New Wave Maths - Teachers Guides: Level C - Ages 7-8 by Teacher Superstore

RIC–1086 11.8/588

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

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Robert Dayman 2003

RIC–1086 ISBN 978-186311-707-4 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.

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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 C – Teachers Guide • iii •

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

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Teachers Notes and Answers

Additional Activities

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

Assessment

Grid Paper ......................................................................................................................................... 198–201 Number Charts and Cards ..................................................................................................... 202–204 Number Lines ............................................................................................................................................. 205 Place Value Charts .................................................................................................................................... 206 Spinners – Blank .............................................................................................................................. 207–208 Calendar – Any year ................................................................................................................................... 209 Clocks .............................................................................................................................................................. 210 Money .............................................................................................................................................................. 211 Bingo Cards ...................................................................................................................................... 212–215 Sorting Circles ................................................................................................................................ 216–217 Venn Diagram – Blank ............................................................................................................................. 218 Carroll Diagram – Blank .............................................................................................................................................. 219 Line or Bar Graph – Blank ......................................................................................................................................... 220 3-D Shapes ................................................................................................................................................... 221 Tangrams ........................................................................................................................................................ 222 Graph and Table – Blank ........................................................................................................................ 233 Map ................................................................................................................................................................... 224

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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 .................................................................................. 226 Primary School Mathematics ................................................................................................. 227–228 Problem-solving Strategies ................................................................................................................... 229 Concrete to Mental ................................................................................................................................. 230 Mathematical Learning Areas .............................................................................................................. 231 Homework Policy ..................................................................................................................................... 232

• iv • New Wave Maths Book C – 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. 3. Students should develop their capacity to use mathematics in solving problems individually and collaboratively. 4. Students should learn to communicate mathematically. 5. Students should learn techniques and tools which reflect modern mathematics. 6. Students should exercise the processes through which mathematics develops.

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 (c) engage in the mathematical study needed for further education and employment. 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 (c) communicate mathematically to a range of audiences. 7. appreciate: (a) that mathematics is a dynamic field with its roots in many cultures; and (b) its relationship to social and technological changes.

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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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New Wave Maths Book C – 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):

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

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 constr uct conceptual under standing 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 8. modelling positive attitudes towards mathematics.

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• 2 • New Wave Maths Book C – 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 supportive, 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. • 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 The school and classroom setting should be safe and conducive to effective learning. These perspectives have several implications for teaching. They are listed as:

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• a supportive environment for learning; • appropriate mathematical challenge is provided; and • fostering processes which enhance learning. 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.

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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 C – 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; 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

Teachers need to be aware of the individual differences of all students and provide learning •f orr e vi ewa levelpofu r pand oindependence seso n l y•To do this, experiences which develop success for each student.

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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 C – Teachers Guide

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General Content Outline Goals and Guidelines Once Year 2 has been completed and is understood, students may then proceed to Year 3. 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 curricula 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 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 students' family as this is the centre of their 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.

The teaching of processes isu necessary to develop independent problem-solvers. Therefore, © R . I . C . P b l i c a t i o n s 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 •f or r e vi e w pu r p ose so nl y• Branch, Ministry of Education, 1989, publication Learning Mathematics: Pre-Primary to Stage

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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; 5. reflection in actions to formulate ideas; 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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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:

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New Wave Maths Book C – 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. The Curriculum Framework, 1998 (pages 183–193) identifies seven clusters of outcomes, some of these being:

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Appreciating Mathematics

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Students appreciate mathematics by 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. The development of ideas should be done using a wide range of familiar materials in a problemsolving situation that has meaning to the students. Relating activities to home communities and developing pleasure and confidence in mathematics supports the value of mathematics.

Working Mathematically

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, 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. 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.

• 6 • New Wave Maths Book C – Teachers Guide

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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. discussing findings and interpretations; 2. identifying patterns and relationships; 3. using symbols and words; 4. drawing pictures, diagrams and graphs; 5. constructing models; 6. translating between relationships; 7. making lists and tables; 8. drawing conclusions; 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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1. observing and identifying; 2. comparing, ordering and classifying; 3. making patterns and arrangements; 4. constructing models; 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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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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Number

Students should be able to count in one-to-one correspondence situations, develop cardinal and ordinal concepts to 10 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

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New Wave Maths Book C – Teachers Guide • 7 •

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. Students continue to be introduced to experiences with larger numbers through grouping and trading activities. Base 10 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 recognition of decimal numbers in symbolic format. During Year 3, students should be able to recall most of the basic facts for addition and subtraction. The New Wave Maths book provides further development of this knowledge as well as developing experience with the basic multiplication and division facts.

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Recommended Progression for Algorithms Year 1

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• Use concrete materials to manipulate and arrange objects with either oral or written answer in addition and subtraction. • Counting equivalent sets by two, threes, fours and fives up to 20. • Sharing objects in practical situations.

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

17 +2

43 + 24

21 23 + 14

372 + 416

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

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54 – 22

469 – 217

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

18 + 19 =

76 – 25 =

21 + 14 + 37 = 256 + 48 = 329 + 257 =

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100 – 60 =

700 – 300 =

638 – 73 =

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

40 x 2 =

42 =

34 x 2 =

200 =

x 21 x 40

6 x 100 = 30 x = 90 • Division is set out as shown in the examples below. 6 4 24

24 ÷ 4 = 6

Year 4

• Addition and subtraction with regrouping and up to two decimal places; emphasise use of linear measure and money. • Written multiplication of sums as shown by these examples.

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54 x 2

18 x 3

• Initially using basic facts in division, such as: 5 5 25

8r1 6 49

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30 x 6

• Later with dividend less than 100 and divisor up to 10, such as: 3 96

5 76

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New Wave Maths Book C – Teachers Guide • 9 •

Measurement Initially, students will make judgments of more or less, bigger or smaller, and equal to or not equal to when measuring 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. 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.

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Chance and Data

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Students will be involved in investigations that develop the use and understanding of the language of chance and from this, make a statement about the likelihood that an event will occur. A range of activities in classifying objects will help develop classification skills. Results may be represented in graph form—concrete or pictorial. Comparisons of records may then be made. Students should now be able to commence tallying and representing data in lists, tables and graph form. The complexity of recording and representation increases with the knowledge and experiences gained.

© R. I . C.Publ i cat i ons Space activities should relate to the students' environment and the objects within it. Making models ofr familiar parts ofw the environment using a variety of objects helps in developing spatial •f o r e v i e p u r p o s e s o n l y • awareness and an understanding of the interrelation between component parts. Movement of Space

components and parts thereof develops a knowledge of the understanding of transformation.

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Students are now able to use models of three-dimensional shapes and pictorial representations of two-dimensional shapes.

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• 10 • New Wave Maths Book C – 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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• 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. As a computational aid, the calculator can:

attention to focus on mathematical processes by allowing calculations to be done ©• enable R . I . C.Publ i cat i ons swiftly and accurately by all children; for example, in problem-solving or investigative activities; •f or• r ev i e w ptou pos einvestigated, sonbyl y •many examples enable rules or patterns ber discovered and generating

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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. 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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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.

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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 C – 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:

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• 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. • 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. 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; workor project-based assessment; collected samples of students’ independent work; individual homework assignments; group reports; anecdotal records; self-assessment; and peer assessment. 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)

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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 C – Teachers Guide

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

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 C – Teachers Guide • 13 •

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• 14 • New Wave Maths Book C – 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

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New Wave Maths Book C – Teachers Guide • 15 •

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

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

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

Resources have been listed to aid organisation before the lesson.

Unit 14–3

Student page 42

Skills

• • • • •

discussing deducing working independently manipulating using a calculator

Resources

• Base 10 MAB or counters • calculator

Language

• • • •

add multiply subtract number stories

Notes

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.

Number (N2.3)

• Addition of three whole numbers less than 10 with regrouping.

Main Activity (N2.2, WM2.3) Warm up • Ask students to take out their calculator and follow your instructions: Key in 3, then +, then =, then =, then = • Ask students to explain what happens.This is called the ‘constant function’. It is a shortcut to add the same number to itself or to a previous given starting point; e.g. 5 + 3 = = =. • Work through a couple of examples with the class.

What to do • Direct the class to find the answers to the problems using a calculator if necessary and/or Base 10 MAB. • Explain to the class what is required in the second activity. All answers must equal 20.The first example asks what is required to be added to 10 to make 20.The answer is … ! (10) • Use the Base 10 MAB or counters to assist in finding the answers to the number stories on the page. • Repeat explanations until satisfied the students are able to continue independently.

• 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.

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A space for you to record notes relevant to the lesson has been provided. This space could be used for any purpose. Some suggestions:

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Outcomes

N2.3, N2.2, WM2.3

Skills relevant to the main activity have been listed.

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.

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.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46 – 47, 56 – 57. • 76 • New Wave Maths Book C – Teachers Guide

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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.

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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 C – Teachers Guide

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

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 224. Teachers may photocopy and use them with their class(es). adhesive tape

felt-tip pens

school buildings and grounds

analog clock/watch

fishing line

scissors

atlas/street directory

flip array

shapes – 2-D

fraction cake

shapes – 3-D

fraction chart

small squares

fraction grid

Smarties™ or similar

geoboards

spinners

geometric blocks

stopwatch

grain

straws

blackboard ruler

glue

student stationery

books – fiction and nonfiction

heavy card – coloured or plain – A4

streamers – paper

attribute blocks balance balloons balls bathroom scales

boxes – various shapes and sizes

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Base 10 MAB

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street directory or town plan

building or house plans

interlocking cubes

string

bundles of 10s and 1s

lead pencil

sun safety equipment

butcher paper

light card – coloured and plain – A4

tangrams • page 222

calculator

and A3

tape measure

unit cubes

can

magazines

washers

cardboard strips

measuring containers (mL/L)

water

cardboard tubes

metre stick

wool

cars

mirror/mira

1-cm grid paper • page 199

centicubes

modelling clay

2-cm cubes

classmates

money (coins/notes)

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classroom

newspapers

classroom furniture

number chart 1–100 • page 202

clocks • page 210

objects for weighing activities

clock stamp

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coloured counters coloured pencils coloured rods

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overhead projector overheads

paper – coloured and plain – A4 and

community map • page 224 containers – large and small

paper strips

cutting tools for clay

pattern blocks

dice – six-sided

pegboards

digital clock/watch

pipe-cleaners

dominoes

plastic polygons

duster

playground

eggtimer

popsticks

elastic bands

ruler

environment

sand

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calendar • page 209

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New Wave Maths Book C – Teachers Guide • 17 •

Term One Week Unit Outcomes

Page

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

N2.1a—Locate numbers on a 1–100 grid according to specific questions.

M2.2—Measure distances using paces and handspans.

2 N2.1a—Locate ordinal and cardinal numbers on a number grid.

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

N2.1a—Use a number grid to assist in rounding activities.

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3 S2.1, WM2.2—Draw a plan for a specific purpose.

N2.4—Investigate and describe patterns.

M2.3—Estimate the length or amount of given items.

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4 N2.4—Identify and describe number patterns.

N2.1a—Record results of trading games with Base 10 MAB.

5 S2.2, WM2.2—Identify 3-D shapes in the environment.

N2.1a, S2.2, WM2.2—Record results of trading games with Base 10 MAB. Build models with cubes. 6

M2.2, N2.4—Compare the area of objects and regions.

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

N2.1a—Recognise coin values and count amounts of money.

7 S2.3—Identify symmetry in 2-D shapes.

N2.1b—Recognise fractional amounts using diagrams. N2.2, N2.4, S2.2, WM2.2—Build models with cubes and describe the number patterns made.

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8 N2.4—Use a number grid to find and describe patterns.

C&D2.2—Classify items in categories. 9

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9 S2.4, S2.2—Use spatial criteria to identify attributes of 3-D and 2-D objects.

N2.1b—Recognise fractional amounts using diagrams. 10

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6 WM2.2, WM2.3—Work mathematically to explain and compare the best approach to solve a problem.

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C&D2.1, C&D2.3—Investigate and record chance activities.

M2.2, WM2.1—Recognise times on analog clocks.

10 N2.1a, N2.4—Use a number grid to find and describe patterns.

21 22 23 24 25 26 27 28

C&D2.2, M2.2, WM2.1—Classify items in categories.

N2.1a—Recognise coin values and count and make up amounts in different ways.

• 18 • New Wave Maths Book C – Teachers Guide

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

Term Two Week Unit Outcomes

Page

1 11 S2.2, M2.2, WM2.3—Identify shapes that tessellate.

N2.1a—Recognise coin values and count and share amounts of money.

M2.2—Use arbitrary units and a balance beam to order given items by mass.

12 N2.1a—Recognise coin values and count and make up amounts in different ways.

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

N2.2—Use concrete materials to assist in solving number stories.

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13 S2.2—Record features and draw figures of 2-D shapes.

N2.2, WM2.3—Use a calculator to solve number problems involving a constant function. WM2.1, WM2.2—Analyse objects to brainstorm mathematical concepts related to a real-life activity.

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14 N2.2, WM2.2—Use concrete materials to assist in creating number stories.

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C&D2.1, C&D2.2, C&D2.4—Investigate, record and explain results of chance activities.

N2.2—Use a calculator to assist in solving multiplication and repeated addition problems. Use Base 10 MAB to assist in solving number stories.

15 S2.2—Draw 2-D shapes according to specific instructions.

N2.1a—Calculate the number of cents in dollar amounts. 6

M2.2, WM2.1—Recognise times on analogue clocks.

16 N2.1a—Calculate amounts of money.

C&D2.1—Investigate, record and explain results of chance activities. 7

N2.1a—Calculate amounts of money.

17 S2.2—Draw mirror images of triangles.

18 N2.2, N2.3—Use knowledge of multiples to solve related multiplication and division problems.

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C&D2.4—Interpret information on a graph to answer questions. 9

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N2.1a—Share amounts of money equally.

19 S2.3—Identify symmetry in 2-D and 3-D shapes.

N2.3, WM2.2—Work out number problems logically. 10

M2.2, WM2.1—Record times of the day using a shadow stick.

20 N2.1a, N2.2—Share amounts of money equally.

C&D2.3—Record data in a Venn diagram.

N2.3—Solve addition and subtraction problems.

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37 38 39 40 41 42 43 44 45 46 47 48

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M2.2, WM2.1—Measure time reading a calendar.

N2.1a—Calculate amounts of money.

51 52 53 54 55 56 57 58 59 60

New Wave Maths Book C – Teachers Guide • 19 •

Term Three Week Unit Outcomes

Page

1 21 S2.1, WM2.2—Identify facilities on a map and discuss the location of facilities in their community.

WM2.3—Work mathematically to identify and conjecture about number patterns.

M2.2, N2.3—Measure lengths in metres and centimetres.

22 N2.4—Solve pictorial number patterns.

C&D2.2, C&D2.4—Collect, record and analyse data in categories. 3

N2.1a—Order prices from most to least expensive and answer related questions.

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23 S2.1, WM2.2—Draw a plan for a specific purpose.

N2.1a—Calculate the amount of change needed for given amounts. M2.2, WM2.3—Measure the volume of containers in cups.

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

N2.1a—Calculate amounts of money and change needed for given amounts.

25 S2.2—Make constructions from written instructions.

N2.3, WM2.4—Work out number problems logically.

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4 24 N2.2, N2.3—Use knowledge of multiples to solve patterns and combinations of multiplication and division problems.

M2.2—Double and halve numbers of shapes.

26 N2.3—Add and subtract multiples of ten.

C&D2.2, C&D2.4, WM2.2—Collect, record and analyse data. 7

N2.3, N2.2—Solve number sentences using a calculator or Base 10 MAB.

27 S2.3—Complete shapes to make them symmetrical.

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

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M2.2, WM2.2—Draw shapes on a grid with a set area and compare the perimeter.

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N2.4—Solve number patterns.

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81 82 83

N2.3—Use rounding to approximate whether answers to addition and subtraction problems are possibly correct or incorrect.

9 29 S2.3, WM2.2—Work out which shapes will make larger copies of the original when four are placed together.

N2.3—Use knowledge of multiples to solve addition problems.

M2.2, S2.2—Complete pictorial patterns and area activities with 2-D shapes.

30 N2.3—Use knowledge of multiples to solve subtraction and addition problems.

87 88

C&D2.4—Interpret information from a given graph.

N2.4—Solve pictorial and written number problems.

• 20 • New Wave Maths Book C – Teachers Guide

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

Term Four Week Unit Outcomes

Page

1 31 S2.1, WM2.3—Draw paths on a grid according to specific instructions.

N2.1a, N2.4—Use a number grid to find multiples.

M2.2—Measure the area and perimeter of shapes.

2 32 N2.1a—Calculate amounts of money.

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

N2.1a—Calculate amounts of money and exchange for a single coin.

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3 33 S2.3—Explain how to manoeuvre 2-D shapes to fit given outlines.

N2.1a—Exchange amounts of money.

M2.2—Estimate then measure given items with arbitrary units and a balance beam.

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4 34 N2.3—Use knowledge of multiples to work out number problems.

100

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C&D2.2—Order and analyse data.

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N2.3, N2.1a—Use knowledge of multiples to calculate prices.

102

5 35 S2.3, S2.2—Make and draw constructions of models from written instructions. N2.1b—Recognise fractional amounts using diagrams.

103 104

WM2.2, WM2.3—Work mathematically to explain and compare the best approach to solve a problem.

105

6 36 N2.1a, N2.1b—Double and halve amounts of money.

106

C&D2.2, C&D2.4—Record and analyse data in Carroll diagrams.

N2.4, WM2.2—Solve a mathematical problem logically.

107 108 109

N2.1b—Recognise fractional amounts using diagrams.

110

M2.2, WM2.3—Compare area of shapes using different units.

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7 37 S2.1—Follow paths on a given map.

8 38 N2.3—Solve subtraction number sentences that use a constant subtrahend of 10.

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N2.4, WM2.2—Solve and describe pictorial number patterns.

111 112 113 114

9 39 S2.1, WM2.2—Draw a plan for a specific purpose.

115

N2.1b—Recognise fractional amounts using diagrams.

116

M2.1—Select appropriate units of measure to measure a variety of items.

117

10 40 N2.3—Use a calculator to solve number sentences involving multiplication.

118

C&D2.3, C&D2.4—Collect, record and analyse data on a Venn diagram.

119

N2.1a, N2.4—Identify ordinal numbers; solve calendar activities; identify multiples of five.

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New Wave Maths Book C – Teachers Guide • 21 •

Unit 1–1

Student page 1

Outcomes

Indicators

N2.3, S2.1

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

Skills • drawing • following instructions • logical thought • counting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencils • coloured pencils

Language • add • pattern • smallest • border • region

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Notes

Main Activity (S2.1) Warm up

• Show students on the blackboard/whiteboard or overhead how to draw a scribble pattern. • Emphasise the need for large pieces to the pattern and the need to touch the edge of the design area on all sides.

What to do

• Ask students to draw their own scribble pattern using a lead pencil. • When the pattern is drawn tell the students that they are now to colour their pattern. When colouring, the following guidelines are to be used: – No two adjoining pieces are to be coloured using the same colour. – Use as few colours as possible to complete the colouring. • Check with students to see what was the least number of colours used to complete the pattern. • Display the finished patterns.

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• Addition of one-digit by one-digit whole numbers.

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• 22 • New Wave Maths Book C – Teachers Guide

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Unit 1–2

Student page 2

Outcomes

Indicators

N2.3, N2.1a

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.

Skills • counting

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • 1–100 number chart – see page 202 • counters

• add • grid • before • after • greater than • less than

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Notes

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• Addition of one-digit by one-digit whole numbers with no regrouping.

Main Activity (N2.1a) Warm up

• Ask the class as a whole to count from 40 to 80.

What to do

• Ask the class what number comes before 27, 34, 52 and 18. • Use a large chart or overhead of a 100 grid. • Point to 6 and ask what number is 2 greater than 6. (Place a counter on 6 in the workbook.) • Repeat for 25 and 59. • Work with the class as a whole group to answer the questions in the workbook.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 32–33. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 23 •

Unit 1–3

Student page 3

Outcomes

Indicators

N2.3, M2.2

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

Skills • measuring using uniform units • reasoning • recording data • speaking and listening

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil • blackboard ruler • teacher’s desk • storage trolley • bookshelf • pin-up board • maths book

Language • add • pace • tally • hand span • total • length • width • distance • greatest

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Main Activity (M2.2) Warm up

• Ask students how they could measure a large distance—e.g. the length of the oval—if they do not have a measuring tape. • Discuss the practicality of each option given.

What to do

• Organise the class into small groups then set them to measure the length of the oval using their pace or stride. Remind them to try to keep their stride consistent. Record result. • Continue to measure width of oval and length of classroom. • When completed, use a hand span—thumb to little finger extended—to measure the items listed in the workbook. Record the measures. • Discuss reasons why measures are different for different students. • Would the measures be the same if you repeated the exercise? Discuss responses. If time, check. (A pedometer could also be used to compare measures in the pacing activity.)

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• Addition of one-digit by one-digit whole numbers with no regrouping.

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

Unit 1—Answers

Student pages 1–3 Unit 1–2

Unit 1–1

1. (a) 8 (b) 8 (c) 8 (d) 9 (e) 7 (f) 9 2. (a) 56 (b) 65 (c) 1, 12, 23, 34, 45, 56, 67, 78, 89, 100 (d) 85 (e) 23 (f) 12, 4 (g) 68 (h) 18, 3 (i) 16, 20 (j) 58

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

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

Consolidation 1–2

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1. (a) 9 (b) 9 (c) 7 (d) 9 (e) 5 (f) 9 2. Teacher check 3. Teacher check

• Students work in a group of three or four with a display 1–100 grid. In turn, they make up their own questions while others find and point to the answer(s).

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R.I.C. Publications®

Consolidation 1–3

• Use hand spans and paces to measure distances between items and places at home. Record.

New Wave Maths Book C – Teachers Guide • 25 •

Unit 2–1

Student page 5

Outcomes

Indicators

N2.3, N2.1a

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.

Skills • following directions • counting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils

Language • subtract • grid • square

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Notes

Main Activity (N2.1a) Warm up

• Walk around the class counting the students using ordinal numbers. Students must remember the number they were assigned. Call out various numbers such as 8th, 21st etc. Students must stand up. If confusion ensues, all students count with teacher from 1st until correct student is located.

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• Ask students to look at the 100 grid in their workbook. • For students who may have difficulties, it may be useful to have them complete the blank squares prior to answering the question. • Ask students to put their finger in the second, twenty-first, fiftieth and eighty-sixth squares. Check each time to see that students understand the request. • Tell the students that they will be colouring squares as directed. Using the colours as asked, work through the exercise as a whole class directed by the teacher. • Add further squares to colour if time or have students work in pairs to check squares with each other. • Work with a partner taking turns to throw the die. Each student places a counter on the square shown on his/her throw of the die. With the second and subsequent throws, move the counter on the number of squares shown on the die. • Who is the first to reach 50? • Repeat activity with ten throws of the die to see who finishes closest to 100. • Take turns to throw the die, moving on each turn to see who reaches 100 first.

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What to do

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• Subtraction of one-digit by one-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 32–33. • 26 • New Wave Maths Book C – Teachers Guide

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Unit 2–2

Student page 5

Outcomes

Indicators The student is able to: • make block graphs using real data. • read and compare frequencies from lists and simple one way tables.

N2.3, C&D2.3, C&d2.4

Skills • reading a calendar • collecting information • recording information • graphing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • classmates • coloured pencils • calendar with birthdates of students

• subtract • graph • birthday • days of the week • axis • axes

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Notes

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

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• Subtraction of one-digit by one-digit whole numbers with no regrouping.

• Have a calendar handy to check the days of the week the student’s birthdays fall on. • Explain to students that information collected is sometimes shown on a graph so that it is easier to read. A graph has two axes—vertical and horizontal. Each axis tells some information about the collected data. One axis is often the number of items collected. Draw an example of the graph in the workbook to show students and explain the two axes.

What to do

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• To complete the graph, students will need to give their birthdate and day of the week it falls on. If the day is not known, check it on the calendar. • Use the Carroll diagram to record the number of students with birthdays on each day of the week. • Show students how this information is transferred to the graph—one square represents one person. • Complete the graph by colouring the squares to show each person on the graph. Use a different column for each bar. • Explain that the bars showing the number of students with birthdays on each day is why this is called a bar graph. • Answer the questions relating to the information shown on the graph.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 27 •

Unit 2–3

Student page 6

Outcomes

Indicators

N2.3, N2.1a

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.

