave Maths Book B – Teachers Guide

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Unit 21–2

Student page 62

Indicators

Outcomes N2.3, N2.2

The student is able to: • use materials and diagrams to represent division stories which can be thought of either as repeated subtraction or ‘sharing out’. • use multiples (i.e. equivalent groups) to count and compare collections.

Skills • grouping • sharing

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • add • share • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of whole numbers.

Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

• Direct students to select six items. Asks students to share these items between two groups. How many in each group? (3) • Ask students to explain what they have done. ‘I have six items shared between two groups. I have three items in each group.’ • Repeat this many times with different numbers of items to 20 shared evenly into specified groups of 2, 3, 4 or 5. • Written records of these activities may be made in the workbook. Use concrete materials if required. • Activity 3 may be completed using the diagrams or by having the students use concrete materials to represent each drawing.

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Main Activity (N2.2, N2.3)

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New Wave Maths Book B – Teachers Guide • 103 •

Unit 21–3

Student page 63

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • estimate the number of times a unit of length which he/she can handle will fit along an object and show improvement in his/her estimates as a result of testing.

N2.3, M2.2, M2.3

Skills • estimating length • measuring length

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • Base 10 MAB longs • Base 10 MAB flats • cubes

Language

• add • estimate • longs • cubes • height • length

• measure • trade • flats • width • span

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, M2.3) Warm up

• Distribute the Base 10 MAB longs, flats and large cubes. Direct students to use them to measure items within their group.

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• Ask students to open their workbook and record an estimate of how many longs it would take to measure the width of the desk. Write the estimate in the space provided. • Continue to make an estimate for each of the items to be measured. • Use longs to measure the width of the desk. Write in the space provided the actual number of longs used. • Can you trade these longs for a flat? How many longs do you need to make a flat? (10) If you can trade, do so. Record the number of flats and longs you now have in the space provided. • Repeat the measurement for each item, trading if able. Ask how many flats are required to make a large cube. If enough flats are made from trading the longs, trade them for a large cube. Record the pieces of wood traded in the space provided.

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• The focus for this unit is addition of whole numbers.

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• 104 • New Wave Maths Book B – Teachers Guide

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Unit 21—Answers

Student pages 61 – 63

Unit 21–1 1. (a) 18 (b) 20 (c) 17 2. (a) 2 (b) 4 (c) 3 (d) 4 3. (a) 10 (b) 10 (c) 9

(d) 18

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1. (a) 7 (b) 5 (c) 1 (d) 6 2. (a) star (b) house (c) yacht

Unit 21–2

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(d) 20

• Complete further dot-to-dot activities with numbers extending beyond 20.

Consolidation 21–2

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1. (a) 22 (b) 23 (c) 19 2. Teacher check

• Provide further opportunities to share pictures of objects into specified equal groups.

Consolidation 21–3

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• Estimate, then measure, how many rulers will match the length or width of each item listed.

New Wave Maths Book B – Teachers Guide • 105 •

Unit 22–1

Student page 64

Indicators

Outcomes N2.3, N2.1a, N2.2

The student is able to: • count coins, including in multiples of 5c, 10c 20c, 50c, $1 and $2, and record total amounts. • use materials and diagrams to represent division stories which can be thought of either as repeated subtraction or ‘sharing out’.

Skills • grouping • adding money

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials • plastic coins

Language • add • groups • how many • lots of • sum

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a, N2.2) Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

• Direct students to select eight items. Put these items into lots of two. How many lots of two are there? (4) Students may say this as: eight is equal to four lots of 2. • Repeat this many times with up to twenty items shared into lots of 2, 3, 4 or 5. • Students say what they have done each time. • Written records of this activity can be found in the workbook. • Plastic coins may be used to assist students in Exercise 4. Add the coins to find the total value of the coins shown.

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• The focus for this unit is addition of whole numbers.

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• 106 • New Wave Maths Book B – Teachers Guide

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Unit 22–2

Student page 65

Indicators

Outcomes

The student is able to: • describe ways in which his/her social behaviour is regulated by numbers and measurements. • recognise as mathematical some common ways of doing things. • know that the numbers, position and movement of the hands on clocks reflect the passage of time. • ask questions about objects or pictures following the modelling of questions by the teacher.

WM2.1, WM2.2

Skills • working mathematically • recognising numbers • explaining • questioning

Resources • pencil • examples of photographed items (optional) – digital radio/ alarm clock – computer keyboard – TV/video remote control – mobile phone

Language • number • numeral • digit • digital radio/alarm clock • computer keyboard • TV/video remote control • mobile phone

r o e t s Bo Notes r e p ok u S

What to do

• The aim of the activity is for students to identify the object in each photograph and explain what the numbers are used for on each. • The activity can be completed individually, with a partner or small group, or as a class. • Direct students to look at each photograph in their workbook. Individually, or after class, partner, or small-group discussion, students identify the items and write an explanation about what the numbers are used for. • Words and phrases could be written on the blackboard/whiteboard before students write in their workbooks.

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New Wave Maths Book B – Teachers Guide • 107 •

Unit 22–3

Student page 66

Indicators

Outcomes

N2.3, N2.2

Skills • sharing out • grouping

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials

Language

• add • equal share • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of single digit whole numbers.

Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

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Main Activity (N2.2, N2.3)

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• 108 • New Wave Maths Book B – Teachers Guide

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Unit 22—Answers

Student pages 64 – 66

Unit 22–1 (d) 25

Possible answers Radio alarm clock • digital 12-hour time in a.m or p.m. • FM/AM station guide Keyboard • (top row) function keys for computer commands • (second top row) numeral keys for typing numbers • numeral keys to the right on keyboard TV/Video remote control • numbers to change TV channels Mobile phone • number keys for phone numbers • number keys to be used in SMS messages. • digital time on screen

r o e t s Bo r e p ok u S

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1. (a) 26 (b) 24 (c) 21 3 2. (a) 5 (b) 3. Teacher check 4. (a) 15c (b) 50c (c) $1 (d) $1

Unit 22–2

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• Provide further opportunities for students to draw their own diagrams to show ‘lots of ’ stories as in Exercise 3.

Consolidation 22–2

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1. (a) 9 (b) 9 (c) 6 2. (a) 2 (b) 3 (c) 4 (d) 5

• Students can identify other items in the classroom, school or home environment that use numbers, and describe how they are used.

Consolidation 22–3

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• Provide further opportunities to students to share pictures of items or concrete materials among a specified number.

New Wave Maths Book B – Teachers Guide • 109 •

Unit 23–1

Student page 67

Indicators

Outcomes N2.3, S2.3, WM2.4

The student is able to: • make symmetrical pictures using a variety of means which include cut-out figures and flipping and drawing around templates. • respond to questions such as ‘Is your working correct?’ by checking each stage of the work.

Skills • mirror imaging • exploring symmetry

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • mirror/mira • coloured pencils/ crayons

Language • add • copy • pattern • mirror image • how many • squares

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of single-digit whole numbers.

Warm up

• If mirrors are available, distribute these to groups of students. Allow time for students to explore using the mirrors. Encourage students to explain what they can see when looking into the mirror.

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• Direct students to their workbook. Place a mirror on the dotted line – look into the mirror to see the mirror image. Draw the image. • An explanation of how to complete the drawing may be required. If so, start at the top of the drawing, draw a line two squares long (using your ruler as a guide) along the top line to the right of the dotted line. Ask where the next line goes. (Down the page for one square.) Draw the line. • Continue to ask the class where the next line is to be drawn and how long it will be, then have students draw the line. • If the drawing is accurate, they will finish on the line one square up from the bottom of the grid. • Students colour both sides of the drawing, using different colours. • Answer the questions and provide an explanation for the answer given to Exercise 4(d). Share explanations.

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Main Activity (S2.3, WM2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26 – 27. • 110 • New Wave Maths Book B – Teachers Guide

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Unit 23–2

Student page 68

Indicators

Outcomes N2.3, N2.2, N2.1a

Skills • counting on • sharing

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language •add •how much •altogether •how many •share

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of single digit whole numbers.

Warm up

• Distribute concrete materials among groups of students and allow time for free play.

What to do

• Direct students to select three lots of four items. How many items altogether? This may be said as: 3 lots of 4 = 12. • Repeat this many times with lots of 2, 3, 4 or 5 to a total of 20. • Students state what they are doing with each grouping. • Ask students to select twelve items. Share these among four groups. How many in each group? • This may be stated as: 12 divided by 4 = 3 or 12 shared among 4 = 3. • Repeat this many times with up to 20 items shared equally into groups of 2, 3, 4 or 5. • Written examples of these activities may be made in the workbook. Use concrete materials to represent the drawings if this will assist working out.

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Main Activity (N2.2, N2.3, N2.1a)

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New Wave Maths Book B – Teachers Guide • 111 •

Unit 23–3

Student page 69

Indicators

Outcomes

The student is able to: • locate in time and order regular activities. • identifies number patterns on a calendar.

N2.3, M2.2, N2.4

Skills • following instructions • recognising patterns • reading a calendar

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils/ crayons • calendar

Language

• multiply • calendar • weeks • days • pattern

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, N2.4) Warm up

• Display a calendar month. Ask students to tell you what they can see—days of the week, number of days in the month, the day of the week the month starts etc.

• Ask students to open to the calendar in their workbook. • Ask what a full week means to them. For this calendar it is Sunday to Saturday. Which is the first full week? (Sunday 6 to Saturday 12) • Colour the first three full weeks blue. How many days are coloured? • Ask students to draw a red cross on every third day. What pattern is shown? (Counting by threes) • Mark the birthdays shown using a green circle. What pattern can you see? (All Tuesdays or every seventh number starting from 1)

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• The focus for this unit is basic facts of multiplication.

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• 112 • New Wave Maths Book B – Teachers Guide

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Unit 23—Answers

Student pages 67 – 69

Unit 23–1 1. (a) 2 (b) 13 (c) 8 2.

(d) 4

Unit 23–2 1. (a) 4 (b) 5 (c) 4 (d) 3 2. (a) 20c (b) 40c (c) 16 (d) 12 3. (a) 2 (b) 3

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3. Teacher check 4. (a) 34 (b) Teacher check (There should be the same number.) (c) Teacher check (There should be the same number.) (d) Teacher check

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Consolidation 23–2

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• Provide further opportunities to share items among specified numbers.

Consolidation 23–3

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• Use the calendar to devise other questions where a pattern will emerge.

New Wave Maths Book B – Teachers Guide • 113 •

Unit 24–1

Student page 70

Indicators

Outcomes N2.3, N2.2

Skills • grouping

Number (N2.3)

Resources • Base 10 MAB • counters • pencil

Language • multiply • how many • groups • lots of

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.3) Warm up

• Provide groups of students with counters. Allow time for free exploration.

What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

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• 114 • New Wave Maths Book B – Teachers Guide

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Unit 24–2

Student page 71

Indicators

Outcomes N2.3, M2.2, C&D2.4

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • read and compare frequencies from lists and simple one-way tables. • comment on information in displays of data produced by himself/herself and peers.

Skills • measuring length • comparing • collecting data • analysing data

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • Base 10 MAB longs

Language • multiply • measure length • list • longest • shortest • how many • altogether • tally • total

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, C&D2.4) Warm up

• Organise the class into groups of four. • Distribute Base 10 MAB longs to the groups of students. Direct students to use the longs to measure items of their choosing.

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• Ask students to write their name and the names of the other three group members in the space provided on the table in the workbook. • Use longs to measure the length of his/her own foot. • Make a tally to show the number of rods required to measure the foot. • Count the tally to find the total number of longs used. • Copy the tally and total recordings from other group members next to his/her name in the workbook. • Answer the questions using information from the table. • Ask all students with blonde hair to stand. Students stay standing if they also have blue eyes. • Record the list of students with blonde hair and blue eyes in the space provided. • Answer the questions, with teacher’s help if required.

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• The focus for this unit is basic facts of multiplication.

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New Wave Maths Book B – Teachers Guide • 115 •

Unit 24–3

Student page 72

Indicators

Outcomes

N2.3, N2.2, N2.1b

The student is able to: • use materials and diagrams to represent division stories. • use multiples to count and compare collections. • link the action of sharing into two equal portions with the language of ‘half ’. • use halving based on symmetry as the basis for partitioning continuous quantities.

Skills • grouping

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • concrete materials • fraction cake • paper

Language

• add • equal share • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute concrete materials to groups of students. Allow time for free play. • Provide groups of students with counters. Allow time for free exploration.

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• Direct students to select ten counters. See how many groups of five you can make. How many groups did you make? (2) • Students may say this as: 10 can be shared in to 2 lots of 5, or 10 = 2 lots of 5. • Repeat this many times using up to 20 items to be made into groups or lots of 2, 3, 4 or 5. • Written records of this activity may be made in the workbook. Use concrete materials to assist if students are having difficulties sharing using the drawings. • Use a fraction cake to show halves and fourths (quarters). Invite students to discuss what they see and understand, or, use an A4 sheet of paper, fold it in half, then either cut or tear it to show the two halves. • Fold the two halves in half again and cut or tear to make fourths. Better understanding may be gained by starting with a fresh piece of paper, folding it in half and then in half again. Open the paper out to show the four segments (fourths) then cut out. • Students can record this activity by completing the exercise in their workbook.

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Main Activity (N2.2, N2.3, N2.1b)

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• 116 • New Wave Maths Book B – Teachers Guide

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Unit 24—Answers

Student pages 70 – 72

Unit 24–1 1. (a) 15 (b) 12 (c) 9 2. Teacher check 3. Teacher check 4. Teacher check 5. Teacher check

(d) 6

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1. (a) 10 (b) 8 (c) 6 (d) 4 2. (a) 2 (b) 4 (c) 7 (d) 3 (e) 4

Unit 24–2

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• Continue grouping activities with pictures or concrete materials but ask students to write what they have done as equations; e.g. two lots of four makes eight – 2 x 4 = 8.

