9780230401235 text by Cherie chals

C A R I B B E A N P R I MARY MAT HE MAT IC S

Second edition

Teacherâ&#x20AC;&#x2122;s Book 5 Laurie Sealy and Sandra Moore

Macmillan Education 4 Crinan Street London N1 9XW A division of Macmillan Publishers Limited Companies and representatives throughout the world ISBN 978-0-230-40123-5 Text ÂŠ Laurie Sealy and Sandra Moore 2014 Design and illustration ÂŠ Macmillan Publishers Limited 2014 First published 2014 All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, transmitted in any form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publishers. Designed by Macmillan Education Typeset by EXPO Holdings Illustrated by TechType These materials may contain links for third party websites. We have no control over, and are not responsible for, the contents of such third party websites. Please use care when accessing them. Although we have tried to trace and contact copyright holders before publication, in some cases this has not been possible. If contacted we will be pleased to rectify any errors or omissions at the earliest opportunity. 2018 2017 2016 2015 2014 10 9 8 7 6 5 4 3 2 1

Contents General introduction

About teaching Mathematics

Scope and sequence for level 5

About using Teacher’s Book 5

Unit by unit: Overview, Teaching suggestions and Sample lesson plans Unit 1 Number

Unit 2 Patterns, sequence and order 19 Unit 3 Operations – addition and subtraction 23 Unit 4 Decimals

Unit 5 Multiplication

Unit 6 Division

Unit 7 Fractions

Unit 8 Geometry

Unit 9 More decimals

Unit 10 Measurement

Unit 11 More fractions

Unit 12 Percentages, ratio and proportion 69 Unit 13 Measurement – time

Unit 14 Statistics, data and probability 77 Answers to Student’s Book 5

Answers to Workbook 5

121

CD-ROM activity directory (list of topics) for level 5

138

Link to Caribbean Teacher Resources website

140

General introduction Bright Sparks provides a different kind of Teacher’s Book. Each book gives experienced teachers new and useful ideas, while supporting novice or untrained teachers with concept explanations and lesson details. Every Teacher’s Book includes that year’s Scope and sequence, all Student’s Book answers, all Workbook answers, a CD-ROM activity directory, and Teacher Resources website link. For every unit in the Student’s Book, the Teacher’s Book provides a breakdown of its objectives, resources for suggested activities, a plan of operation with main ideas, specific lesson ideas and teaching tips, extensions, differentiation ideas, assessment possibilities, and notes for where to use CD-ROM activities. Each unit has a Sample lesson plan incorporating all of these elements. Bright Sparks Teacher’s Books highlight and are built on the following key emphases. These emphases are woven into the suggestions and ideas offered for the various units and lessons throughout the series. • Problem-solving and developing reasoning skills are essential. • Teamwork, partner work and social learning lead to deeper understanding. • Student engagement is essential to student learning. • Teaching should be concept-based, with lessons built around the ‘big idea’, exploring the concept and then applying it. Procedures are necessary steps but should follow, and not be the focus of, a lesson. • New information which is linked to prior knowledge is more easily understood and used. Well-prepared teachers break down the topic into manageable parts and help students connect it together once it is well understood.

Introduction • Bright Sparks Teacher’s Book 5

• The language of Mathematics is semiotic, including both words and symbols. Teachers need to specifically teach this language and how it is used. • Everyone learns differently. Teaching the same concept using multiple representations (verbal, symbolic, graph/chart, diagram, model, and physical objects) ensures more students learn, and that students have a deeper understanding. • Differentiating lessons means adjusting the content for all learners, including students with particular needs (e.g. processing, physical limitations, gifted). • Mental Mathematics is not computation, but rather is learning to think, to explain one’s thinking to others, to question and to justify one’s answers. • Task or project-based learning calls on students to use a variety of skills as they identify a problem, explore strategies, choose and then explain their solution. • Good mathematical games and activities engage students while practising essential skills. • Assessment is intended to inform teaching and learning. The results of student assessments should be used to identify what concepts or skills need attention and where individual students need support or challenge. Assessment is on-going, processoriented and takes different forms, including self-assessment, formative and summative assessment. Teachers will be able to choose that which best suits their own classroom needs from the teaching suggestions and the subject matter in each Teacher’s Book.

About teaching Mathematics Steps for lessons Mathematics education research confirms that students construct their understanding of concepts, such as numbers, through real world experiences, and that the beginning of those experiences is with the use of concrete materials.

1 Students first work with concrete materials to model and perfect their understanding. 2 Next, students use visual representations, such as pictures. It is at this point that some of the lessons in the Student Book are introduced, and then practised. 3 Once these levels are strong, the symbolic representation may be introduced. The symbolic representation, for example, might be the use of the addition sign and a number sentence. The order of teaching and learning, then, best begins with the concrete, then moves to the visual or pictorial, and finally to the abstract, or symbols.