Skills • counting • following instructions • early rounding skills

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil • 1–100 number chart – see page 202

Language • grid • subtraction • squares • closer

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Main Activity (N2.1a) Warm up

• Display a counting chart 1–100. • Ask the class to count from 1–100. • Look at the chart and ask students ‘Is 4 closer to 0 or 10?’; ‘Is 18 closer to 10 or 20?’

What to do

• Work through Exercise 2 (a) with the whole class. • Set students to complete the rest of Exercise 2 on their own. Continue to assist those who need help. • Ask students to consider how they answered 2 (g). Direct students to write their thoughts to complete Exercise 3.

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• Subtraction of one-digit by one-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 66–67. • 28 • New Wave Maths Book C – Teachers Guide

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

Unit 2—Answers

Student pages 4–6 Unit 2–2

Unit 2–1

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

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1. (a) 3 (b) 2 (c) 3 (d) 3 (e) 3 (f) 3 2. Activity One Teacher check Activity Two Teacher check Activity Three Teacher check Activity Four Teacher check

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• Try similar activities with a partner using a ten-sided die.

Consolidation 2–2 • Use a Carroll diagram to collect information about students’ favourite colours and record on a bar graph.

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1. (a) 5 (b) 8 (c) 4 (d) 3 (e) 9 (f) 2 2. (a) 50 (b) 90 (c) 30 (d) 50 (e) 70 (f) 20 (g) halfway between 3. 45 is halfway between 40 and 50 so it is not closer to either number.

Consolidation 2–3

• Students practise rounding activities in a group of three or four using a display 1–100 grid.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 29 •

Unit 3–1

Student page 7

Outcomes

Indicators

N2.3, S2.1, WM2.2

The student is able to: • place important things in his/her environment in order on a map. • describe the location of an object as ‘between’ two other locations. • represent a problem with a sketch or diagram.

Skills • discussing • reasoning and logical thinking • planning • organising • designing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil • classroom

Language • add • plan • arrange • layout

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Notes

Main Activity (S2.1, WM2.2) Warm up

• Talk to the class about how the furniture is arranged. Ask students if they would need to rearrange the furniture in the class if the room was used for another activity; e.g. drama, dance. Ask students to explain their answers. • Tell the class they are to plan the layout of the furniture in the room for a class party.They have responsibility for the arrangements.

What to do

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• Addition of one-digit by one-digit whole numbers with no regrouping.

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• Working in small groups may help. Encourage students to discuss the furniture needs for a party and how best these needs can be met. • Draw the plan showing the furniture arrangements. • Each group presents its arrangements. • Choose some of the arrangements and have the students organise the class according to their plan. Check whether it is practical. (Ideally, have a party.)

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 12–13. • 30 • New Wave Maths Book C – Teachers Guide

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

Unit 3–2

Student page 8

Outcomes

Indicators

N2.3, N2.4

The student is able to: • write a pattern of numbers to fit a particular pattern and use it to predict the number needed for later terms.

Skills • discussion • colouring • describing • analysing

Number (N2.3)

Resources

Language • add • pattern • describe

• Base 10 MAB or counters • calculator • coloured pencils • centicubes

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Notes

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• Addition of one-digit by one-digit whole numbers with no regrouping.

Main Activity (N2.4) Warm up

• Ask students what a number pattern is. • Acknowledge that patterns in mathematics do not always include numbers, although numbers may be involved. • Look at the pattern in the workbook. What do you see?

What to do

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• Complete the next three bars using coloured pencils to repeat the pattern. • Describe the pattern using your own words. • If students experience difficulties, ask them to construct the pattern using centicubes or similar. • Share descriptions of patterns.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 31 •

Unit 3–3

Student page 9

Outcomes

Indicators

N2.3, M2.3

The student is able to: • estimate distance in a familiar unit such as a pace, and show improvement in their estimates as a result of pacing to measure the distances. • judge by ‘looking’ which containers will hold about the same as, more than or less than a given container, and by ‘hefting’ which objects will be about the same, heavier or lighter than a given object.

Skills • discussion • estimating • reasoning • debating

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil

Language • add • estimate • length • area • capacity • mass • time • long • wide

• cover • fill • weigh • about

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Main Activity (M2.3) Warm up

• When measuring we use a variety of units depending on the type of measurement— centimetres and metres for length; grams and kilograms for mass; millilitres and litres for volume; square centimetres and square metres for area; and minutes, hours and days for time. • Organise the class into small groups.

What to do

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• Addition of one-digit by one-digit whole numbers with no regrouping.

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• Ask the groups to discuss and then estimate the measures for the examples provided. Write the agreed measure but do not actually measure. • When all groups have finished, share and discuss findings. Reach consensus where there is a wide difference.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 88–89, 94–95. • 32 • New Wave Maths Book C – Teachers Guide

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

Unit 3—Answers

Student page 10 Unit 3–1

1. (a) 7 (b) 4 (c) 9 (d) 6 (e) 9 (f) 9 2. The number of blocks increases by 2. The colour pattern repeats red – blue, red – blue etc. 3. The number of blocks increases by 2. The colour pattern repeats yellow – green – red, yellow – green – red etc.

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1. (a) 7 (b) 8 (c) 9 (d) 6 (e) 8 (f) 7 2. Teacher check

Unit 3–2

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• Draw a plan of a home or farm.

Consolidation 3–2 • Use centicubes, attribute blocks etc. to make their own patterns. Discuss with a partner.

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1. (a) 7 (b) 8 (c) 5 (d) 8 (e) 5 (f) 9 2. Teacher check

Consolidation 3–3

• Brainstorm other things students can estimate.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 33 •

Unit 4–1

Student page 10

Outcomes

Indicators

N2.3, N2.4

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

Skills • discussion • describing • reasoning

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencils

Language • add • pattern • number • double

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Notes

Main Activity (N2.4) Warm up

• Talk about number patterns. Counting numbers form a pattern—one larger than the previous. Counting by twos forms a number pattern as does counting by tens. • Ask students to describe some number patterns of their own.

What to do

• Look at the number pattern in the workbook. Who can see a pattern? How would you describe the pattern? What would be the next two numbers in the pattern? • Complete the next pattern activity. • Double the numbers shown. How can you double a number? Add the number to itself or multiply by two. • Halve the numbers shown by dividing by two.

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• Addition of a two-digit number to a one-digit number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 38–39. • 34 • New Wave Maths Book C – Teachers Guide

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

Unit 4–2

Student page 11

Outcomes

Indicators

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

The student is able to: • identify possible results of an action or event by collecting data. • make block graphs using real data.

Skills • discussing • throwing a die • recording • reasoning • deducing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • six-sided die • 2-cm cubes • felt-tip pens • coloured pencils

• add • die • guess • most likely • record • chance • bias

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Notes

Main Activity (C&D2.1, C&D2.3) Warm up

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• Addition of a two-digit number to a one-digit number with no regrouping.

• Arrange the class in small groups. Ask what happens when a die is thrown. Which number is most likely to turn up? Why?/Why not?

What to do

• Explain that in their groups they will have the opportunity to test their guess. • Take it in turns to throw the die 20 times. Record on the graph the number that shows up on each throw. • Ask which number occurred most often. Record on the blackboard/whiteboard the number of times each number turned up from each group. Are the totals gained different from each group? Why?/ Why not? • Make a six-sided die from a 2-cm cube and repeat the experiment. • Is there a bias in the die or are the results due to chance? Ask students to explain their answers.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 100–101, 108–109. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 35 •

Unit 4–3

Student page 12

Outcomes

Indicators

N2.3, N2.1a

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.

Skills • discussing • throwing a die • trading MAB

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • six-sided die

Language • add • trade • cubes • value

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

Main Activity (N2.1a) Warm up

• Distribute Base 10 MAB and allow small groups to have a brief period of free play. • Discuss the relationship between the small cubes, longs (sticks), flats and large cubes. Emphasise that they are only pieces of wood and they represent what we want them to represent. • Discuss trading—when you have 10 small cubes, these may be traded for one long; ten longs may be traded for one flat; one flat may be traded for one large cube.

What to do

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• Addition of a two-digit number to a one-digit number with no regrouping.

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• Take turns to throw the die and add the number of small cubes to the group pile to correspond with the number on the die. When 10 small cubes have been collected, trade these for one stick. Continue with five more throws. • Repeat the activity a number of times—trading as required. • Repeat the activity using 10 throws.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 34–35. • 36 • New Wave Maths Book C – Teachers Guide

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

Unit 4—Answers

Student pages 10–12 Unit 4–1 1. (a) 19 (b) 18 (c) 18 (d) 18 (f) 17 2. Teacher check 3. Teacher check

(e) 19

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1. (a) 14 (b) 17 (c) 11 (d) 18 (e) 16 (f) 15 2. (a) Numbers increase by 2; odd numbers (b) 13, 15 3. (a) 30, 32, 34 (b) 49, 47, 45 (c) 23, 26, 29 (d) 55, 50, 45 4. (a) 8 (b) 6 (c) 20 (d) 10 (e) 12 (f) 30 (g) 22 (h) 14 (i) 18 (j) 100 5. (a) 6 (b) 4 (c) 10 (d) 8 (e) 5 (f) 50 (g) 15 (h) 20 (i) 9 (j) 25

Unit 4–2

• Make up number patterns for other students to solve.

Consolidation 4–2 • Use a 10-sided die to complete a similar activity.

Consolidation 4–3

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(e) 39

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1. (a) 29 (b) 37 (c) 48 (d) 57 (f) 28 2. Teacher check 3. Teacher check

• Partners take turns choosing numbers 1–99 to show longs and cubes.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 37 •

Unit 5–1

Student page 13

Outcomes

Indicators

N2.3, S2.2, WM2.2

The student is able to: • identify mathematical shapes such as cones or rectangles on which familiar things are based. • pose questions suggested by collected data, after going on a ‘shape’ walk.

Skills • discussion • observing • recording • analysing • drawing • relating findings

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • school buildings and grounds • 3-D shapes

Language • subtract • shapes • natural • built • sphere • cube • cylinder • rectangular prism

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Notes

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

• Display models of 3-D shapes (or distribute to small groups for examination). • Discuss features of the shapes and where they might be found.

What to do

• Explain to the class that they will be walking quietly around the school looking for the shapes. When a shape is found, it is to be recorded as natural or built (made by people), stating where the shape was found. • Draw the shape in their workbook. • Share findings with whole class.

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• Subtraction of a two-digit number from a two-digit number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4–5. • 38 • New Wave Maths Book C – Teachers Guide

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

Unit 5–2

Student page 14

Outcomes

Indicators

N2.3, N2.1a, S2.2, WM2.2

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. • copy pictures composed of simple geometric figures. • represent a problem with concrete materials.

Skills • subtracting • trading MAB • building cubes • counting cubes

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • 2-cm cubes

• subtract • trade • cubes • findings • compare • build • count

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Notes

Main Activity (N2.1a, S2.2, WM2.2) Warm up

• Distribute Base 10 MAB and allow small groups to have a brief period of free play. • Revise relationships between pieces of wood (Unit 4.3). • Discuss trading (Unit 4.3).

What to do

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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• Students select a handful of small cubes. • Count and trade the small cubes for longs. • Select a handful of longs. • Count and trade for flats. • How many flats, longs and small cubes do you have in total from both selections and trades? • Write the amount of wood you have in the table in the workbook. • Check with other members of the class and write the totals of wood they have collected. • Compare the collections—who had the most wood? • Distribute 2-cm cubes to groups of students. • Ask students to build the three cubes shown and count to find the total number of cubes used in each block. • Record the number of cubes used in the space provided.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 36–37. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 39 •

Unit 5–3

Student page 15

Outcomes

Indicators

N2.3, M2.2, N2.4

The student is able to: • compare the area of two regions directly by superimposing one over the other. • Identify number patterns in shapes.

Skills • comparing • counting • drawing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • eraser • ruler • pencil sharpener • pencil • scrapbook • scissors

Language • subtraction • cover • small squares • large • number • pattern

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

Main Activity (M2.2, N2.4) Warm up

• We can compare the area of an object by matching it against something else. One useful item is our hand. By covering an object with our hand, we can say whether it is smaller, the same size or larger than our hand.

What to do

• For this activity you will need an eraser, a pencil sharpener, a ruler, a pencil, a scrapbook and a pair of scissors. • See which items you can cover with your hand. Circle them in your workbook. • Another way to find the area of an object is to break it up into small squares then count the squares. Patterns can also be made if the starting shape is a square. • Count the small squares inside the larger squares and write the number you find. • Draw the next square in the pattern and find how many small squares there are in the large squares.

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• Subtraction of a one-digit whole number from a two-digit whole number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. • 40 • New Wave Maths Book C – Teachers Guide

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

Unit 5—Answers

Student pages 13–15 Unit 5–1

1. (a) 4 (b) 1 (c) 5 (d) 1 (e) 5 (f) 5 2. (a) Teacher check (b) Teacher check (c) Teacher check 3. Teacher check 4. 8, 27, 64

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

Unit 5–2

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• Create a 3-D display of objects from home and school to categorise.

Consolidation 5–2

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1. (a) 31 (b) 41 (c) 51 (d) 61 (e) 81 (f) 72 2. Teacher check 3. (a) 4 (b) 9 (c) 16 4.

• Work in pairs to make prisms that differ in height, width and length.

Consolidation 5–3

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R.I.C. Publications®

• Estimate then measure the number of cubes needed to cover a variety of items.

New Wave Maths Book C – Teachers Guide • 41 •

Unit 6–1

Student page 16

Outcomes

Indicators

WM2.2, WM2.3

The student is able to: • ask questions about collected objects or pictures following the modelling questions of their teacher. • compare ways of representing a problem. • make conjectures (often guesses) about shapes and measurements.

Skills • discussing • problem solving • explaining • cooperating

Main Activity (N2.1a)

• pencil • coloured pencils

Language • counting • brainstorm • decide • decision • problem

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• The aim of the activity is for students to devise a method of the best way to count the sprinkles on the bread. • This activity is designed for students working collaboratively in groups. As students will need to discuss their opinions and ideas, allow enough time so they do not feel rushed and for ideas to evolve. Open-ended tasks such as these are a good opportunity for students to ‘take a risk’ with maths.When completing such tasks, some students may be more successful in mixed-ability groups rather than same-ability groups. • Encourage students to think divergently and to explore all options. • Some groups will be able to work independently while others may need guidance. • When each group has decided on the best way to count the sprinkles, members can use words and pictures/diagrams to write their explanations in the workbook. • Students can then share their ideas with the class. Record findings on the blackboard/ whiteboard. A tally could be made of the same methods. Encourage thorough discussion of each method and improvements. For example; if a group decided to count the sprinkles one-by-one the problem of keeping track of where you were up to could occur. An improvement could be to mark a 3 x 3 grid with a knife, count the amount in one square and multiply by 9. Some students may suggest using a magnifying glass! You will be surprised at some of the ingenious answers! • After discussion, students decide whether their original method is still the best way to count the sprinkles or if one of the other ways is superior.

Notes

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What to do

Resources

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• 42 • New Wave Maths Book C – Teachers Guide

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

Unit 6–2

Student page 17

Outcomes

Indicators

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

The student is able to: • read and compare frequencies from lists and simple one-way tables. • organise data by classifying items in categories they have created.

Skills • recording • counting • timing • discussing • observing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • cars • pencil

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• add • tally • colour • biggest • smallest • most • least • common

Notes

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

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• Addition of two-digit by two-digit whole numbers with no regrouping.

• Explain to the class that when recording information we keep a tally to assist in counting the total later. • Show the recording of a tally as a set of five. • Ask students to give the total of several tallies from the blackboard/whiteboard; e.g. //// //; //// ////; //// ////.

What to do

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• The activity is best completed in small groups and in a set time—10 minutes. • Students work together observing and use one or two recorders. As each coloured car passes a tally mark is made on the recording sheet. • At the end of the time, all students transfer the tally to their own workbook. • Working together, the group answers the questions related to the tally. • The second exercise is completed in the same manner by observing the colour of the cars in the car park. This may be best completed first as it is easier to record the colours of the stationary cars.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 43 •

Unit 6–3

Student page 18

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • read amounts of money and make up that amount with coins in different ways.

Skills • adding

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • add • coins • cost

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

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups and allow students to explore them. • Direct the groups to make one dollar using 10c, 20c and 50c coins.

What to do

• Use the workbook activity to find the totals of the coins shown and write the answer in the book. • Use the coins, if necessary, to show the prices of the items. Combine the two prices as shown to find the total of the purchases. Write them in the workbook.

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• Addition of two-digit by two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 44 • New Wave Maths Book C – Teachers Guide

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

Unit 6—Answers

Student pages 16–18 Unit 6–1

1. (a) 22 (b) 27 (c) 25 (d) 29 (e) 26 (f) 24 2. (a) white (b) blue (c) white, red, other, black, blue 3. Teacher check

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Answers will vary. Possible methods the students may decide upon could include: • counting the sprinkles one-by-one, • using a magnifying glass to assist, • making a 3 x 3 or 4 x 4 grid with a knife and counting the sprinkles within each square, • counting in colours and adding the total.

Unit 6–2

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• Work out the best way to count other items such as poppy seeds or sesame seeds on a loaf of bread or a bread roll.

Consolidation 6–2

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1. (a) 54 (b) 67 (c) 73 (d) 76 (e) 95 (f) 76 2. (a) $1.00 (b) $1.30 (c) 60c 3. (a) 85c (b) $1.35 (c) 80c (d) $1.20 (e) $1.10

• Make a tally of other things; e.g. types of rubbish found in the playground.

Consolidation 6–3

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R.I.C. Publications®

• Select cards with written prices and match with plastic coins.

New Wave Maths Book C – Teachers Guide • 45 •

Unit 7–1

Student page 19

Outcomes

Indicators

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 • observing • manipulating • discussing • sharing • reporting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 3-D shapes • modelling clay • fishing line • cutting tools • pencil • ruler

Language • subtract • shapes • exactly • same • divide • original • halves • symmetrical

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Notes

Main Activity (S2.3) Warm up

• Distribute 3-D shapes to small groups of students. Allow students to manipulate and examine the shapes.

What to do

• Distribute modelling clay to the groups and ask students to make models of 3-D shapes. • Using the fishing line cutter, ask students to show where and how they can cut the models into three smaller shapes each exactly the same size. Discuss the results. • Use the 2-D shapes in the workbook to divide into smaller shapes the same shape as the original. Discuss the results. • Explain symmetry—one half is exactly the same as the other. Show using a rectangle. • Ask students to draw a line to cut the given shapes in half. Check to see if the halves are symmetrical. Share findings.

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• Subtraction of a one-digit whole number from a two-digit whole number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26–27. • 46 • New Wave Maths Book C – Teachers Guide

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

Unit 7–2

Student page 20

Outcomes

Indicators

N2.3, N2.1b

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.

Skills • discussing • demonstrating • sharing • dividing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • strips of paper

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

• subtract • bigger • divide • one • strip • whole • equal parts • quarters • greater • sum of • difference between • total

Notes

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

Main Activity (N2.1b) Warm up

• Discuss parts of a whole—halves, thirds, quarters. Show these using strips of paper. Ask students to demonstrate to the class how they would show parts of a whole.

What to do

• In the workbook the students are to divide the strip into four equal parts. How many sections in each part? (2) • Use the second strip in the workbook to answer the questions below.This may be completed as a whole-class exercise. • Encourage interaction among students as they discuss their findings. • Look at the diagram of the netball court in the workbook. How many equal parts is it divided into?

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 30–31. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 47 •

Unit 7–3

Student page 21

Outcomes

Indicators

N2.3, N2.2, N2.4, S2.2, WM2.2

The student is able to: • use materials and diagrams to represent multiplication stories. • solve a constant addition pattern. • copy pictures composed of simple geometric figures. • represent a problem with concrete materials, sketch or a diagram.

Skills • manipulating • recording • following directions • drawing • analysing • discussing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 2-cm cubes

Language • subtract • cubes • second • layer • record • total • third • fourth • fifth

• number • pattern

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

Main Activity (N2.2, N2.4, S2.2, WM2.2) Warm up

• Distribute 2-cm cubes to small groups of students, allow time for free play.

What to do

• Students are to make the 2 x 2 cube shape as shown in their workbook. • Ask students to record the number of cubes used in the space provided. • Add a layer to the top of the model. How many cubes used now? Record in the space provided. • Add a third, fourth and fifth layer of cubes, recording the total number of cubes used in each model. • Draw at least two of the models that were made. • Look at the record of the number of cubes used and discuss in your groups any number patterns found. Share these with the whole class.

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. • 48 • New Wave Maths Book C – Teachers Guide

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

Unit 7—Answers

Student pages 19–21

Unit 7–1 1. (a) 64 (b) 84 (c) 42 (d) 53 (f) 72 2. Yes

(e) 35

Unit 7–2 1. (a) 25 (b) 24 (c) 32 (d) 37 (f) 21 2.

(e) 17

4 2 1 3 3. (a) No (b) /4 (c) /4 (d) /4 (e) /4 2 4 (f) /4 (g) 4 (h) /4 4. 3

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4. (a) Yes (b) Yes (c) Yes (d) Yes (e) Yes (f) Yes (g) Yes (h) Yes

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• Examine symmetry in the environment.

Consolidation 7–2 • Cut items in their lunch boxes in halves and quarters.

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1. (a) 39 (b) 23 (c) 36 (d) 17 (e) 54 (f) 28 2. (a) 4 (b) 8 (c) 12 (d) 16 (e) 20 (f) Counting by four 3. Teacher check

Consolidation 7–3

• Repeat the activity using two, three or five cubes as a base.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 49 •

Unit 8–1

Student page 22

Outcomes

Indicators

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 with an adding rule.

Skills • following directions • colouring • counting • analysing

Number (N2.3)

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

Language • multiply • patterns • grid • fifth • square • fourth • second • list • numbers

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

Notes

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

• Explain to the class that mathematics is frequently understood by the patterns that are found in it. The exercise to follow is about discovering patterns and understanding them.

What to do

• Follow the directions as a whole class, firstly by colouring each fifth square red. The fifth square is numbered … ? (5) The next fifth square is numbered … ? (10), and so on. • Repeat, putting a cross in each fourth square. • Repeat, putting a dot in each second square. • Describe the patterns made by colouring each fifth square; putting a cross on each fourth square; and putting a dot on each second square. Discuss these patterns. • Find the answers to the final five questions using the completed grid.

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Teac he r

• Multiplication of one-digit by one-digit whole numbers.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. • 50 • New Wave Maths Book C – Teachers Guide

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

Unit 8–2

Student page 23

Outcomes

Indicators

N2.3, C&D2.2

The student is able to: • organise data by classifying items in categories he/she has created.

Skills • discussing • recording • working independently

Teac he r

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • pencil

• multiply • list

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

Notes

• Completion of number sentences using multiplication of single-digit whole numbers.

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Main Activity (C&D2.2) Warm up

• Remind students that there are many different ways to record data. Ask them to describe some. Focus attention on lists as the means of recording for this activity. • Ask students where they might use a list to record something.

What to do

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• Direct students to complete the activity using lists as asked. This work is best completed independently.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 51 •

Unit 8–3

Student page 24

Outcomes

Indicators

N2.3, N2.1b

The student is able to: • understand that constructing a number of fair shares from a whole requires splitting the whole into equal parts.

Skills • observing • discussing • colouring

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils • fraction cake

Main Activity (N2.1b) Warm up

• Show students parts of a whole using a fraction cake. If enough, distribute fraction cakes to small groups for them to explore. • Focus attention on the equality of each part when breaking the whole into parts. Ask students to show the equivalent parts to the class as they make a whole. • Discuss the parts of a whole using fraction notation; e.g. fourth (or quarter), third, half, sixth, eighth.

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• multiply • shapes • part

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

• Completion of number sentences using multiplication of one-digit by one-digit whole numbers.

What to do

Language

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• Working with the whole class, ask students to colour the diagrams as requested. • Check work as it is being completed to ensure understanding.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 28–29. • 52 • New Wave Maths Book C – Teachers Guide

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

Unit 8—Answers

Student pages 22–24 Unit 8–1

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

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1. (a) 24 (b) 20 (c) 18 (d) 30 (e) 8 (f) 21 2. (a) Teacher check (b) Teacher check (c) Teacher check (d) Colour Counting by fives Cross Counting by fours Dot Counting by twos (e) 20, 40, 60, 80, 100 (f) 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (g) Counting by tens, even numbers (h) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100 (i) 20, 40, 60, 80, 100

Unit 8–2

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• Use another 1–100 grid to explore patterns such as counting in 2s, 3s and 4s.

Consolidation 8–2

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

• Brainstorm other ideas to make personal lists about and compare with classmates.