Consolidation 24–2

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• Use longs to measure the arm length of himself/herself and three friends.

Consolidation 24–3

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• Draw more ‘space’ food and use lines to show it being cut into halves and fourths (quarters).

New Wave Maths Book B – Teachers Guide • 117 •

Unit 25–1

Student page 73

Indicators

Outcomes N2.3, S2.3

The student is able to: • make symmetrical pictures using a variety of means which include cut-out figures and flipping and drawing around templates. • repeat multiple copies of two or three figures in a recognisable pattern for decorative purposes.

Skills • following patterns • exploring symmetry

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 2-D shapes • ruler

Language • multiply • drawings • turn • sideways • upside down • pattern • shape • cover

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute 2-D shapes to groups of students. Direct them to find pairs of shapes and explore patterns they can make with each pair. Encourage students to discuss the patterns.

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• Ask students to turn patterns made using pairs of shapes through a quarter turn, then half a turn, and describe what they see. • Refer students to their workbook to look at the drawings. • Ask students to turn the page on its side and describe what they see. • Turn the page upside down. What do they see? Record the findings. • Direct students to use a ruler and pencil to continue the pattern shown so that it covers the page.Those needing assistance may be asked what the next square in the row will look like and/or the next square in the first column. • Repeat these questions for subsequent squares in the row and other columns as required.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26 – 27. • 118 • New Wave Maths Book B – Teachers Guide

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Unit 25–2

Student page 74

Indicators

Outcomes N2.3, N2.2

Skills • counting on • sharing

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • multiply • share • equally • evenly • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute concrete materials among groups of students. Allow time for free play.

What to do

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Main Activity (N2.2, N2.3)

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 119 •

Unit 25–3

Student page 75

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • estimate the number of times a unit of length which they can handle will fit along an object and show improvement in their estimates as a result of testing.

N2.3, M2.2, M2.3

Skills • estimation • measuring length

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • matchstick • ruler • eraser • maths book • sharpener • duster

Language

• multiply • shorter • longer • estimate • measure

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, M2.3) Warm up

• Ask groups of students to collect a pencil, ruler, eraser, maths book, pencil sharpener, duster and matchsticks. • Explain estimation. Look at an object then make an educated guess; in this case, whether the object is longer or shorter than a matchstick. No direct measuring is involved. Use examples. Estimate who is taller—you or me? Which is longer—the desk or my table? etc.

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• Choose the pencil—estimate whether it is longer or shorter than a matchstick. Colour, circle or tick the shorter or longer box. • Repeat for the other objects. • Use matchsticks to check to see which is longer—the object or the matchstick—and record object or matchstick to show which is longer. • Actual comparison of the number of matchsticks needed to equal the length of object may be made.

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• The focus for this unit is basic facts of multiplication.

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• 120 • New Wave Maths Book B – Teachers Guide

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Unit 25—Answers

Student pages 73 – 75

Unit 25–1 1. (a) 18 (b) 25 (c) 20 2. (a) 2 (b) 4 (c) 2 (d) 3 (e) 2

(d) 15

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Unit 25–2

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• Create patterns on strips of 2-cm grid paper and give to a classmate to continue.

Consolidation 25–2

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• Continue similar activities using concrete materials and verbalising their actions to others.

Consolidation 25–3

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• Complete the same activity using an informal unit of measure such as a Base 10 MAB long or a 2-cm cube.

New Wave Maths Book B – Teachers Guide • 121 •

Unit 26–1

Student page 76

Indicators

Outcomes N2.3, N2.2

Skills • grouping

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • multiply • how many groups • left over

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.3) Warm up

• Distribute concrete materials to groups of students and allow time for free play.

What to do

• Direct students to select seven items. Ask students to share these items into groups of two. How many groups are made? How many items are left over? • Ask students to explain what they have done. ‘I have seven items shared into groups of two. I have three groups of two and one left over.’ • Repeat this many times with different numbers of items to 21 shared so that there is always some left over. Items to be shared into groups of 2, 3, 4 or 5. • Written records of these activities may be made in the workbook. Use concrete materials if required.

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• The focus for this unit is basic facts of multiplication.

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• 122 • New Wave Maths Book B – Teachers Guide

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Unit 26–2

Student page 77

Indicators

Outcomes N2.3, C&D2.3, C&D2.4

The student is able to: • make graphs using ‘real’ data. • comment on information in displays of data produced by himself/herself and peers.

Skills • sorting • recording data

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials

Language • multiply • sort • Carroll diagrams • organise • information

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.3, C&D2.4) Warm up

• Distribute materials to groups of students and allow time for free play. • Direct students to pick a handful of items then sort these into two groups. Describe how they sorted the items.

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• Sort the two groups into another two groups so there are now four groups. Describe how they sorted the two groups into four groups. • Repeat these several times for different selections of items. • Ask the boys in the class to stand together. Ask the girls to stand together. The class is sorted into boys and girls. • Ask the class how the groups may be further sorted. Perhaps left-handed and right-handed or oldest in the family, not oldest. Show these sortings. • Return each time to groups of boys and girls. • Sort on birthdays—those boys born on 1 January to 30 June in one group, 1 July to 31 December in another. Girls from 1 January to 30 June in one group and 1 July to 31 December in another. • Count the number in each group and record the total in the correct box or write student names (given name or initials).

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• The focus for this unit is basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 108 – 109. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 123 •

Unit 26–3

Student page 78

Indicators

Outcomes

N2.3, N2.2

Skills • grouping • counting

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • Base 10 MAB small cubes and longs

Language

• multiply • how many • cubes • longs

r o e t s Bo Notes r e p ok u S

Main Activity (N2.2, N2.3) Warm up

• Distribute Base 10 MAB small cubes and longs to groups of students. Allow time for free play.

• Direct students to use small cubes to make one long. Select different cubes. Do you need the same number of small cubes each time to make one long? • If you have 10 small cubes could you exchange it for one piece of wood that is the same length? (Yes, one long.) • Open the workbook and use small cubes to see how many are required to make each of the four sets of cubes shown. • In the next exercise, circle the correct number of small cubes required. Now find how many sets of cubes can be made from all the cubes in Exercise 3(b) first then 3(c). Record findings.

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What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

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• 124 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 26—Answers

Student pages 76 – 78

Unit 26–1 1. (a) 2 (b) 3 (c) 5 (d) 4 2. Teacher check 3. Teacher check

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1. (a) 1 (b) 2 (c) 4 (d) 5 2. (a) 2 groups of four. 1 left over (b) 3 groups of two. 1 left over (c) 4 groups of three. 1 left over (d) 2 groups of ten. 1 left over (e) 5 groups of three. 1 left over

Unit 26–2

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(d) 1

• Complete similar activities with concrete materials where items will be left over after grouping in specified numbers.

Consolidation 26–2

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1. (a) 3 (b) 1 (c) 5 2. (a) 10 (b) 3 (c) 5 (d) 4 3. (a) three cubes (b) 6 (c) 4

• Write the results of the warm-up activity sorting boys and girls into oldest and not oldest on to a Carrol diagram.

Consolidation 26–3

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R.I.C. Publications® www.ricpublications.com.au

• Continue using Base 10 MAB, small cubes and longs to group sets of cubes in specified numbers.

New Wave Maths Book B – Teachers Guide • 125 •

Unit 27–1

Student page 79

Indicators

Outcomes N2.3, S2.2

The student is able to: • copy pictures composed of simple geometric figures so that the main components are recognisable in shape, position and orientation.

Skills • following patterns • constructing 3-D shapes

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 2-cm cubes

Language • multiply • build • shapes • model • twice • long • wide • table

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute 2-cm cubes to groups of students and allow time for free play. • Direct students to select three cubes and make as many different arrangements as they are able to with the three cubes. Describe arrangements made.

What to do

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Main Activity (S2.2)

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• Open workbooks and make models of the drawings shown. In the space provided write how many cubes it takes to make each shape. • In the next activity, direct students to use five cubes to build as many different shapes as they can. Explain that each cube must not overlap another cube but fit face on a face. Shapes can be drawn in the space provided. (They need only be drawn in 2-D form.)

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• 126 • New Wave Maths Book B – Teachers Guide

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Unit 27–2

Student page 80

Indicators

Outcomes N2.3, N2.4

The student is able to: • use materials and diagrams to group numbers into tens and ones.

Skills

Resources • Base 10 MAB • counters • pencil

• counting on • sharing

Teac he r

Number (N2.3)

Language • multiply • change • fewer • pieces • value

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute Base 10 MAB materials to groups of students. Allow time for free play.

What to do

• Direct students to pick up a small handful of Base 10 MAB cubes. Ask if the pieces can be changed for other pieces of wood without changing the value of the wood. How? Students explain what they are doing. (Changing or trading small cubes for equivalent longs. Changing longs for equivalent flats and where applicable, changing flats for large cubes.) • Repeat this many times. • Written records of this activity may be made in the workbook.

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Main Activity (N2.4)

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 127 •

Unit 27–3

Student page 81

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • comment on information in displays of data produced by himself/herself and peers.

N2.3, M2.2, C&D2.4

Skills • estimation • measuring length

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • Base 10 MAB longs • coloured pencils/ crayons

Language

• multiply • measure • length • graph

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, C&D2.4) Warm up

• Organise the class into groups and provide each group with Base 10 MAB longs. Allow students to explore measurement of objects using the long.

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• Direct students to measure the length of their desk using the long. How many longs did it take? • Students select a coloured pencil/crayon and colour one space above the desk for each long used to measure the length of their desk. • Direct students to select four other items to measure with the long and colour the graph in the same way. Record the name of the object on the graph and/or draw a picture of the object. • Some objects may require more than twelve longs to measure it. Ask students how they can show the correct measure. Invite open discussion and direct it towards practical solutions—draw more spaces or just write the total number used.

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What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

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• 128 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 27—Answers

Student pages 79 – 81

Unit 27–1

1. (a) 3 (b) 4 (c) 5 (d) 2 2. two longs exactly 3. four longs with two cubes left over 4. Traded for three longs with four left over. (i) Cubes can be crossed off ten at a time and the number of tens counted. (ii) The total amount of cubes can be counted and the number divided by ten.

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1. (a) 3 (b) 1 (c) 4 (d) 2 2. (a) 2 (b) 4 (c) 3 (d) 3 (e) 5 3. Answers will vary. Some possible answers are:

Unit 27–2

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• Use six or seven 2-cm cubes and build different arrangements of shapes.

Consolidation 27–2

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1. (a) 4 (b) 3 (c) 6 (d) 4 2. Teacher check

• Group varying numbers of interconnecting cubes into tens and count the number of tens and ones.

Consolidation 27–3

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• Use another informal unit such as an eraser or pencil case to measure the same items on the graph.

New Wave Maths Book B – Teachers Guide • 129 •

Unit 28–1

Student page 82

Indicators

Outcomes N2.3, N2.4

The student is able to: • use materials and diagrams to group numbers into tens and ones.

Skills • grouping • adding • subtracting

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • Base 10 MAB materials • 6-sided die • 10-sided die

Language • multiply • trade • addition • equal • subtract

r o e t s Bo Notes r e p ok u S

Main Activity (N2.4) Warm up

• Distribute Base 10 MAB materials, 6- and 10-sided die to groups of students. Allow time for free play. • Ask each group to select a Base 10 long. What other wood do you have that matches this stick? Students answers will vary—two common answers should be other longs and/or ten small cubes. • Explain to the class that 10 small cubes and 1 long are equal value, one may be exchanged or traded for the other.

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• Ask each group to throw the six-sided die once and select small cubes to match the number shown on the die. Continue to do this, adding to the collection of small cubes. When students have collected 10 or more small cubes trade 10 small cubes for one long. • Practise this several times. • Introduce the trading game. Follow the instructions as set out in the workbook. • Play the game several times. • Ask students to put the 6-sided die aside and select one flat for the group. Ask students how they might take one small cube from the flat. Trade the flat for 10 longs. Can a small cube be taken now? (No) What do you need to do? (Trade one long for 10 small cubes.) One small cube may now be taken. • Repeat this several times, varying the amount of wood to be taken away. • Refer students to the second trading game in their workbook. Follow the instructions to find the winner. • Repeat the game several times. • For the final activity, students may circle longs and small cubes in lots of 10 to find the smallest amount of wood required to show the total. If this is difficult, students should select wood to match the drawing and then trade to find the smallest amount of wood required to show the equivalent of what is there.

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What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

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• 130 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 28–2

Student page 83

Indicators

Outcomes N2.3, C&D2.2, C&D2.3

The student is able to: • apply unambiguous and familiar criteria to sequence data consistently. • compare heights (or lengths) of the columns in a block graph to place categories in order. • understand the need for a baseline and space blocks regularly (in provided grids) to allow comparisons to be made.

Skills • sorting • recording data • graphing

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language • multiply • shapes • large • square • triangle

• tally • graph • small • circle • total

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.3) Warm up

• Review the use of tally marks. After four strokes, draw a line across the four to show a group of five when the fifth item is located; i.e. 1111.

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• Students are to open their workbooks and colour all large circles blue. Colour all small circles red. Colour all large squares green. Colour all small squares yellow. Colour all large triangles orange. Colour all small triangles brown. • Find the large squares—make a tally mark for each large square as you find it. Put a tick beside the large square to show you have counted it already. • Write the total of large squares in the space. • Continue for the other shapes. • Transfer the information collected to the graph by colouring one space for each of the shapes found.

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What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

o c . che e r o t r s super

For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107 and 108 – 109. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 131 •

Unit 28–3

Student page 84

Indicators

Outcomes

N2.3, N2.1a

The student is able to: • count coins, including in multiples of 5c, 10c, 20c, 50c, $1 and $2, and record total amounts. • decide whether he/she has more or less money than the price and whether to expect change.