Teaching concepts In the outline of the units that follow, some suggestions for using activities will be made. However, teachers will come up with many other great ideas. The key is to introduce every new concept with many opportunities to model it using concrete materials and multiple representations. Research confirms that this process ensures long term learning, and should be encouraged. The more familiarity students have with the concrete materials and visual representations, the more easily they will be able later to adapt that learning to more abstract conceptual forms. Manipulatives, then, are not for the teacher to show the class or do demonstrations. They are for all

students to hold and use and physically manipulate. Students should have time to explore, to model, and to explain to others their understanding. Through their manipulation of the materials and through their discussion, the level of understanding and learning will be made clear. When there is an obvious gap in student learning, hearing the student describe what he or she is doing can give the teacher clues as to where the gap in understanding lies.

Multiple representations Even with limited resources, teachers should use different materials and different approaches to teach a single concept. Using multiple representations of one idea, whether concrete, pictorial or symbolic, deepens the conceptual understanding for a student. It also ensures a greater chance that all students, based on their inherent learning abilities, will respond to and understand at least one of the different approaches the teacher offers. On a practical level, if a particular object always represents one idea, then some students who did not understand may stay stuck on that image, but if different objects and approaches are used to represent a concept, then gradually the students see what all the objects have in common.

Peer teaching and teamwork Active learning works best when teachers have clear expectations for the classroom environment when students work in groups, or work with materials. Exploration and discussion can encourage learning, provided these key strategies are conducted within an organised classroom where students know what is expected, how to speak with one another and how to comment when questioning another studentâ&#x20AC;&#x2122;s reasoning. Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Introduction

When teaching students how to have Mathematics conversations, teachers will need to help students learn to show respect for other peopleâ&#x20AC;&#x2122;s views and to take turns when talking over their ideas with a partner or in a small group. When reporting back to the whole class, some teachers first help students appoint a group leader. To keep materials sorted and organised, some teachers use colours

Introduction â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

for groups, and put the same colour on a bin with Mathematics resources for that group. Each group then has one person whose job it is to return the bin to the shelf. These are a few suggestions of ideas that work well in different classrooms of the region, but each teacher will use what works best based on his or her students and school environment.

Scope and sequence for level 5 Major concept

Knowledge and skills

Number

Apply counting skills to practical situations Count numbers between two numbers Use ordinal numbers to 100th Read/write numbers to 100 000 State the value or place value to 5 digits Write expanded forms for up to 5-digit numbers Write and name decimals to two places Compare and order 1- to 5-digit numbers

Patterns, functions, algebra

Recognise and extend patterns in a series of numbers or shapes Calculate missing values in sequences Work with problems involving consecutive numbers or patterns (poles and spaces) Discuss patterns and generalise Create a pattern with up to 5 variables Solve for the unknown represented by a symbol x or variable (n) Substitute values for n in a simple function input/output model Write equations to represent word problems and vice versa

Operations and relations

Mentally add 2-digit numbers Add up to 5-digit numbers with or without regrouping Mentally subtract from a 1- or 2-digit number from a number up to 100 Subtract up to 5-digit numbers, with or without regrouping Multiply 1- to 3-digit numbers by multiples of 10 Multiply a 1- to 3-digit numbers by a 1- or 2-digit number, with or without regrouping State and use the times tables to 12x List multiples of a 1-digit number and find the LCM of 2 or 3 whole numbers by listing multiples Divide a 1- to 5-digit number by a 1- or 2-digit numbers using more than one algorithm Deal with the remainder in reasonable ways during problem solving (reword) List factors of numbers and explain what they are, and find the GCF/HCF of 2 or 3 numbers Estimate reasonable results to practical situations Round numbers to 4 digits Use rounding skills to estimate and check results

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Introduction

Major concept

Knowledge and skills

Add, subtract and multiply decimal numbers Apply skill with operations to problem solving involving more than one operation Explain why a solution is reasonable Demonstrate skill using a calculator for all four operations Use mathematical language Use mental mathematics strategies demonstrating number sense Explain problem solving approaches used and justify answers Use arithmetic skills to complete fact families using addition and subtraction/ multiplication and division Compare addition and subtraction inverse processes Compare multiplication and division inverse processes Add a series of numbers, combining to make multiples of 10 Recognise commutative, identity properties of + and x Explore the associative and distributive properties (BZ, TT) Use the distributive property of multiplication to solve equations

Money skills

Use the calculator to add, subtract, multiply dollars and cents Round money to the nearest dollar and estimate total cost Find total cost and make change from $100 Calculate profit and loss Calculate simple hire purchase costs Calculate VAT or tax in simple problems Describe and use notes/bills circulating in own country ($1), $5, $10, $20, ($50), $100 Add, subtract, multiply or divide money using the decimal point, with or without renaming Estimate the total cost of several items given the unit cost, or the rate

Measurement

Review: tell the time in hours and minutes Record time in hours and minutes, and with 24-hour clocks Add, subtract, multiply hours and minutes Discuss and calculate elapsed time, using days, hours or minutes, Convert hours to minutes and minutes to hours Use measurement in problem solving and practical situations Estimate, measure and record lengths using m, cm, mm (metre stick and ruler) Compare lengths using mm, cm, m, km Round to nearest cm or 5 mm Estimate to nearest m in practical situations Measure the lengths of sides to find perimeter in polygons using cm