Consolidation 8–3

o c . che e r o t r s super

R.I.C. Publications®

• Cut out food pictures from magazines and draw lines showing 1/2, 1/3 etc.

New Wave Maths Book C – Teachers Guide • 53 •

Unit 9–1

Student page 25

Outcomes

Indicators

N2.3, S2.4, S2.2

The student is able to: • respond to ‘Tell me the shape of this (object, place or mathematical model)’ using language such as ‘flat’, ‘curved’, ‘corner’, ‘side’, ‘round’, ‘square’, ‘edge’. • identify mathematical shapes such as cones or rectangles on which familiar things are based.

Skills • observing • discussing • examining • relating information

Number (N2.3) Main Activity (S2.4, S2.2)

• Base 10 MAB or counters • calculator • duster • can • ruler • ball • environment

Language • divide • rolls • slides • bounces • flat sides • curves • corners • hard • soft

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

Warm up

• Engage the class in a discussion of the attributes of an object—what it looks like, is made of, feels like, can be made to do and so on.

What to do

• Organise the class into small groups and ask one person from each group to collect a duster, can, ruler and a ball. • Each group examines each object to complete the grid to indicate with a tick if it has the attribute named. • Discuss group findings as a whole class. • Send the groups to walk quietly around the school to find where the four shapes listed are located. • Share findings with the whole class.

• square • rectangle • triangle • circle

Notes

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• Division of basic facts.

Resources

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 14–15. • 54 • New Wave Maths Book C – Teachers Guide

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

Unit 9–2

Student page 26

Outcomes

Indicators

N2.3, N2.1b

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. • see the need to check that the ‘halves’ are the same size and attempt to monitor portions.

Skills • observing • discussing • colouring • identifying • comparing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • coloured pencils • fraction grid • fraction cake

• divide • grid • fraction equivalents • tenths • fifths • half • whole

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

Notes

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Teac he r

• Completion of number sentences using division of basic facts.

Main Activity (N2.1b) Warm up

• Display a large fraction grid in the class for all to see. • Show students one whole on the fractions chart and the fraction cake. Show that two halves is equivalent to one whole; ‘equivalent’ being ‘the same as’. Show that three thirds and four quarters are equivalent to two halves and one whole. • Show that one half and two quarters are equivalent. Repeat this process with several fractions—use students to show the class.

What to do

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• Use the fraction grid in the workbook to complete the exercises as a whole class. Work through each one using the grid and reinforcing with the fraction cake as required.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 30–31. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 55 •

Unit 9–3

Student page 27

Outcomes

Indicators

N2.3, M2.2, WM2.1

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.

Skills • reading an analog clock • recording

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • analog clock

Language • divide • time • nearest • minute • clock face

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

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

• Use a large analog clock for this activity. Explain to students the importance of telling the time and the difference between an analog clock and a digital clock. • Set the clock to a variety of times and ask the students to tell the time to the nearest five minutes. Remind students of the importance of the hour hand.

What to do

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• Completion of number sentences using basic facts of division.

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• When satisfied that the class is ready, ask them to complete the workbook activity. Assist those with difficulties. • Regroup if required and work with the group using the clock to assist.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 98–99. • 56 • New Wave Maths Book C – Teachers Guide

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

Unit 9—Answers

Student pages 25–27 Unit 9–1

1. (a) 4 (b) 5 (c) 3 (d) 3 (e) 4 (f) 4 2. (a) 2 (b) 5 (c) one (d) five (e) three (f) ten (g) four (h) six (i) five (j) eight 3.

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

Unit 9–2

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• Bring four toys from home to use instead of the objects in Exercise 2.

Consolidation 9–2

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1. (a) 24 (b) 32 (c) 12 (d) 27 (e) 12 (f) 16 2. (a) 3.00 (b) 10.20 (c) 6.50 (d) 11.55 (e) 2.35 (f) 4.40 (g) 5.00 (h) 8.35 (i) 11.50 (j) 9.00 (k) 4.05 (l) 1.20 (m) 2.25 (n) 1.25 (o) 8.40 (p) 10.05

• Cut scrap paper into quarters, thirds, tenths etc.

Consolidation 9–3

• Direct students to look at the classroom clock throughout the day and nominate the time to the nearest five minutes.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 57 •

Unit 10–1

Student page 28

Outcomes

Indicators

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 with an adding rule.

Skills • counting • analysing • describing • recording • interpreting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils

Language • add • patterns • grid • tenth • square • fifth • odd number

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

Notes

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

• Remind students of previous work using pattern grids.

What to do

• Working as a whole class, ask students to colour each tenth square blue. • What pattern has been formed? Write this in the workbook. • Colour every square with an odd number green. Describe this pattern and write it in the workbook. • Complete the final questions in the book.

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Teac he r

• Addition of two-digit by two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. • 58 • New Wave Maths Book C – Teachers Guide

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

Unit 10–2

Student page 29

Outcomes

Indicators

N2.3, C&D2.2, M2.2, WM2.1

The student is able to: • organise data by classifying items in categories they have created. • locate in time and order regular activities. • connect mathematical ways of ordering times of day and year to the ways we order times by natural events.

Skills • discussing • observing • recording • drawing • describing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • coloured pencils • pencil

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

• add • seasons • year • hottest months • coldest • summer • winter • autumn • spring

Notes

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Teac he r

• Addition of two-digit by two-digit whole numbers with no regrouping.

Main Activity (C&D2.2, M2.2, WM2.1) Warm up

• Discuss with students the weather at different times of the year. The changes in weather are known as seasons. The four seasons are summer, autumn, winter and spring. • Ask the students to describe the weather in each season and name the months in each season.

What to do

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• List the four seasons at the top of the chart in the workbook. Under the season list sports or activities students like to do during this season. Draw a picture of the sport or activity. • In the second chart, list the three hottest and the three coldest months of the year. Describe the things they like to do most during these months. • Share lists with the class.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 96–97. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 59 •

Unit 10–3

Student page 30

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways.

Skills • coin recognition • addition • exploration • reporting • exchanging coins

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • add • total value • row • coins • difference between • exchange

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

Main Activity (N2.1a) Warm up

• Distribute coins to small groups and allow free play for a brief time.

What to do

• Find the total value of the coins in the two rows. • Find the difference in the value of the two rows of coins. • Find one coin that each row can be exchanged for. • Encourage the groups to explore with their coins to make each total shown using five, ten and twenty cent coins only. Find as many different ways as possible. • Ask groups to share some of their findings.

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Teac he r

• Addition of two-digit by two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 60 • New Wave Maths Book C – Teachers Guide

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

Unit 10—Answers

Student pages 28–30

Unit 10–1

1. (a) 78 (b) 78 (c) 89 (d) 99 (e) 87 (f) 56 2. Teacher check 3. Teacher check

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

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Teac he r

1. (a) 55 (b) 79 (c) 38 (d) 59 (e) 68 (f) 44 2. (a) Teacher check (b) Teacher check (c) Teacher check (d) Blue Counting by tens Cross Counting by fives Dot Counting by twos using odd numbers (e) 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (f) No (g) No. Every second square with a cross is an even number. (Two odds make an even; e.g. 5+5=10) (h) None (i) 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (j) Yes

Unit 10–2

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(e) 88

• Continue to use blank 1–10 grids to explore other number patterns.

Consolidation 10–2

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• Sort students’ birthdays into the season each occurs.

Consolidation 10–3

• With a partner, practise exchanging plastic coins for amounts of money written on cards.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 61 •

Unit 11–1

Student page 31

Outcomes

Indicators

N2.3, S2.2, M2.2, WM2.3

The student is able to: • select materials and methods to achieve the ends they have in mind. • compare the area of two regions directly by superimposing one over the other. • make conjectures (often guesses) about shapes and measurement.

Skills • manipulating • discussing • experimenting • recording • reasoning • observing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils • 2-D shapes

Language • subtract • shapes • tessellate

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

Notes

Main Activity (S2.2, M2.2, WM2.3) Warm up

• Distribute a variety of 2-D shapes to small groups for students to manipulate. • After free play, direct students to find which shapes fit together—tessellate—with themselves and/or with other shapes. Encourage students to discuss freely their findings and experiments.

What to do

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Teac he r

• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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• Ask students to complete the activity in their workbook by colouring the shapes that fit together without leaving gaps.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 2–3. • 62 • New Wave Maths Book C – Teachers Guide

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

Unit 11–2

Student page 32

Outcomes

Indicators

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

Resources

Language

• Base 10 MAB or counters • calculator • plastic coins

• subtract • coin • total value • share • number

• coin recognition • counting

Number (N2.3)

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

Notes

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Teac he r

• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups for students to play with. • Work through some coin recognition activities—note the animals featured on each coin, the head on the reverse, the colour, size and shape.

What to do

• In the workbook count the number of each different value coin and write the total in the space provided. Find the total value of all the coins of each type. If need be, use the plastic coins to assist. Write the total value in the space provided. • For the final exercise ask students to make up $1.20 using 20c coins. Then ask how many people could have 20c if the $1.20 were to be shared. • Repeat for $2.50 and $2.00.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 62–63. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 63 •

Unit 11–3

Student page 33

Outcomes

Indicators

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 • weighing • recording • graphing • ordering • discussing • analysing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • paper clips • balance scales • pen • sharpener • pencil • eraser

Language • subtract • balance scales • draw • graph • lightest • heaviest

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

Main Activity (M2.2) Warm up

• Ask the class how they would be able to arrange objects in order of their mass. Encourage a range of answers. • Discuss use of a balance scale and ensure students understand how it works.

What to do

• Explain that they are to use paper clips to balance given objects.When an object is balanced a graph is to be drawn to show the number of paper clips used. Students draw one paper clip for each paper clip used. Demonstrate this on the blackboard/whiteboard. • Organise the class into small groups to complete the weighing and graphing. • When the graphing is completed, use the graph to order the objects from lightest to heaviest.

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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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 C – Teachers Guide

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

Unit 11—Answers

Student pages 31–33

Unit 11–1 1. (a) 20 (b) 10 (c) 30 (d) 20 (e) 30 (f) 10 2. (b), (c), (d), (e)

Unit 11–2 1. (a) 70 (b) 60 (c) 70 (d) 80 (f) 40 2.

(e) 50

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3. (a) 6 (b) 5 (c) 8 (d) 30 (e) 5 (f) 11

• Use attribute blocks of the same thickness to discover other shapes and patterns that tessellate.

Consolidation 11–2

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(e) 22

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Consolidation 11–3

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R.I.C. Publications®

• Use other informal units to balance objects (counters, cubes etc.)

New Wave Maths Book C – Teachers Guide • 65 •

Unit 12–1

Student page 34

Outcomes

Indicators

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. • read amounts of money and make up the amount with coins in different ways.

Skills • coin recognition • discussing • following directions • exchanging coins

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • multiply • how many • coins

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

Notes

Main Activity (N2.1a) Warm up

• Distribute coins to small groups for free play. • Ask students to match groups of coins with a single coin so that both have the same value; e.g. 4 x 5c and 20c.

What to do

• Ask students to take out a 20c coin. Show the number of 5c coins required to make 20c. Write the answer in the space provided. • Repeat for $1 and 20c coins; for $2 and 50c coins; and $1 and 10c coins. • Ask students to make 40c using three coins. Which three were used? Record this. • Repeat to complete the exercise.

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Teac he r

• Completion of number sentences using basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 66 • New Wave Maths Book C – Teachers Guide

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

Unit 12–2

Student page 35

Outcomes

Indicators

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

The student is able to: • pose questions suggested by collected data. • comment on information in displays of data produced by themselves and peers.

Skills • recording • analysing • discussing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • pencil

• multiply • tally • month • most • least

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Notes

Main Activity (C&D2.2) Warm up

• Revise tallying and the way a tally is kept.

What to do

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• Completion of number sentences using basic facts of multiplication.

• Students are to have their workbooks open ready to make their tally. In turn, ask each student in which month he or she was born. All students make a tally mark in the space beside the month named. Continue until all students have named their birth month. • Use the tally sheet to answer the two questions. • The second exercise asks students to list their favourite weekday television program and answer the questions. • Have students share their favourite programs. Perhaps keep a class tally on the blackboard/ whiteboard to see which program is the overall favourite.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 67 •

Unit 12–3

Student page 36

Outcomes

Indicators

N2.3, N2.2

The student is able to: • use addition/subtraction relationships and number partitions to write sets of related number statements. • use materials and diagrams to represent multiplication/division stories which can be thought of as repeated addition/subtraction.

Skills • manipulating • working independently

Teac he r

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • multiply • number stories • equal

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• Completion of number sentences using basic facts of multiplication.

Warm up

• Organise the class into small groups, each group having Base 10 MAB available. • Students have a brief period of free play with the MAB.

What to do

• Explain to the class what is required in this activity. In the first set, all answers must equal 10. The first example asks what is required to be added to 1 to make 10. The answer is … ! (9). • Another example shows 10 and asks what is to be taken away from or subtracted from 10 to make 10. The answer is … ! (0) • Use the Base 10 MAB or counters to assist you to find the answers to the number stories on the page. • Repeat explanations until satisfied students are able to continue independently.

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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. • 68 • New Wave Maths Book C – Teachers Guide

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

Unit 12—Answers

Student pages 34–36

Unit 12–1

1. (a) 4 (b) 9 (c) 6 (d) 3 (e) 5 (f) 4 2. Teacher check 3. Teacher check

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1. (a) 3 (b) 4 (c) 9 (d) 7 (e) 2 (f) 9 2. (a) 4 (b) 5 (c) 4 (d) 10 (e) 20c, 10c, 10c (f) 50c, 50c (g) 10c, 10c, 10c, 10c, 10c or 20c, 10c, 10c, 5c, 5c (h) 10c, 5c, 5c (i) 20c, 20c, 20c, 20c, 20c or 50c, 20c, 20c, 5c, 5c

Unit 12–2

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• Create further examples of Exercise 2 for students to practise.

Consolidation 12–2

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1. (a) 40 (b) 50 (c) 35 (d) 27 (e) 16 (f) 45 2. (a) 9 (b) 8 (c) 7 (d) 4 (e) 5 (f) 1 (g) 8 (h) 7 (i) 4 (j) 3 (k) 0 (l) 15 (m) 14 (n) 19 (o) 1 (p) 5 (q) 2 (r) 1 (s) 10 (t) 1 3. (a) 4 (b) 11 (c) 13 (d) 2 (e) 1 (f) 10 (g) 6 (h) 4 (i) 3 (j) 8 (k) 3 (l) 5 4. Teacher check

• Brainstorm other ideas for students to tally and then discuss results.

Consolidation 12–3

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R.I.C. Publications®

• Complete activities using different numbers to solve number stories.

New Wave Maths Book C – Teachers Guide • 69 •

Unit 13–1

Student page 37

Outcomes

Indicators

Resources

N2.3, S2.2

The student is able to: • draw figures to show the essential spatial features of named geometric shapes. • make things which will meet criteria or needs relating to a function.

• Base 10 MAB or counters • calculator • squares and rectangles • hexagons and pentagons • equilateral triangles • string • ruler • paper • pencil

Skills • observing • recording • measuring • checking

Number (N2.3)

Language • divide • features • shapes • corners • sides • distance around • square • hexagon • triangle • pentagon • rectangle

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Notes

Main Activity (S2.2) Warm up

• Organise the class into small groups. Distribute 2-D shapes to each group. Allow students to explore the shapes.

What to do

• Focus attention on the attributes of the shapes as outlined in the table in the workbook. • Ask students to discuss in their groups these attributes then write their answers in the space provided. • Ask students how they intend to measure the perimeter of each shape. Encourage ideas and experimentation to see which is best. • Check shapes for tessellation properties. More paper may be required.

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• Completion of number sentences of basic facts of division.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 6–7. • 70 • New Wave Maths Book C – Teachers Guide

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

Unit 13–2

Student page 38

Outcomes

Indicators

N2.3, N2.2, WM2.3

The student is able to: • use materials and diagrams to represent multiplication stories/ division stories which can be thought of as repeated addition/ repeated subtraction or ‘sharing out’. • use a calculator to test their conjectures about numerical expressions.

Skills • using a calculator • working in pairs • discussing • cooperating • deducing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator

• divide • multiply • add • subtract

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Notes

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• Completion of number sentences using basic facts of division.

Main Activity (N2.2, WM2.3) Warm up

• Ask students to take out their calculator and follow your instructions: * Key in 3, then +, then =, then =, then = • Ask students to explain what happens. This is called the ‘constant function’. It is a shortcut way to add the same number to itself or to a previous given starting point; e.g. 5 + 3 = = =. • Work through several examples with the class. Direct the class to work in pairs to find the answers to their own use of the constant function.

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* Note: Not all calculators work this way. Some require: 3 + + = or + 3 = = etc.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46–47, 56–57. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 71 •

Unit 13–3

Student page 39

Outcomes

Indicators

WM2.1, WM2.2

The student is able to: • provide examples of their families measuring things for a purpose. • recognise as mathematical some common ways of doing things. • ask questions about collected objects or pictures following the modelling of questions by their teacher.

Skills • problem solving • categorising • working mathematically • discussing • explaining

Resources • pencil

Language • brainstorm • utensils • counting • measuring • weighing • timing • temperature • grams • kilograms • millilitres • litres • cupfuls • spoonfuls

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Main Activity (WM2.1, WM2.2)

• The aim of the activity is for students to identify a practical purpose for the items pictured on the page and to describe some mathematical concepts that would be involved in their use. • Encourage students to think divergently as well as practically. The activity is designed for students to complete independently; however, some may need to work with a partner. • For Question 1 students answers would include making a cake, muffins, cooking etc. • In Question 2 students categorise the items into groups of their own choice. The most obvious are cooking ingredients and utensils. Further groupings could be measuring utensils, mixing utensils and utensils to hold mixtures. The ingredients could be sorted into dry and wet etc. • There are many mathematical concepts in the answer to Question 3. Ingredients need to be measured, weighed and/or counted. Timing is involved in how long to beat the eggs, stir the mixture, cook in the oven, cool on a tray etc. Decisions have to be made on the correct measuring item for specific ingredients. • Students can then share their ideas with the class. Record findings on the blackboard/ whiteboard and encourage discussion. • After discussion, students can then write extra ideas they did not think of in their workbook.

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What to do

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• 72 • New Wave Maths Book C – Teachers Guide

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

Unit 13—Answers

Student pages 37–39

Unit 13–1 1. (a) 3 (b) 5 (c) 6 (d) 3 (e) 7 (f) 5 2.

Unit 13–2 1. (a) 32 (b) 40 (c) 27 (d) 30 (e) 28 (f) 18 2. (a) 20 (b) 20 (c) 10 (d) 10 (e) 9 (f) 9 (g) 8 (h) 8 (i) 21 (j) 21 (k) 9 (l) 2 (m) 10 (n) 2 (o) 8 (p) 2 (q) 3 (r) 2 (s) 5 (t) 2 (u) 5 (v) 16 (w) 2 (x) 10 (y) 9 (z) 5

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3. All of the given shapes tessellate. 4. Teacher check

Answers will vary. Refer to the teachers notes on page 72 for possible answers.

Consolidation 13–2

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• In pairs, students can use a calculator to create and record their own problems.

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• Solve ‘What am I?’ puzzles involving various 2–D shapes.

Consolidation 13–3

• Students participate in a cooking activity using the items pictured and any others necessary to bake a cake, muffins etc.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 73 •

Unit 14–1

Student page 40

Outcomes

Indicators

N2.3, N2.2, WM2.2

The student is able to: • use addition/subtraction relationships and number partitions to write sets of related number statements. • use materials and diagrams to represent multiplication stories/ division stories which can be thought of as repeated addition/repeated subtraction or ‘sharing out’. • represent a problem with an appropriate number operation.

Skills

• brainstorming • recording • adding • subtracting • multiplying • dividing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • add • number stories

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Notes

Main Activity (N2.2, WM2.2) Warm up

• Write the number 10 on the blackboard/whiteboard. Ask students to tell you all they can about the number 10 including how it can be made. Record all answers given. If possible, arrange answers in groups for addition, subtraction, multiplication and division. • When possibilities are exhausted or sufficient time has been provided to have a range of answers, switch attention to the workbook.

What to do

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• Addition of three whole numbers each less than 10 with no regrouping.

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• Students are to write their own number stories about 12. • Next they are to choose their own number and write as many number stories as they are able about this number. Use MAB or counters to assist. • Finally, using their age, write as many number stories as possible. • Have students share their answers. Write these on the board if desired.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 48–49, 50–51. • 74 • New Wave Maths Book C – Teachers Guide

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

Unit 14–2

Student page 41

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 themselves and peers.

Skills • discussing • brainstorming • throwing dice • recording • graphing • explaining

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • dice

• add • dice • total • record • possible • most • least

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Notes

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

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• Addition of three whole numbers less than 10 with no regrouping.

• Discuss chance—what does it mean? Can we be sure of what will happen? Give some examples of chance events; e.g. meeting your best friend in the street; having a day off school. • Ask students to provide other examples.

What to do

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• Organise the class into small groups, each with two dice. • Ask students to provide the possible totals if the two dice are rolled together. • Ask which total they would expect to occur most often? Least often? Why? • Set students to take turns to roll the dice 20 times, recording the total on the graph provided. • Discuss the results with reports from each group on frequency of total occurrence. • Ask the class to explain any differences. • Repeat the activity and check results, this time against previous results.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 75 •

Unit 14–3

Student page 42

Outcomes

Indicators

N2.3, N2.2, WM2.3

Skills • discussing • deducing • working independently • manipulating • using a calculator

• Base 10 MAB or counters • calculator

• add • multiply • subtract • number stories

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• Addition of three whole numbers less than 10 with regrouping.

Main Activity (N2.2, WM2.3) Warm up

• Ask students to take out their calculator and follow your instructions: Key in 3, then +, then =, then =, then = • Ask students to explain what happens. This is called the ‘constant function’. It is a shortcut to add the same number to itself or to a previous given starting point; e.g. 5 + 3 = = =. • Work through a couple of examples with the class.

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• Direct the class to find the answers to the problems using a calculator if necessary and/or Base 10 MAB. • Explain to the class what is required in the second activity. All answers must equal 20. The first example asks what is required to be added to 10 to make 20. The answer is … ! (10) • Use the Base 10 MAB or counters to assist in finding the answers to the number stories on the page. • Repeat explanations until satisfied the students are able to continue independently.

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What to do

Language

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Number (N2.3)

Resources

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 46–47, 56–57. • 76 • New Wave Maths Book C – Teachers Guide

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

Unit 14—Answers

Student pages 40–42

Unit 14–1

1. (a) $9 (b) $9 (c) $7 (d) $8 (e) $8 (f) $9 2. (a) Teacher check (b) Teacher check (c) More chance of throwing a total of 7 than any other number. Less chance of throwing a total of 2 than any other number. (d) No, not if results are pure chance. However, a small sample may cause some variations.

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1. (a) 6c (b) 7c (c) 9c (d) 9c (e) 9c (f) 7c 2. Teacher check 3. Teacher check 4. Teacher check

Unit 14–2

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• Roll a die or two dice. Use the number to write + or – number stories. (Number between 1 and 12.)

Consolidation 14–2

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1. (a) $15 (b) $15 (c) $15 (d) $18 (e) $19 (f) $15 2. (a) 5 (b) 27 (c) 3 (d) 30 (e) 4 (f) 16 (g) 6 (h) 28 (i) 4 (j) 15 (k) 4 (l) 24 3. (a) 10 (b) 11 (c) 3 (d) 1 (e) 8 (f) 3 (g) 5 (h) 2 (i) 6 (j) 5 (k) 27 (l) 5 (m) 4 (n) 9 (o) 30 (p) 10 (q) 2 (r) 19 (s) 2 (t) 4 4. Teacher check

• Complete a similar activity using dominoes chosen randomly from the pack.

Consolidation 14–3

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R.I.C. Publications®

• Roll three dice. Use this number to write +, – or x number stories. (Number between 7 and 18.)

New Wave Maths Book C – Teachers Guide • 77 •

Unit 15–1

Student page 43

Outcomes

Indicators

N2.3, S2.2

The student is able to: • draw figures which show the essential spatial features of named geometric shapes.

Skills • drawing • sharing • discussing • problem-solving

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil • coloured pencils • ruler • 2-D shapes

Language • subtract • grid • connect • shapes • enclose

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Notes

Main Activity (S2.2) Warm up

• Organise the class into small groups and distribute a variety of 2-D shapes to each group. Allow students to explore the shapes. • Demonstrate on an overhead how shapes can be made by connecting dots on a dot grid. Ask students to demonstrate so that the rest of the class can see. • Demonstrate how shapes can be made so that they enclose a given number of dots.