Skills • grouping • counting • adding coins • subtracting coins

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • plastic coins

Language

• multiply • add • subtract • cost • paid • change

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute plastic coins to groups of students. Direct them to challenge each other to find different combinations of coins to make one specific coin; e.g. 50c, $1, 20c etc.

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• Use the coins if required to find the difference between the money values given in the workbook; e.g. you have 5c, take away 5c, what do you have left? You have 15c, take away 10c, what do you have left? • Use coins to show the sums in the second activity. Find the total, extra coins needed or difference between the money values shown to find the answers; e.g. I have 20c, what do I need to take away to be left with 10c? Suggest that 20c is shown using other coin values. Show the 10c left by removing other coin(s). How much was removed? • Work with students as required. • The final activity may need reading for students. Suggest that they use coins to work through the sum to find the answer, or leave as a problem for students to find the answers to.

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What to do

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Main Activity (N2.1a)

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• 132 • New Wave Maths Book B – Teachers Guide

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Unit 28–Answers

Student pages 82 – 84

Unit 28–1

1. (a) 4 (b) 2 (c) 5 (d) 3 2. Shapes Tally Total

Large squares

Small squares

Large circles

r o e t s Bo r e p ok u S Small circles

Large triangles

Small triangles

Number of shapes

6 5

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Teac he r

1. (a) 4 (b) 2 (c) 1 (d) 3 2. Teacher check 3. Teacher check 4. 3 flats, 5 longs, 7 ones

Unit 28–2

4 3 2 1

Large Small Large squares squares circles

Small Large Small circles triangles triangles

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• Provide further opportunities to play the trading games. Generally, students will have more difficulty with the subtracting practice game than the addition practice game.

Consolidation 28–2

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1. (a) 5 (b) 2 (c) 4 (d) 1 2. (a) 0c (g) 5c (b) 10c (h) 15c (c) 5c (i) 0c (d) 45c (j) 10c (k) 20c (e) 5c (f) 30c (l) 15c 3. (a) 10c (g) 15c (b) 5c (h) 5c (c) 10c (i) 10c (d) 25c (j) 20c (e) 10c (k) 20c (f) 15c (l) 30c 4. 20c

• Use handfuls of attribute blocks to tally and then graph the amount of large yellow circles, small yellow circles etc.

Consolidation 28–3

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• Provide further opportunities to complete addition and subtraction problems with amounts of money.

New Wave Maths Book B – Teachers Guide • 133 •

Unit 29–1

Student page 85

Indicators

Resources

The student is able to: • describe the location of an object as ‘between’ two other locations. • find paths on informal maps and mazes.

• Base 10 MAB • counters • pencil • coloured pencils/ crayons • map of students’ school/classroom • map of school (see page 231)

Outcomes N2.3, S2.1

Skills • following paths • mapping

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Main Activity (S2.1) Warm up

• Show a map of the school or classroom or use the school map on page 231. Ask students to describe a path between two different points. Ask for alternative directions. Repeat for different paths.

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• Ask students to open their workbooks and look at the map. • Ask students to identify features—railway line, train station, school, shopping centre, police station, recreation centre, corner store, streets and Kelly and Paul’s houses. • Ask students to look at the map and find the path they would follow to walk from Kelly’s house to Paul’s house. Select a student to describe the path to be used. • Ask for students who selected a different path. Choose one to describe his/her path. • Ask for students who have another path they had chosen. Have the path described. • Within reason, choose as many different alternatives as are offered. • Students are to write the directions they would give to another person to follow the path from Kelly’s house to Paul’s house.

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What to do

• multiply • directions

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Teac he r

Number (N2.3)

Language

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 12 – 13. • 134 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 29–2

Student page 86

Indicators

Outcomes N2.3, N2.4

The student is able to: • identify, copy, continue and describe repeating patterns.

Skills • recognising patterns • describing patterns

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • interconnecting cubes • concrete materials • beads

Language • multiply • continue • pattern • fourth • shape • sixth • sort • third

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of multiplication.

Warm up

• Distribute concrete materials to groups of students and direct them to make patterns. • Direct students to copy or continue patterns made by other members of their group. • Ask individuals to describe their patterns to either the group or the whole class.

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• Ask students to open their workbook and look at the patterns displayed. • In the first pattern what will the next shape be? Why? Draw it. What shape will follow? Why? Draw it. Continue the pattern for two more shapes. • Look at the second pattern. Describe it. How many different shapes are used? How many shapes in total are used in the pattern? Write this number in the space in the workbook. • Point to the fourth shape. It is a … Write the word ‘square’ in the space provided. Write the name for the sixth shape in the space provided. • Use your pencil and draw a short line after every third bead. Did you have an even group of three at the end? If not, check your groups of three. Describe the pattern—multiples of 3 or counting by 3.

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What to do

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Main Activity (N2.4)

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 135 •

Unit 29–3

Student page 87

Indicators

Outcomes

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure area. • estimate the number of times a unit of area which he/she can handle will fit over an object and show improvement in his/her estimates as a result of testing.

N2.3, M2.2, M2.3

Skills • estimation • measuring length

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • 2-D shapes of uniform size and shape; e.g. pattern blocks

Language

• multiply • shapes • objects • estimate

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2, M2.3) Warm up

• Distribute 2-D shapes among groups of students and direct them to use shapes to cover their maths book. Allow time for this to be completed. (Ensure each shape is the same size and shape.) • Ask students to select an object, other than their maths book, to use to cover with the shapes. Write the name of the object in the space provided in the workbook. • Discuss estimation—an ‘educated’ guess.

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• Estimate how many shapes it will take to cover the object you have chosen. Write your estimate in the space provided. Use 2-D shapes to cover the object. Write the total number used in the space provided. • Continue with five different objects. Write the estimate first then measure. • Ask students whether their estimation became better. Discuss their answers. • Students write the reason they thought their estimates got better or did not.

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What to do

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Teac he r

• The focus for this unit is basic facts of multiplication.

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• 136 • New Wave Maths Book B – Teachers Guide

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Unit 29—Answers

Student pages 85 – 87

Unit 29–1 1. (a) 4 (b) 2 (c) 3 (d) 1 2. Teacher check

Unit 29–2 1. (a) 4 (b) 3 (c) 5 (d) 1 2. Teacher check 3. (a) 12 (b) square (c) triangle 4.

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5. Teacher check; counting in threes

• Read and follow the written directions offered by other students in Exercise 2.This will enable students to see how clear their directions were.

Consolidation 29–2

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1. (a) 6 (b) 4 (c) 3 (d) 7 2. Teacher check

• Make shape/number patterns using attribute blocks. Describe his/ her pattern to a classmate or the classmate identifies and describes the pattern.

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R.I.C. Publications® www.ricpublications.com.au

Consolidation 29–3

• Choose further objects to practise estimating and measuring the area using a uniform unit of measure.

New Wave Maths Book B – Teachers Guide • 137 •

Unit 30–1

Student page 88

Indicators

Outcomes N2.3, N2.1a

The student is able to: • decide whether he/she has more or less money than the price and whether to expect change.

Skills • adding money • giving change

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • plastic coins • shop

Language • add • how much • change • bought

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition using money.

Warm up

• Distribute plastic coins among groups of students. Suggest they find as many combinations of coins as they can to make one coin; e.g. 10c, 20c, 50c, $1 or $2. Alternatively, set up a classroom shop and have students purchase items up to $2 in value and receive change for their purchase.

What to do

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Main Activity (N2.1a)

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• Use the warm up examples as shopping exercises to find the change required.This may be done in the groups with students taking turns at being the shopkeeper and distributing the correct change to the students. As the shopkeeper they can keep a record of the change that they gave. This will mean repeating the exercise several times. • If students wish, they may complete the answers by themselves.

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• 138 • New Wave Maths Book B – Teachers Guide

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Unit 30–2

Student page 89

Indicators

Outcomes N2.3, N2.4, S2.3

The student is able to: • identify, copy, and continue repeating patterns. • repeat multiple copies of two or three figures in a recognisable pattern for decorative purposes.

Skills • recognising patterns • describing patterns

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • variety of shapes • matchsticks • pop sticks or similar

Language • add • set • pattern

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of whole numbers using money.

Warm up

• Distribute materials to groups of students and direct them to make patterns. • Ask others in the group to describe the pattern. • Direct students to make patterns by rotating the materials they use, or alter their existing pattern by rotating materials. Describe how the pattern was changed and what the new pattern is.

• Ask students to look at the arrangements in their workbook. Which of the three is a pattern? Why is it a pattern? Why are the others not patterns? • Students may like to make patterns of their own using matchsticks or pop sticks. • Look at the three patterns using shape. Describe the patterns. Extend the patterns by at least two shapes.

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What to do

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Main Activity (S2.3, N2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 24 – 25. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 139 •

Unit 30–3

Student page 90

Indicators

Outcomes

N2.3, N2.1a

Skills • adding money

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • canteen • copies of restaurant menus • plastic coins

Language

• add • how much • cost • buy • menu

r o e t s Bo Notes r e p ok u S

• The focus for this unit is basic facts of addition using money.

Warm up

• Take the class for a visit to the canteen and discuss the menu and costs of items with the manager or use restaurant menus to discuss items and costs and explain how menus work by showing people what their purchases will cost.

What to do

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Main Activity (N2.1a)

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• Using plastic coins to assist if required, ask students to find the two items listed and write the price for each in the space provided: banana = 25c, carrot = 5c. Find the total cost of the two items and write this in the space provided. • Complete the rest of the activities in this manner, or, if students are comfortable, allow them to proceed on their own.

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• 140 • New Wave Maths Book B – Teachers Guide

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Unit 30—Answers

Student pages 88 – 90

Unit 30–1

1. (a) 9c (b) 6c (c) 8c (d) 6c 2. (b) is the only pattern. Teacher check 3. (a) Teacher check (b) Teacher check (c) Teacher check

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Teac he r

1. (a) 6c (b) 8c (c) 11c (d) 7c 2. (a) 25c (b) 20c (c) 10c 3. (a) 20c (b) 5c (c) 15c (d) 30c (e) 0c (f) 10c

Unit 30–2

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Consolidation 30–2

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1. (a) 11c (b) 15c (c) 13c (d) 13c 2. (a) 25c + 5c = 30c (b) 15c + 10c = 25c (c) 5c + 20c = 25c (d) 5c + 25c + 15c = 45c (e) 15c + 5c = 20c (f) 20c + 5c + 10c = 35c (g) 25c + 10c + 15c = 50c (h) 15c + 25c + 25c = 65c

• Create patterns using matchsticks or pop sticks for other students to extend.

Consolidation 30–3

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R.I.C. Publications® www.ricpublications.com.au

• Use actual canteen prices to practise adding costs. Prices will obviously be higher and many students may need assistance in working out the cost.

New Wave Maths Book B – Teachers Guide • 141 •

Unit 31–1

Student page 91

Indicators

Outcomes WM2.2, WM2.3, M2.2

The student is able to: • ask questions about collected objects or pictures. • offer suggestions in response to a ‘What would happen if …’ question pitched at or just beyond their mathematical level. • make conjectures (often guesses) about shapes and measurements. • respond to a request to ‘convince me’ which of two different container ‘holds more’ by pouring from one to the other or by pouring from each into two identical containers.

Skills • estimating capacity • problem-solving • working mathematically

Resources • pencil • five different sized and shaped transparent containers • coloured liquid

Language • cordial • contains • most • more • full • pour

• container • capacity • least • less • level

r o e t s Bo Notes r e p ok u S

What to do

• The aim of this activity is to answer the question: As liquids take the shape of the container, how is the capacity of different shaped and sized containers determined? (It has a strong link with the science learning area.) • Each of the containers has had the same amount of cordial poured into it. At this stage of development, many students will not be able to identify this. One container will appear to hold more cordial in it in their opinion. It could be Container A as it is the most filled, Container C as it is the widest or Container D as it is filled higher than any others. • Direct students to look at the containers in their workbooks. Ask them questions about the shape, size width and height of the containers and cordial levels in each. Words and phrases can be written on the blackboard/whiteboard. • Ask students to circle the letter of the corresponding container they think holds the most. Students then give a reason(s) for their answer. • Discuss the various answers with the class. • The same amount of cordial could now be poured into the five different container provided by the teacher. Further discussions and comparisons with the activity in their workbook could be made.

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Teac he r

Main Activity (WM2.2, WM2.3, M2.2)

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• 142 • New Wave Maths Book B – Teachers Guide

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Unit 31–2

Student page 92

Indicators

Outcomes N2.3, N2.1a, N2.4

The student is able to: • read, write and say the numbers in order to beyond 100 and count on or back from any number to 100. • describe patterns in lines in a hundred chart.

Skills • recognising patterns • describing patterns • counting

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 1–100 grid (see page 206) • coloured pencils/ crayons

Language • add • number grid • fifth • third • fourth

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of whole number using money.

Warm up

• Use a 1–100 grid and seat class around the grid. Ask individual students to place counters on numbers as you ask. Initially nominate whole numbers; e.g. 2, 4, 6, 8, 10. What can you tell me about these numbers? Try 10, 20, 30, 40, 50. What can you tell me about these numbers? • Other combinations may be used.

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• Ask students to place counters on the 1–100 grid on every second number up to 30. What numbers have been covered? • Leave the counters there and cover every fourth number. What numbers have been covered this time? • Leave all counters there. Cover every fourth number. What numbers have you covered this time? • Which numbers have two counters on them? • Which numbers have three counters on them? • Refer students to their workbook to complete colouring the grid as directed. • Answer the questions related to the grid.

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What to do

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Main Activity (N2.1a, N2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44 – 45. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 143 •

Unit 31–3

Student page 93

Indicators

Outcomes

The student is able to: • locate in time and order regular activities.

N2.3, M2.2

Skills • measuring time • reading calendars

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • coloured pencils/ crayons • calendar

Language

• add • calendar • day • week • date • month

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Use a large display calendar to ask students any of the following questions: How many months in the year? How many full weeks in most months? How many days in a week? Choose one month. What is the day that the 1st of the month falls on? What is the date of the second Sunday? What are the dates of all Wednesdays? What is the date three days before the 27th?