Introduction â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

Major concept

Knowledge and skills

Estimate, measure, record and compare mass using g and kg Choose appropriate units of measurement for mass in practical situations Compare mass using balance scales Estimate, measure, record and compare capacity using mℓ and ℓ Explore the concept of volume, using centimetre cubes (cm3) Find the area of squares and rectangles using cm2 and m2 Recognise and determine perimeter or area in practical situations Count squares or half squares to determine area on a square centimetre grid Explore temperature in practical situations Geometry

Recognise lines, line segments, straight or curved lines Recognise, describe, compare and name plane shapes (2D) Recognise, describe, compare and name 5 solid shapes (3D) Make models of solid shapes, and identify or describe the shape of each face, determine number of edges and vertices Identify solid shapes in the environment Identify right angles in plane figures and name the properties of squares, rectangles and triangles Find right angles and angles less or greater than right angles (acute and obtuse) in the environment, in flat or solid shapes Explore angles Recognise parallel, perpendicular and intersecting lines Identify diameter and radius and centre point on a circle Compare flat surfaces, recognise and use tessellation to create new shapes and patterns Recognise and draw lines of symmetry in plane figures Recognise rotational symmetry in simple shapes Recognise congruence in simple plane figures Explore and predict patterns and shapes with simple transformations

Fractions

Name the fraction, whole number or mixed number represented in part of a set of objects or a shaded part of a figure Identify equivalent fractions, and use to simplify to lowest terms or cancel (LCM) Add and subtract fractions with or without like denominators Identify and solve real world problems using fractions, and use in practical situations Compare and convert mixed numbers, improper and proper fractions Find fractional parts of given quantities Order a set of simple fractions Multiple a fraction by a fraction, and cancel Bright Sparks Teacher’s Book 5 • Introduction

Major concept

Knowledge and skills

Decimals

Identify the decimal point, relate to money Identify the tenths, hundredths and thousandths place Divide and multiply decimal numbers by multiples of 10 (10, 100, 1000) Multiply and divide to 2 decimal places by a whole number Add and subtract decimal numbers to 2 decimal places Estimate and round to nearest whole number Write decimal fractions as common fractions

Data/statistics

Collect, organise and display data using a pictograph, tally chart, frequency table, bar graph, line graph, block graph or pie graph, with 1, 2, 5 or 10 scale Interpret data, apply the data to problems, compare information shown to draw conclusions or make predictions of outcomes Construct a graph from a simple list of data Discuss how data is collected through different methods and the ways it is represented Read, understand, interpret and compare how data is represented and presented on different graphs, and why some graphs better fit certain uses

Probability

Determine how likely the result of an event, after experimentation

Set theory

Work with the concepts of subset, union and intersection of sets Use simple Venn diagrams to display commonalities, explain what is represented, and how it relates

Percentages, ratio, proportion

Express simple fractions or decimals as percentages Find the percentage of a whole, using calculation Work with simple problem solving, involving ration and proportion Find mean (average) of a series of numbers Explore the concept of proportion, and use in problem solving

Introduction â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

About using Teacher’s Book 5 How to get the most from the Student’s Books and Teacher’s Books The Scope and sequence, Table of contents and Student’s Book index outline the concepts covered throughout the school year. Some topics are ‘Enrichment’ within the units, where not every syllabus in the region includes that concept. These topics may still be used to extend student learning or for advanced students, or may be left out. Teachers will feel free to use the Bright Sparks materials that best fit their local needs and their particular class in any given year. The Student’s Books are used to supplement Mathematics instruction and provide an opportunity for examples and written practice to follow practical activities. After first learning the mathematical concepts through active participation, manipulation of concrete models, discussion, problem posing and a variety of approaches, students can then be guided through the exercises in the Student’s Book that supplement that learning. The examples and explanations support classroom teaching and provide prompts as students work independently, while the features (Hint, Challenge, etc) push student thinking and help students to remember. Teachers and students sometimes face overcrowding, limited space, high noise levels from adjoining classes, multi-age classrooms, limited resources and varied support. It is challenging to try to find materials, time and even space to carry out practical activities. This is the reality for many teachers in the region. The Teachers Book gives some ideas and suggestions for lessons and games that help students become interested and involved, without using commercial products that are hard to obtain. Teachers will gradually collect

additional ideas for activities and games from colleagues, workshops and through Internet or book research. Students easily become excited and engaged when involved in activities and when they see Mathematics as fun, even as they solidify their learning. As teachers, we hope to keep this enthusiasm kindled and build the confidence that comes with their new skills and knowledge. Teachers may need to be confident voices in favour of students doing activities or games in Mathematics, rather than following the pencil and paper approaches that are sometimes expected. Research and experience prove that student engagement – being interested and actively involved, including in classroom discussions – leads to better problem solvers with stronger mathematical thinking skills. Teachers may need to be strong advocates for change, helping to educate parents and others who are not yet aware of these proven approaches. Teamwork and problem-solving skills develop through these types of classroom strategies.