What to do

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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• Direct students to use coloured pencils to draw any 2-D shape of their choice to enclose 3, 4, 5 or 6 dots. • Try with different shapes—change colours for ease of finding the shapes. • Try with other shapes. • Share results. Discuss any problems.

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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 C – Teachers Guide

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

Unit 15–2

Student page 44

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways. • decide whether they have more or less money than the price and whether to expect change.

Skills • coin recognition • working independently • converting dollars to cents

Number (N2.3)

Resources

Language subtract, cents, amounts, money, change

• Base 10 MAB or counters • calculator • plastic coins and notes

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Notes

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• Subtraction of a one-digit whole number from a two-digit whole number with no regrouping.

Main Activity (N2.1a) Warm up

• Discuss with the class the number of cents in $1, $2, $3, $4, $5, $6 etc. • Provide examples to find the total in cents by adding prices given in dollars; e.g. $1 and $3 is $4 equals 400c. Use $2 and $2; $3 and $2; and $4 and $1. If difficulties occur, try further examples. • Explain to students that it is easier to work in dollars and then change the answer to cents.

What to do

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• Set students to work, assisting as required. • With the final activity, again recommend working in dollars and then converting answers to cents.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 60–61. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 79 •

Unit 15–3

Student page 45

Outcomes

Indicators

N2.3, M2.2, WM2.1

Skills • reading time • working independently • recording

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • analog clock

Language • subtract • clock • time • twelve-hour time • quarter hour • half hour

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

• Use a large analog clock for this activity. Explain to students the importance of telling the time and the difference between an analog clock and a digital clock. • Set the clock to a variety of times and ask the students to tell the time to the nearest quarter of an hour, half hour or five minutes. • Remind students of the importance of the hour hand.

What to do

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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• When satisfied that the class is ready, ask them to complete the workbook activity. Assist those with difficulties. • Regroup if required and work with the group, using the clock to assist.

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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 C – Teachers Guide

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

Unit 15—Answers

Student pages 43–45

Unit 15–1

1. (a) 41c (b) 62c (c) 22c (d) 32c (e) 43c (f) 51c 2. (a) 600c (b) 200c (c) 500c (d) 400c (e) 300c (f) 800c 3. (a) 1000c (b) 700c (c) 500c (d) 600c (e) 1100c (f) 900c 4. (a) 400c (b) 500c (c) 600c (d) 700c (e) 300c (f) 400c (g) 100c (h) 200c (i) 0c (j) 200c (k) 300c (l) 200c

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1. (a) $2 (b) $6 (c) $2 (d) $4 (e) $4 (f) $3 2. Teacher check

Unit 15–2

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• Use geoboards to recreate the shapes made in Exercise 2.

Consolidation 15–2

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1. (a) 18c (b) 27c (c) $38 (d) $41 (e) 13c (f) $24 2. (a) 8.00 (b) 10.30 (c) 8.45 (d) 1.15 (e) 7.05 (f) 3.40 (g) 11.55 (h) 2.25 3. (a) 6.30 (b) 9.15 (c) 1.45 (d) 8.30

• Complete Exercise 4 using change from $8 instead of $9.

Consolidation 15–3

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R.I.C. Publications®

• Students practise reading times using cardboard clocks. Also read times on clocks with Roman numerals, no numbers etc.

New Wave Maths Book C – Teachers Guide • 81 •

Unit 16–1

Student page 46

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • count coins and record total amounts.

Skills • addition • addition of money

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • cost • add • buy

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Notes

Main Activity (N2.1a) Warm up

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

What to do

• Ask students to find the cost of a stick of celery and a glass of milk (10c and 10c). • What is the total of these two items? Can you use the coins to show the cost of each item and the total cost? • In the workbook find the cost of a piece of pizza and one apple. Write the cost of each item next to the question (a). Use coins if students need help to find the total cost of the two items. Write the total cost in the space provided. • Continue with the rest of the questions. Use the coins if necessary to help to find the total cost.

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• Addition of three two-digit numbers with no regrouping.

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• 82 • New Wave Maths Book C – Teachers Guide

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

Unit 16–2

Student page 47

Outcomes

Indicators

N2.3, C&D2.1

The student is able to: • identify possible results of an action or event by collecting data. • describe familiar events as being more or less likely to happen.

Skills • throwing dice • recording • following directions • discussing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • 2-cm cubes • felt-tip pen • coloured pencils

• add • numbers • face • most likely • as expected

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Notes

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• Addition of three two-digit whole numbers with no regrouping.

Main Activity (C&D2.1) Warm up

• Remind students that they have thrown dice already to find out the frequency of a number or the total of two dice occurring. Revise these results. • Organise the class into small groups and provide a 2-cm cube to each group. • Direct students to use a felt-tip pen to mark the sides so that 1 and 6 are opposite each other, 2 and 5 are opposite and 3 and 4 are opposite.

What to do

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• What results would be expected from ten throws? Make ten throws recording the results. Is this as expected? Explain. • Repeat the exercise several times if time permits to see if results change.To enable recording, have one person from each group record each repeat.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 100–101. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 83 •

Unit 16–3

Student page 48

Outcomes

Indicators

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

Resources • Base 10 MAB or counters • plastic coins

• coin recognition • working independently

Number (N2.3)

Language • add • count • coins • total

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Main Activity (N2.1a) Warm up

• Distribute plastic coins and allow students free play in small groups. • Encourage students to make different amounts with the coins and let the other group members work out the total.

What to do

• Focus attention on the workbook activity. Plastic coins may be used if required. • Find the totals as shown on the page and write the answers in the space provided.

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• Addition of three two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 84 • New Wave Maths Book C – Teachers Guide

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

Unit 16—Answers

Student pages 46–48

Unit 16–1

1. (a) 98 (b) 99 (c) 88 (d) 88 (e) 97 (f) 59 2. (a) None; there is a one in six chance of each number occurring (b) Teacher check 3. (a) Teacher check (b) Teacher check

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1. (a) 48 (b) 38 (c) 59 (d) 49 (e) 45 (f) 55 2. (a) $1.40 (b) $2.05 (c) 65c (d) 60c (e) $1.55 (f) $1.95 (g) 45c (h) $2.25 (i) $1.35 (j) $2.15

Unit 16–2

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• Make up realistic prices for items on their lunch boxes and add up combinations as for Exercise 2.

Consolidation 16–2

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1. (a) 79 (b) 88 (c) 69 (d) 89 (e) 86 (f) 69 2. (a) $12 (b) $2.50 (c) 25c (d) $1 (e) $6 (f) 80c (g) $2.60 (h) 45c

• Complete a similar activity using randomly selected dominoes.

Consolidation 16–3

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• With a partner, practise exchanging amounts of money with amounts written on cards.

New Wave Maths Book C – Teachers Guide • 85 •

Unit 17–1

Student page 49

Outcomes

Indicators

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 • demonstrating • explaining • drawing • assisting others

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 2-D shapes • pencil • ruler

Language • subtract, • triangles • mirror image

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

Notes

Main Activity (S2.2) Warm up

• Distribute 2-D shapes to small groups. Allow students to manipulate the shapes in a free environment.

What to do

• Direct students to find shapes that are placed so that they are the mirror image of each other. Explain mirror image as the reflection seen in the mirror (reversed image). • Ask students to demonstrate and explain their mirror image. • Direct students to draw three different types of triangles in the spaces provided in their workbook. • Draw a mirror image of each triangle in the box beside the original drawing—use the centre line as the mirror. • Check within the group to assist each other.

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• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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

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

Unit 17–2

Student page 50

Outcomes

Indicators

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 • coin recognition • discussing • working with peers

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • plastic coins

• count • total • money

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

Notes

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Teac he r

• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups. Allow free play. • Ask students to make up combinations of money for others in the group to find the total.

What to do

• Use coins if required, to find the total of the coins shown in the workbook. Work with others in the group to find answers.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 87 •

Unit 17–3

Student page 51

Outcomes

Indicators

N2.3, M2.2, WM2.1

The student is able to: • locate in time and order regular activities. • connect mathematical ways of ordering times of the day and year to the ways we order time by natural events or cultural events.

Skills • discussing • reading a calendar • recording

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • calendar showing all holidays • coloured pencils

• subtract • calendar • days of the week • months of the year

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

• Generate a discussion on the calendar—how it is made up (of months); the days in the months; weeks, names of months; leap year; and any other points that arise.

What to do

• Complete the exercises as a whole-class activity. • As tasks are completed, remind students that the calendar in the workbook is not this year’s calendar; therefore days and dates may not correspond to the current year. • When completed, check with the current year calendar to see where any differences occur. School holiday dates, Easter, Foundation Day and Labour Day will differ.

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• Subtraction of a two-digit whole number from a two-digit whole number, both multiples of 10, with no regrouping.

Teac he r

Language

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• 88 • New Wave Maths Book C – Teachers Guide

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Unit 17—Answers

Student pages 49–51 Unit 17–2

Unit 17–1

1. (a) 24 (b) 22 (c) 44 (d) 21 (e) 23 (f) 33 2. (a) 10c (b) 40c (c) 15c (d) 35c 3. (a) 25c (b) 60c (c) 50c (d) 50c

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1. (a) 53 (b) 31 (c) 43 (d) 55 (e) 33 (f) 24 2. Teacher check

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• Draw different pentagons and the mirror image of each.

Consolidation 17–2 • In pairs, take turns using plastic money to make up amounts to be added and recorded.

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1. (a) 10 (b) 10 (c) 10 (d) 10 (e) 10 (f) 40 2. (a) 30 January (b) 12 April (c) 29 April (d) 5 July (e) 23 July (f) 27 September (g) 14 October (h) 18 December (i) Teacher check (j) 1 March (k) 30 November

Consolidation 17–3

• Keep a yearly calendar on display for students to refer to for dates and events in the future.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 89 •

Unit 18–1

Student page 52

Outcomes

Indicators

N2.2, N2.3

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

Skills • following directions • manipulating • sharing • trading

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • multiply • divide

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

Notes

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

• Distribute Base 10 MAB and/or counters to small groups of students; allow a brief period of free play.

What to do

• Direct students to take 12 small cubes or counters and arrange these in as many different ways as they can. Choose members from each group to report back to the class. Groups check to see if they have the same arrangements. Focus on arrays of 1 x 12; 2 x 6; 3 x 4; 4 x 3; 6 x 2; and 12 x 1. Explain that these arrangements show factors of 12. • Again, using the 12 small cubes or counters, share into three groups; then four groups; then six groups; then two groups. Discuss findings in each case. Explain that sharing is division. • Ask students to take out 7 lots of 5 small cubes. Rather than counting them all, ask how else the total might be found. (By trading 10 small cubes for one long.) Repeat this trading several times. • Students should now attempt the exercise in their workbook. Assist as required.

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• Multiplication of property of zero; i.e. (number) x zero is zero.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 52–53, 56–57. • 90 • New Wave Maths Book C – Teachers Guide

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

Unit 18–2

Student page 53

Outcomes

Indicators The student is able to: • interpret block graphs produced by others.

N2.3, C&D2.4

Skills • reading graphs • recording • graphing • analysing

Number (N2.3)

Resources

Language

• counters • calculator • chart or overhead of line graph – see page 220

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

• multiply • graph • temperature • hottest • coolest • same • degree • most • time

Notes

Main Activity (C&D2.4) Warm up

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Teac he r

• Multiplication of basic facts.

• Revise the features of a line graph—vertical and horizontal axis, title, plotted points and line joining the points. Show students how to read the graph—temperature for a given day. Which day had a particular temperature?

What to do

• Work with the class as a whole to complete the activities for the line graph.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 91 •

Unit 18–3

Student page 54

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • read amounts of money and make up the amount with coins in different ways. • count coins and record total amounts.

Skills • multiplication • coin recognition • sharing • adding coins

Number (N2.3)

Resources • counters • calculator • plastic coins

Language • multiply • coin • equal shares • how many • value • altogether

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

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups of students and allow time for free play.

What to do

• Direct students to make a collection of coins that matches the coins in the workbook. • Share these coins into three equal groups so that the groups have the same monetary value and the same number of coins. • Using the groups of coins, answer the questions in the workbook.

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• Multiplication of basic facts.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 92 • New Wave Maths Book C – Teachers Guide

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

Unit 18—Answers

Student pages 52–54

Unit 18–1

1. (a) 12 (b) 14 (c) 10 (d) 6 (e) 18 (f) 8 2. (a) Friday (b) 30° (c) Tuesday and Thursday (d) 6° (e) Monday (f) 34° (g) 30° (h) Wednesday (i) 36° (j) Saturday

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1. (a) 0 (b) 0 (c) 0 (d) 0 (e) 0 (f) 0 2. (a) 80, 80, 8, 10 (b) 10, 10, 2, 5 3. (a) 14, 14, 7, 2 (b) 45, 45, 5, 9 (c) 60, 60, 6, 10 (d) 15, 15, 5, 3 (e) 18, 18, 3, 6 (f) 30, 30, 5, 6 (g) 36, 36, 9, 4 (h) 21, 21, 3, 7 (i) 27, 27, 3, 9 (j) 32, 32, 4, 8 (k) 18, 18, 9, 2 (l) 40, 40, 5, 8

Unit 18–2

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• Complete similar activities using different combinations.

Consolidation 18–2 • Brainstorm ideas with the class for constructing other line graphs and discuss results.

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1. (a) 12 (b) 21 (c) 6 (d) 15 (e) 24 (f) 18 2. (a) 2 (b) 2 (c) 2 (d) 6 (e) 70c (f) $2.10 (g) 6

Consolidation 18–3

• Participate in sharing amounts of money in a group of two, three or four.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 93 •

Unit 19–1

Student page 55

Outcomes

Indicators

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 • drawing • division • understanding symmetry

Number (N2.3)

• counters • calculator • pencil • ruler • mira

• divide • line of symmetry • shape • square • equilateral triangle • rectangle • pentagon • hexagon • isosceles triangle

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

Main Activity (S2.3) Warm up

• Explain symmetry, in particular line of symmetry. Use a student as an example. If we were to cut a person in half lengthways, the left and right halves would be (almost) the same. Draw a rectangle on the blackboard/whiteboard. Ask a student to draw in a line of symmetry. Check with the class. Ask if there are any others. Ask if students can see any objects in the class that have lines of symmetry. Show these to the class. • If miras* are available, distribute these and explain how they work.

What to do

Language

Notes

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• Division of basic facts.

Resources

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* A mira is a plastic maths tool which both reflects what is in front and lets you see through to what is behind.

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• Students are to find lines of symmetry in the shapes drawn in the workbook. Use a mira if required. • When completed, ask students to draw shapes or objects from within the classroom and show their line(s) of symmetry.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26–27. • 94 • New Wave Maths Book C – Teachers Guide

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

Unit 19–2

Student page 56

Outcomes

Indicators The student is able to: • represent a problem with an appropriate number operation. • use materials and diagrams to solve both story problems and symbolically expressed additions and subtractions.

N2.3, WM2.2

Skills • division • using a calculator • following directions • working independently • addition • subtraction

Number (N2.3)

Resources

Language

• counters • calculator

• divide • how many • largest • smallest

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

Notes

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• Division of basic facts.

Main Activity (N2.3, WM2.2) Warm up

• Explain to the class that this exercise is an investigation by them. As such, you, the teacher, will only be available to assist if a student can not understand the problem or is having difficulties working the problem out. • Students may use a calculator if they wish.

What to do

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• Read the instructions on the page to the class. Invite students to ask questions if they do not understand any parts of the instructions. • Set students to work to complete the exercises.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 68–69. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 95 •

Unit 19–3

Student page 57

Outcomes

Indicators

Resources

Language

N2.3, M2.2, WM2.1

The student is able to: • recognise key times on an analog clock. • know that the numbers, position and movement of the hands on clocks reflect the passage of time.

• calculator • counters • stick/pencil/pop stick • playground • cardboard/butcher’s paper • tape • felt-tip pens • tape measure • modelling clay

shadow, time, length

Skills • measuring • discussing • drawing • designing • constructing • analysing • evaluating

Number (N2.3)

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

• Explain to students that there are many items used to tell the time. Ask students to give examples and list them on the blackboard/whiteboard. • If a shadow stick is not mentioned, tell the class that this is a method that has been used in the past. By noting where the shadow of a stick or equivalent falls on a flat surface, the actual time can be told.

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• The task for the lesson is for a group of students to discuss, sketch and construct their own shadow stick.This can be made by placing a pencil (or similar) into modelling clay and attaching it to the middle of a large sheet of cardboard or paper. • The shadow stick is to be placed outside in a sunny spot and checked to see if it works. • Students mark and record the length of the shadows at approximately hourly intervals. • Discuss the results and any problems experienced. • The task can be repeated on another day—preferably at another time of the year when the sun is lower or higher in the sky. Compare results.

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What to do

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• Division of basic facts.

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• 96 • New Wave Maths Book C – Teachers Guide

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

Unit 19—Answers

Student pages 55–57

Unit 19–1 1. (a) 9 (b) 3 (c) 6 (d) 5 (e) 4 (f) 7 2.

1. (a) 1 (b) 9 (c) 6 (d) 4 (e) 5 (f) 7 2. (a) 65 (b) 24 (c) 4 (d) 6 (e) 53 (f) 33 (g) 7 (h) 14 (i) No

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3. Teacher check

Unit 19–2

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• Create symmetrical paper doilies.

Consolidation 19–2 • Use the class sizes of their own class and two others to repeat the activity, substituting the numbers.

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1. (a) 5 (b) 4 (c) 8 (d) 2 (e) 9 (f) 6 2. Teacher check 3. Teacher check

Consolidation 19–3

• Investigate how a sundial was used to tell the time.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 97 •

Unit 20–1

Student page 58

Outcomes

Indicators

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

The student is able to: • use materials and diagrams to represent division stories which can be thought of as repeated addition. • count coins and record total amounts.

Skills • addition • coin recognition • exchanging coins • working independently • recording • sharing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • add • share • how much • equally

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

Notes

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

• Distribute plastic coins to small groups and allow a brief free play period.

What to do

• Ask students to take out a 10c coin. How can this one coin be shared between two students? (The coin needs to be changed to two 5c coins then shared.) • Repeat this with 20c, 50c and $1 coins to develop understanding of the need to exchange one coin for other coins to enable sharing to take place. • Repeat using combinations of coins; e.g. 10c and 20c is shared between 2. How much each? • Ask students to work through the workbook exercises using the coins to assist.

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• Addition of three single-digit whole numbers with regrouping.

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• 98 • New Wave Maths Book C – Teachers Guide

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

Unit 20–2

Student page 59

Outcomes

Indicators

N2.3, C&D2.3

The student is able to: • suggest ways of efficiently counting how many there are in several categories.

Skills • recording • working independently

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • pencil • class members • Venn diagram outline – see page 218

• add • Venn diagram • record • results • preference • multiples

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Notes

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Teac he r

• Addition of two two-digit whole numbers with no regrouping.

Main Activity (C&D2.3) Warm up

• There are many means of recording data for ease of reading and understanding. One method is a Venn diagram. A Venn diagram usually consists of overlapping circles. Data to be shown are placed in the correct circle, or in the overlap if they can belong to more than one group. If there are data that do not fit at all, they are placed in the space outside of the circles. • Demonstrate these breakdowns—boys and girls in the class. All the boys belong to one circle while all the girls to another. • Demonstrate these breakdowns—boys and girls with brothers only (one group), sisters only (another group), brothers and sisters (overlap group), single child (placed outside the circles). Repeat with other breakdowns.

What to do

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• Complete the apples and oranges exercise using student initials only. Students will need to put their hands up or stand up to show their preference as asked and be recorded. • Students should try the multiple exercise on their own.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 108–109.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 99 •

Unit 20–3

Student page 60

Outcomes

Indicators

N2.3

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.

Skills • adding • subtracting • logical thinking

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencil

Language • add • subtract

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

Main Activity (N2.3) Warm up

• Ask students in turn to choose three numbers between 1 and 9. Write on the board as an addition sum and solve as a class. Repeat.

What to do

• The activities in this exercise are straightforward addition and subtraction sums. • Ask students to look for combinations when adding that will make the operation easier. Ask students to provide examples of easier combinations: – pairs adding to ten – doubling • Direct students to mark examples they can see that have combination pairs that add to ten or involve doubling. • Set the class to work to complete the sums.

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• Addition of two two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 64–65. • 100 • New Wave Maths Book C – Teachers Guide

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

Unit 20—Answers

Student pages 58–60 Unit 17.1

1. (a) 16c (b) 16c (c) 18c (d) 19c (e) 18c (f) 19c 2. (a) 5c (b) 25c (c) 25c (d) 50c (e) 30c (f) 80c

Unit 17.2 1. (a) 59c (b) 68c (c) 67c (d) 99c (e) 88c (f) 35c 2. Teacher check 3.

Multiples of 2

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Multiples of 3 3, 9, 15, 21 ,27

6, 12, 18, 24, 30

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Multiples of both 2 and 3

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• Solve further written examples using coins to assist.

Consolidation 20–2 • Brainstorm other pairs of foods, colour etc. to complete Venn diagram activities.

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1. (a) $88 (b) $69 (c) $99 (d) $88 (e) $77 (f) $58 2. (a) 12 (b) 14 (c) 16 (d) 18 (e) 15 (f) 16 (g) 12 (h) 16 (i) 12 (j) 12 3. (a) 18 (b) 12 (c) 19 (d) 10 (e) 15 (f) 14 (g) 10 (h) 16 (i) 17 (j) 17 (k) 14 (l) 10 (m)15 (n) 18 (b) 8 (c) 9 (d) 6 (e) 8 4. (a) 7 (f) 6 (g) 8 (h) 4 (i) 5 (j) 11

Consolidation 20–3

• Roll 0–9-sided die three or four times to use as numbers to add up.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 101 •

Unit 21–1

Student page 61

Outcomes

Indicators

Resources

N2.3, S2.1, WM2.2

The student is able to: • describe the location of an object as ‘between’ two other locations. • ask questions about collected objects or pictures following the modelling of questions by their teacher.

• Base 10 MAB or counters • calculator • local area map • pencil • felt-tip pen • community map – see page 224

Skills

• subtraction • reading a map • discussing • recognising symbols • sharing • reasoning • thinking logically

Number (N2.3)

Language • subtract • map • facilities

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Notes

Main Activity (S2.1, WM2.2) Warm up

• Ask students to name all the facilities they can think of that are available in their neighbourhood. List them on the blackboard/whiteboard. • Enlarge the community map on page 224 or use as an overhead. Discuss the facilities, location of houses, streets etc.

• Distribute or display a copy of a local area map. Street directories could also be used where appropriate. Ask students to locate the facilities that they named in the map which are close to each other. Use a felt-tip pen to show each facility. Does the map have a key to assist in locating the facilities? If so, what symbol is used to show each facility? • Make a note in the workbook of the facilities that are close together. Explain why these are placed this way. • Share the findings as a class. • Students write thoughts and list the facilities they would like to see located close together for Exercise 3. Share ideas across the class.

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What to do

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Teac he r

• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 12–13. • 102 • New Wave Maths Book C – Teachers Guide

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

Unit 21–2

Student page 62

Outcomes

Indicators The student is able to: • offer suggestions to ‘What would happen if …’ questions pitched at or just beyond their mathematical level.

WM2.3

Skills • exploring patterns • problem-solving • skip counting

Resources

Language

• pencil • flip array

• number pattern • flip array

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Main Activity (WM2.3)

Teac he r

What to do

Notes

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• The aim of the activity is for students to identify number patterns on a 1–100 grid and explore option when presented with a ‘what if …’ problem. • Remind students that maths is largely logic and patterns. • The activity is designed for students to complete independently; however, some may need to work with a partner. • Direct students to look at the numbers in black on the flip array and to write the first 10. This may help them to focus and identify possible patterns. • Students write in their workbook the number pattern(s) they identified. • Direct students to look at the numbers in red on the flip array. What pattern(s) can they see now? Write the answer(s) in the workbook.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 103 •

Unit 21–3

Student page 63

Outcomes N2.3, M2.2

Skills • measuring • recording • problem-solving • using a calculator

Number (N2.3)

Indicators

Resources

The student is able to: • use a ruler or tape measure to measure and make things to the nearest centimetre. • remember many basic addition and subtraction facts and work out the others.

• Base 10 MAB or counters • calculator • basketball court • classroom • oval • metre stick • ruler

Main Activity (M2.2, N2.3) Warm up

• Ask students what measuring device and unit they could use to find the length of the school oval. Discuss choices. • Organise the class into small groups. • Issue each group with a metre stick and explain to them that they are to use the metre stick to measure the length of the basketball court, the oval and the classroom. Discuss some of the problems they might encounter and how these may be overcome; e.g. forgetting when counting (keep a tally).