What to do

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Teac he r

• The focus for this unit is addition of whole numbers, with some using money.

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• Further questions of this type may be asked if required. • Direct students to their workbook. Working with the whole class, ask each question in turn and have students respond orally then write the correct answer.

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• 144 • New Wave Maths Book B – Teachers Guide

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Unit 31—Answers

Student pages 85 – 87

Unit 31–1

1. (a) 10c (b) 16c (c) 18c (d) 16c 2. (a) 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 (b) 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48 (c) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 (d) 15, 30, 45 (e) 20, 40 (f) 12, 24, 36, 48

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Teac he r

1. Teacher check 2. Teacher check 3. Teacher check

Unit 31–2

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• Provide further opportunities for students to experience pouring the same and/or different amounts of liquid into various containers and discuss their findings.

Consolidation 31–2

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1. (a) 18c (b) 17c (c) 8 (d) 5 2. (a) Friday (b) 18th (c) 24th, 25th, 26th, 27th, 28th, 29th, 30th (d) 12th and 19th (e) Friday (f) Saturday 30th (g) Thursday (h) Monday (i) 13th

• Use a 1–100 grid to count in twos, threes, fours, fives and tens.

Consolidation 31–3

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R.I.C. Publications® www.ricpublications.com.au

• In a group of three or four, make up further questions for other group members to solve using the calendar.

New Wave Maths Book B – Teachers Guide • 145 •

Unit 32–1

Student page 94

Indicators

Outcomes N2.3, N2.1a

The student is able to: • count coins, including in multiples of 5c, 10c 20c, 50c, $1, and $2, and record total amounts. • decide whether they have more or less money than the price and whether to expect change.

Skills • adding money • giving change

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • plastic coins

Language • add • how much • change • buy • bought • least • most

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a) Warm up

• Distribute plastic money among groups of students. Direct students to make up activities that provide change; e.g. I have 20c and I spend 10c, how much change will I receive? Allow reasonable time for this activity.

What to do

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Teac he r

• The focus for this unit is revision of basic facts of addition.

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• Students may undertake the workbook activities as a shopping exercise. • Use the workshop examples as shopping exercises to find the change required.This may be done in the groups with students taking turns at being the shopkeeper and distributing the correct change to the students. As the shopkeeper, they can keep a record of the change that they gave. This will mean repeating the exercise several times. • If students wish they may complete the answers by themselves.

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• 146 • New Wave Maths Book B – Teachers Guide

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Unit 32–2

Student page 89

Outcomes

Indicators

Resources

N2.3, C&D2.2, C&D2.4

The student is able to: • in answer to the question, ‘How could we find out?’, suggest collecting objects or information and offer suggestions about what data to collect. • offer suggestions about how to classify objects or information. • comment on information in displays of data produced by himself/herself and peers.

• Base 10 MAB • counters • pencil • hoops • concrete materials

Skills • sorting • recording data

Number (N2.3)

Language • add • Venn diagram

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.4) Warm up

• Distribute two hoops and concrete materials to groups of students. Allow time for free play. • Direct students to collect a handful of items and sort them into two groups, placing one group in each hoop. Do any items belong to both groups? If yes, how might we show this? (Overlap the hoops.) • Repeat with different items, encouraging the use of common classifications or sortings.

What to do

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Teac he r

• The focus for this unit is revision of basic facts of addition.

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• Direct students to their workbook where a written record of this type of sorting may be kept. • To complete the second activity, ask the students to list water sports and land sports. Students select a number of each to write in the correct list.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 106 – 107. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 147 •

Unit 32–3

Student page 96

Indicators

Outcomes

N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways.

Skills • adding money • recognising equivalency of money

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • plastic coins

Language

• add • change • money • coins • exchange • trade

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition.

Warm up

• Distribute plastic coins to groups of students. Suggest they pick a small handful of coins then change them into the smallest amount of money of equivalent value, or exchange them for coins of a given denomination to an equivalent value. Each student in the group may take turns to complete this activity with others watching and checking.

What to do

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Main Activity (N2.1a)

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• Students may use the plastic coins to assist in completing the activities in the workbook which all involve trading or exchanging a range of coins for those of a given denomination.

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• 148 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 32—Answers

Student pages 94 – 96

Unit 32–1

1. (a) 7 (b) 14 (c) 11 (d) 10 2. Out of water – towel, sandcastle, sunglasses In water – shark, fish, seahorse, sea star In and out of water – seagull, shell, crab, flippers, mask Note: Answers may vary depending on the point of view of the student. 3. Teacher check

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 8 (b) 5 (c) 5 (d) 7 2. (a) 5c (b) 10c (c) 15c (d) ruler, sharpener, eraser, pencil (e) box of crayons (f) ruler and eraser

Unit 32–2

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• Label items in their desks with a price 50c or less. Work out how much change from 50c or $1 they would receive if each item or a combination was ‘bought’.

Consolidation 32–2

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1. (a) 8 (b) 16 (c) 15 (d) 10 2. 3 3. 2 4. 2

• Suggest further items that could be placed in one of the sections of the Venn diagram.

Consolidation 32–3

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• Provide further opportunities as described in the warm up where students exchange coins of equivalent value.

New Wave Maths Book B – Teachers Guide • 149 •

Unit 33–1

Student page 97

Indicators

Outcomes N2.3, M2.2

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length.

Skills • modelling • measuring • counting • finding perimeter

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • geoboard • elastic bands • coloured pencils/ crayons

Language • add • geoboard • rectangle • squares • perimeter • units • different • shape

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition.

Warm up

• Distribute geoboards and elastic bands to groups of students. Allow time for free play. Stress safety issues when using elastic bands.

• Direct students to make a square with sides of one unit. Show shape. Repeat for sides of 2 or 3 units. • Direct students to make a rectangle with a side of 1 unit and the long side of 2 units. How many units are there around the shape? What is the perimeter of the shape? Repeat with different length sides. • Ask students to make a shape with a perimeter of 10 units. Show the shape. • Make a shape with a perimeter of 14 units. Can you make other shapes with a perimeter of 14 units? Draw all the shapes with a perimeter of 14 units on the grid in the workbook.

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What to do

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Main Activity (M2.2)

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• 150 • New Wave Maths Book B – Teachers Guide

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Unit 33–2

Student page 98

Indicators

Outcomes N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways.

Skills • recognising equivalency of money • adding money

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • plastic coins

Language • add • circle • coins • trade

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition—adding on.

Warm up

What to do

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Main Activity (N2.1a)

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• Students may use the plastic coins to assist in completing the activities in the workbook which all involve trading or exchanging a range of coins for those of a given denomination.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 151 •

Unit 33–3

Student page 99

Indicators

Outcomes N2.3, M2.2

Skills • measuring perimeter and area • comparing perimeter and area

Number (N2.3)

The student is able to: • use a ruler or tape measure to measure and make things to the nearest centimetre. • compare the area of two regions directly by superimposing one over the other.

Resources

• Base 10 MAB • counters • pencil • ruler • 1-cm cubes

Language

• add • around • below • length • order • longest • perimeter

• draw • space • measure • compare • shortest • area • pattern

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Ask students to draw around their hand, or have a partner draw around their hand for them, in the space in the workbook.

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• Use your ruler to measure the length of your hand. Remember that the zero mark is placed at the point you wish to start measuring. • Write the length of your hand inside your drawing of your hand. • Compare the length of your hand with five friends. How might you do this? Measure the hand or the drawing with a ruler, piece of string or the like; make a direct comparison of each person’s hand; superimpose drawings or actual hands on a drawing. Other suggestions may arise. • Write the names of your classmates’ hands in order from shortest to longest. • Use 1-cm cubes to find the perimeter (ask what perimeter is—the distance around the outside) and the area (ask what area is—the surface or space inside the perimeter or boundary) of two shapes drawn in the workbook. • Write the perimeter and the area of each shape in the space provided. • Look at the perimeter and the area of each shape. How does the area compare with the perimeter? For shape one the area is 12 units and the perimeter is 14 units. For shape two the areas is 10 units and the perimeter is 14 units.The perimeter is the same but the area is different. Note: There is no relationship between area and perimeter.

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What to do

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Teac he r

• The focus for this unit is revision of basic facts of addition – adding on.

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• 152 • New Wave Maths Book B – Teachers Guide

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Unit 33—Answers

Student pages 97 – 99

Unit 33–1

1. (a) 3 (b) 3 (c) 2 (d) 1 2. four 3. two 4. 50c 5. 5 6. $1

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Teac he r

1. (a) 10 (b) 17 (c) 16 (d) 11 2. Teacher check

Unit 33–2

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• Use dotted grid paper (see page 198) to draw shapes that have a perimeter of 12 or 16 units.

Consolidation 33–2

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1. (a) 9 (b) 6 (c) 3 (d) 8 2. Teacher check 3. Teacher check 4. (a) Shape 1 – Area 12 Perimeter 14 Shape 2 – Area 10 Perimeter 14 (b) The area changed and the perimeter stayed the same.

• Provide further opportunities as described in the warm up where students exchange coins of equivalent value.

Consolidation 33–3

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• Try making shapes with a perimeter of 14 units and check the area to see what happens. Students may wish to check the activity in Unit 33–1 where they made drawings of a number of shapes with a perimeter of 14 units.

New Wave Maths Book B – Teachers Guide • 153 •

Unit 34–1

Student page 100

Indicators

Outcomes N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways.

Skills • recognising equivalency of money • adding money

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • plastic coins

Language • add • change • coins • share • evenly

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a) Warm up

• Distribute plastic coins to groups of students. Suggest that they pick a small handful of coins then change them into the smallest amount of money of equivalent value, or exchange them for coins of a given denomination to an equivalent value. Each student in the group may take turns to complete this activity with others watching and checking.

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• Students may use the plastic coins to assist in completing the activities in Exercise 2 in the workbook which all involve trading or exchanging a range of coins for those of a given denomination. • Ask students to select four 50c coins. Share these coins evenly among four people. How much will each person get? • Repeat this several times for specified common coin value.Then ask for a selection of coins to a total value of 20c, 40c, 60c, $1 etc. Ask students to share these coins so that each person receives the same amount of money; e.g. a group of 2, 5, 3, 4 etc. • Direct students to complete activities in their workbook.

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What to do

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Teac he r

• The focus for this unit is revision of basic facts of addition – adding on.

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• 154 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 34–2

Student page 101

Outcomes

Indicators

N2.3, C&D2.3, C&D2.4, C&D2.1

The student is able to: • make graphs and plots using oneto one correspondence between ‘real’ data and a representation. • compare heights (or lengths) of the columns in a block graph to place categories in order. • describe how his/her graph shows the results of the data collection. • identify possible results of an action or event by collecting data.

Skills • graphing • investigating chance

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons • die

Language • add • grid • birthday • month • most • least • difference between

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition—adding on.

Warm up

• Ask students to name the months of the year. Ask students if they know which month of the year they were born in. Tell those who don’t know or are unsure.

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• Direct students to take out their workbook. • Ask all students who have a January birthday to stand. Colour one square for each student standing. Tell the individual to sit when a square for him/her has been coloured. • Repeat for all months, changing colours for each month so that no two consecutive months are coloured the same. • Work with the whole class to answer the questions on the page. • Issue each student with a die if available, or distribute a die to small groups. • Each student takes a turn to roll the die and record the number showing on its face by colouring one space on the graph in the appropriate space. Each student has fifteen throws in turn. • Answer the questions on the page. Focus discussion on why there are differences in the findings. (Chance processes—no uniformity or definite knowledge of any one number occurring more likely than another.)

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What to do

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Main Activity (C&D2.3, C&D2.4, C&D2.1)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 110 – 111. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 155 •

Unit 34–3

Student page 96

Indicators

Outcomes

N2.3, N2.1a

The student is able to: • count coins, including in multiples of 5c, 10c, 20c, 50c, $1 and $2, and record total amounts.

Skills • adding money • recognising equivalency of money

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • plastic coins

Language

• add • coins • value • number sentence • true

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition—adding on.

Warm up

• Distribute coins among groups of students. Direct students to select two or three coins and find the total value of their selections. Ask other groups members to check the accuracy of totals.

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• Ask students to select two or three specific coins and find the total; e.g. 5c and 10c—total is 15c; 20c and 10c and 20c—total is 50c. • Repeat this several times. • Ask students to select two or three specified coins and another larger value. Find the value of the missing coin—10c and 20c and ___c = 50c. The missing coin is? (20c) 50c and 20c and 20c and ___c = $1. The missing coin is? (10c) • Repeat with other combinations. • Written records of these activities may be made in student workbooks.

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What to do

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Main Activity (N2.1a)

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• 156 • New Wave Maths Book B – Teachers Guide

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Unit 34—Answers

Student pages 100 – 102

Unit 34–1

1. (a) 8 (b) 6 (c) 7 (d) 9 2. (a) Teacher check (b) Teacher check 3. (a) Teacher check (b) Teacher check (c) Teacher check

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Teac he r

1. (a) 6 (b) 4 (c) 8 (d) 7 2. (a) 20c (b) 50c (c) 10c (d) $2 3. (a) 20c (b) 10c (c) 5c (d) 10c

Unit 34–2

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• Repeat the activity of asking students to share coins so that each person will receive the same amount even if made up of different denominations; e.g. 50c or 20c, 20c, 10c.

Consolidation 34–2

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1. (a) 7 (b) 4 (c) 3 (d) 3 2. (a) 10c (b) 25c (c) 40c (d) $1 3. (a) 10c (b) 5c (c) 20c

• Repeat the die activity again and compare the results. Compare other students’ results.

Consolidation 34–3

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• Provide opportunities for similar activities as in Exercise 3 where students write the value of the missing coins to complete number sentences.