How to use the Unit Check and summary, Assessments 1–10 and Workbook Self-checks The underlying objective – assessing Mathematics learning – needs to be kept in the forefront. The Unit Check can be used as a tool for self-assessment, introducing students to the opportunity to check themselves and see how well they are learning. You may also wish to use it as a formative assessment tool, to chart student progress in concept areas and plan further teaching. The longer Assessments 1–10 give a broader overview of learning in more than one concept area. In Workbook 5 there are seven ‘Reviews’ at the end which can be used by students Bright Sparks Teacher’s Book 5 • Introduction

as ‘Self-checks’. These reviews work well for student self-assessment, if students are taught how to use the results to recognise their strengths and their needs.

Informal assessment Teachers will, as usual, carry out informal checks on student progress. Such informal assessment can be approached systematically, deciding in advance what concepts or skills will be assessed, and for which students, on a weekly basis. In this way, teachers can build up notes on every student, checking for strong or weak understanding and identifying students who have trouble formulating or articulating their reasoning.

Mathematical language / Teaching English language learners The language of Mathematics needs to be discretely taught. Students may enter school with a home use of language somewhat different from the Standard English expected in school. In Belize, in particular, and in some other parts of the region, there are students entering school for whom English is not their first language. Techniques to help students’ transition to English while learning the language of Mathematics include: • specifically teaching the Mathematics vocabulary (e.g. ‘times’, ‘length’), particularly those words which carry more than one meaning (e.g. ‘line’, ‘match’) • using hand movements to demonstrate while teaching

Introduction • Bright Sparks Teacher’s Book 5

• using activities that include singing, modelling, describing, and hand-held objects • encouraging visual learning, such as using sketches in problem solving to show what we know and what we need to find out • ‘revoicing’ – where teachers encourage students to speak in class and then repeat back what the student is trying to say, using the appropriate language/ mathematical terms.

Focus on the ‘big idea’ The Teacher’s Books offer suggestions for ideas to engage students and point out correlating activities on the CDROM or Teacher Resources website. The Workbooks, in addition, state which specific lesson in the Student’s Book each practice exercise supports. The Teacher’s Books address the key teaching points, the main concepts or the ‘big ideas’ mathematically. In addition, the common misconceptions, or weak areas that are sometimes seen, will be noted, with ideas for bridging these gaps before they become deterrents to learning. As before, units will have ideas for differentiating lessons to reach all learners, teaching tips, ideas for resources (which teachers will supplement with their own activities), extension ideas and sample lesson plans.

UNIT BY UNIT: Overview, Teaching suggestions and Sample lesson plans Lessons should continue to be based on practical activities, diagrams, models and word problems which connect Mathematics to the real world. Use student discussion frequently, to help students refine their reasoning and to give you insights into their learning. Provide opportunities for students to question, and plan in advance what probing questions you will ask that will help bring out the

main ideas of the lesson. Give students time for individual work, where you can observe and check with them one-on-one. Include the essential wrap-up at the end of the lesson, using discussion and questions for students to review, recount and remember, even as you informally assess their learning and make adjustments to your plan for the next level of teaching.

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Introduction

UNIT 1 Number Place value and number words, Value, Expanded form, More expanded large numbers with regrouping, Strategy: forming numbers, Assessment 1

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Read whole numbers to the millions place • Write whole numbers to the millions place • Express the value of whole numbers to millions • Express the place value of whole numbers to millions • Expand whole numbers in more than one way • Regroup expanded numbers

RESOURCES Unifix cubes/base-10 blocks, if available; flash cards with whole numbers 0–9; place value poster; place value charts.

Teaching the content of the unit In this unit we learn about other number systems than our own. Our knowledge of value and place value is extended to millions and we learn to expand and regroup numbers.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit.

Unit 1 • Bright Sparks Teacher’s Book 5

Each title is for the lesson in the Student’s Book and the reference in brackets is for the specific section. For example, ‘1.5’ refers to the Student’s Book Unit 1, lesson 5. Practice exercises in the Workbook are noted as ‘WB’ and may be used in class or for homework. Each WB exercise is cross referenced back to the Student’s Book lesson. CD-ROM activities are noted by the relevant lessons below.