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Teac he r

• subtract • metre stick • measure • length • half • double

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

• Subtraction of a two-digit whole number from a two-digit whole number, both multiples of 10 with no regrouping.

• When these items have been measured, the lines shown in the workbook are to be measured using a ruler. Show students how to measure with the zero point at the end of the line, not the end of the ruler. • After measuring the lengths of the lines, write down half the length or double the length as directed. Use a calculator to assist if required.

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What to do

Language

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 78–79. • 104 • New Wave Maths Book C – Teachers Guide

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

Unit 21—Answers

Student pages 61–63 Unit 21–2

Unit 21–1 1. 2. 3. 4.

Teacher check 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Answers will vary. These could include: • even numbers • counting in twos • two times table • columns of numbers increasing by 10 Answers will vary. These could include: • odd numbers • counting in twos starting at number one • columns of numbers increasing by 10

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1. (a) $10 (b) 30c (c) 20c (d) $50 (e) 40c (f) $20 2. Teacher check 3. Teacher check

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• Study facilities on other community maps.

Consolidation 21–2 • Form another pattern on a flip array or 1–100 grid for students to identify.

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1. (a) $70 (b) $10 (c) 40c (d) 10c (e) 50c (f) $52 2. Teacher check 3. (a) 2 cm (b) 3 cm (c) 2.5 cm (d) 4 cm (e) 3.5 cm 4. (a) 20 cm (b) 24 cm (c) 14 cm (d) 18 cm (e) 22 cm

Consolidation 21–3

• Measure other features around the school grounds.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 105 •

Unit 22–1

Student page 64

Outcomes

Indicators

N2.3, N2.4

The student is able to: • draw a pictorial pattern of numbers to fit a given pattern and use it to predict what is needed for later terms.

Skills • addition • describing patterns • observing • reasoning

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • small squares or 1-cm square grid paper • counters

Language • add • patterns

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Notes

Main Activity (N2.4) Warm up

• Write the following on the blackboard/whiteboard: 1, 2, 3, 4, 5, 6, 7 … Explain to students that this is a number pattern. What is the next number in the pattern? (8) Describe the pattern? (The numbers increase by one each time.) • Write the following on the blackboard/whiteboard: ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo …Explain to students that this is a pictorial representation of a number pattern. What is the next display in the sequence? Describe the pattern?

What to do

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• Addition of three whole numbers with an unlike extension of places and no regrouping.

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• Using the materials provided, ask students to write the next two sequences in the patterns shown in their workbook. • Describe each pattern.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 40–41. • 106 • New Wave Maths Book C – Teachers Guide

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

Unit 22–2

Student page 65

Outcomes

Indicators

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

The student is able to: • organise data by classifying items in categories they have created. • write a few sentences to describe the results of their data collection.

Skills • addition • counting • recording • reading • analysing

Number (N2.3)

Resources

Language • add • tally • total • most common

• Base 10 MAB or counters • calculator • reading book • library book • pencil

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Notes

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

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• Addition of three whole numbers with unlike extension of places with no regrouping.

• When counting more than one set of items at the same time it is very difficult to keep track of the total for each set. To overcome this, we use a tally to assist. • A tally consists of a set of five marks on a piece of paper or on the board. Each set is made up of four vertical lines with a fifth line drawn diagonally across the four. • As markings are in sets of five, they are easy to count later. Make a series of tallies on the board for students to find the total.

What to do

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• Direct students to their task. Select a paragraph from either a reading book or a library book and count the number of 3-, 4-, 5- and 6-letter words in the paragraph. Keep a tally of each word as it occurs according to its size. • When completed, answer the questions. • Repeat with another paragraph from a different book. (Both paragraphs will need to have almost the same number of words to be able to compare accurately.)

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 107 •

Unit 22–3

Student page 66

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • decide whether they have more or less money than the price and whether to expect change.

Skills

Resources • Base 10 MAB or counters • calculator • plastic money

• addition • ordering • coin recognition

Number (N2.3)

Language • add • order • list • most expensive • least expensive • difference in value • coins

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Main Activity (N2.1a) Warm up

• Arrange class into small groups and distribute plastic money for a brief period of free play.

What to do

• Ask each group to make up the prices, as shown in their workbook, using the plastic money. • Arrange the money in order from most to least in value. Use this to order the items shown from most expensive to least expensive. • Use the money to find the difference in price between the most and least expensive items. • Use the money to show the three coins needed to buy the sugar and the two coins to buy the jam.

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• Addition of two whole numbers with an unlike extension of places and no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 60–61. • 108 • New Wave Maths Book C – Teachers Guide

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

Unit 22—Answers

Student pages 64–66

Unit 22–1 1. (a) 69 (b) 88 (c) 99 (d) 87 (e) 79 (f) 47 2. (a)

(b)

(c)

(d)

1. (a) 79 (b) 78 (c) 58 (d) 59 (e) 87 (f) 69 2. (a) Teacher check (b) Teacher check (c) No 3. Teacher check

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Unit 22–2

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• Complete similar activities using triangular or rectangular shapes.

Consolidation 22–2

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1. (a) 257 (b) 477 (c) 337 (d) 197 (e) 247 (f) 187 2. cereal, ice cream, jam, juice, bread, sugar, milk, soup 3. (a) $3.55 (b) $1.20, 10c (c) $2, 10c

• Use two paragraphs with a larger number of words and compare the results.

Consolidation 22–3

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R.I.C. Publications®

• Cut out items from toy catalogues and order from most to least expensive.

New Wave Maths Book C – Teachers Guide • 109 •

Unit 23–1

Student page 67

Outcomes

Indicators

N2.3, S2.1, WM2.2

Skills • subtraction • reading plans • tracing • discussing • analysing • drawing • sharing

Number (N2.3)

The student is able to: • place important things in their environment in order on their map. • pose questions suggested by collected data.

Resources • Base 10 MAB or counters • calculator • pencil • ruler • house or building plans (large) • copies of house plans from newspapers

• subtract • draw • plan • outside • external • most common • shapes

Main Activity (S2.1, WM2.2) Warm up

• Display the house or building plans for the students to see. Explain that the plan looks down from above. Trace over the outside or external walls shown on the plans.

What to do

• Break the class into small groups and distribute house plans from newspapers to each group. • Ask students to trace over the outside walls. • Ask students to think about their own house or the school and what it would look like if they drew only the external walls. • Ask students to draw a plan of their house or the school showing just the external walls. A bird’s-eye view may be beyond some of the students. (If the student’s house or the school is two-storey, two plans can be drawn. Also, use only part of the school if there are several buildings.) • Share drawings with the class. Discuss the most common shape and why this shape is so common.

Notes

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• Subtraction of a two-digit whole number from a two-digit whole number, both multiples of 10, with no regrouping.

Teac he r

Language

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4–5. • 110 • New Wave Maths Book C – Teachers Guide

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

Unit 23–2

Student page 68

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • decide whether they have more or less money than the price and whether to expect change.

Skills • coin recognition • subtraction • identifying change

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • plastic coins

• subtract • change • buy

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

Notes

Teac he r

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• Subtraction of a three-digit whole number from a three-digit whole number both multiples of 100 with no regrouping.

Main Activity (N2.1a) Warm up

• Arrange the class into small groups and distribute plastic coins to each. Allow a brief period of free play.

What to do

• Ask students to use the coins to show the price tag’s value for each toy in the workbook. • For the exercise, you have 50c to spend. Find how much change you would receive from 50c when you buy each item. Work with the groups and write answers in the space provided. • Repeat to find change from $1.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 60–61. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 111 •

Unit 23–3

Student page 69

Outcomes

Indicators

Resources

N2.3, M2.2, WM2.3

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. • make conjectures (often guesses) about shapes and measurements.

• Base 10 MAB or counters • calculator • plastic cups • sand, grain, water • five large containers; e.g. icecream container, bucket, large can, small box, class rubbish bin

Skills • subtraction • recording • measuring • analysing • reasoning

Number (N2.3)

• subtract • tally • number • fill • most • least • difference • largest • smallest

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

• Revise keeping a tally.

What to do

• Arrange the class into small groups. Each group is to have five large containers, a small plastic cup and either sand, grain or water. • Explain to the class that the small cup is to be used to fill each of the large containers in turn. As each cupful is emptied into the large container, a tally mark is made to record it. When all containers have been filled, answer the questions. • Five containers may be too many for some students. Use fewer or smaller containers.

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• Subtraction of a three-digit whole number from a three-digit whole number, both multiples of 100, with no regrouping.

Teac he r

Language

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• 112 • New Wave Maths Book C – Teachers Guide

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

Unit 23—Answers

Student pages 67–69

Unit 23–1

1. (a) 300 (b) 300 (c) 200 (d) 300 (e) 300 (f) 100 2. (a) 35c (b) 15c (c) 20c (d) 25c (e) 30c (f) 5c (g) 10c (h) 40c 3. (a) 70c (b) 90c (c) 80c (d) 55c (e) 75c (f) 60c

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1. (a) 30 (b) 40 (c) 20 (d) 30 (e) 40 (f) 30 2. Teacher check

Unit 23–2

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• Draw a plan of a relative or friend’s house.

Consolidation 23–2 • Cover boxes in wrapping paper. Make labels with prices for students to attach and choose ‘gift’ combinations to add and give change from a set amount.

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Consolidation 23–3

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R.I.C. Publications®

• Repeat the activity using a different container(s). Estimate the number of cups before measuring.

New Wave Maths Book C – Teachers Guide • 113 •

Unit 24–1

Student page 70

Outcomes

Indicators

N2.3, N2.2

The student is able to: • use multiples (i.e. equivalent groups) to count and compare collections. • use materials and diagrams to represent multiplication/division as repeated addition/subtraction or ‘sharing out’.

Skills • working independently

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • multiply • divide

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Notes

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

• Invite students’ participation in the following examples: Blackboard/Whiteboard 2 x 5 = and ask for the answer; 2 x 50 = and ask for the answer; 2 x 500 = and ask for the answer. Repeat for 4 x 3 = ; 4 x 30 = ; 4 x 300 = ; and 3 x 7 = ; 3 x 70 = ; 3 x 700 = . Ask students to describe any patterns that are emerging.

What to do

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• Multiplication of basic facts.

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• Try numbers 1–10 in the workbook. Allow students to use their calculator if necessary. • The final exercise is a revision of basic facts showing the four combinations of the one fact. Students should be directed to work through these by themselves. Allow the use of a calculator if required.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 52–53, 56–57. • 114 • New Wave Maths Book C – Teachers Guide

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

Unit 24–2

Student page 71

Outcomes

Indicators

N2.3, C&D2.4

The student is able to: • interpret block graphs produced by others.

Skills • multiplication • recording • graphing • interpreting graphs

Number (N2.3)

Resources

Language • multiply • survey • bar graph • pie graph • most • least • order

• Base 10 MAB or counters • calculator • students • coloured pencils • block/bar graph – see page 223

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Notes

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Teac he r

• Multiplication of basic facts.

Main Activity (C&D2.4) Warm up

• Explain to the class that graphs are a convenient means of displaying information for easy reading. • Revise the features of a block graph—vertical and horizontal axes, colouring plotted squares, title.

What to do

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• Ask students to choose their favourite fast food and stand in the line for chicken and chips, fish and chips, hamburgers or pizza. Write total for each line on the board and ask students to complete their graph. • A pie graph shows information in a different way. Explain that in a pie graph the largest piece of the pie shows the most or greatest number. • Explain how to read the pie graph then work with the class through the exercise in the workbook.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 115 •

Unit 24–3

Student page 72

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • decide whether they have more or less money than the price and whether to expect change. • count coins and record amounts.

Skills • multiplication • coin recognitions • subtracting

Number (N2.3)

Resources • counters • calculator • plastic coins

Language • multiply • zero • change

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

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups and allow a brief period of free play.

What to do

• Ask students to use the coins to show the amount displayed on the price tags. • Explain to the students that they have $1 to spend. Find how much change will be received from the dollar for each present purchased.

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Teac he r

• Multiplication of basic facts, multiplication property of zero.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 60–61. • 116 • New Wave Maths Book C – Teachers Guide

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

Unit 24—Answers

Student pages 70–72

Unit 24–1

1. (a) 15 (b) 45 (c) 35 (d) 30 (e) 25 (f) 40 2. Teacher check 3. (a) swimming (b) basketball (c) swimming, netball, cricket, baseball, basketball (d) Teacher check

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1. (a) 16 (b) 32 (c) 8 (d) 28 (e) 20 (f) 24 2. (a) 18, 180, 1800 (b) 14, 140, 1400 (c) 24, 240, 2400 (d) 30, 300, 3000 (e) 35, 350, 3500 (f) 4, 40, 400 (g) 0, 0, 0 (h) 48, 480, 4800 (i) 24, 240, 2400 (j) 12, 120, 1200 3. (a) 27, 27, 3, 9 (b) 35, 35, 7, 5 (c) 28, 28, 7, 4 (d) 18, 18, 9, 2 (e) 30, 30, 5, 6 (f) 32, 32, 4, 8 (g) 35, 35, 5, 7 (h) 24, 24, 6, 4

Unit 24–2

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• Create five problems similar to Exercise 3 for students to solve.

Consolidation 24–2

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1. (a) 0 (b) 0 (c) 0 (d) 0 (e) 0 (f) 0 2. (a) 75c (b) 50c (c) 90c (d) 60c (e) 20c (f) 10c (g) 45c (h) 40c 3. (a) 80c + 60c = $1.40 (b) 25c + 50c = 75c (c) 40c + 60c = $1.00 (d) 10c + 50c = 60c (e) 90c + 10c = $1.00 (f) 55c + 25c = 80c

• Create bar graphs or pie graphs with the students, showing hair colours etc.

Consolidation 24–3

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R.I.C. Publications®

• Use a different starting amount to find the change and make up new examples.

New Wave Maths Book C – Teachers Guide • 117 •

Unit 25–1

Student page 73

Outcomes

Indicators

N2.3, S2.2

The student is able to: • make constructions from visual instructions.

Skills • division • following directions • folding • cutting

Number (N2.3) Main Activity (S2.2)

• counters • calculator • A4 paper (recycled) • scissors • pencil

• divide • fold • longways • half • rectangle • small • square • triangle

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Warm up

• Explain to the class that origami is a Japanese art form of paper folding. If you have access to an example, show the class. Another form of simple paper folding is to make a paper aeroplane. This is an exercise that may be completed with the class. • Distribute a sheet of A4 paper to each class member. Ask for a description of a rectangle. Ask for an example (the sheet of paper).

Notes

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• Demonstrate how to fold the sheet of paper longways in half, ensuring edges meet accurately. The class copies this. • Demonstrate folding in half to make a smaller rectangle. The class copies this. • Cut one of the small rectangles from the large sheet. • Distribute another sheet of paper and repeat the process to make a square by folding across a corner so the short side folds onto the long side. Cut off the excess. Fold in half and half again to give a small square. Cut the small square from the sheet. • Distribute three more sheets of paper and ask the class to make small triangle, a tree and a person. Students may draw a simple diagram on the folded paper to make the tree and the person. • Display results.

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What to do

Language

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Teac he r

• Division of basic facts.

Resources

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4–5. • 118 • New Wave Maths Book C – Teachers Guide

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

Unit 25–2

Student page 74

Outcomes

Indicators

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. • use informal methods based on partitioning to solve two-digit addition and subtraction problems.

Skills • logical reasoning • supporting ideas • calculating

Number (N2.3)

Resources

Language

• counters • calculator

• divide • sum • different • answer • correct

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Notes

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• Division of multiples of 10 by 10.

Main Activity (N2.3, WM2.4) Warm up

• This activity may be completed independently or in small groups. • Explain to the class that mathematics is mostly about patterns and logic. • This activity relies heavily on logic.

What to do

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• Explain that a sum is given to two students and each arrives at a different answer. Both students are very strong in their determination that their answer is correct. • Look at the sum in the workbook and see which answer is correct. Support your decision by explaining why you reached your decision and how this decision is right.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 68–69. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 119 •

Unit 25–3

Student page 75

Outcomes

Indicators

N2.3, M2.2

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

Skills • explaining • working in groups • division • doubling • halving

Number (N2.3)

Resources • counters or plastic money • calculator • squares or cubes

Language • divide • length • double • area • half • shapes

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Main Activity (M2.2) Warm up

• Organise the class into small groups. • Distribute small cubes or Base 10 MAB or a number of small squares. Allow a brief period of free play.

What to do

• Ask students to make a small line with the cubes/squares. Double the length of the line. Ask for an explanation from the groups as to what they did—how long to start, when doubled? • Repeat several times. • Complete the first activity in the workbook. • Ask each group to arrange a small group of cubes/squares using even numbers. Ask the group to halve the number of cubes/squares. Ask for an explanation from the groups of what they did—what was the starting area (number of cubes/squares)? What was the final area? • Repeat several times. • Complete the second activity in the workbook.

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• Division of basic facts using money.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80–81. • 120 • New Wave Maths Book C – Teachers Guide

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

Unit 25—Answers

Student pages 73–75

Unit 25–1

1. (a) 2 (b) 8 (c) 7 (d) 5 (e) 3 (f) 4 2. (a) Both were correct. (b) Brett subtracted the smaller number from the larger number and Rochelle added both. 3. (a) 98 (b) 57 (c) 69 74 11 41 (Answers may vary if calculations are multiplied or divided.)

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1. (a) 6 (b) 1 (c) 4 (d) 5 (e) 9 (f) 3 2. Teacher check

Unit 25–2

• Complete similar activities as for Exercise 3.

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• In pairs, experiment with paper folding to make, for example, a paper aeroplane.Write instructions for others to follow.

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1. (a) $7 (b) $6 (c) 9c (d) 6c (e) $7 (f) 9c 2. (a) 2 (b) 6 (c) 8 (d) 10 3. (a) 5 (b) 4 (c) 3 (d) 1

Consolidation 25–3

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R.I.C. Publications®

• Use other concrete materials such as counters or buttons to double and halve amounts.

New Wave Maths Book C – Teachers Guide • 121 •

Unit 26–1

Student page 76

Outcomes

Indicators

N2.3

The student is able to: • use informal methods based on partitioning to solve one- and twodigit addition and subtraction problems.

Skills • manipulating • adding • subtracting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • add • subtract

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

Notes

Main Activity (N2.3) Warm up

• Organise the class into small groups and distribute Base 10 MAB. Allow a brief period of free play.

What to do

• Explain to the class that they will be subtracting multiples of ten from multiples of ten. The sum is an extension of basic facts of subtraction only now there are tens and ones involved. All ones columns are filled with zeros. The actual working out is focused on the tens column. • Ask students to take out MAB to show 50. Ask them how many tens (5) and how many ones (0). • Take away 30. What is left? (20) • Repeat for 70 – 10; 40 – 20; 60 – 50; and 80 – 60. • Direct students to complete the work in their workbook. Encourage them to use the Base 10 MAB. • Addition problems are worked in the reverse manner; e.g. 70 + 10; 40 + 20; 60 + 30; and 40 + 50. • Again encourage students to use the Base 10 MAB.

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Teac he r

• Addition of a two-digit whole number to a two-digit whole number with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 70–71, 72–73. • 122 • New Wave Maths Book C – Teachers Guide

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

Unit 26–2

Student page 77

Outcomes

Indicators

N2.3, C&D2.2, C&D2.4, WM2.2

The student is able to: • organise data by classifying items in categories they have created. • read and compare frequencies from lists and simple one-way tables. • pose questions suggested by the collected data.

Skills • observing • recording • timing • analysing • interpreting • adding

Number (N2.3)

Resources

Language • addition • tally • most common • least common

• Base 10 MAB or counters • calculator • vehicles passing the school • sun safety equipment • watch • pencil

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

Notes

Main Activity (C&D2.2, C&D2.4, WM2.2) Warm up

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Teac he r

• Addition of a two-digit whole number by a two-digit whole number with no regrouping.

• Revise tallying. Ask a student to show on the blackboard/whiteboard how a tally of 12 would be shown. Select other students to show a tally of 6, 15, 21 and 20.

What to do

• Explain to the class that they will be going in groups to the edge of the school grounds to take a tally of all the different types of vehicles that drive past the school. Suggest that each group member is responsible for keeping a tally of one type of vehicle only—one for cars, another for bikes (motor and push), another for trucks, another for buses and one for other vehicles. • Keep a 15-minute time slot open for the recording. One the time is up, students transfer the group’s recordings to their own workbook. • Complete the questions. • Repeat the activity at another time of the day to see if there is a difference.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 123 •

Unit 26–3

Student page 78

Outcomes

Indicators

N2.3, N2.2, N2.3

The student is able to: • use their understanding of number partitions and the relationship between addition and subtraction to solve ‘hidden number’ questions. • remember basic addition and subtraction facts. • use counting strategies such as combining.

Skills • adding • subtracting • reasoning

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • add • number sentence

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

• Completing number sentences is a common activity. Simple number sentences such as 2 + 6 = and 4 + 3 = are common. Ask students how they would complete a number sentence such as 4 + _ = 12. Ask for alternative solutions. • Repeat for 14 – _ = 6.

What to do

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Teac he r

• Addition of three two-digit numbers with no regrouping.

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• Set students to complete activities on their page in the workbook. Allow students to use a calculator and MAB if required—particularly for some problems in Exercise 4.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 64–65. • 124 • New Wave Maths Book C – Teachers Guide

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

Unit 26—Answers

Student pages 76–78

Unit 26–1

1. (a) 68c (b) 82c (c) 91c (d) 74c (e) 53c (f) 74c 2. Teacher check

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Teac he r

1. (a) 68c (b) 82c (c) 91c (d) 74c (e) 53c (f) 86c 2. (a) 4 (b) 40 (c) 4 (d) 40 3. (a) 20 (b) 20 (c) 10 (d) 10 (e) 30 (f) 10 (g) 10 (h) 20 (i) 20 (j) 30 50 (c) 9 (d) 90 4. (a) 5 (b) 5. (a) 60 (b) 60 (c) 60 (d) 90 (e) 90 (f) 70 (g) 90 (h) 100 (i) 80 (j) 70

Unit 26–2

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• With practice, students should be able to complete similar problems without using Base 10 MAB.

Consolidation 26–2

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1. (a) $67 (b) $95 (c) $69 (d) $79 (e) $78 (f) $69 2. (a) 13 (b) 13 (c) 5 (d) 16 (e) 16 (f) 9 (g) 10 (h) 10 (i) 4 (j) 13 (k) 13 (l) 7 (m) 17 (n) 17 (o) 9 3. (a) 6 (b) 3 (c) 6 (d) 7 (e) 7 (f) 7 (g) 9 (h) 9 (i) 9 (j) 8 (k) 8 (l) 4 (m) 5 (n) 6 (o) 6 4. (a) 200 (b) 400 (c) 36 (d) 80 (e) 200 (f) 900 (g) 9 (h) 7 (i) 128 (j) 134 (k) 800 (l) 150 (m) 200 (n) 90 (o) 180

• Complete the activity again from the front of their house at different times.

Consolidation 26–3

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R.I.C. Publications®

• With practice, students should be able to complete most of these problems without the use of a calculator.

New Wave Maths Book C – Teachers Guide • 125 •

Unit 27–1

Student page 79

Outcomes

Indicators

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 • drawing • using a ruler • following directions • multiplication • understanding symmetry

Number (N2.3)

Resources • counters • calculator • pencil • ruler

Language • multiply • draw • shapes • symmetrical

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Notes

Main Activity (S2.3) Warm up

• Revise symmetry. Ask students to explain symmetry. (If necessary, use a student as an example. ‘If we were to cut a student in half lengthways, the left and right halves would be (almost) the same.’) • Draw a half diagram on the blackboard/whiteboard of a flower or shape. Ask a student to complete the drawing, making it symmetrical with the original. • Repeat a number of times.

What to do

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• Multiplication of basic facts using money.

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• Direct students to complete the drawings in the workbook. Remind students that for one square shown on one side of the dotted line there must be an equivalent square shown on the other side. • Check work and assist as required. Remind students to use a ruler when drawing.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 26–27. • 126 • New Wave Maths Book C – Teachers Guide

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

Unit 27–2

Student page 80

Outcomes

Indicators

Resources

N2.3, N2.4

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

• counters or plastic money • calculator

Skills • writing numbers • halving numbers • doubling numbers • exploring patterns • multiplication

Number (N2.3)

Language • multiply • double • half • numbers • complete • pattern

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Notes

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Teac he r

• Multiplication of basic facts using money.