New Wave Maths Book B – Teachers Guide • 157 •

Unit 35–1

Student page 103

Indicators

Outcomes N2.3, S2.3, N2.4

The student is able to: • repeat multiple copies of two or three figures in a recognisable pattern for decorative purposes. • describe a rule which could have been used to generate an adding or subtracting sequence and test.

Skills • recognising patterns • continuing patterns

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language • add • grid pattern

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of addition—adding on.

Warm up

• Ask students to open their workbooks and look at the pattern shown on the page.

What to do

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Main Activity (S2.3, N2.4)

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• Ask students to describe the pattern. Student responses may differ and differences should be encouraged and explored. Descriptions may focus on one side of the dotted lines and see the pattern as a mirror image. Alternatively, the pattern may be viewed as a whole and the dotted line ignored other than a control point to assist in describing the location of the squares. • Once the pattern has been established, ask students to choose coloured pencils/crayons to complete the pattern continuing down the grid. • After completing the pattern, ask students to write a description of the pattern in their own words. Again, the descriptions may vary.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26 – 27. • 158 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 35–2

Student page 98

Indicators

Outcomes N2.3, N2.1b, N2.2

The student is able to: • understand that constructing a number of fair shares from a whole requires splitting all of the whole into equal parts (that is, with approximate equality and exhaustion). • use materials and diagrams to represent multiplication stories which can be thought of as repeated addition.

Skills • grouping • sharing • multiplying

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • concrete materials • fraction cake

Language • take • pieces • how many • share • equally • altogether

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision or basic facts of subtraction.

Warm up

• Distribute concrete materials and direct students to make sets or lots of in their groups. Share the description of the sets.

What to do

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Main Activity (N2.1b, N2.2)

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• Show a fraction cake of thirds. Ask students how many people could receive an equal share. • Repeat for fourths, fifths, halves. • Ask students to make sets of the following—3 lots of 4; 2 lots of 6; 4 lots of 3; 4 lots of 2; 2 lots of 5; 2 lots of 3. • Students describe what they have in their sets—three lots of four make (equal) twelve. • Written records of both activities may be made in the workbook.

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New Wave Maths Book B – Teachers Guide • 159 •

Unit 35–3

Student page 105

Indicators

Outcomes

The student is able to: • respond to a request to ‘convince me’ which of two different containers ‘holds more’ by pouring from one to the other or by pouring from each into two identical containers. • use repetitions of a uniform unit consistently and carefully to measure area. • use a ruler or tape measure to measure and make things to the nearest centimetre.

N2.3, M2.2

Skills • measuring

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • paper cup, shoe box, cereal packet, jar • sand or rice • ruler • Base 10 MAB • string

Language

• take • pour • container • smallest • capacity • length • shortest

• fill • into • empty • largest • area • longest • order

r o e t s Bo Notes r e p ok u S

Main Activity (M2.2) Warm up

• Organise the class into groups and have a member of each group collect a paper cup, shoe box, cereal packet, jar and sand or rice. A second group member is to collect Base 10 MAB. Allow time for group members to explore the materials.

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• Direct students to fill each container in turn with sand or rice. Pour the sand or rice into a jar. Count the number of full jars that are poured from each container and write the total under the capacity next to the name of the container. • Open out each container and use either flats, longs or large cubes to cover the surface of the open container.This is the area. Record the area in the space provided by counting the number of pieces of wood used. • Check to see if the capacity and the area are in the same order. • In groups, ask students to measure the lengths of their arms. This may be best done by using a piece of string laid along arm then measuring the length of the string with a ruler or a metre ruler. • Write the names of the students in order, with the student with the longest arm on the top.

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What to do

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Teac he r

• The focus for this unit is revision of basic facts of subtraction.

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• 160 • New Wave Maths Book B – Teachers Guide

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Unit 35—Answers

Student pages 103 – 105

Unit 35–1

1. (a) 3 (b) 7 (c) 8 (d) 5 2. (a) 3 (b) 4 (c) 5 3. (a) 8 (b) 20 (c) 16 (d) 15

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Teac he r

1. (a) 8 (b) 8 (c) 6 (d) 4 2. Teacher check 3. Teacher check

Unit 35–2

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• Use a line of symmetry on grid paper, create a pattern around it and give it to a classmate to continue.

Consolidation 35–2

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• Cut items from their lunchboxes into halves, fourths etc. • Count in twos to work out the number of legs in the classroom or by tens to work out the number of fingers in a group.

Consolidation 35–3

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• Repeat Exercise 2 using different containers such as a tissue box or takeaway food container.

New Wave Maths Book B – Teachers Guide • 161 •

Unit 36–1

Student page 106

Indicators

Outcomes N2.3, N2.1a

The student is able to: • count coins, including in multiples of 5c, 10c, 20c, 50c, $1 and $2, and record total amounts.

Skills • addition of money

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • plastic coins

Language • take • count • coins • total

r o e t s Bo Notes r e p ok u S

Main Activity (N2.1a) Warm up

• Distribute plastic coins among groups of students. Direct students to select up to five coins and challenge the rest of the group to find the total value of the coins they have used.

What to do

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• The focus for this unit is revision of basic facts of subtraction.

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• Direct students to select combinations of the same coin to find the total value of the coins selected; e.g. three 5c coins—total is 15c; two 20c coins—total is 40c; five 10c coins —total is 50c; three $2 coins—total is $6; five $1 coins—total is $5; five 5c coins—total is 25c; three 10c coins—total is 30c; four 20c coins—total is 80c. • Written records of this type of activity may be made in the workbook.

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• 162 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 36–2

Student page 107

Indicators

Outcomes N2.3, C&D2.2,. C&D2.4, C&D2.3

The student is able to: • apply unambiguous and familiar criteria to sequence data consistently. • compare heights (or lengths) of the columns in a block graph to place categories in order. • read and compare frequencies from lists and simple one-way tables.

Skills • recording data • sorting • interpreting data

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • attribute blocks • 2-D shapes

Language • take • graph • circle • shape • triangle • square • straight • curved • sides

r o e t s Bo Notes r e p ok u S

Main Activity (C&D2.2, C&D2.3, C&D2.4) Warm up

• Distribute attribute blocks and 2-D shapes to groups of students. Direct students to find different ways to sort the shapes. Share these ways among the group.

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• Ask students to turn to their workbook and look at the first activity. • There are three shapes shown; use the graph to record the number of each shape by colouring one box for each different shape. Mark the shape graphed by placing a tick next to the shape as it is graphed. • Use the graph to answer the questions. • In the second activity, only shapes with straight sides are to be graphed in the first row; shapes with curved sides in the second row; and shapes with both straight and curved sides in the third row. Graph each sort of shape by colouring a box and then tick the shape off. • Answer the questions using the finished graph.

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What to do

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Teac he r

• The focus for this unit is revision of basic facts of subtraction.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 110 – 111. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 163 •

Unit 36–3

Student page 108

Indicators

Outcomes

N2.3, N2.4, WM2.2

The student is able to: • use materials to create a pictorial pattern. • represent a problem with concrete materials and manipulate the materials to find a solution. • represent a problem with a sketch or diagrams.

Skills • discussing patterns • creating patterns

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • counters (red, green, and blue) • coloured pencils/ crayons

Language

• solve • different patterns

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of addition and subtraction of whole numbers.

Warm up

• Distribute 4 red, 4 green and 4 blue counters to each student. Students may work in groups, pairs or individually. Direct students to make patterns with their counters.

What to do

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Main Activity (N2.4, WM2.2)

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• Discuss patterns within the group or with the whole class as selected. • Ask students to open their workbook and, using any or all of the twelve counters available, make patterns to be drawn on the page. Counters may be used and then traced around with a matching coloured pencil/crayon. • Several different patterns may be made or students may prefer to make one continuous pattern.

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• 164 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 36—Answers

Student pages 106 – 108

Unit 36–1

Number of this shape

1. (a) 1 (b) 6 (c) 4 (d) 3 2. (a) 1 6 8 (b) 5 (c) 13 4 3

r o e t s Bo r e p ok u S 2 1

3. (a) 7 (b) 4

Straight Curved Both 1

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1. (a) 8 (b) 2 (c) 7 (d) 4 2. (a) 20c (b) 50c (c) 60c (d) $1.50 (e) $4 (f) $1 (g) $2

Unit 36–2

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• Continue activities using varying amounts of same value coins to count the total.

Consolidation 36–2

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1. (a) 20 (b) 17 (c) 3 (d) 8 2. Teacher check

• Make a block graph to record the groups of attribute blocks and 2-D shapes sorted in the warm-up activity.

Consolidation 36–3

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• Use different amounts of the same coloured circles or extra colours to make a new pattern. Discuss and compare with classmates.

New Wave Maths Book B – Teachers Guide • 165 •

Unit 37–1

Student page 109

Indicators

Resources

The student is able to: • describe the location of an object as ‘between’ two other locations. • find paths on informal maps and mazes. • attend to order and betweenness in describing a path which fits a simple criterion.

• Base 10 MAB • counters • pencil • map of school buildings (copy of page from workbook if unable to find one of own school – transfer to overhead) or (copy of school map on page 231) • coloured pencils/ crayons

Outcomes N2.3, S2.1

Skills • mapping • tracing paths • describing location

Teac he r

Number (N2.3)

Language • add • grid pattern

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of whole numbers.

Warm up

• Show students a large map of their own school or an overhead picture of the map of the school in the workbook or the school map on page 231.

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• Select a student to trace the path he/she would use to move from one site to another. Ask for alternative paths to be shown by other students. • Select another student and ask for the path he/she would use to move from one site to another visiting two or three places on the way. Ask other students to show alternative paths. • Both these activities may be repeated several times. • Students are to be directed to their workbook, select a coloured pencil then show the path they would take to go from TA4 to their office. • Using a different colour show the path used to move as directed from TA16 through the other sites.

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What to do

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Main Activity (S2.1)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 12 – 13. • 166 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 37–2

Student page 110

Indicators

Outcomes N2.3, WM2.2

The student is able to: • produce simple variations on problems explored. • compare ways of representing a problem. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

Skills • working mathematically • problem-solving • counting

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil

Language • add • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is addition of whole numbers.

Warm up

• Direct students to their workbook. Examine the picture.What do you see? (Three children, two dogs and dog leads. )What might you assume from the picture? Encourage different ideas from students.

What to do

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Main Activity (WM2.2, N2.3)

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• Read the questions to the students and the final instructions. • Ask students to complete the questions themselves and to explain how they know how many dogs ran away. Answers may vary. If the explanation is sound, accept the answers.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 167 •

Unit 37–3

Student page 111

Indicators

Outcomes

The student is able to: • locate in time and order regular activities. • recognise ‘key times’ on an analog clock and tell the time of day on digital clocks in hours and minutes. • connect mathematical ways of ordering times of day and year to the ways we order time by natural events.

N2.3, M2.2, WM2.1

Skills • measuring time

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • large analog clock face

Language

• multiply • activities • school day • hands • clock • times

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of multiplication.

Warm up

• Use a large analog clock face to show different times of the day. Ask students to read the time, if able. Assist students with hour hand and minute hand reading. Students don’t need to be proficient in all time reading at this stage.

What to do

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Main Activity (M2.2, WM2.1)

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• After practice at reading the clock, ask students to open their workbook. • Display the time shown on the first clock face. Ask what the time shows. (9 o’clock) Ask students what activity they would be doing at 9 o’clock on a school day.Write a description of the activity in the space provided. • Repeat for each time shown. The last two times are after school hours.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 96 – 97. • 168 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 37—Answers

Student pages 103 – 105

Unit 37–1

1. (a) 3 (b) 3 (c) 9 (d) 10 2. (a) 4 (b) 6 (c) Teacher check. The most common answer would be because there are four leads not attached to dogs any more, there would be four dogs that ran away.

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Teac he r

1. (a) 27 (b) 29 (c) 23 (d) 23 2. Teacher check 3. Teacher check

Unit 37–2

• Use the map to complete further activities, selecting the paths they would take from one place to another. Begin at different teaching areas.

Consolidation 37–2

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1. (a) 6 (b) 20 (c) 5 (d) 3 2. Teacher check

• Encourage divergent thinking in other working mathematically problems. Discuss as a class, so those students who find it difficult can listen, learn and gradually participate more fully.

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R.I.C. Publications® www.ricpublications.com.au

Consolidation 37–3

• Repeat the activity using a Saturday or Sunday to answer the question.

New Wave Maths Book B – Teachers Guide • 169 •

Unit 38–1

Student page 112

Indicators

Outcomes N2.3, WM2.2

The student is able to: • represent a problem with a sketch or diagrams. • compare ways of representing a problem. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number.

Skills • following instructions • working mathematically • problem-solving

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • coloured pencils/ crayons

Language • multiply • how many

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of multiplication.

Warm up

• Direct students to examine the picture in their workbook and describe what they see.

What to do

• Read the instructions to the class. • Ask students to draw a picture of the hat rack to show what it would look like if seven children collect their hats. • Discuss any differences in drawings. Are these real differences or just different descriptions of the same answer?

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Main Activity (WM2.2, N2.3)

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• 170 • New Wave Maths Book B – Teachers Guide

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Unit 38–2

Student page 112

Indicators

Outcomes N2.3, C&D2.2, C&D2.4

The student is able to: • apply unambiguous and familiar criteria to sequence data consistently. • comment on information in displays of data produced by himself/herself and peers.

Skills • modelling • graphing • classifying

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • attribute blocks • 2-D shapes

Language • multiply • shapes • Venn diagram • straight • edges • curved • groups

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of multiplication.

Warm up

• Distribute attribute blocks and 2-D shapes and direct students, in their groups, to find different ways of sorting the shapes. Describe how they sorted their shapes to the rest of the group.