Place value (1.1) Read through SB 1.1 with the students, explaining the ideas contained within it. Practise reading the numbers in the blue example box before Ex 1.1 A out loud. Look for pointers that help in the naming of the correct place value. Ask questions – ‘Which place comes immediately to the left of hundreds? ...ten thousands? Which place comes immediately to the right of ones? ...millions? How many places are there in a number that is in the thousands place? ...ten thousands? ...hundred thousands?’ Discuss the fact that when looking at place value, the value of the numbers increases by multiples of ten as we move to the left, and decreases by divisors of ten as we move to the right. Practise the spelling of the place value names. Complete SB 1.1 A. Use with WB Unit 1, Ex 1 Allow the students to read on and complete the individual question in the box by themselves. Put the students into pairs according to their seating and have them complete the Partner Activity. Check that answers are correct while moving around

Ex 1.1 B 1 2 3 4 5

Hundred Ten Thousands Hundreds Thousands Thousands

1 6

5 4

the class as the exercise is being done. Discuss the meaning of the term ‘place value’. We are being asked for the name of the position a particular digit occupies e.g. 45 361 – the 5 is in the thousands column, therefore its place value is thousands. Draw a place value chart on the board or use a place value poster (see chart above.) With assistance from the class, place the numbers in SB 1.1 B into the correct columns. The exercise can then be completed according to the instructions. Use with WB Unit 1, Ex 2 For the reading and writing of numbers, the students need to know that numbers are viewed in groups of three starting from the right. At this stage they have learnt to read 3-digit numbers but review is always useful, so some 3-digit numbers can be displayed for the students to read. Now put another digit in front of one of these 3-digit numbers and ask them to read it again. Then put another digit in front of this and yet another. We now have a 6-digit number. If this 6-digit number is seen as 2 groups of 3 digits, the reading of it becomes less of an issue. Look at the numbers in the box below. Thousands

Ones

835

107

351

462

When we look at the ones with a 4-digit number, there is only one digit in the thousands, in this case, four thousand. The other digits are ones – eight hundred

3 1 0 5

Tens

Ones

5 8 5 0 0

7 0 9 9 9

and thirty-five ones; the number is four thousand, eight hundred and thirty-five. With a 5-digit number we start on the right as before, which leaves only 2 digits in the thousands. This number is twenty-nine thousand, one hundred and seven. In the 6-digit number, three hundred and fifty-one represents the thousands; four hundred and sixty-two represents the ones. The number is read: three hundred and fifty-one thousand, four hundred and sixty-two. Ask students to do the Challenge question using this method. Discuss it as a class, noting which students are struggling with the ideas covered. Instruct the students to complete SB 1.1 C. Go round to check on the students who may have difficulties. Use with WB Unit 1, Ex 3 1.1 D – Use of a place value chart is helpful to sort out which digits go into which columns. When the students can see the digits in the correct places they can fit in zeros in the missing places and have a better understanding of the number they are building. Following this the exercise SB 1.1 D can be completed. Use with WB Unit 1, Ex 4 Enrichment: Other number systems This is an informational page and should be read and discussed with the class. Simple questions can be created to give the students practice using Roman numerals as these are still used to number pages and exercises in some text books, and also on some analogue clock faces. Bright Sparks Teacher’s Book 5 • Unit 1

Enrichment: Hieroglyphics and IT project – the Mayan system of numbers This is another informational page. These provide a background for our number system and give the students the opportunity for comparison. Follow up on the suggested activities.

Value / Expanded form (1.2 and 1.3) Once the students understand the place value of digits it should be an easy step to determine the value of these digits. The place name supplies all the information needed – ones are worth 1; we multiply the digit in the ones place by 1. Tens are worth 10; we multiply the digit in the tens place by 10. Hundreds are worth 100; we multiply the digit in the hundreds place by 100. Practise orally before completing SB 1.2 A. Oral practice is vital to aid understanding. Use with WB Unit 1, Ex 5 and 6 SB 1.2 B – Remind the students that zero has no value and is therefore not expanded. Do a few examples together with the students before completing the exercise. Use with WB Unit 1, Ex 7

Expanded form (1.3) Look at the different forms of expanding and discuss the differences and similarities. SB 1.3 A gives further practice of expanding and follows on from SB 1.2 B. Use with WB Unit 1, Ex 8 In Ex 1.3 B, the reverse of expanding is now practised. Encourage the students to look at the number of digits that follow the largest value. This will guide them in determining the number of places in the completed answer. Remind them that in the same way that we did not expand zeros there will be places not represented in the expansions because they had zero

Unit 1 • Bright Sparks Teacher’s Book 5

value. Discuss how they should deal with this. Do SB 1.3 B. Use with WB Unit 1, Ex 9 Expanded numbers with regrouping Read the note with the students and reinforce the teaching points. These are that both sides of an equals sign should have the same value and that treating the work in the same way as subtraction regrouping will simplify it. When 1 hundred is taken from the hundreds place, cross out the digit in the hundreds place and replace it with one number less. e.g. 34H 12T 6 Ones lace the 1 that is subtracted from the P hundreds before the digit in the tens column. We are left with 3H 12T 6 Ones. Practise some together using the subtraction regrouping method. When the students can do them fairly comfortably, SB 1.3 C can be attempted. Faster students can also attempt the Challenge. Use with WB Unit 1, Ex 10 SB 1.3 D – This offers further practice writing numbers in short form. Encourage the students to look carefully at the work as it combines different types of regrouping. Point out the Hint box to them. SB 1.3 E 1–10 uses basic expanding but 11– 20 encourages them to use an alternative method. Each place is written in the long form and put into brackets. Practise this with the students before instructing them to complete 11–20. Use with WB Unit 1, Ex 11 The Enrichment box deals with very large numbers. Students will enjoy thinking of occasions when they need to use large numbers.