Main Activity (N2.4) Warm up

• Remind students that mathematics is largely logic and patterns. • The simplest number pattern is the set of counting numbers. • Another form of a number pattern is the doubling and halving of numbers. Ask students to double 1, 5, 3 and 6. Ask for half of 4, 8 and 14. • Other patterns are made up of sequences; e.g. multiples of 2—2, 4, 6, 8 … what are the next two numbers? • What is this sequence 10, 20, 30, 40 … ?

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• Work with the whole class to complete the activities in the workbook. Work through each activity together. More able students may work ahead.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 41–42, 44–45. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 127 •

Unit 27–3

Student page 81

Outcomes

Indicators

Resources

N2.3, M2.2, WM2.2

The student is able to: • compare the area of two regions directly by superimposing one over the other. • express measurements using ‘between’ or refer to the part units in some way. • represent a problem with a sketch or diagram.

• counters or plastic money • calculator • pencil • ruler

Skills • analysing relationships • measuring • drawing • counting • multiplication

Number (N2.3)

Language • multiply • area • shapes • perimeter • grid

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

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

• Ask the class to tell you what they know or understand about perimeter and area. Ask if they know of any relationships between perimeter and area; for example, if we change one will it change the other? If we keep one the same can we change the other?

What to do

• Explain to the students they will be given an area of 18 squares.They are to draw a number of different shapes on the grid but each shape must have 18 squares. All squares must have a full side in contact with the full side of another square in the shape. • After drawing several shapes with 18 squares as their area, count the number of edges of squares on the perimeter. • What did they find? Write about this in the space provided.

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• Multiplication of basic facts using money.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80–81. • 128 • New Wave Maths Book C – Teachers Guide

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

Unit 27—Answers

Student pages 79–81

Unit 27–1

1. (a) 15c (b) 16c (c) 27c (d) 10c (e) 21c (f) 24c 2. (a) 40 (b) 12 (c) 10 (d) 4 (e) 2 (f) 30 (g) 18 (h) 20 (i) 16 (j) 24 3. (a) 10 (b) 5 (c) 7 (d) 2 (e) 4 (f) 8 (g) 6 (h) 3 (i) 9 (j) 1 4. (a) 32, 64 (b) 24, 48 (c) 20, 24 (d) 20, 25 5. (a) 15, 18 (b) 15 (c) 14, 17 (d) 15 (e) 17, 22 (f) 31 6. (a) 18, 12 (b) 20, 10 (c) 12, 9 (d) 11, 7

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1. (a) 28c (b) 15c (c) 16c (d) 30c (e) 40c (f) 20c 2. Teacher check

Unit 27–2

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• Investigate number patterns by creating their own with a partner. Share with the class.

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• Use graph paper to create a shape for another student to complete symmetrically.

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1. (a) $45 (b) $32 (c) $24 (d) $35 (e) $36 (f) $15 2. The perimeter will change.

Consolidation 27–3

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• Share the shapes he/she made with other students to compare findings.

New Wave Maths Book C – Teachers Guide • 129 •

Unit 28–1

Student page 82

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • use multiple (i.e. equivalent groups) to count and compare collections. • read amounts of money and record total amounts.

Skills • discussing • adding • multiplying • doubling • using a calculator • division

Number (N2.3)

Resources • counters or plastic money • calculator

Language • divide • multiply • add

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Notes

Main Activity (N2.1a, N2.3) Warm up

• Ask students how many have been shopping. Ask them if they buy more than one of the same item. Ask how they would work out the total price for multiple lots of the same item. Allow full discussion of different methods used. Ensure adding, multiplying, doubling are included, as well as using a calculator.

What to do

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Teac he r

• Division of basic facts using money.

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• Set students to work to find out the cost of the purchases as set out in their workbook. • At the end of the session, ask students how they worked out their answer. If students used several different means, ask them which one they considered to be the best and why.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 56–57. • 130 • New Wave Maths Book C – Teachers Guide

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

Unit 28–2

Student page 83

Outcomes

Indicators

Resources

N2.3, C&D2.4

The student is able to: • interpret graphs produced by others. • write a few sentences to describe the results of their data collection.

• counters or plastic money • calculator • pencil

Skills • division • interpreting graphs • reading graphs • compiling a list

Number (N2.3)

Language • divide • pie graph • most • how long, • same • time • list

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Notes

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Teac he r

• Division of basic facts using money.

Main Activity (C&D2.4) Warm up

• Revise features of pie graphs (title, circular in shape, portions of the circle showing parts of the whole—hence its name). Use student hair colour to make a pie graph and display the results on the blackboard/whiteboard or overhead. Explain how each portion of the pie is made up of part of the whole of the class numbers.

What to do

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• Using this information, lead the class through the pie graph in the workbook, explaining that the size of the segments shows relative size of each activity as part of the day. Students provide responses to questions and write answers in their books. • Students, after a class discussion in relative times they take to participate in a variety of activities, complete the table at the bottom of the page. • Share student responses with the class.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 131 •

Unit 28–3

Student page 84

Outcomes N2.3, WM2.4

Skills • division • addition • subtraction

Number (N2.3)

Indicators

Resources

The student is able to: • round sensibly to estimate and to check answers to additions and subtractions. • respond to questions such as ‘Is your working correct?’ by checking each stage of the work.

• counters or plastic money • calculator

Language • divide • approximation • correct • incorrect • addition • subtraction

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Main Activity (N2.3, WM2.4) Warm up

• Ask which multiple of ten the following numbers are closest to (for example, 26 rounds to 30, whereas, 24 rounds to 20): 26, 51, 34, 47, 18, 72. • Round these numbers to their closest ten then add them—27 and 43 ≈ 70; 51 and 29 ≈ 80; 66 and 18 ≈ 90.

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• Taking a number to its closest ten (rounding) allows us to make approximate, educated guesses of answers, without actually working out the answer. • Use this technique to make approximations to see whether the answers given to the sums are possibly correct or incorrect. For example, Question 1(a), nearest 10 to 47 is 50 and the nearest 10 to 31 is 30. 50 plus 30 is 80. Is 98 (rounded to 100) nearly correct? No. Put a cross next to the answer. • Repeat with the students for (b), (c) and (d) before allowing students to approximate the subtraction examples. • Check the accuracy of the approximations by working out the actual answers using the sums on the lower half of the page. • Discuss the results as a whole class.

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What to do

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Teac he r

• Division of basic facts using money.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 66–67. • 132 • New Wave Maths Book C – Teachers Guide

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

Unit 28—Answers

Student pages 82–84 Unit 28–2

Unit 28–1

1. (a) $3 (b) $8 (c) 8c (d) $5 (e) $7 (f) 10c 2. (a) sleeping (b) 6 hours (c) eating and watching TV 3. Teacher check

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Teac he r

1. (a) 6c (b) $8 (c) 9c (d) 4c (e) $7 (f) $6 2. (a) $6 (b) $30 (c) $20 (d) $28 (e) $5 (f) $18 (g) $24 (h) $100 (i) $20 (j) $1 (k) $32 (l) $70 (m) $2 (n) $12 (o) $15 (p) $50 (q) $27 (r) $16 (s) $12 (t) $18

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• Choose items from the school canteen and work out the total price for multiple lots.

Consolidation 28–2

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1. (a) 4c (b) 8c (c) $7 (d) $6 (e) 3c (f) $5 2. (a) incorrect (b) correct (c) incorrect (d) correct (e) incorrect (f) correct (g) correct (h) incorrect 3. (a) incorrect (b) correct (c) incorrect (d) correct 4. (a) incorrect (b) correct (c) correct (d) incorrect

• Students could attempt to make a pie graph as accurately as possible to show their time use during the day.

Consolidation 28–3

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R.I.C. Publications®

• Practise rounding numbers between 1–100. (If a number ends in 5 it should be rounded up to the closest ten.)

New Wave Maths Book C – Teachers Guide • 133 •

Unit 29–1

Student page 85

Outcomes

Indicators

N2.3, S2.3, WM2.2

The student is able to: • explain their choice of simple figures which are ‘the same’ with language such as turn, turn over, slide along. • represent a problem with concrete materials and manipulate the materials to find a solution.

Skills • manipulating shapes • recognising shapes • enlarging • discussing • addition

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic shapes (squares, parallelograms, trapeziums, equilateral triangles) • pencil • ruler

Language • add • same shape • small • larger • square • parallelogram • trapezium • equilateral triangle • original

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Notes

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

• Organise the class into small groups and distribute the shapes. Allow students to manipulate the shapes for a short time.

What to do

• Ask students to take out a square. • Ask students if they are able to make a larger square using four of the smaller squares. Check results and invite comments on results. • Ask students to show a parallelogram. Ask students if they are able to make a large parallelogram using four of the smaller parallelograms. Discuss results and ask students to draw their discovery. • Repeat for the other three shapes. Students may need to make an L shape using three squares. The enlargement will be of four L shapes of three squares each. • Finish off using other shapes of students’ own choosing.

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• Addition of two whole numbers with unlike extension of places and no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 20–21. • 134 • New Wave Maths Book C – Teachers Guide

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

Unit 29–2

Student page 86

Outcomes

Indicators

N2.3

The student is able to: • use informal methods based on partitioning to solve one-, two- and three-digit addition problems. • use multiples to count collections.

Skills • addition

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator

• add • total • sum

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Notes

Main Activity (N2.3) Warm up

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• Addition of two three-digit whole numbers with no regrouping.

• Discuss with the students how this page will be completed according to the chosen suggestion(s) below.

What to do

• This page is a revision of work undertaken to date. • Suggested use of the page: – revision – test of retained knowledge – group interactive session with more able students assisting less able students – mental activity – calculator activity – introduce estimation skills and try these.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 64–65. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 135 •

Unit 29–3

Student page 87

Outcomes

Indicators

N2.3, M2.2, S2.2

The student is able to: • compare the area of two regions directly by superimposing one over the other. • draw figures which show the essential spatial features of named geometric shapes.

Skills • manipulating resources • drawing • comparing • exploring patterns • addition • area

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 2-D shapes • 2-cm cubes

Language • add • draw • shapes • pattern • cover • cube • square shapes

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Main Activity (M2.2, S2.2) Warm up

• Organise the class into small groups and distribute 2-D shapes and 2-cm cubes. Allow a period of free exploration.

What to do

• Ask students to look at the shapes in the pattern at the top of the page. Ask them to find the pattern and draw the next two shapes. • Shapes may be covered by other shapes to find how many are required so that comparisons in size of shapes can be made—that is, a comparison of area. • Two-centimetre cubes have been nominated as the shape to cover the squares drawn on the page. Use the cubes to find how many cover the first shape, the second shape and the third shape. • Use the cubes to make a square shape with 16 cubes, draw it and then make one with 25 cubes. Draw this shape also.

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• Addition of two three-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 2–3, 80–81. • 136 • New Wave Maths Book C – Teachers Guide

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

Unit 29—Answers

Student pages 85–87

Unit 29–1

1. (a) 999 (b) 777 (c) 396 (d) 767 (e) 888 (f) 976 2. (a) 7, 70, 700 (b) 6, 60, 600 (c) 8, 80, 800 (d) 6, 60, 600 (e) 8, 80, 800 (f) 8, 80, 800 (g) 9, 90, 900 3. (a) 20 (b) 21 (c) 25 (d) 30

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Teac he r

1. (a) 179 (b) 799 (c) 886 (d) 588 (e) 498 (f) 398 2. (a) Yes (b) No (c) No (d) Yes 3. Teacher check

Unit 29–2

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7-sided shape

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3. 4 cubes, 9 cubes 4. Teacher check

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• Compare the results of shapes drawn in Exercise 3.

Consolidation 29–2 • Create number patterns using 1-cm cubes or by drawing dots, shapes or pictures.

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1. (a) 785 (b) 888 (c) 978 (d) 598 (e) 965 (f) 558 2.

Consolidation 29–3

• Make and draw rectangular shapes with 1- or 2-cm cubes.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 137 •

Unit 29–3

Student page 87

Outcomes

Indicators

N2.3, M2.2, S2.2

The student is able to: • compare the area of two regions directly by superimposing one over the other. • draw figures which show the essential spatial features of named geometric shapes.

Skills • manipulating resources • drawing • comparing • exploring patterns • addition • area

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 2-D shapes • 2-cm cubes

Language • add • draw • shapes • pattern • cover • cube • square shapes

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

Main Activity (M2.2, S2.2) Warm up

• Organise the class into small groups and distribute 2-D shapes and 2-cm cubes. Allow a period of free exploration.

What to do

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Teac he r

• Addition of two three-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 2–3, 80–81. • 138 • New Wave Maths Book C – Teachers Guide

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

Unit 29—Answers

Student pages 85–87

Unit 29–1

1. (a) 999 (b) 777 (c) 396 (d) 767 (e) 888 (f) 976 2. (a) 7, 70, 700 (b) 6, 60, 600 (c) 8, 80, 800 (d) 6, 60, 600 (e) 8, 80, 800 (f) 8, 80, 800 (g) 9, 90, 900 3. (a) 20 (b) 21 (c) 25 (d) 30

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Teac he r

1. (a) 179 (b) 799 (c) 886 (d) 588 (e) 498 (f) 398 2. (a) Yes (b) No (c) No (d) Yes 3. Teacher check

Unit 29–2

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6-sided shape

7-sided shape

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3. 4 cubes, 9 cubes 4. Teacher check

www.ricpublications.com.au

• Compare the results of shapes drawn in Exercise 3.

Consolidation 29–2 • Create number patterns using 1-cm cubes or by drawing dots, shapes or pictures.

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1. (a) 785 (b) 888 (c) 978 (d) 598 (e) 965 (f) 558 2.

Consolidation 29–3

• Make and draw rectangular shapes with 1- or 2-cm cubes.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 139 •

Unit 30–3

Student page 90

Outcomes

Indicators

N2.3, N2.4

The student is able to: • write a pattern of numbers to fit a particular pattern and use it to predict the numbers needed for later terms. • describe a rule which could have been used to generate an adding or subtracting sequence and test.

Skills • reasoning • observing • correcting • addition

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils

Language • add • errors • patterns

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Main Activity (N2.4) Warm up

• Number patterns are an important part of understanding mathematics.

What to do

• Using sound reasoning and observation skills, students are to look at the patterns in their workbook to find and correct any mistakes. Each pattern contains at least one error. • When the error is located, students are to neatly cross out the error and enter the correct item to ensure the pattern is accurate. • Share findings at the end of the lesson.

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• Addition of two three-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 44–45. • 140 • New Wave Maths Book C – Teachers Guide

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

Unit 30—Answers

Student pages 88–90

Unit 30–1

1. (a) 720 (b) 850 (c) 670 (d) 380 (e) 960 (f) 970 2. (a) June (b) Rochelle (c) Rochelle 100 cm Brett 102 cm Ron 110 cm Coleen 112 cm Bob 113 cm June 115 cm (d) Coleen and Bob (e) 2 cm (f) Ron and Coleen, Bob and June (g) 1 cm (h) 12 cm

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Teac he r

1. (a) 527 (b) 668 (c) 687 (d) 799 (e) 875 (f) 699 2. (a) 3, 30, 300 (b) 3, 30, 300 (c) 4, 40, 400 (d) 2, 20, 200 (e) 4, 40, 400 (f) 3, 30, 300 (g) 5, 50, 500 (h) 2, 20, 200 3. (a) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 (b) 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 (c) 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 (d) 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Unit 30–2

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Consolidation 30–2 • Choose six children of varying heights from the class to construct a bar graph and answer similar questions.

Consolidation 30–3

• Make up number patterns of their own and give to a classmate to solve. (Classmates will need to be of similar ability.) Explain the answer if it cannot be solved.

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(d) 100, 95, 90, 85, 80, 75, 70, 65 (e) 5, 9, 13, 17, 21, 25, 29, 33

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• Practise counting in 6s, 7s, 8s, 9s and 10s.

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1. (a) 700 (b) 800 (c) 400 (d) 800 (e) 900 (f) 900 2. Patterns should be:

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 141 •

Unit 31–1

Student page 91

Outcomes

Indicators

N2.3, S2.1, WM2.3

The student is able to: • give instructions for creating paths on squared paper or computer screens which require movements to be done in order. • test their conjectures with a single trial.

Skills • drawing • problem-solving • addition • defining paths

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • coloured pencils • overhead projector • grid transparency (see pages 199 or 200) • overhead pens

Language • add • path • square • grid • different

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Notes

Main Activity (S2.1, WM2.3) Warm up

• Display a grid, using an overhead projector, for the whole class to see. • Ask a student to draw a path through all the squares in one row. Repeat for one column. Repeat for two or three rows. • Ask if there are other ways this can be done. Allow a student to demonstrate on the grid.

What to do

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• Addition of whole numbers with unlike extension of places and no regrouping.

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• Direct students to their workbook and ask them to draw the path they would follow through the grid, passing through each square once. Use one coloured pencil to draw the path. • Ask the students to write and explain whether there are other paths they could have followed. • If they think there are other paths, ask them to draw these in a different colour on the same grid or on the grids at the bottom of the page.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 10–11. • 142 • New Wave Maths Book C – Teachers Guide

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

Unit 31–2

Student page 92

Outcomes

Indicators 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 with an adding rule.

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

Skills • counting • following directions

Number (N2.3)

Resources

Language • add • multiples • grid • nearest • square

• Base 10 MAB or counters • calculator • coloured pencils • markers

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Notes

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Teac he r

• Addition of whole numbers with unlike extension of places and no regrouping.

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

• Ask the class to count to 50 in unison. • Ask the class to count to 30 by twos. • Ask a student to count to 30 by threes. • Ask another student to count to 20 by fours. • Explain that the answers to counting by twos, threes or fours are the multiples of 2, 3 and 4. Multiples are found by multiplying one number by another.

What to do

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• The grid at the top of the page in the workbook is to have the multiples of 3 coloured. Remind the class that this is the three times table or every third square that is to be coloured. • Working as a whole class, direct students to place counters on the numbers shown in the workbook. Now move the counter to the nearest coloured marker. Was the counter moved forwards or backwards? Check with each number. • Repeat for multiples of four and five.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 56–57. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 143 •

Unit 31–3

Student page 93

Outcomes

Indicators

N2.3, M2.2

The student is able to: • use repetitions of a uniform unit consistently and carefully to measure length. • compare the area of two regions directly by superimposing one over the other.

Skills • measuring • counting • recording • adding • finding perimeter

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • add • table • distance around • shape • number of squares • area • perimeter

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

Main Activity (M2.2) Warm up

• Select a number of items in the classroom. Discuss with the students the distance around the perimeter and covering the surface area. Explain that area is usually measured in squares.

What to do

• Open the workbook and explain to the class that they are to complete the blank spaces on the diagram by measuring the distance around each shape and counting the number of squares in each shape. • Ask how they will measure around the shapes. (A ruler could be used.) For this exercise, students can measure by counting the units (sides of the squares on the outer edges). To help with counting, mark the unit they start at. • When all shapes have been counted, answer questions 2(a) and 2(b). • Complete Exercise 3 using 12 1-cm cubes.

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• Addition of two two-digit whole numbers with no regrouping.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80–81. • 144 • New Wave Maths Book C – Teachers Guide

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

Unit 31—Answers

Student pages 91–93

Unit 31.1

1. (a) 28 (b) 53 (c) 77 (d) 28 (e) 24 (f) 39 2. Teacher check 3. Teacher check 4. Teacher check

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1. (a) 15 (b) 13 (c) 19 (d) 17 (e) 48 (f) 18 2. Yes, Teacher check (These diagrams show three possible answers.)

Unit 31.2

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Consolidation 31–2 • Practise 2x, 3x, 4x and 5x tables. Extend to 6x, 7x, 8x, 9x and 10x and repeat activity using those multiples.

Consolidation 31–3

• Use other amounts of 1-cm cubes to experiment with measuring the perimeter and area.

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(a) Shapes A, B, C, D and E cover the same area. (b) Shape A 3. Teacher check

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• Participate in maze activities.

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1. (a) 76 (b) 78 (c) 49 (d) 37 (e) 67 (f) 74 2.

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 145 •

Unit 32–1

Student page 94

Outcomes

Indicators

N2.3, N2.1a

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

Skills • working cooperatively • discussing • counting money • subtracting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • subtraction • count • coins • total

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

Notes

Main Activity (N2.1a) Warm up

• Distribute plastic coins to small groups of students and allow a period of free play. • Ask students to select any three coins. In their groups, tell each other the total amount of the coins. Repeat for five coins, four coins, three coins of the same value, five coins of the same value.

What to do

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Teac he r

• Subtraction of a one- or two-digit number from a two-digit number with no regrouping.

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• Direct students to the activity in their workbook. Suggest they use the plastic coins if this will help find the answers. Work in groups and help each other as required. • Complete the activities.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 146 • New Wave Maths Book C – Teachers Guide

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

Unit 32–2

Student page 95

Outcomes

Indicators

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

The student is able to: • make block graphs using ‘real’ data. • interpret block graphs produced by others.

Skills • measuring • recording • working cooperatively • problem-solving • graphing • analysing data

Number (N2.3)

Resources

Language • subtraction • Base 10 MAB • measure • length • graph • longest • shortest

• Base 10 MAB or counters • calculator • coloured pencils • classmates • streamers • string • scissors

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Notes

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Teac he r

• Subtraction of a one- or two-digit number from a two-digit number with no regrouping.

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

• Organise the class into groups of six students. Complete Exercise 1 in the groups.

What to do

• Organise the class into groups of four students. • Provide each group with streamers, string, scissors and Base 10 MAB sticks/longs. • Explain to the class that they are to measure the length of each group member’s arm using the Base 10 MAB sticks/longs. • The first task within the groups is to decide how to measure the length of one arm. Once this is decided, complete the measures and record them on the graph provided. Colour one block for each long used. • After completing the graph, answer the questions at the bottom of the page.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 147 •

Unit 32–3

Student page 96

Outcomes

Indicators

N2.3, N2.1a

Skills • exchanging money • subtraction

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

Language • subtraction • exchange • coins

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

Main Activity (N2.1a) Warm up

• Arrange the class into small groups and distribute plastic coins. Allow a brief period of free play with the coins. • Ask the students to select two coins. Ask if these can be exchanged for one other coin. If so, exchange the coins. Repeat several times, use more than two coins to start with. Remind students that it is not always possible to exchange the coins for one other.

What to do

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Teac he r

• Subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

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• The activity in the workbook focuses on the exchange of coins for one coin. Encourage the students to use the plastic coins if it helps. • Work through the activities as a group.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. • 148 • New Wave Maths Book C – Teachers Guide

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

Unit 32—Answers

Student pages 94–96

Unit 32.1

1. (a) 44 (b) 92 (c) 73 (d) 18 (e) 27 (f) 32 2. Teacher check 3. Teacher check

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1. (a) 2 (b) 4 (c) 2 (d) 2 (e) 24 (f) 22 2. (a) 60c (b) 35c (c) 80c (d) $5 (e) $14 (f) 90c (g) 65c (h) 60c

Unit 32.2

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• In pairs, choose a certain number of coins at random and work out the totals.

Consolidation 32–2

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1. (a) 24 (b) 36 (c) 30 (d) 10 (e) 80 (f) 43 2. (a) 50c (b) 20c (c) $1 (d) $2 (e) $1 (f) $1 (g) $2

• Use a tape measure to measure their arms and repeat Question 3 by creating a new graph.

Consolidation 32–3

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R.I.C. Publications®

• In pairs, choose different coins—50c, 20c etc.—to list as many different ways as they can to make up the amount.

New Wave Maths Book C – Teachers Guide • 149 •

Unit 33–1

Student page 97

Outcomes

Indicators

N2.3, S2.3

The student is able to: • explain their choice of simple figures which are ‘the same’ with language such as turn, turn over, slide along.

Skills

• drawing • explaining • analysing • multiplication • identifying • translating

Number (N2.3)

Resources • counters • calculator • triangles, trapeziums, rectangles, pentagons • pencil

Language • multiply • shapes • fit • outliner • triangle • trapezium • rectangle • pentagon • rotate

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Notes

Main Activity (S2.3) Warm up

• Hold a rectangular piece of paper up horizontally for the class to see. Ask what you need to do to the piece of paper to display it vertically. Rotate it through 90° or one-quarter turn. Are there other ways? Show as the students describe to check for accuracy. • The shapes shown in the workbook should be distributed to small groups for experimenting with.

What to do

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Teac he r

• Basic facts of multiplication.