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• Direct students to their workbook and the first activity. Remind students how a Venn diagram works. Items are grouped in the space if they are the same. Where items have shared or common features they are grouped in the overlap. • Ask students to state the number identifying each shape with straight edges only. These numbers are placed in the left side of the diagram. • Repeat for curved edges and those with both straight and curved edges. • In the second activity, the shapes with any straight edges are grouped, using their number, on the top box. Those with any curved edges are grouped in the bottom box. • The next column of boxes show the shapes with just straight edges in the top box, those with straight and curved edges in the middle box and those with only curved edges in the bottom box. • All shapes are identified by the number inside them.

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What to do

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Main Activity (C&D2.2, C&D2.4)

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 171 •

Unit 38–3

Student page 114

Indicators

Outcomes

N2.3, WM2.2, WM2.4

The student is able to: • represent a problem with a sketch or diagrams. • respond to questions such as ‘Is your working correct?’ by checking each stage of the work. • expect two approaches to a counting task to produce the same result and express surprise if they do not.

Skills • working mathematically • problem-solving • counting

Teac he r

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil

Language

• multiply • counted • how many • altogether

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of multiplication.

Warm up

• Direct students to their workbook and ask them to examine the page. Ask them to describe what they see. Ask for different versions.

What to do

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Main Activity (WM2.2, WM2.4)

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• Read the instructions to the class. • Ask students to think how they can decide who was correct. • Ask students to think of ways they can make the counting of the counters easier. Students may use actual counters to manipulate if this helps. • Students record their ideas then share them with the class.

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• 172 • New Wave Maths Book B – Teachers Guide

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Unit 38—Answers

Student pages 112 – 114

Unit 38–1 1. (a) 40 (b) 8 (c) 12 (d) 3 2. Teacher check. Three hats will be left.

Unit 38–2 1. (a) 18 (b) 21 (c) 15 (d) 50 2. straight edges 3

4 6

straight and curved edges

curved edges

7 10

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straight edges

1, 3, 4, 6, 7, 8, 10

straight edges only

3, 4, 6, 8 straight and curved edges

1, 7, 10 curved edges only

2, 5, 9

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Teac he r

curved edges

1, 2, 5, 7, 9, 10

5 9

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• Encourage divergent thinking in other working mathematically problems. Discuss as a class, so those students who find it difficult can listen, learn and gradually participate more fully.

Consolidation 38–2

m . u

1. (a) 4 (b) 3 (c) 10 (d) 3 2. Teacher check. Karen was correct as there are 26 counters.

• Create a pictograph to show shapes with straight sides only, curved sides only and straight and curved sides.

Consolidation 38–3

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• Encourage divergent thinking in other working mathematically problems. Discuss as a class, so those students who find it difficult can listen, learn and gradually participate more fully.

New Wave Maths Book B – Teachers Guide • 173 •

Unit 39–1

Student page 115

Indicators

Outcomes N2.3, S2.1

The student is able to: • place important things in his/her environment in order on the map. • describe the location of an object as ‘between’ two other locations.

Skills • scale drawing

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • ruler

Language • multiply • draw • picture • classroom • same sizes • largest

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of multiplication.

Warm up

• Ask students to have a good look at their classroom then, as asked, describe what they see. Bring focus to placement of the furniture, in particular the teacher’s table and the students’ desks.

What to do

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Main Activity (S2.1)

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• Ask students to draw, using a ruler to make straight lines, the position of the teacher’s table and the students’ desks. • When drawings are finished, ask students whether all desks were the same size. Ask whether they have been drawn the same size. Ask for explanations as to why desks are or are not the same size. • If desks are not the same size, ask which are larger.

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• 174 • New Wave Maths Book B – Teachers Guide

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Unit 39–2

Student page 116

Indicators

Outcomes

The student is able to: • represent a problem with an appropriate number operation. • use counting strategies such as combining collections and counting the lot, counting on from the first number, counting on from the largest number. • use a calculator to add and subtract numbers arising in daily activities, entering subtractions in the correct order.

N2.3, WM2.2

Skills • problem-solving • working mathematically • counting

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • calculator

Language • multiply • how many • away • present • groups

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of basic facts of multiplication.

Warm up

• Discuss with students places where mathematics is used in everyday life—shopping, driving, cooking, building etc. • Explain to students that teachers use mathematics in their classrooms every day. The activities in the workbook show some of these uses.

What to do

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Main Activity (WM2.2, N2.3)

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• Work with the students to read the questions and find the answers. If needed, students may use counters or a calculator to assist in finding answers to sums after the type of sum and the numbers involved have been established.

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R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 175 •

Unit 39–3

Student page 117

Indicators

Outcomes

The student is able to: • select or reject units as relating or not relating well to the attribute to be measured. • use repetitions of a uniform unit to measure area.

N2.3, M2.1, M2.2

Skills • measuring area

Number (N2.3)

Resources

• Base 10 MAB • counters • pencil • 1- or 2-cm cubes

Language

• multiply • approximate • area • shape

r o e t s Bo Notes r e p ok u S

Main Activity (M2.1, M2.2) Warm up

• Distribute counters and cubes to groups of students. Direct students to use the materials to cover and find the area of small objects; e.g. workbook, pencil case, diary or similar.

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• Explain to the students that they will be asked to use counters only to find the area of three different shapes in their workbook.The counters will not cover the shapes perfectly. Students will need to decide what they wish to do about uncovered and/or overlapping pieces. • Record the number of counters used to cover each shape in the space provided. • Repeat using cubes. • Encourage students to discuss whether counters or cubes were better to use, giving supporting argument for their case. • Students make their own choice and write it in the workbook, then give their reasons why they chose either counters or cubes.

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What to do

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Teac he r

• The focus for this unit is revision of basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80 – 81. • 176 • New Wave Maths Book B – Teachers Guide

R.I.C. Publications® www.ricpublications.com.au

Unit 39—Answers

Student pages 115 – 117

Unit 39–1

1. (a) 4 (b) 2 (c) 3 (d) 5 2. Teacher check

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Teac he r

1. (a) 2 (b) 4 (c) 4 (d) 1 2. Teacher check (a) Teacher check (b) Teacher check

Unit 39–2

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• Draw a plan of another room in his/her school with attention to scale.

Consolidation 39–2

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1. (a) 1 (b) 4 (c) 3 (d) 2 2. Teacher check

• Devise further questions to ask about the classroom. Share ideas and solve as a class.

Consolidation 39–3

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• Use counters and cubes to measure the area of other 2-D shapes such as a triangle, pentagon or an oval. Discuss whether counters or cubes were better to use.

New Wave Maths Book B – Teachers Guide • 177 •

Unit 40–1

Student page 118

Indicators

Outcomes

N2.3, WM2.2

Skills • problem-solving • working mathematically • counting

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • library • calculator

Language • multiply • how many

r o e t s Bo Notes r e p ok u S

Main Activity (WM2.2) Warm up

• Take students to the school library and ask the librarian or library assistant to explain how a bulk loan works. Ensure discussion includes acknowledgment that all books are not always returned.

What to do

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Teac he r

• The focus for this unit is revision of basic facts of multiplication.

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• Ask students to look at the picture of the bulk loan of encyclopaedias. How many books are in the set? • Look at the picture of the returned books. How many have been returned? • Ask students how many books are missing. • Ask students to write an explanation saying how they found the number of missing books. • Share these findings with the class.

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• 178 • New Wave Maths Book B – Teachers Guide

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Unit 40–2

Student page 119

Indicators

Outcomes N2.3, C&D2.3, C&D2.4

The student is able to: • compare heights (or lengths) of the columns in a block graph to place categories in order. • understand the need for a baseline and space blocks regularly (in provided grids) to allow comparisons to be made. • comment on information in displays of data produced by themselves and peers.

Skills • collecting data • graphing • analysing data

Teac he r

Number (N2.3)

Resources • Base 10 MAB • counters • pencil • 1-cm cubes • coloured pencils/ crayons

Language • add • block graph • most • how many • altogether • least

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of addition of basic facts using money.

Warm up

• Distribute 1-cm cubes to all students.

What to do

• Introduce a discussion on pets. Ask how many students have a pet. • Focus on the number of students who have a dog as a pet—record this number by placing a 1-cm cube on each space to represent one student until all students have been shown. • Repeat for each of the other pets. • To keep this record, ask students to colour the spaces under each cube. • Work with the class as a whole to find the answers to the questions.The teacher may read the questions or select a student to read the questions. Refer students back to the graph to find the answers.

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Main Activity (C&D2.3, C&D2.4)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 110 – 111. R.I.C. Publications® www.ricpublications.com.au

New Wave Maths Book B – Teachers Guide • 179 •

Unit 40–3

Student page 120

Indicators

Outcomes

N2.3, WM2.4

The student is able to: • respond to questions such as ‘Is your working correct?’ by checking each stage of the work.

Skills

Resources

• Base 10 MAB • counters • pencil

Language

• add • errors • patterns

• problem-solving • discussing patterns • creating patterns • working mathematically

Teac he r

Number (N2.3)

r o e t s Bo Notes r e p ok u S

• The focus for this unit is revision of addition of whole number using money.

Warm up

• Ask students to make a pattern, or think of a pattern then draw it on the blackboard/ whiteboard. Other students check to see that it is a recurring pattern that has been drawn.

What to do

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Main Activity (WM2.4)

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• Ask several different students to draw patterns. • Direct students to their workbook. Students may work independently, in pairs or small groups. • Ask students to examine each pattern carefully in turn to find the error. • Once the error has been identified, students are to redraw the patterns accurately. • Share correct patterns with the class. Students either show or explain to the class what the error was and explain how the error was corrected.

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• 180 • New Wave Maths Book B – Teachers Guide

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Unit 40—Answers

Student pages 118 – 120

Unit 40–1

1. (a) 14c (b) 16c (c) 7c (d) 10c 2. Teacher check

r o e t s Bo r e p ok u S

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Teac he r

1. (a) 7 (b) 3 (c) 2 (d) 3 2. (a) 9 (b) Teacher check

Unit 40–2

• Use counters and cubes to measure the area of other 2-D shapes such as a triangle, pentagon or an oval. Discuss whether counters or cubes were better to use.

Consolidation 40–2

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1. (a) 9c (b) 17c (c) 9c (d) 14c 2.

• Construct a pictograph of the types of pets, ensuring the pets are drawn the same size or within squares the same size.

Consolidation 40–3

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• Create patterns with an error for a classmate to identify.

New Wave Maths Book B – Teachers Guide • 181 •

Teac he r

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• 182 • New Wave Maths Book B – Teachers Guide

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Additional Activities

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New Wave Maths Book B – Teachers Guide • 183 •

Space Activities S2.1 1. Involve students in discussions as to how the classroom can be best arranged to provide for more floor space at the front, in the rear or between desks.

2. Involve students in discussions as to how seating might be arranged within the classroom – single desks, groups, rows, direction to face.

3. Students plan pin-up displays of their own.

4. Draw a bird's-eye view of the classroom showing where the desks and tables are. Discuss relative size of desks and tables.

r o e t s Bo r e p ok u S

5. Give each student a copy of a plan of the school buildings and grounds. Walk the whole class around the grounds, identifying buildings and areas that are used for specific purposes.

1. Students may be directed to make models of similar shapes or structures to those in the environment using boxes, building blocks or construction kits.

2. Make a simple model using blocks or boxes then make it longer, higher and wider.

3. Use the sun to make shadows with the body. Trace around the shadows with chalk. Make a longer, shorter, wider and narrower shadow. Trace around each one—perhaps use a different coloured chalk for each shadow.

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S2.2

Discuss with students what they did each time.

A similar activity may be done using large shapes and the sun, or smaller shapes and the overhead projector.

4. Use modelling clay to make shapes and alter them by squeezing, stretching, dropping and pushing against a firm surface. Students describe what happens in each case.

S2.3

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• colour every second row red;

• colour every fifth column green; or

• colour every fourth square blue; or

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5. Use 1-cm grid paper to make patterns by colouring according to predetermined instructions given by the teacher. For example:

• as determined by the students who should be able to describe their patterns. These activities should be repeated often using 1-cm square paper or 1-cm triangle grid paper on pages 199 and 201 of New Wave Maths Teachers Guide.

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1. Use the grids on pages 198 – 201 to create tessellating patterns.

2. The grids on pages 199 and 200 can also be used to reduce and enlarge simple pictures, or complete symmetrical pictures or shapes.

3. Introduce symmetry in the shapes students use and follow up with symmetry that may be identified in objects in the classroom. 4. Use 2-D shapes to make patterns. Use the shapes to make the pattern initially. Repeat the exercise later and have students trace around the individual shapes to draw the pattern. Students should use shapes that do and do not fit together in both exercises.

• 184 • New Wave Maths Book B – Teachers Guide

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Space Activities cont.

5. Using concrete materials, students make their own patterns and describe them. Where possible, number patterns should be noted by students. These activities should be done regularly. If possible, have students keep a written record of their patterns and/or have a classmate describe the pattern and add the next two to five parts of the pattern.

1. Students should be encouraged to examine their environment for shapes similar to given shapes they have been working with; for example, boxes and 3-D models.

2. Attribute blocks can be used to assist students in comparing and classifying shapes according to shape, size, colour and thickness. The Venn diagram on page 223 of the New Wave Maths Teachers Guide may be used to assist with the classifying.

3. Students should be encouraged to classify according to directed attributes or choose their own. In either case they need to be able to substantiate their basis for classification; for example, size, colour, material, with holes, with wheels, shape.

4. Students may make a tally of shapes found in their environment and identify where the shape is found and how many of them there are in the environment.

Discovery of shapes should be in conjunction with open discussion to develop understanding of the reason why objects are certain shapes.

5. Discuss with students relative size of objects and why they are different in size. A comparison of student furniture with other student furniture and adult furniture is a good starting point.

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6. Use straws, popsticks, matchsticks or other materials to make shapes with 3, 4, 5 and 6 sides. Have students find out how many different kinds of each shape they can make. Check each shape made to see how many sides and corners there are in each shape. Is there a pattern? Students may chart their findings. For example:

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New Wave Maths Book B – Teachers Guide • 185 •

Measurement Activities M2.1

Students should discuss freely what they are doing. 2. Students are to use a lump of modelling clay to make a shape. The shape is balanced on a balance scale with a number of object of students' choice; for example, 2-cm cubes. Record the results.