More expanded numbers with regrouping (1.4) The teaching points mentioned before completing SB 1.3 C should be reviewed before completing 1.4 A and 1.4 B. More able students should do the Challenge. Use with WB Unit 1, Ex 12

out numbers of varying size while the students manipulate the papers to form their answers. In this oral session, use each term and discuss its meaning, to aid understanding. Students do the Partner Activity, then SB 1.5 can be completed. Use with WB Unit 1, Ex 13

Strategy: Forming numbers (1.5)

Assessment 1

(See also sample lesson plan below.)

Assessment 1 at the end of this unit can now be completed. It is separated into two parts and tests knowledge of value, place value, expanding and writing numbers to the millions place. The Challenge is directed towards those students who complete the assessment quickly.

Knowledge of the terms largest, smallest, greatest, least, odd and even must not be assumed, therefore oral practice is suggested. As a preliminary activity, each child can write the four digits needed on separate pieces of paper. Call

Sample lesson plan UNIT 1 1.5 Strategy: Forming numbers

Objectives (for the specific lesson)

RESOURCES

• To understand that the position of digits affects the value of the number

Bristol board or paper cut to the size of playing cards, some with the digits 0 – 9 and some with the place values Ones to Thousands. (Cut enough cards for everyone in the class to have a digit card and for at least half the class to have a place value card.)

• To consolidate the meaning of mathematical vocabulary: greatest, smallest, even, odd

Engaging the students’ interest / Connections

Share the cards among the students so there is an equal distribution of digits and place value terms. Ask the students with digits to keep theirs a secret and have individuals describe theirs (in terms of size and shape). The rest of the class should try to guess which number they have. Alternatively a form of 20 questions could be asked, with the other members of the class asking questions to ascertain the digit possessed. The students are exposed to open expression of the fact that one digit has greater or lesser value than another. They can also see why this number value by itself does not dictate the overall value of the number when paired with a place value. The language of mathematics is being developed as they see the different facets that determine value.

Bright Sparks Teacher’s Book 5 • Unit 1

Teaching the lesson

Ask the students who have place value terms to hold them up in turn. Discuss the different names as they are displayed. Next, pair the holders of place value cards with holders of digits. Put 2 pairs together and they all try to determine which pair has the larger number. Match a pair of students holding 1 Thousand (or other pair with small digit value) with a pair holding 9 Tens. Discuss why the 9 does not make this number bigger than the 1 Thousand. The reason is that the place value is more powerful than the digit itself. The students can now stay in their fours and each child should be given a card with a digit on it (each group will have four different digits). They can, among themselves, rearrange the cards to make a variety of four digit numbers. Appoint a scribe for each group and have them record and label each number created e.g. largest, smallest, largest even, largest odd, etc. Groups present these answers to the class, who check for accuracy. SB 1.5 can be completed at this point. WB Unit 1, Ex 13 gives further practice of this skill.

Differentiating for different learning styles

Be prepared to assign problems with Tens of Thousands to those who are quick to show understanding. Any students who have difficulties can be given only three digits to deal with instead of four. They can be given four digits at a later stage.

Assessment

Make informal assessment as groups work together. Make notes on the degree of participation of each member of the group.

Summary of key points

The value of the digit is only one factor determining size. The position of the digit in relation to the other digits plays a great part in determining size.

Extension activities

The students can be challenged to games of speed with numbers containing 6 or more digits. How quickly can they rearrange these digits to make the type of number called?

Unit 1 â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

UNIT 2 Patterns, sequence and order Ordering numbers, Counting and ordering, Problem solving, Patterns, Revision, Unit 1 and Unit 2 check and summary

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Recognise patterns and sequences of numbers • Sequence numbers in ascending order • Sequence numbers in descending order • Fill in missing elements in patterns/ sequences • Understand and use correct mathematical language for ordering

RESOURCES Flash cards with whole numbers 0–9.

Teaching the content of the unit This unit deals with building patterns, and putting numbers and designs into sequential order.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit. Practice exercises in the Workbook are noted as ‘WB’ and may be used in class or for homework. Each WB exercise is cross referenced back to the Student’s Book lesson. CD-ROM activities are noted by the relevant lessons below.

Ordering numbers (2.1) Discuss how we know that one number is larger than another, using an example containing a 2-digit, a 3-digit and a 4digit number. The students should be able to verbalise that the 4-digit number has thousands as the highest place value and this makes it the largest number. Present a few examples of this type of ordering. Next, discuss what can be done when the group of numbers all have the same number of digits. The work previously completed on value and place value should have prepared students for this type of question. The answer is to start with the highest place and compare these values. The largest value will determine the largest number. If these are all the same, go to the next place and compare these values and so on until one number stands out as being the largest. Eliminate this number from the group and compare the ones left to find the next in order. The teaching points are these: 1) start by looking at how many digits are in the number; 2) compare the digits in the highest place; 3) repeat this step until all of the numbers are positioned. Discuss the terms ‘ascend’ (to go up) and ‘descend’ (to come down). Ask the students to think up a clue or trick to remind them of the meaning of each word. Students remember tips/clues that they help to formulate more easily. Complete SB 2.1. CD-ROM exercises in Block A give further practice and extension of this concept. Bright Sparks Teacher’s Book 5 • Unit 2

Counting and ordering (2.2)

Patterns (2.4)

(See also sample lesson plan below.)