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• Explain to the groups that the shapes shown in the workbook are to be redrawn as shown by the dotted outlines. The group’s task is to explain how each shape is to be moved to change it from its original position to the new position. Write the explanation in the space provided. • Share explanations with the class. Discuss any alternatives or differences.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 22–23. • 150 • New Wave Maths Book C – Teachers Guide

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

Unit 33–2

Student page 98

Outcomes

Indicators

N2.3, N2.1a

Skills • exchanging money • working cooperatively

Number (N2.3)

Resources

Language

• counters • calculator • plastic coins and notes

• multiply • coins • notes • exchange • how many

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

Notes

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• Basic facts of multiplication.

Main Activity (N2.1a) Warm up

• Distribute coins and notes to small groups, allowing free play for a brief period. • Ask the groups to take turns to select a coin for the others to exchange for several coins; e.g. 20c for 2 x 10c or 4 x 5c coins or 1 x 10c and 2 x 5c coins.

What to do

• Direct the students to their workbook and ask them to exchange the coins and notes shown for the coins or notes requested. Work in the groups to assist each other.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 58–59. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 151 •

Unit 33–3

Student page 99

Outcomes

Indicators

N2.3, M2.2

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

Skills • working cooperatively • weighing • recording • analysing data

Number (N2.3)

Resources • counters • calculator • balance scales • 2-cm cubes • tennis ball, golf ball, softball, cricket ball, T-ball, beanbag • washers

Language • multiply • balance • estimate • actual • table • heaviest • lightest

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

Main Activity (M2.2) Warm up

• Arrange the class in small groups with each group to collect a balance scale, 2-cm cubes and the balls as well as the other items to weigh. • Ensure students understand how to use the balance scales.

What to do

• Set students to work in their groups to balance each item in turn against the 2-cm cubes. Record the number of cubes required. • When all balancing is complete, answer the questions. • Repeat the activity using washers. • Discuss results with the whole class.

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• Basic facts of multiplication.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 86–87. • 152 • New Wave Maths Book C – Teachers Guide

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

Unit 33—Answers

Student pages 97–99 Unit 33.2

Unit 33.1

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

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1. (a) 9 (b) 30 (c) 5 (d) 7 (e) 5 (f) 3 2. Teacher check. Answers should demonstrate the following: (a) flip vertically (b) quarter turn anticlockwise (90°) (c) quarter turn anticlockwise (or clockwise) (d) flip vertically

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• Use the shapes to fit into different outlines and explain what they needed to do.

Consolidation 33–2

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1. (a) 32 (b) 18 (c) 0 (d) 0 (e) 21 (f) 18 2. Teacher check 3. Teacher check

• Practise, in particular, the four and five times tables.

Consolidation 33–3

• Repeat using different items instead of the balls— stapler, book, empty lunch box, toy etc.

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 153 •

Unit 34–1

Student page 100

Outcomes

Indicators

N2.3

The student is able to: • use multiples (i.e. equivalent groups) to count and compare collections.

Skills • problem-solving • discussing • working cooperatively • recording • dividing • multiplying

Number (N2.3)

• counters • calculator

Language • divide • problems • how many • share • equally, • take away • sets

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

Main Activity (N2.3) Warm up

• Explain to the class there are times when we are required to solve problems. At these times we need to think about what is being asked, decide what the problem is about and how to solve it. Most problems are presented in word form.

What to do

• Work with the class as a whole on the first problem. What does it tell us? There are seven children. Each child needs three pencils. What do we need to find? The total number of pencils. How can this be done? Add seven lots of three or multiply 7 by 3. Answer is 21. • Encourage students to use Base 10 MAB or counters to assist. • Students may work in pairs or groups to develop discussion to assist in problem solving. • Share final solutions with the class. Discuss different methods of reaching the solution.

Notes

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• Basic facts of division.

Resources

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 54–55. • 154 • New Wave Maths Book C – Teachers Guide

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

Unit 34–2

Student page 101

Outcomes

Indicators

N2.3, C&D2.2

The student is able to: • apply unambiguous and familiar criteria to sequence data consistently.

Skills • ordering • analysing data • dividing • making lists

Number (N2.3)

Resources

Language

• counters • calculator • students

• divide • arrange • tallest • shortest • tenth • sixth • fourteenth

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Notes

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• Basic facts of division.

Main Activity (C&D2.2) Warm up

• This activity would be particularly applicable on days when class photographs were being taken. • Explain to students that there are times when information (data) to be collected has special importance. It is therefore necessary to know and understand ways and means of doing this. • There are times when organising people into groups or a special order is important, such as is for class photographs when each class is arranged in order from tallest to shortest.

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• Ask students to stand and line up in order from tallest to shortest. Ask neighbouring students to help with checking. Double-check the order. • List the students in order on the blackboard/whiteboard. Students copy this order into their workbooks. • Ask students to answer the questions at the end of the list. • Discuss answers.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 155 •

Unit 34–3

Student page 102

Outcomes

Indicators

N2.3, N2.1a

The student is able to: • Use multiples to count and compare collections. • read amounts of money and make up the amount with coins in different ways.

Skills • adding • multiplying • dividing

Number (N2.3)

• counters • calculator • plastic money and notes (or photocopy money on page 211)

Language • divide • how much • cost • money • multiply • add

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

Main Activity (N2.3, N2.1a) Warm up

• Distribute plastic money and notes (photocopied) to groups of students and allow a few minutes of free play.

What to do

• Tell the groups that they will be going shopping using their workbooks. They will be asked to buy a number of the same item and find the total cost of the purchase. If a toy costs $10 and you were to buy four of them, how much would they cost? ($40) • Allow the students to use the money to show how much each purchase will cost. Discuss in their groups to determine whether there is any disagreement. Once agreement has been reached, write the total cost in the space provided. • Each group member should take turns at using the notes to show the total cost. • If plastic notes are not available, print tokens or use Base 10 MAB to show $10, $20 and $50 notes—$10 as small cubes, $20 as sticks and $50 as flats.

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• Basic facts of division.

Resources

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 56–57. • 156 • New Wave Maths Book C – Teachers Guide

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

Unit 34—Answers

Student pages 100–102 Unit 34.2

Unit 34.1

1. (a) 18 (b) 3 (c) 3 (d) 24 (e) 16 (f) 28 2. Teacher check

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1. (a) 3 (b) 8 (c) 4 (d) 5 (e) 30 (f) 56 2. (a) 21 (b) 24 (c) 4 (d) 4 (e) 6 (f) 7 (g) 5 (h) 7 (i) 5 (j) 10c (k) 7 (l) 3

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• Complete similar word problems created by the teacher or themselves.

Consolidation 34–2

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Number 1. (a) 3 (b) 8 (c) 7 (d) 2 (e) 8 (f) 7 Main Activity 2. (a) $160 (b) $270 (c) $210 (d) $300 (e) $120 (f) $80 (g) $180 (h) $200 (i) $320 (j) $240 (k) $180 (l) $60 (m) $400 (n) $80 (o) $420

• Arrange the students in their class from oldest to youngest and list.

Consolidation 34–3

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R.I.C. Publications®

• Students should practise their multiplication tables if having difficulty finding the cost.

New Wave Maths Book C – Teachers Guide • 157 •

Unit 35–1

Student page 103

Outcomes

Indicators

N2.3, S2.3, S2.2

The student is able to: • use multiple copies of a simple prism to decide whether repetitions will stack or pack and make repeating patterns. • make constructions from visual instructions.

Skills • manipulating materials • making models • modifying • following instructions • addition

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencils • 2-cm cubes

Language add, copy, drawing, model, double, height, width, length, triple

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

Notes

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

• Organise the class into small groups and distribute 2-cm cubes to each group. Allow a brief period of free play. • Ask each group to take one cube and place it on the desk or floor. Make a model that is double the height. How high is it? (2 cubes) Have the width or length changed? (No). • Make a second model double the width of the first. How wide is it? (2 cubes) Have the height or length changed? (No). • Make a third model that is double the length of the first model. How long is it? (2 cubes) Have the height or width changed? (No). • In each case, only one dimension (length, width or height) has changed.

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• Explain to the students that in their workbooks is a diagram using three cubes. Make one model of the diagram using the 2-cm cubes. Make each of the models of the original as asked. Draw the model in the workbook when it has been made. (It will need to be drawn smaller.) • Keep a copy of each model for the teacher to check.

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What to do

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• Revision of addition of three single-digit whole numbers.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 4–5. • 158 • New Wave Maths Book C – Teachers Guide

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

Unit 35–2

Student page 104

Outcomes

Indicators

N2.3, N2.1b

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. • use halving based on symmetry as the basis for partitioning continuous quantities into 4 parts and 8 parts.

Skills • working cooperatively • sharing

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • fraction cake • pencil • ruler • boxes of Smarties™ (or similar)

• add • divide • parts • equal share • whole

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

Notes

Teac he r

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• Revision of addition of three single-digit whole numbers and two two-digit whole numbers, the latter with no regrouping.

Main Activity (N2.1b) Warm up

• Ask four students to stand at the front of the class. Give one of them a bag of small boxes of Smarties™ or similar, use Base 10 MAB longs if preferred. Ask the student how he or she will share the whole packet with the others. Being a caring, sharing child this will be done equally! Share the goods.

What to do

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• Organise the class into small groups and provide each group with a fraction cake. Ask each group to choose or show how they would share a whole cake with a total of four people and another with a total of three people. • Explain that each part is part of a whole and each part has a name depending on how many parts a whole is divided into. Ask the name of each part if a whole is divided into two equal parts; three equal parts; four equal parts; five equal parts; eight equal parts; or ten equal parts. • Direct students to complete the activities in their workbook.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 28–29. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 159 •

Unit 35–3

Student page 105

Outcomes

Indicators

WM2.2, WM2.3

The student is able to: • ask questions about collected objects or pictures. • compare ways of representing a problem. • offer suggestions in response to ‘What would happen if…’ questions. • make conjectures about shapes and measurement.

Skills • discussing • problem-solving • explaining • cooperating

Resources • calculator • pencil

Language • counting • brainstorm • decide • decision • problem

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

Main Activity (WM2.2, WM2.3)

• The aim of the activity is for students to devise a method to find the best way to count the money displayed on the page. • This activity is designed for students working collaboratively in groups. As students will need to discuss their opinions and ideas, allow enough time so they do not feel rushed and for their ideas to evolve. Open-ended tasks such as these are a good opportunity for students to ‘take a risk’ with maths. When completing such tasks, some students may be more successful in mixed-ability groups rather than same-ability groups. • Encourage students to think divergently and to explore all options. • Some groups will be able to work independently while others may need guidance. • When each group has decided on the best way to count the money, members can use words and pictures/diagrams to write their explanation in their workbooks. • Students can then share their ideas with the class. Record findings on the blackboard/ whiteboard and discuss each method. • After discussion, students decide whether their original method is still the best way to count the money. • Direct students to consider how they would count the money if they were blindfolded. This could be done in groups, with partners or individually. Share findings as a class.

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What to do

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• 160 • New Wave Maths Book C – Teachers Guide

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

Unit 35—Answers

Student pages 103–105

Unit 35–1

1. (a) $13 (b) 17c (c) 18c (d) 87c (e) 79c (f) $79 2. Teacher check 3. whole, half, one third, one fourth (quarter)

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1. (a) 8c (b) 9c (c) $9 (d) $8 (e) $18 (f) $17 2. Teacher check 3.

Unit 35–2

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Answers will vary. These could include: • sorting into gold and silver coins and adding the total • sorting into coin values, adding these and combining all totals. 2. Teacher check 3. Teacher check 4. Answers will vary. Most students will say to feel the money and sort by size and shape.

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• Make a simple model of their own using at least three and no more than six cubes and repeat the activity.

Consolidation 35–2

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• Cut food from their lunch boxes or use fruit to cut into equal shares.

Consolidation 35–3

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R.I.C. Publications®

• Work out the best way to count Smarties™ in a box.

New Wave Maths Book C – Teachers Guide • 161 •

Unit 36–1

Student page 106

Outcomes

Indicators

N2.3, N2.1a, N2.1b

The student is able to: • see the need to check that the ‘halves’ are the same size and attempt to monitor portions. • count coins, including in multiples of 5c, 10c, 20c, 50c, $1 and $2, and record total amounts.

Skills • working cooperatively • sharing information • converting money • subtracting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • plastic coins

• subtract • half • double

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

• Organise the class into small groups and distribute plastic coins. Allow a brief period of free play.

What to do

• Ask the group to take out a 20c, $1, 50c and 10c coin. Using other coins below each, show half the value of the given coin. Below that again, show double the value of the original coin. Ask a member of the group to explain what the group has shown. Ask for any other answers. • Set the class to work on the activities in the workbook. Encourage students to discuss their findings.

Notes

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• Revision of subtraction of one- and two-digit whole numbers from a two-digit whole number with no regrouping.

Teac he r

Language

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• 162 • New Wave Maths Book C – Teachers Guide

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

Unit 36–2

Student page 107

Outcomes

Indicators

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

The student is able to: • offer suggestions about how to classify objects or information. • comment on information in displays of data produced by themselves and peers.

Skills • gathering data • collating information • recording • analysing data • subtracting

Number (N2.3)

Resources

Language • subtraction • Carroll diagram • preferences • more • how many • differences

• Base 10 MAB or counters • calculator • student footwear • students

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

Notes

Teac he r

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

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• Revision of subtraction of a two-digit whole number from a two-digit whole number with no regrouping.

• Explain to the class that a Carroll diagram is a useful way to compare selected items, or a collection of different information from a set collection of items.

What to do

• In the workbooks, information on the type of footwear worn by boys and girls separately is to be collected. Ask boys with shoes to stand in the correct line (check recording is correctly completed). Continue for the rest of the footwear for boys. Repeat this process for the girls’ footwear. • The second diagram calls for information about boys and girls and whether they are left- or right-handed. Collect the information as above. • Answer the questions on the page, either individually or as a whole class.

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

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 163 •

Unit 36–3

Student page 108

Outcomes

Indicators

N2.3, N2.4, WM2.2

The student is able to: • ask questions about collected objects or pictures following the modelling questions of their teacher. • describe a rule which could have been used to generate an adding or subtracting number sequence and test.

Skills • discussing • problem-solving • exploring • explaining • subtracting

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencils

Main Activity (N2.4, WM2.2) Warm up

• Develop discussion among students as to how they could find out whether there was more of one item than another in a collection of two different items, without counting the total number of each different item. • Encourage students to think divergently and to explore all options.

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Teac he r

• subtraction • counting

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

• Revision of subtraction of one- and two-digit whole numbers from a two-digit whole number with no regrouping.

What to do

Language

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• Issue groups of students with two sets of different coloured counters and ask them to trial suggestions and explore other options. • Put into practice the preferred option by finding whether there are more dots than crosses shown on the page in the workbook. • Ask students to write their explanation on the page.

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• 164 • New Wave Maths Book C – Teachers Guide

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

Unit 36—Answers

Student pages 106–108

Unit 36–1

1. (a) $45 (b) 30c (c) $40 (d) $51 (e) 25c (f) 73c 2. Teacher check 3. Teacher check

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Teac he r

1. (a) $4 (b) $1 (c) 52c (d) 83c (e) 22c (f) $7 2. (a) 50c (b) 25c (c) $1 (d) 40c (e) 60c (f) $2 3. $4 4. $1.75 5. $7.70

Unit 36–2

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• Brainstorm other ideas to record using a Carroll diagram.

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• In pairs, continue to solve halving and doubling quantities of coins.

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1. (a) $30 (b) 50c (c) $25 (d) 11c (e) 44c (f) $23 2. Teacher check

Consolidation 36–3

• Encourage divergent thinking in other mathematical 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®

New Wave Maths Book C – Teachers Guide • 165 •

Unit 37–1

Student page 109

Outcomes

Indicators

Resources

N2.3, S2.1

The student is able to: • find paths on informal maps and mazes.

• counters • calculator • coloured pencils • street directory or town plan

Skills • working cooperatively • reading maps • following paths • problem-solving • drawing • multiplying

Number (N2.3)

Language • multiply • map • path

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

Notes

Main Activity (S2.1) Warm up

• If available, provide small groups with a copy of a street directory or a plan of the town or locality. • Ask students to open the directory at the page that shows their school. • In groups, ask the students to find the local school and any other significant features—shops, other schools, ovals, sporting or recreation facilities etc. • Allow the groups to explore ways of moving between given locations. Share group suggestions with all groups. Discuss why different paths were taken.

• Using the experience of following paths within their own locality, students are to plan and draw the path they would follow, as individuals, on the Daytown map provided in the workbook. • Share the path with other group members and discuss why there were different choices, if there were any.

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What to do

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Teac he r

• Revision of basic facts of multiplication.

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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 C – Teachers Guide

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

Unit 37–2

Student page 110

Outcomes

Indicators The student is able to: • attempt to produce equal shares of discrete quantities through dealing out and counting.

N2.3, N2.1b

Skills • working cooperatively • problem-solving • displaying fractions • discussing • sharing solutions • dividing

Number (N2.3)

Resources

Language

• counters • calculator • coloured pencils • ruler • paper streamers

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

• divide • separate • equal parts • part of • diagram • quarters • fifths • half

Notes

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Teac he r

• Revision of basic facts of division.

Main Activity (N2.1b) Warm up

• Distribute previously cut lengths of paper streamers to small groups of students. • Ask students, in their group, to show two equal parts of a streamer by folding it. Use another streamer to show three equal parts by folding and a third to show four equal parts by folding. • Explain in each case what was done and how it was done.

What to do

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• Turn to the workbook and complete the activities shown. Encourage groups to work together to assist each other in finding the answers. • Share answers from each group with the whole class. Ask students to explain how they reached their answer.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 30–31. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 167 •

Unit 37–3

Student page 111

Outcomes

Indicators

Resources

N2.3, M2.2, WM2.3

The student is able to: • compare the area of two regions directly by superimposing one over the other. • offer suggestions in response to ‘What would happen if…’ questions pitched at or just beyond their mathematical level.

• Base 10 MAB or counters • calculator • 1-cm cubes • 2-cm cubes • cardboard cutouts in a variety of shapes

Skills • estimating • discussing • measuring • comparing • checking • explaining • adding

Number (N2.3)

Language • add • cover • shapes

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

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

• Organise the class into small groups and distribute 1-cm and 2-cm cubes as well as cardboard cut-outs to each group. • Ask the class to find out which shape has the biggest area. Use the cubes to find out. • Discuss the results. Does it make a difference which cubes you use? • Ask if there is another way of comparing area by direct comparison.

What to do

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Teac he r

• Revision of addition of two and three two-digit whole numbers with no regrouping.

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• Direct students to their workbook and ask them to consider the question posed there. • Write answers in the space provided. • Use 2-cm and 1-cm cubes to check estimates. • Write an explanation to explain the findings and any difference from the original estimation. If original estimate was correct, write an explanation for their findings.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 80–81. • 168 • New Wave Maths Book C – Teachers Guide

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

Unit 37—Answers

Student pages 109–111

Unit 37–1 1. (a) 18c (b) 14c (c) $32 (d) $25 (e) 36c (f) $27 2. Teacher check

Unit 37–2 1. (a) $9 (b) $7 (c) 9c (d) $3 (e) 5c (f) $8 2.

r o e t s Bo r e p ok u S 5. 6.

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Teac he r

7. (a) 2 (b) 8 (c) 5 (d) 10 (e) 3 (f) 11 (g) 4 (h) 15

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• As a class, devise a list of other paths to take. In pairs, students choose three of the paths and use different coloured pencils to show each. Compare results.

Consolidation 37–2

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• Practise cutting various sized pieces of scrap paper into stated equal parts. Include squares, rectangles, circles etc.

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R.I.C. Publications®

Consolidation 37–3

• Write up the results of the activities in the warm up. Draw a diagram to show the shape and write the number of 1- and 2-cm cubes used.

New Wave Maths Book C – Teachers Guide • 169 •

Unit 38–1

Student page 112

Outcomes

Indicators

N2.3

The student is able to: • use a calculator (if necessary) to add and subtract numbers arising in daily activities, entering subtractions in the correct order.

Skills • using a calculator • subtracting • discussing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator

Language • add • subtract • number sentences • constant

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

Notes

Main Activity (N2.3) Warm up

• Using their calculator, ask students to enter 15 – 5 = ; 23 – 5 = ; 13 – 5 =; 25 – 5 = ; 22 – 5 = ; 32 – 5 = ; and explain the answers. (May need 32 – 5 = = = as keystrokes vary among calculator models.) • Look for the terms ‘constant’, ‘same’ to describe the final digit when subtracting a constant and the unit number is the same. • Ask if students really need a calculator. Try without to find the answers to these: 27 – 5 = ; 37 – 5 = ; 17 – 5 = ; 46 – 5 = ; 26 – 5 = ; 16 – 5 = ; 21 – 5 = ; 41 – 5 = ; 31 – 5 = .

What to do

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Teac he r

• Revision of addition of three one- and two-digit numbers with no regrouping.

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• Without using a calculator, try to find the answers to the number sentences in the workbook.

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• 170 • New Wave Maths Book C – Teachers Guide

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

Unit 38–2

Student page 113

Outcomes

Indicators

Resources

N2.3, C&D2.3, S2.4

The student is able to: • make graphs and plots using oneto-one correspondence between ‘real’ data and a representation. • respond to ‘Tell me about the shape of this’, using language such as ‘curved’, ‘straight’ etc.

• Base 10 MAB or counters • calculator • plastic shapes to match those in the workbook • mira

Skills • sorting • classifying • categorising • using miras • adding

Number (N2.3)

Language • add • shapes • diagram • symmetrical • straight edges • curved edges • non-symmetrical

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

Notes

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Teac he r

• Revision of addition of whole numbers with no regrouping.

Main Activity (C&D2.3, S2.4) Warm up

• Organise the class into small groups and distribute a variety of shapes to each group for their free investigation. • Ask students to sort the shapes into those that are symmetrical and those that are not symmetrical. Discuss line of symmetry—each side of the central line is a mirror image of the other. (Some shapes will have several lines of symmetry.) If you have access to miras, distribute these to the groups to use. When placed on the centre of a shape, the image seen in the mira should be superimposed over the half of the shape seen.

What to do

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• Sort the set of shapes in the workbook in the same way, then make a subset of each set with straight edges and one with curved edges.These two sets are then sorted into those with only straight edges, those with only curved edges and those with straight and curved edges. • Repeat for the non-symmetrical set.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 14–15. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 171 •

Unit 38–3

Student page 114

Outcomes

Indicators

N2.3, N2.4, WM2.2

The student is able to: • write a pattern of numbers to fit a particular pattern and use it to predict the number needed for later terms. • represent a problem with concrete materials.

Skills • working cooperatively • finding patterns • making structures • discussing

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • 2-cm cubes • coloured pencils

Language • add • pattern • blocks • first • fifth • fourth • grid • second • third

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

Main Activity (N2.4) Warm up

• Arrange the class into small groups, each group to have access to 2-cm cubes. Allow a brief period of free play.

What to do

• Ask students to arrange three blocks in the pattern shown in their workbook. How many blocks used in each step arrangement? (3, 6, 10) • Ask how many blocks are likely to be needed for the next step. Listen to answers. Ask for reasons. Some students may identify the pattern—rows of 1, 2, 3, 4—next will be 5, making a total of 15. • Allow students to build and find out for both the fourth and fifth steps. Find the total of all blocks used to build all four steps. • Use coloured pencils to design a pattern on the grid. Remind students that the first and second items are the same and the third and fifth items are the same. • Display and discuss patterns.

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Teac he r

• Revision of addition of whole numbers with no regrouping.

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• 172 • New Wave Maths Book C – Teachers Guide

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

Unit 38—Answers

Student pages 112–114

Unit 38–1

1. (a) 79 (b) 69 (c) 87 (d) 173 (e) 366 (f) 499 only straight edges 2. 6, 9

straight edges symmetrical

1, 3, 4, 5, 6, 9, 10

1, 5, 6, 9

straight & curved

1, 5

curved edges

1, 3, 4, 5, 10

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only curved edges

3, 4, 10 only straight edges

straight edges

non-symmetrical

2, 7, 8, 11

curved edges

straight & curved

2, 7, 11

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Teac he r

1. (a) 87 (b) 88 (c) 67 (d) 98 (e) 88 (f) 77 2. (a) 55 (i) 71 (q) 12 (b) 66 (j) 39 (r) 89 (c) 48 (k) 22 (s) 7 (d) 65 (l) 18 (t) 34 (e) 77 (m) 83 (u) 79 (f) 43 (n) 2 (v) 26 (g) 85 (o) 42 (w) 36 (h) 27 (p) 68 3. (a) 3 (i) 14 (q) 73 (b) 53 (j) 6 (r) 54 (c) 24 (k) 75 (s) 46 (d) 11 (l) 86 (t) 64 (e) 37 (m) 1 (u) 23 (f) 44 (n) 82 (v) 32 (g) 61 (o) 19 (w) 76 (h) 58 (p) 41 4. The number in the tens column decreases by 1 but the value decreases by 10.