Remodel the modelling clay and repeat the activity.

Repeat this task several times. Students should reflect on what is happening to the mass of the modelling clay each time it is reshaped.

3. Discuss how the tallest container may not hold the most juice as it isn't as wide as another.

4. Decide by hefting, rather than visual size, which is the heavier of two pieces of fruit.

1. Students make direct comparisons of objects. Arranging objects in order shows the level of understanding.

2. Arbitrary units may be used to ascertain lengths or heights of objects. Popsticks, Base 10 MAB longs and coloured rods are useful measuring units.

3. Larger objects may be measured with paper streamers or string/wool and glued to a chart for display.

4. Compare the distance around a lid and its area to other lids. Use counters to cover the lid; for example, count these to see if the lid with the biggest perimeter also has the greatest area.

5. Compare objects of the same height to see if they have the same mass. Use a balance scale.

6. Compare objects of the same height to see if they have the same capacity by pouring the contents from one to the other.

7. Use a variety of free-play sessions including art to allow students to paint, colour, cover pages or surfaces of objects.

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1. Manipulation of puzzles, including jigsaws, simple puzzles and pattern blocks, develops an awareness of area.

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8. Find lids with the same area. Measure their perimeter to see if they are the same. Use wool to measure the perimeter.

9. Compare the capacity of containers with the same area base. What do you notice about those that have the larger capacity?

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10. Make an assortment of boxes filled with different materials and coverings.

• 186 • New Wave Maths Book B – Teachers Guide

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Measurement Activities cont. 11. Fill containers of the same size with different ingredients, water, grain etc. and compare their mass.

1. Students should be allowed many opportunities to estimate amounts, then pour and fill containers with a variety of materials (water, sand, grains). Focus on discussion of how much the container holds, which holds the most, the same and so on.

Encourage students to understand the need to pour easily and note which containers are easiest to pour from.

2. Estimate, then fill containers with different objects such as blocks or balls to see how many are required to fill it.

3. Use a variety of materials in free-play situations, using balances, where students are able to verbalise their perceptions of the mass of different objects.

Teacher questions should develop the concepts of heavier and encourage the use of balance scales to support the students' claims.

4. Discuss with students an estimate of how long before an event happens, and how long an event was, before and after it happened.

5. Discuss days of the year, seasons, times of the year, the activities that take place and the clothes worn at these times.

6. Students should estimate before completing the following activities.

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M2.3

Use an eggtimer to time the duration of the following, or other, activities:

• the number of times a ball can be bounced

• the number of times students can write their name

• the number of shapes students can make

• the distance students can walk around the netball court.

Use a stopwatch to see how long it takes students to:

• walk across the oval and back

• tie shoelaces

• count backwards from 20

• tidy their desk.

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In five or ten minutes see how much of the following activities students can complete:

• draw and colour a picture; or

• write a story.

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New Wave Maths Book B – Teachers Guide • 187 •

Number Activities N2.1a 1. When sorting and classifying, students should justify their sorting and be able to answer open and closed questions relating to the total items sorted, comparisons of part of the items and totals of combinations of some of the sorted items.

Sorting charts are provided on pages 223 – 224 of the New Wave Maths Teachers Guide.

Students' verbalisation of their work is of great importance.

2. Seriate objects and discuss placement of the order of individual objects. Arrangements may be at student discretion or as directed by the teacher. 3. Play games using the bingo cards on pages 212 – 215 of New Wave Maths Teachers Guide to assist students in recognising the numbers 1 – 100.

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5. Use plastic coins or photocopy the notes and coins on page 211 of the New Wave Maths Teachers Guide. Students can participate in shopping activities.

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4. The number lines on page 205 of New Wave Maths Teachers Guide can be distributed to students to assist in counting activities.

6. Use number tracks provided on pages 203 – 204 of The Teacher Resource Guide to play games. Make dice with numbers or symbols to indicate forward or backward movement. Use a 2-cm cube with green numbers 1, 2 and 4 for forward movement and red numbers 3 and 5 for backward movement and a black dot for miss a turn. First to reach 20 or 30 wins. 7. Use the coins shown on page 215 of the New Wave Maths Teachers Guide to assist students in recognising coins and their value.

Use the following instructions:

• Put a cross on two coins where their combined value is equal to 10c.

• Tick the two coins that you could exchange for 20c.

• Circle the three coins you would need to use to exchange for 50c.

• Colour the $1 and $2 coins yellow.

• Colour the 5c coins grey, 10c coins green, 20c coins blue and 50c coins red.

N2.1b 1. Use symmetry to assist in cutting paper into halves, thirds etc. or marking fractions in diagrams of rectangles, squares etc.

2. Cut fruit or items from their lunch boxes into fractions.

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1. Use concrete materials and diagrams to assist in solving addition, subtraction, multiplication and division number stories and number calculations.

2. Use students’ experiences to create number stories involving the four operations.

1. Hold competitions in groups, using basic addition and subtraction facts and multiplication tables.

2. Use the templates on page 203 of New Wave Maths Teachers Guide to make personal basic facts charts.

1. Use a flip array or number grid chart to identify rules or create number patterns for other students to identify.

2. Use concrete materials such as attribute blocks or matchsticks to create a pattern of numbers.

N2.3

N2.4

Use coins to make money patterns.

• 188 • New Wave Maths Book B – Teachers Guide

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New Wave Maths Book B – Teachers Guide • 189 •

Student Outcomes

Working Mathematically

Chance and Data

WM2.1 The student describes some of the ways self, friends and family use ideas about space, number, measurement and chance in daily life.

C&D2.1 The student distinguishes possible from impossible events, and describes familiar, easily-understood events as being more likely or less likely to happen.

WM2.2 The student poses mathematical questions prompted by similar or related questions and represents questions using objects, pictures, symbolic statements or mental images.

C&D2.2 The student realises that we can answer some questions ourselves by collecting, classifying and sequencing data and applies unambiguous and familiar criteria consistently when classifying and sequencing.

WM2.3 The student responds to ‘What would happen if … ?’ type questions about numbers, shapes, data and measurements and tests ideas with at least a single trial.

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S2.1

S2.2

S2.3

S2.4

Number

N2.1a The student reads, writes, says and counts with whole numbers to beyond 100, using them to The student attends to order and betweenness on compare collection sizes and describe order. informal maps and in descriptions of locations and N2.1b The student understands the meaning of ‘half ’ and paths. ‘quarter’, splitting quantities into ‘fair’ shares and The student meets simple criteria relating to shape partitioning quantities repeatedly into halves. or structure in making and drawing things, making N2.2 The student understands the meaning and recognisable copies of arrangements of shapes. connections between counting, number partitions, The student uses multiple copies of shapes to addition and subtraction and uses this understanding construct repetitive patterns and follows and to represent situations involving all four basic describes simple movement rules for generating operations. such patterns. N2.3 The student counts, partitions and regroups in order The student sorts things according to everyday to add and subtract one- and two-digit numbers, spatial criteria and, prompted, uses spatial language drawing mostly on mental strategies for one-digit to describe the shape of things. numbers and a calculator for numbers beyond their present scope.

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Measurement

N2.4

M2.1

The student distinguishes the attributes of length, area, capacity and mass when comparing things and chooses things which relate well to the attribute of interest to use as units.

M2.2

The student directly compares and orders things by length, area, capacity, mass and time; indirectly compares lengths and capacities; and uses uniform units carefully to measure lengths.

M2.3

The student estimates the order of things by length, area, mass and capacity and makes numerical estimates of length using a unit that can be seen or handled.

M2.4

Attention should be directed toward Level 3.

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Space

C&D2.4 The student describes what own and classmates’ displays of data show.

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WM2.4 The student expects to get the same answer to counting, computation and measuring tasks each time they are carried out and, when prompted, checks and corrects answers.

C&D2.3 The student displays and summarises data based on one-to-one correspondence between data and representation.

The student recognises, continues, represents and describes patterns involving counting, grouping and constant addition or subtraction of whole numbers.

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M3.4a The student understands and measures perimeter directly and used straightforward arithmetic to determine perimeters, elapsed time and other measurements which cannot be obtained directly. M3.4b The student attends informally to scale when making and using plans, maps and models. • 190 • New Wave Maths Book B – Teachers Guide

Extracted from Mathematics Outcomes and Standards Framework – Student Outcome Statements, Education Department of Western Australia 1998.

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Working Mathematically—Record Sheet

Apply and Verify

Mathematical Strategies

Investigate Mathematically

Comment

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Student Name

Contextualise Mathematics

Outcome Category

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New Wave Maths Book B – Teachers Guide • 191 •

Space—Record Sheet

Reason Geometrically

Represent Transformations

Comment

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Student Name

Represent Shape

Represent Location

Outcome Category

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Measurement—Record Sheet

Indirect Measure

Estimate

Direct Measure

Comment

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Student Name

Understand Units

Outcome Category

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New Wave Maths Book B – Teachers Guide • 193 •

Chance and Data—Record Sheet

Interpret Data

Summarise and Represent Data

Comment

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Student Name

Collect and Organise Data

Understand Chance

Outcome Category

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• 194 • New Wave Maths Book B – Teachers Guide

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Number—Record Sheet

Reason about Number Patterns

Calculate

Understand Operations

Comment

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Student Name

Understand Numbers

Outcome Category

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New Wave Maths Book B – Teachers Guide • 195 •

Proforma This proforma has been provided for you to copy and use with your class. You can either: • select an activity and evaluate the whole class; or • select a small group of students and evaluate their work. The indicators are found on the relevant page in the New Wave Maths Teachers Guide.

1. Photocopy this page.

2. Write the appropriate date, strand, outcome(s) and indicators.

3. Photocopy enough for one per student being assessed.

4. Inform the students they are being assessed on the activity they are about to complete. 5. Students complete the activity in the workbook. 6. Mark the work completed by the student.

r o e t s Bo r e p o u k Mathematics Proforma S 7. Attach the proforma to the appropriate workbook page.

8. Record evaluation as required.

Date

Strand

Outcome(s) Demonstrated

Indicators

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Needs Further Opportunity

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Mathematics Proforma Strand

Indicators

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Demonstrated

Needs Further Opportunity

Classroom Teacher • 196 • New Wave Maths Book B – Teachers Guide

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Photocopiable Resources

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New Wave Maths Book B – Teachers Guide • 197 •

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1-cm dot grid paper.

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1-cm grid paper.

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New Wave Maths Book B – Teachers Guide • 199 •

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2-cm grid paper.

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• 200 • New Wave Maths Book B – Teachers Guide

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1-cm triangle grid paper.

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New Wave Maths Book B – Teachers Guide • 201 •

Number Cards

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Photocopy onto coloured card. Cut out and laminate. You may wish to enlarge to A3.

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New Wave Maths Book B – Teachers Guide • 203 •

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• 204 • New Wave Maths Book B – Teachers Guide

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5 1

10 6

r o e t s Bo r e 50 45 p 55o u k S

G l u e

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26 27 28 29

36 37 38 39

51 52 53 54

70 66 67 68 69

56 57 58 59

75 71 72 73 74

76 77 78 79

G l u e

90u 95 n 100 © R. I . C.P bl i cat i o s orr ev e u po eso y 82 • 83 f 84 86 87 i 88 w 89 p 91r 92 93s 94 96 n 97l 98 • 99

0 5

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35 31 32 33 34

46 47 48 49

61 62 63 64

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11 12 13 14

20 G l u 16 17 18 19 e 40

25 21 22 23 24

32 34 o c . che e r o t r s sup 50 er 12 14 16 18

22 24 26 28

10 15 20 25 30 35 40 45

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36 38

100

55 60 65 70 75 80 85 90 95 2/ 3

1/ 3

1/ 2

1 3/ 4

New Wave Maths Book B – Teachers Guide • 205 •

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100 Chart

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• 206 • New Wave Maths Book B – Teachers Guide

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0 – 99 Chart

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New Wave Maths Book B – Teachers Guide • 207 •

Basic Facts

8 0 8 16 24 32 40 48 56 64 72 80

9 0 9 18 27 36 45 54 63 72 81 90

10 0 10 20 30 40 50 60 70 80 90 100

X 0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 0 2 4 6 8 10 12 14 0 3 6 9 12 15 18 21 0 4 8 12 16 20 24 28 0 5 10 15 20 25 30 35 0 6 12 18 24 30 36 42 0 7 14 21 28 35 42 49 0 8 16 24 32 40 48 56 0 9 18 27 36 45 54 63 0 10 20 30 40 50 60 70

8 0 8 16 24 32 40 48 56 64 72 80

9 0 9 18 27 36 45 54 63 72 81 90

10 0 10 20 30 40 50 60 70 80 90 100

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• 208 • New Wave Maths Book B – Teachers Guide

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9 8

9 7

9 6

9 5

9 4

9 3

9 2

9 1

8 8

8 7

8 6

8 5

8 4

8 3

8 2

8 1

8 0

7 7

7 6

6 6

6 5

6 4

6 3

6 2

6 1

6 0

5 5

5 4

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9 0

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4 2

4 1

3 3

3 3 2. t1

3 0

2 2

2 1

1 1

1 0

4 0

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Photocopy onto coloured card. Cut out and laminate. You may wish to enlarge to A3.

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These pairs of number added or multiplied (either order) and their reciprocal subtraction and division facts constitute the basis of the basic number facts.