Practise counting in different multiples. Count up and down, encouraging the students to look for the difference between the numbers. There are some patterns that do not ascend or descend in multiples. Some sequences double as they progress, some sequences have a difference that ascends or descends by 1 or more each time. Introduce some sequences that give practice looking for these. SB 2.4 A, 2.4 B and 2.4 C can be completed.

Practise counting on from various points in the number sequence, e.g. 50, 51, 52 ... ask the students to continue. 97, 98, 99, ... . Count backwards from various points e.g. 87, 86, 85, ... ; 200, 199, 198, ... . Practise also counting forward and back in twos, threes and fives. Give adequate practise then instruct the students to complete SB 2.2 A. Use with WB Unit 2, Ex 1 SB 2.2 B gives further practise of ordering. Review the meaning of ascend and descend and the necessary method before completing SB 2.2 B. CD-ROM exercises in Block A give further practice and extension of this concept. Use with WB Unit 2, Ex 2–3

Problem solving (2.3) Discuss problem-solving terminology. Certain words or groups of words suggest certain actions. Have an interactive session to see what the students remember. The word ‘altogether’ prompts us to make a total. Sometimes this is done by adding and sometimes by multiplying. Ask for an example of each. Ask which other words prompt us to make totals. How many ...? What is the sum/total ...? How long ...? There are also words that prompt us to subtract to find the answer. What is the difference ...? How many more ...? How much less/many fewer ...? How many short ...? Two different methods of finding the difference are suggested. Go through these with the students before instructing them to complete SB 2.3. Faster students can do the Challenge.

Unit 2 • Bright Sparks Teacher’s Book 5

Use with WB Unit 2, Ex 4 SB 2.4 D can be completed without the need for further teaching. Refer to the page on Enrichment: Other number systems for help with Roman numerals, if needed. Use with WB Unit 2, Ex 5 When students have had an opportunity to try the Challenge, discuss it as a class.

Revision (2.5) Revision of SB Units 1 and 2 – This revises place value, expanding numbers, ordering and comparing, pattern making and problem solving. It is up to the teacher if this is done after advising students to revise or as an impromptu exercise. The term ‘ordinal number’ (a number defining the position in a series e.g. first, twentieth, etc.) should be reviewed. Use with WB Unit 2, Ex 6

Assessment Unit 1 and Unit 2 Check and summary will show if key points on numbers patterns and sequences have been grasped.

Sample lesson plan UNIT 2 2.2 Counting and ordering

Objectives (for the specific lesson)

RESOURCES

• To understand that numbers have a natural sequence

Individual digits (on card) may be used to create sequences; paper; colours; pencils.

• To be able to count and skip numbers in ascending and descending order • Use place value in a practical way to sequence numbers

Engaging the students’ interest / Connections

Begin by playing a counting game. First, count as a class up to a pre-determined number. Next, count in other multiples. That being done well, try counting backwards in similar multiples. Then introduce the game. Choose a particular number. The students are to count around the class, but may neither say this number nor any multiple of it, out loud. (If 4 is the chosen number, they cannot say 4, 8, 12 or any number in the 4 x table.) When they arrive at these multiples, an animal noise such as a bark should replace the number. When an error is made, that child may not participate for the remainder of that round. Start the count over again or continue from where the error is made when that child drops out of the game. Other multiples can be chosen. You make the rules and decide when to move on to the next stage of the lesson. This game reviews counting as well as using multiples and sequencing skills. Next, call a series of numbers to the class and ask them what follows. Call a few of these. Make sure to do some decreasing sequences. Encourage some class members to make up some sequences that can also be asked of the class.

Teaching the lesson

Discuss how we know that one number is larger than another. What do we look for to determine size? It could be the number of digits, size of digits. Do a few of these together on the board. Be careful to include simple fractions and some sums of money, as this introduces decimals. Tell the class that they are going to have the opportunity to show off their skills in the areas just practised. Now turn to Section 2.2 and read the instructions with the students. Clarify any instruction or part of instruction that they do not understand. Complete one or two similar problems together. Assign SB 2.2 A and 2.2 B. Use with WB Unit 2, Ex 1, 2 and 3

Differentiating for different learning styles

It will become clear that some students can complete the entire page with no assistance and some will need help. Make discreet notes to yourself about this and work with those who need help, while the more able ones can create their own sequences and challenge other able students with them. Bright Sparks Teacher’s Book 5 • Unit 2

Assessment

Assessment can be fairly informal. Read answers, listen to the type of questions asked, and assess orally. Take notes on the areas of weakness so that specific help can be given. A later lesson could be geared to any weaknesses.