Unit 38–2

2, 7, 11

only curved edges

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• Take away a different constant—e.g. ‘8’—and solve problems with a calculator at first and then without when a pattern emerges.

Consolidation 38–2

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1. (a) 677 (b) 367 (c) 757 (d) 896 (e) 988 (f) 697 2. (a) 15 (b) 21 (c) 34 3. Teacher check 4. Teacher check

• Draw other shapes and use to complete the same activity.

Consolidation 38–3

o c . che e r o t r s super

R.I.C. Publications®

• Design different grid patterns and describe the pattern.

New Wave Maths Book C – Teachers Guide • 173 •

Unit 39–1

Student page 115

Outcomes

Indicators

N2.3, S2.1, WM2.2

The student is able to: • place important things in their environment in order on their map. • pose questions suggested by collected data.

Skills • drawing • mapping • observing • recording • locating features • discussing • working cooperatively • subtraction

Number (N2.3)

Resources • Base 10 MAB or counters • calculator • pencils • ruler

Language • subtract • map • features • located • correct place

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

Notes

Main Activity (S2.1, WM2.2) Warm up

• Take the class for a walk around the school. Ask students to identify key features—buildings, play area, oval, gardens etc. Perhaps take a clipboard and paper and make notes or even rough sketches to remember where various features are and their proximity to each other.

What to do

• On return to class, ask students to locate the features they observed on the page in their workbook. Each feature should be in as close a placement to its true location as possible. • Allow students to discuss placement of features with each other. Completing the exercise in small groups may be beneficial. • Display and discuss (if necessary) final drawings.

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Teac he r

• Revision of subtraction of whole numbers with no regrouping.

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• 174 • New Wave Maths Book C – Teachers Guide

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

Unit 39–2

Student page 116

Outcomes

Indicators

N2.3, N2.1b

The student is able to: • use halving based on symmetry as the basis for partitioning continuous quantities into parts. • understand that constructing a number of fair shares from a whole requires splitting all of the whole into equal parts.

Skills • subtraction • identify fractions • finding equivalent fractions

Number (N2.3)

Resources

Language

• Base 10 MAB or counters • calculator • fraction cake • paper (recycled) • coloured rods

• subtract • fractions • quarters • fourths • half • equivalent • fractions

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

Notes

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Teac he r

• Revision of subtraction of whole numbers with no regrouping.

Main Activity (N2.1b) Warm up

• Distribute fraction cakes and/or coloured rods to groups of students. Allow students time for free play.

What to do

• Direct students to display two objects that show halves of a whole; for example, two white rods that make one red rod. Ask students to explain how the objects show halves. • Ask students to show four quarters and two halves with the objects, each showing the same whole; for example, four rods equivalent to two rods equivalent to one rod. Explain what is shown. Ask ‘How many quarters?’, ‘How many halves?’, ‘How many quarters make one half?’ • The diagram in the workbook shows the same. Fill in the answers. • Distribute a sheet of paper to each student. Ask them to fold the paper in half, then in half again. Open the paper out and colour one half. Colour a separate quarter. Discuss what is shown. A quarter is half of a half, or two quarters equal a half. • Write an explanation of what was done. • Use coloured pencils to colour the fractions shown. Students may need specific guidance. Discuss what is shown—equivalent fractions.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 30–31. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 175 •

Unit 39–3

Student page 117

Outcomes

Indicators

N2.3, M2.1

The student is able to: • select or reject units as relating or not relating well to the attribute to be measured.

Skills

Resources • Base 10 MAB or counters • calculator

• discussing • subtracting • identifying units of measure

Number (N2.3)

Language • subtract • measure • width • surface • volume • time • metres • millilitres • grams • kilogram • minutes

• units • length • distance • capacity • mass • centimetres • square units • litre • hour • seconds

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

Main Activity (M2.1) Warm up

• Hold a general class discussion on units of measures. length—metres, kilometres, centimetres, millimetres area—number of shapes, squares, square centimetres, square millimetres capacity/volume—litres, millilitres mass—grams, kilograms, tonnes time—hour, minute, seconds, day, week, month, year • Ask students to give examples of what they might measure using these units. Encourage a range of ideas—discuss to determine whether the correct units have been selected.

What to do

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Teac he r

• Revision of subtraction of whole numbers with no regrouping.

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• Set students to work independently or in small groups to select the units of measure they would use to measure the items selected in the workbook.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 74–75. • 176 • New Wave Maths Book C – Teachers Guide

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

Unit 39—Answers

Student pages 115–117

Unit 39–1 1. (a) 60 (b) 14 (c) 32 (d) 62 (e) 42 (f) 54 2. Teacher check

Unit 39–2 1. (a) 31 (b) 42 (c) 10 (d) 10 (e) 40 (f) 40 2. (a) 2 (b) 2 3. Teacher check 4. (a) (c)

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(d)

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Teac he r

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• Complete Exercise 4 using rectangular shapes.

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• Repeat the activity using their home or apartment block, relative’s block etc.

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1. (a) 50 (b) 400 (c) 400 (d) 200 (e) 320 (f) 200 2. Teacher check

Consolidation 39–3

• Discuss the selection of units of measure used. Make a list of the best answer for each. (Some may have more than one answer.)

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R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 177 •

Unit 40–1

Student page 118

Outcomes

Indicators

N2.3

The student is able to: • use a calculator to add and subtract numbers arising in daily activities, entering subtractions in the correct order.

Skills • working cooperatively • using a calculator • recording • multiplying

Number (N2.3)

Resources • counters • calculator

Language • multiply • lots of • how many • sets of • share • equal parts • divided

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

Notes

Main Activity (N2.3) Warm up

• Arrange the class into groups and distribute Base 10 MAB and counters. Allow a brief period of free play then ask students to make sets of equal numbers of items and find the total. Each student should take turns at making the sets—e.g. 3 lots of 4—and finding the total. Other group members check the accuracy. • As a whole class, use the calculator to find 5 lots of 6; 7 lots of 4; and 3 lots of 9.

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• Turn to the workbook. Work through the first example of each exercise with the whole class before allowing the group to work together to complete the exercises. • Use the Base 10 MAB or counters to make 7 lots of 3. How many altogether? Record your answer. • How many sets of 7 make 21? How could you find out? Calculator: enter 21 ÷ 7 = . Take 7 counters, another 7 and so on until you have 21 counters. • Share 24 among 4. Use a calculator (24 ÷ 4 = ) or counters to share 24 into 4 equal groups.

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What to do

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Teac he r

• Revision of 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 56–57. • 178 • New Wave Maths Book C – Teachers Guide

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

Unit 40–2

Student page 119

Outcomes

Indicators

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. • read and compare frequencies from lists and simple one way tables.

Skills • collecting data • collating information • recording data • analysing data • reasoning

Number (N2.3)

Resources

Language

• counters • calculator • class survey

• multiply • Venn diagram • survey • results • most • least

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

Notes

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

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Teac he r

• Revision of basic facts of multiplication.

• Revise Venn diagrams as a series of circles used to record information. Where one item has two records this is recorded in the overlap of the two circles. • Survey the class to find who likes a dog as a pet—record their initials on the blackboard/ whiteboard as a list. Repeat for a cat as a pet and a bird as a pet. • Ask students to identify any initials that are in both the dog and the cat list—circle these with a colour. Repeat for dog and bird using a different colour; cat and bird using a different colour; and dog, cat and bird using a different colour.

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• Students can now record those uncircled students in the dog, cat or bird circles. Follow the same procedure for the other parts of the Venn diagram. • What should happen to students without pets? Record outside the circles. • Answer the questions.

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For a relevant assessment activity refer to RIC-0029 Maths Assessment – Level 2 pages 104–105, 108–109. www.ricpublications.com.au

R.I.C. Publications®

New Wave Maths Book C – Teachers Guide • 179 •

Unit 40–3

Student page 120

Outcomes

Indicators

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 on a hundred chart with an adding rule.

Skills • collecting data • recording • graphing • counting • discussing • dividing

Number (N2.3)

Resources • counters • calculator • coloured pencils

Language • divide • record • graph • multiples • grid • problems • nearest

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

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

• Explain that the activities in the workbook are varied and are a revision of several activities. Some students may like to complete the activities on their own and others may need more guidance.

What to do

• Students could say the alphabet with a partner—one letter each per turn. Complete the alphabet activity. • Ask students how Exercise 3 could be completed without using a calculator. (Every seven days from 5 June would be a Monday; i.e. 5, 12, 19 and 26 June.) Count days forwards or backwards from the closest date. • Students can attempt the activity but some may need more help, to work in pairs or make a June calendar with Monday being the 5th to refer to. • For Exercise 4 use coloured pencils to colour the multiples of 5. To ensure the students understand what multiples of 5 are, remind them that they are the answers to the 5 times table. Have students chant the 5 times table and/or count by fives from 5 to 50. • Colour the grid. • Work out the answers to the sums shown (write the answers in the workbook). Place a counter on each of the answers on the grid. • Move the counters to the nearest coloured square. Ask students how they chose the nearest coloured square. Develop the discussion if there is any need.

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Teac he r

• Revision of basic facts of division.

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• 180 • New Wave Maths Book C – Teachers Guide

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

Unit 40—Answers

Student pages 118–120

Unit 40–1

1. (a) 40 (b) 20 (c) 0 (d) 0 (e) 36 (f) 24 2. Teacher check

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Teac he r

1. (a) 8 (b) 27 (c) 18 (d) 12 (e) 24 (f) 20 2. (a) 21 (b) 600 (c) 90 (d) 36 (e) 1600 (f) 30 3. (a) 3 (b) 3 (c) 9 (d) 6 (e) 4 (f) 9 4. (a) 6 (b) 300 (c) 7 (d) 8 (e) 10 (f) 7

Unit 40–2

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• Describe different number problems than those used in the activity in words. Work in pairs.

Consolidation 40–2

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1. (a) 2 (b) 3 (c) 6 (d) 3 (e) 7 (f) 6 2. (a) e (b) i (c) l (d) s (e) y (f) p (g) r (h) h 3. (a) Sunday (b) Saturday (c) Sunday (d) Monday (e) Monday (f) Thursday (g) Wednesday (h) Friday 4.

• Brainstorm other things to record. Survey results of three items; for example, three meals, colours or sports.

Consolidation 40–3

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• Complete Exercise 3 using a different month and given day; for example, the 3rd day of April is a Friday.

New Wave Maths Book C – Teachers Guide • 181 •

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

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New Wave Maths Book C – Teachers Guide • 183 •

Space Activities

S2.2

8. If obtainable, use a plan of the town or local area, to have students see where different facilities are located and give reasons as to why they are located where they are.

1. Use 1-cm grid paper to draw as many different rectangles as possible. It may be helpful to draw each rectangle using a different colour. Discuss the features of the rectangles. 2. Build shapes using different materials: • straws and joiners; • interlocking pieces; or • construction sets. Encourage and use appropriate terminology to discuss the attributes of the structures.

3. Introduce symmetry in the shapes students use and follow up with symmetry that may be identified in objects in the classroom. 4. Use 1-cm dot paper on page 198 of the New Wave Maths Teachers Guide to draw shapes that will enclose 3, 4, 5 or 6 dots. What shapes are made? Can one particular shape, for example, triangle, be drawn to enclose 3, 4, 5 or 6 dots? Draw the shape to find out. Try with other shapes. 5. Each student is given a balloon and a felt-tip pen to draw a straight line on the balloon. Inflate the balloon. Discuss what happens to the line. Let the balloon down and note what happens to the line. Draw a simple picture or shape on the balloon. Re-inflate the balloon. Describe what has happened to the picture or shape. Students suggest what will happen when they let their balloon down. Check to see if the suggestion is correct. 6. Select a number of 2-D shapes cut from thin card or commercial plastic shapes. Suggest what shadows can be made using projections, from an overhead projector, of the shapes. Check to see if the predictions were correct. Experiment to see what other shadow shapes can be made by projecting the shadows using the overhead projector and the same shapes. 7. Students experiment with blocks by making simple models then explore: • doubling, trebling height; • doubling, trebling width; • doubling, trebling length. Describe the result each time.

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1. 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 given purposes. 2. Give directions to move from one point of the school to another. 3. Play games during physical education that require students to stay within boundaries and follow given instructions. 4. Students describe how they can move from a given point (classroom) to another given point within the school (office) by the shortest route and by an alternative route. 5. Use the town map on page 224 of the New Wave Maths Teachers Guide for students to show the paths they would take to leave the school and go to the pet shop, to the park and finish at the library. 6. Use the town map for students to show the paths they would take to go from the lake to the deli, to the school and finish at the church. 7. Look at the town map. Ask students what shapes or close to the shape, do most of the streets make? Why do they think this is so? What other shapes are used? Explain how they think this would be useful in designing a town. Students may be asked to design a simple town plan using streets to make their preferred choice of shape. After designing the town it may be more practical to discuss the benefits or problems with the design.

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• 184 • New Wave Maths Book C – Teachers Guide

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8. Students make models of familiar structures; for example, home or school. When making the models, students should be encouraged to use materials that give approximate representation of differences in size of components of the structures they are modelling.

Space Activities cont. S2.3

1. Use 1-cm grid paper to make patterns by colouring on predetermined instructions given by the teacher. For example: • colour every second row coloured red; • colour every fifth column coloured green; or • colour every fourth square coloured blue; or • 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.

1. Use 3-D shapes to familiarise students with edges, corners and faces. 2. Investigate shapes made by cutting modelling clay into models of 3-D shapes. 3. 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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4. Students draw floor plans of the external walls of familiar buildings or draw the floor plans of familiar rooms. Discuss the shapes used and try to determine why these shapes are the most common.

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2. 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. 3. 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.

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New Wave Maths Book C – Teachers Guide • 185 •

Measurement Activities M2.1

1. Students arrange a set of objects in order from heaviest to lightest by hefting. Check ranking by using balance scales. Objects may be randomly chosen by students or specifically selected by the teacher. 2. Fill boxes of different dimensions with 2-cm cubes to see whether tall boxes may hold more cubes than short, long boxes. 3. Students arrange a set of objects in order from heaviest to lightest by hefting, using a set of objects that are all the same size but filled with different materials. Compare the mass of each using balance scales. (Containers may be honey, yoghurt etc.) Repeat with the same material but different sized containers. (Use sand for simplicity.)

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What conclusions may be drawn from this source of activities? M2.2

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1. Free play pouring water or sand from one container to another to compare capacity of each container. Students will need to have available a wide range of containers they can use. 2. Repeat above but provide some direction. Order the containers used from the one that holds the most to the one that holds the least. 3. Use 20 x 2-cm cubes to build the tallest building they can. Repeat for the longest, and making any other shapes the students can using only the 20 cubes. 4. Students will need a variety of containers and a range of materials to fill the containers; for example, rice, water, sand, peas or beans. Compare the capacity of one container directly with another by pouring the contents of one into another. 5. Use a piece of wool to make a shape. How many 2-cm cubes can be fitted inside the shape? Make other shapes and check whether they can cover the inside of the shapes with the same or a different number of 2-cm cubes. 6. Provide a clear container and a range of objects to be placed in the container when partially filled with water. Partly fill a clear container with water. Mark the water level on the outside of the container with felt-tip pen. Place an object in the container. Mark the water level now. Remove the object and repeat the process with a number of different objects. Have students suggest what to do if an object they have chosen floats. 7. Repeat the above activity but fill the clear container to the top before placing the object into the water. Stand the container in a larger container so the overflow can be collected. Measure the amount of overflow collected. 8. Make a shape from a piece of modelling clay and place in a container partly filled with water. Mark the original water level and the new water level. Remove the modelling clay and ensure the water level is at its original mark. Now reshape the modelling clay. Do not add or take any modelling clay from the original shape. Repeat the process with the new shape. Mark the water level. Repeat this several times and give a reason for the results they find. 9. Balancing different objects on a 'seesaw' balance allows for direct comparison of the mass of two different objects. Use commercial balance scales or have students find a means of constructing their own balance scale and justify its usefulness. 10. Students measure and record their mass at the beginning of each term and the end of the year using bathroom scales, with help from the teacher. Results may be charted or graphed with changes noted on the graph, using a different colour.

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This activity may be done in conjunction with measuring students' heights at the same time and recording them in the same manner.

• 186 • New Wave Maths Book C – Teachers Guide

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Measurement Activities cont. M2.3

1. A set of packages of varying sizes filled with different materials intrigues young students. Range from matchbox to shoe box in size. Focus may be on estimating and finding the heaviest or lightest package, or two that have the same or very similar mass.

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2. Students to be directed to estimate, then lift two different objects to compare the mass. Use relatively large objects, but initially with a noticeable difference in mass. Repeated practice will enable the hefting activities to be done with objects that have less difference in their mass.

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New Wave Maths Book C – Teachers Guide • 187 •

Number Activities

N2.1b N2.2

1. 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. 2. Play games using the 0–99 and 1–100 grid charts on page 202.With a partner, students can take turns in covering a number(s) on the grid with a counter and guessing the number(s). 3. The number lines on page 205 of New Wave Maths Teachers Guide can be distributed to students to assist in counting activities. 4. Use plastic coins or photocopy the notes and coins on page 211 of New Wave Maths Teachers Guide. Students can participate in shopping activities.

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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. 3. Practise using addition/subtraction relationships to solve sets of related number statements. For example; 5 + 3 = 8 so 5 = 8 – 3 and 3 = 8 – 5 and 5 + 3 = 8 so 15 + 3 = 18 and 15 + 13 = 28 4. Practise using multiplication/division relationships to solve sets of related number statements. For example; 4 x 5 = 20 so 5 x 4 = 20 and 4 x 5 = 20 so 20 ÷ 5 = 4 and 20 ÷ 4 = 5

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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. 3. Use a calculator to add and subtract numbers arising from everyday activities. (Ensure students enter numbers in the correct order.) For example; count the total number of students in classes going on an excursion.

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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. 3. Use coins to make money patterns. 4. Use the constant function on a calculator to extend a pattern of numbers beyond their scope.

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

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New Wave Maths Book C – Teachers Guide • 189 •

Student Outcomes Working Mathematically WM2.1 The student describes some of the ways self, friends and family use ideas about space, number, measurement and chance in daily life. WM2.2 The student poses mathematical questions prompted by similar or related questions and represents questions using objects, pictures, symbolic statements or mental images.

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S2.1 The student attends to order and betweenness on informal maps and in descriptions of locations and paths.

C&D2.3 The student displays and summarises data based on one-to-one correspondence between data and representation. C&D2.4 The student describes what own and classmates' displays of data show.

S2.2 The student meets simple criteria relating to shape or structure in making and drawing things, making recognisable copies of arrangements of shapes.

Number © R. I . C.Pu bl i cat i ons N2.1a The student reads, writes, says and counts with whole numbers to beyond 100, using them to • f o rr ev ew ur p osesonl y• S2.3 The student uses multiple copies of i shapes to p compare collection sizes and describe order. construct repetitive patterns and follows and describes simple movement rules for generating such patterns.

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.

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S2.4 The student sorts things according to everyday spatial criteria and, prompted, uses spatial language to describe the shape of things.

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N2.1b The student understands the meaning of 'half' and 'quarter', splitting quantities into 'fair' shares and partitioning quantities repeatedly into halves.

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C&D2.1 The student distinguishes possible from impossible events, and describes familiar, easilyunderstood events as being more likely or less likely to happen.

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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.

M3.4b The student attends informally to scale when making and using plans, maps and models. Chance and Data

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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.

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.

N2.2 The student understands the meaning and connections between counting, number partitions, addition and subtraction and uses this understanding to represent situations involving all four basic operations.

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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.

• 190 • New Wave Maths Book C – Teachers Guide

N2.3 The student counts, partitions and regroups in order to add and subtract one- and two-digit numbers, drawing mostly on mental strategies for one-digit numbers and a calculator for numbers beyond their present scope. N2.4 The student recognises, continues, represents and describes patterns involving counting, grouping and constant addition or subtraction of whole numbers. Extracted from Mathematics Outcomes and Standards Framework – Student Outcome Statements, Education Department of Western Australia 1998. R.I.C. Publications® www.ricpublications.com.au

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Space—Record Sheet

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New Wave Maths Book C – 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. 7. Attach the proforma to the appropriate workbook page. 8. Record evaluation as required.

Date

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Demonstrated Needs Further Indicators Opportunity

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Photocopiable Resources

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Grid Paper ............................................................................................................................... 198–201 Number Charts and Cards ............................................................................................ 202–204 Number Lines ................................................................................................................................... 205 Place Value Charts ......................................................................................................................... 206 Spinners – Blank ..................................................................................................................... 207–208 Calendar – Any year .......................................................................................................................... 209 Clocks .................................................................................................................................................... 210 Money ................................................................................................................................................... 211 Bingo Cards ............................................................................................................................. 212–215 Sorting Circles ........................................................................................................................ 216–217 Venn Diagram – Blank ................................................................................................................... 218 Carroll Diagram – Blank ................................................................................................................ 219 Line or Bar Graph – Blank ........................................................................................................... 220 3-D Shapes ......................................................................................................................................... 221 Tangrams ............................................................................................................................................. 222 Graph and Table – Blank .............................................................................................................. 223 Map ......................................................................................................................................................... 224

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1-cm dot grid paper.

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2-cm grid paper.

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1-cm triangle grid paper.

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100 Chart

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

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70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 • 202 • New Wave Maths Book C – Teachers Guide

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Basic Facts

0 1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10

3 0 3 6 9 12 15 18 21 24 27 30

4 0 4 8 12 16 20 24 28 32 36 40

5 0 5 10 15 20 25 30 35 40 45 50

6 0 6 12 18 24 30 36 42 48 54 60

7 0 7 14 21 28 35 42 49 56 63 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

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2 0 2 4 6 8 10 12 14 16 18 20

3 0 3 6 9 12 15 18 21 24 27 30

4 0 4 8 12 16 20 24 28 32 36 40

5 0 5 10 15 20 25 30 35 40 45 50

6 0 6 12 18 24 30 36 42 48 54 60

7 0 7 14 21 28 35 42 49 56 63 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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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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5 1

41 42 43 44

11 12 13 14

r o e t s Bo r e p 50 45 55o u k S 26 27 28 29

31 32 33 34

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G l u e

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Hundreds

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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 27 © R. I . C.P6u13bl i c at i ons3 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 y3•10 17 30 2 9 16 23 6 13 20 27 31

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11 18 25

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February

o c . October c November December e her r o st super 7

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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

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12 19 26

11 18 25

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12 19 26

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Clocks 12

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Photocopy onto coloured card. Cut out and laminate. You may wish to enlarge to A3.

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Sorting Circles

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Sorting Circles

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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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Carroll Diagram

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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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(Title) • 220 • New Wave Maths Book C – Teachers Guide

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triangular prism

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cube

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Tangrams

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Units of Measure:

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Map

Young Road

Deli

Scott Road

Supermarket

Library

Community Centre

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Duke Street

Video Store

Pizza

Pet Shop

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Newsagent

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School

Robinson Road

Park Avenue

• 224 • New Wave Maths Book C – Teachers Guide

Hill Street

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Parent Information

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Contents

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Expectations of Knowledge of Basic Facts ....................................................................... 226 Primary School Mathematics ......................................................................................... 227–228 Problem-solving Strategies ........................................................................................................ 229 Concrete to Mental ....................................................................................................................... 230 Mathematical Learning Areas ................................................................................................... 231 Homework Policy ........................................................................................................................... 232

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New Wave Maths Book C – Teachers Guide • 225 •

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

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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.

Year 5

Recall basic addition, subtraction, multiplication and division facts.

Years 6 and 7

Automatic response is desirable.

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 flashcards. 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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'Flashcards' – with all combinations of basic facts, hold up, child responds with the answer. Flashcards 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.

• 226 • New Wave Maths Book C – 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 3, 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 initially. 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 C – Teachers Guide • 227 •

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 3. 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 initially. 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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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.

• 228 • New Wave Maths Book C – 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.

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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 them 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 C – Teachers Guide • 229 •

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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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.

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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. Should you encounter any problems, please contact me. Kind regards

Classroom Teacher

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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

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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). 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

• 230 • New Wave Maths Book C – 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

Space

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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 C – Teachers Guide • 231 •

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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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 is crucial to the continued development of your child's mathematical skills.

Kind regards

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Should you encounter any problems, please contact me.

Classroom Teacher

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Dear Parent(s)

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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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Classroom Teacher

• 232 • New Wave Maths Book C – Teachers Guide