Basic Number Facts

New Wave Maths Book B – Teachers Guide • 209 •

Tens

Ones

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Hundreds

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• 210 • New Wave Maths Book B – Teachers Guide

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Spinners

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New Wave Maths Book B – Teachers Guide • 211 •

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Calendar

January

March

15 22 29

12 19 26

16 23 30

13 20 27

10 17 24 31

14 21 28

11 18 25

15 22

15 22 29

12 19 26

16 23

16 23 30

13 20 27

10 17 24

10 17 24 31

14 21 28

11 18 25

16 23

14 21 28

10 17 24

15 22 29

11 18 25

16 23 30

12 19 26

10 17 24 31

13 20 27

11 18 25

14 21 28

12 19 26

15 22 29

June 4

11 18 25

12 19 26

13 20 27

14 21 28

15 22 29

16 23 30

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20 © R. I . C.P6u13bl i c27at i ons 3 10 17 24 July August September • f o r r e v i e w p u r p o s e s o n l y• 30 2 9 16 23 6 13 20 27 3 10 17 31

10 17 24

11 18 25

5 6

14 21 28

11 18 25

15 22 29

12 19 26

16 23 30

13 20 27

10 17 24 31

14 21 28

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Note: By writing the correct day for the current year next to the correct date, this calendar may be used for any year except a leap year.

February

o c . e October c November December her r o st super 7

14 21 28

11 18 25

15 22 29

12 19 26

16 23 30

15 22 29

12 19 26

10 17 24

16 23 30

13 20 27

11 18 25

10 17 24 31

14 21 28

12 19 26

11 18 25

15 22 29

13 20 27

12 19 26

16 23 30

14 21 28

13 20 27

10 17 24

15 22 29

14 21 28

11 18 25

16 23 30

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New Wave Maths Book B – Teachers Guide • 213 •

Clocks

11 2

10 9

3 4

1 2

8 5

10 9

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3 4

10 9

3 4

8 7

• 214 • New Wave Maths Book B – Teachers Guide

3 8

3 4

8 7

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Money

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New Wave Maths Book B – Teachers Guide • 215 •

27 100 14

16 100 28

100 90

100

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100 12

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r o e t s Bo r e p o u 5S 4 35 40 25 k9

100

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r o e t s Bo r e p o u 25 S4 25 100 21 25k

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New Wave Maths Book B – Teachers Guide • 219 •

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Note: This worksheet can be copied onto card and laminated for continuous use. Students name each group on the lines provided before sorting objects.

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Classification Chart

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Sorting Circles

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New Wave Maths Book B – Teachers Guide • 221 •

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Capacity Labels

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• 222 • New Wave Maths Book B – Teachers Guide

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Venn Diagram

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Note: This Venn diagram can be used as required by the students to sort items into categories.

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New Wave Maths Book B – Teachers Guide • 223 •

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Carroll Diagram

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• 224 • New Wave Maths Book B – Teachers Guide

Note: This Carroll diagram can be used as required by the students to sort items into categories.

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Line or Bar Graph

(Title)

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New Wave Maths Book B – Teachers Guide • 225 •

20 19 18 17 16 15 14 13

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Units of Measure:

11 10 9 8 7 6

2 1

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Item

• 226 • New Wave Maths Book B – Teachers Guide

Tally

Total

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2-D Shapes

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New Wave Maths Book B – Teachers Guide • 227 •

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2-D Shapes

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3-D Shapes

r o e t cylinder s Botriangular prism r e p ok u S

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cube

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sphere

square pyramid

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Tangrams

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Waterman Primary School

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New Wave Maths Book B – Teachers Guide • 231 •

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Parent Information

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Contents

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New Wave Maths Book B – Teachers Guide • 233 •

Parent Information

Expectations of Knowledge of Basic Facts Year 1 An informal, general introduction to number and combinations.

Year 2 Discovery approach (manipulating concrete material) to finding and learning addition and subtraction facts.

Year 3

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Discovery and some recall of addition and subtraction facts. Use the terms ‘add’ or ‘subtract’ rather than ‘plus’ or ‘minus’. Learn basic multiplication facts of 2, 3, 4 and 5 and multiples of 10, to 10 times 10.

Year 4

Year 5

Recall basic addition, subtraction, multiplication and division facts.

Year 6 and 7

Automatic response is desirable.

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Consolidate basic sums to 18 and differences taking from 18. Extend recall of basic multiplication and division facts to facts of 6, 7, 8 and 9 times tables.

The following suggestions can be used at home to assist your child in becoming more proficient in gaining automatic recall of the basic number facts. The ideas are not exclusive, many alternatives may be used.

4 5

7 8

‘Snap’ – played with flash cards. Play as for ordinary snap. A variation – write pairs of numbers on cards, or blank playing cards, without operation signs. Child may add, subtract, multiply or divide the pair of numbers to find a matching pair.

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‘Flash Cards’ – with all combinations of basic facts, hold up, child responds with the answer. Flash cards can be easily made from light card (cereal packet) or by purchasing blank playing cards and writing basic facts on these.

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Throw two dice then either add, subtract or multiply the two numbers shown.

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Race the calculator. Call out a basic fact, while you work out the answer using the calculator your child attempts to race you to the correct answer working mentally. ‘Sums, Differences, Products’ (add, take, multiply) – The game is played using a hundred chart. Call a pair of numbers from the basic facts. Your child covers the sum, the difference and the product of the two numbers called on the hundreds chart. Play for a given time; for example, five minutes, or until all of a set of basic facts have been used. ‘Bingo’ – The game is played as for ordinary bingo. You call a basic fact, use basic number fact sheet, your child covers the correct answer if it is on the card. First to cover the card or a line wins the game. When using board games encourage your child to add onto the total when throwing the die, or add the total of the dice, rather than counting on. ‘Numero’ is one of the best mathematical games available which can be used at home to develop mathematics skills.

• 234 • New Wave Maths Book B – Teachers Guide

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Parent Information

Primary School Mathematics The Algorithm The following examples show the recommended method of recording the written algorithm for each of the four processes. These formats are not prescriptive, but are recommendations. In all cases, the ultimate aim is to arrive at the simplest (usually the shortest) form of recording the algorithm. A simplistic progression is shown for the development of each algorithm from Year 1 to Year 7.

Combining and Separating – Addition and Subtraction

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Year 1 Concrete activities are recorded in number sentence form – first written recordings may possibly be made late in Year 1. The same form of recording is used in Years 2 and 3. In year three, adding and subtracting without regrouping are also recorded in vertical form. Vertical recording continues through to Year 7, with regrouping and increased difficulty of examples.

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Year 2 Using basic facts to 9 + 9 = 18 and adding three numbers each less than 6. It is recommended that concrete materials are used.

Year 3 Allow free exploration of addition initally. Focus on commenting with ones for ease of recording. 8

3 2 3 2 5 5c + 5 1 2 + 4 7 2 2c 1 3 + 1 5 7 9 7 + 8c 5 9 1 5c

When subtracting start with the top line number; for example, 3 take 6, can't be done. Regroup, 13 take 6 equals 7.

8 7 $7 0 6 – 2 5 – $3 0 7 6 2 $4 0

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Year 4 Students may still require the use of concrete materials at this stage.

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$2 . 3 7 + 5 6 + $2 . 4 8 9 3 $4 . 8 5

Students may still require the use of concrete materials at this stage. 21

8 3 5

6 .8 0 m – 2 2 7 – 3 . 2 7 m 6 0 8 3 . 5 3 m

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New Wave Maths Book B – Teachers Guide • 235 •

Parent Information

Primary School Mathematics Grouping and Sharing – Multiplication and Division Commencing in Year 2, concrete activities are recorded, using the multiplication symbol in a number sentence from late Year 2 or as ready. Number sentence recording of concrete activities is carried on into year three. The written algorithm is introduced in its extended form in Year 4, working to the abbreviated form when the child understands the process. Year 2 Symbol ‘x’ is introduced to assist with grouping. Use of language to support activities – ‘lots of ’, ‘sets of ’ or ‘groups of ’ to 20 or 30. Division experience is through sorting, sharing and grouping activities using concrete materials. Introduction to open number sentences. For example,

3+2=

4–1=

3 lots of 4 =

Year 3 Allow free exploration of multiplication and division initally. Some students may require the assistance of concrete materials.

5 4

x 7c = 28c x 3 3 1 5

1 0 30

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32 ÷ 4 = 8

Year 4 Some students may require the assistance of concrete materials.

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3 5 35 ➤ x 2 x 3 x 3 8 0 1 5 1 0 5 + 9 0 1 0 5

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Note This is a guide only and students are encouraged to develop progressively through these stages as they are ready. If you have any concerns please make an appointment to discuss them with me. • 236 • New Wave Maths Book B – Teachers Guide

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Parent Information

Problem-solving Strategies To assist your child in solving mathematical problems, the following strategies may help.

1 Understand the problem. (a) Ask relevant questions to determine the operation, pattern, sequence, form of measurement or other mathematical means to begin to work out the problem. (b) Choose a plan or strategy to work out all or part of the problem. (c) Simplify the problem by breaking it into smaller parts and working out each small part. (d) Guess. (e) Work backwards.

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Use appropriate computation: addition; subtraction; multiplication; or division to work out the problem.

To help in working out the problem: (a) Make organised lists or tallies of data. (b) Make tables to show data. (c) Use physical models: objects; pictures; diagrams; graphs; or symbols. (d) Look for patterns and relationships.

Explain, generalise, prove relationships and patterns.

Guess and test facts, hypotheses or rules.

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Write or present conclusions clearly for others to be able to check your findings.

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Check results.

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Some Problem-solving Activities Around the Home

The following suggestions can be used at home to assist your child in becoming more proficient in problem-solving. The ideas are not exclusive, many alternatives may be used.

1 2 3 4 5

When planning the next family holiday, include your child in the planning, budgeting, activities, travelling time, itinerary and allow him/her to help solve any problems which may arise. When renovating your home—painting, replacing flooring, fencing, grassing or reticulating the garden, encourage your child to participate in the planning, costing, measuring and evaluating of the budget. When planning a party, include your child in the planning, catering, shopping and cooking. When fertilising your lawn, invite your child to help you work out how much fertiliser will be required for the area. Also work out the cost and the best way to approach the task to ensure even coverage. When planning your family's next big purchase, encourage your child to help work out a savings plan.

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New Wave Maths Book B – Teachers Guide • 237 •

Parent Information

Concrete to Mental – Including the Calculator

Dear Parent(s) There are a number of different means of completing the four algorithms. Children start by using concrete materials to work through the algorithms to develop understandings. As their knowledge and understanding develop, students move to more abstract means of achieving the solutions to the algorithms. These solutions may be achieved by pencil and paper calculations or by working the solutions mentally (the ultimate aim).

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Should you encounter any problems, please contact me. Kind regards

Classroom Teacher

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Children who have great difficulties in completing algorithms are to be encouraged to use the calculator to find the solutions after first estimating the answer. Estimation skills are essential in showing the development of mathematical knowledge.

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Dear Parent(s)

There are a number of different means of completing the four algorithms.

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Concrete to Mental – Including the Calculator

Children start by using concrete materials to work through the algorithms to develop understandings. As their knowledge and understanding develop, students move to more abstract means of achieving the solutions to the algorithms. These solutions may be achieved by pencil and paper calculations or by working the solutions mentally (the ultimate aim).

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During these developmental phases children will encounter algorithms that are complex, difficult or are a means to another step or the final solution. In such cases, the child should be encouraged to use a calculator to find the solution to the algorithm. The calculator is an invaluable aid in mathematics and its use is to be encouraged from the very beginning of a child’s days at school. Children who have great difficulties in completing algorithms are to be encouraged to use the calculator to find the solutions after first estimating the answer. Estimation skills are essential in showing the development of mathematical knowledge. Should you encounter any problems, please contact me. Kind regards

Classroom Teacher

• 238 • New Wave Maths Book B – Teachers Guide

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Parent Information

Mathematical Learning Areas Mathematics is comprised of a series of learning areas. These learning areas are outlined for teachers in the Student Outcome Statements document produced by the Education Department. There are seven learning areas, each of which is outlined briefly below.

Appreciating Mathematics Appreciate the role of mathematics in their own and other communities.

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Working Mathematically

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Thinking about ideas, investigating, applying, verifying and reasoning mathematically. In brief, problem-solving.

Knowledge of location (place), shape, transformations (changes) and reasoning geometrically (angles, constructions and other geometrical relationships).

Measurement

Understand units of measure, measure objects using measuring units, estimate measures and calculate measurements.

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Understand chance events. Collect and organise data and information. Summarise and represent data. Interpret data.

Number

Understand number and the relationships, order, count, place value. Understand addition, subtraction, multiplication and division and be able to calculate using these operations. Work out number patterns.

Pre-Algebra

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Understand symbols and graphs. Represent variation. Solve equations and inequalities.

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New Wave Maths Book B – Teachers Guide • 239 •

Parent Information

Homework Policy

Dear Parent(s) As part of my Homework Policy I encourage students to regularly undertake given exercises in the reinforcement of mathematical concepts learnt at school. These activities will be within the expected competency level of the children; however, there may be times when, due to unforeseen circumstances, your child does encounter difficulties with the homework. Please take the time to assist with the processes involved, but please encourage your child to ‘have a go’.

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Your encouragement and positive support are crucial to the continued development of your child’s mathematical skills. Should you encounter any problems, please contact me.

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Kind regards

Classroom Teacher

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Homework Policy

As part of my Homework Policy I encourage students to regularly undertake given exercises in the reinforcement of mathematical concepts learnt at school. These activities will be within the expected competency level of the children; however, there may be times when, due to unforeseen circumstances, your child does encounter difficulties with the homework. Please take the time to assist with the processes involved, but please encourage your child to ‘have a go’.

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Occasionally your child will receive a problem to solve. Encourage your child to explore the problem using the problemsolving strategies sheet. Again, encourage your child to ‘have a go’. It is the process of investigation and working mathematically that is the focus of these activities. For this reason it is essential that all steps are written out as the problem is solved. Your encouragement and positive support are crucial to the continued development of your child’s mathematical skills. Should you encounter any problems, please contact me. Kind regards

Classroom Teacher

• 240 • New Wave Maths Book B – Teachers Guide