Summary of key points

Numbers have a natural sequence. New sequences can be made by skipping numbers in a set pattern. Patterns can be made in many ways.

Extension activities

CD-ROM exercises in Block A give further practice and extension of this concept. The students can create sequences of their own and provide a written explanation of how the sequence was formed.

Unit 2 â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

UNIT 3 Operations – addition and subtraction Estimation skills, Properties of addition, Addition with regrouping, Adding large numbers, Subtraction practice, Subtracting large numbers, Regrouping with zeros, Adding and subtracting money, Subtraction practice, Unit 3 check and summary, Assessment 2

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Use estimation to determine the approximate size of an answer • Round numbers to the millions place • Round sums of money to the nearest dollar • Regroup from numbers with more than one zero • Use zeros as place holders for cents in money problems • Understand and use correct terminology for problem solving

RESOURCES Place value charts.

Practice exercises in the Workbook are noted as ‘WB’ and may be used in class or for homework. Each WB exercise is cross referenced back to the Student’s Book lesson. CD-ROM activities are noted by the relevant lessons below.

Estimation skills (3.1) In order to estimate successfully, students should apply their knowledge of rounding numbers. They have already practised rounding to the nearest ten, hundred and thousand. Here we practise grouping the numbers that have the same place value to make the best estimate. Grouping numbers The example box shows the working for grouping the thousands together, then the hundreds and lastly the tens. Introduce some more examples and work them out as a class. Assign SB 3.1 A after appropriate practice is given. Use with WB Unit 3, Ex 1 Review: rounding numbers

Teaching the content of the unit In this unit some properties of numbers are reviewed and some new ones learnt. These properties show how to make numbers work for us. Basic addition and subtraction skills are extended.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit.

(See also sample lesson plan below.) The rules of basic rounding are recorded for review. Discuss them and ask questions to reinforce the rules. E.g. if the digit to the right is 7, what happens to the digit that we are rounding? Ask this using other digits and some specific numbers. Rounding – The same number can be rounded to many different places. When

Bright Sparks Teacher’s Book 5 • Unit 3

we round to a particular place, the places to its left are not changed or omitted. This is a point that students often misunderstand. There should be the same number of places in the rounded answer as there were in the question. Therefore when rounding 24 365 to the nearest hundred our answer will have five places.

Review the basic steps for addition. These are:

1 Numbers are added in columns.

Number to Answer be rounded

2 Two digits cannot be written under one place value, therefore when a 2 digit answer is reached, numbers are regrouped (the higher placed digit is put into the column on the left and added to the values in that place).

24 365

24 write the thousands

SB 3.3 A and 3.3 B can be completed.

24 365

24 400 round the hundreds

(6 tens requires us to round up so 3 hundreds is increased by 1) We know that we are working with the digit in the Hundreds and the Tens places. We also know that the Ten Thousands and Thousands will not change. Write the places that will not change first so they are not forgotten.

Use with WB Unit 3, Ex 4

Adding large numbers (3.4) Repeat the review for the previous page. These numbers have higher place values but the basic knowledge needed is the same. SB 3.4 A and 3.4 B can be completed. A CD-ROM exercise in Block B gives further practice of this concept. Use with WB Unit 3, Ex 5

After writing these, do the appropriate working to round the number to the nearest hundred. SB 3.1 B can be completed.

Subtraction practice (3.5)

Rounding money

1 Numbers are subtracted in columns;

Discuss rounding to the nearest whole dollar. Use the same method as before. When rounding to a particular place, look at the digit to the right of that place. If it is 5 or more, round up, if it is 4 or less, make no change. All numbers to the right of that place become zeros. Complete SB 3.1 C. Use with WB Unit 3, Ex 2

Properties of addition (3.2) Commutative and associative properties as well as the special property of adding zero are defined. Discuss these different properties and how knowledge of them can help us to work more economically. Complete SB 3.2. Ask the students which of these properties they were able to use. Use with WB Unit 3, Ex 3

Addition with regrouping (3.3)

Unit 3 • Bright Sparks Teacher’s Book 5

Review the basic steps of subtraction. These are:

2 The number to be taken away (subtrahend) is always at the bottom. 3 If a digit in this number is larger than one above it, regrouping from the place to the left is practised. Under no circumstances can the smaller digit at the top be taken from a larger digit below it. It is useful to record each step of regrouping by crossing and setting down the new digit. We have previously looked at some of the language of problem solving. This is an opportunity to examine some more subtraction language. The terms used here are: How much/many was/were left? How many years later? What is ... less than? What must I add to ... to make ... ? Discuss the questions. In all cases we can see that the answer required is the difference between the two

numbers given. SB 3.5 A and 3.5 B can be completed.

Subtracting large numbers (3.6) Review the steps as before. The numbers are bigger but the concept remains the same. SB 3.6 A and 3.6 B can be completed. A CD-ROM exercise in Block B gives further practice of this concept. Use with WB Unit 3, Ex 6

Regrouping with zeros (3.7) Regrouping from 1 zero can be challenging. Regrouping when there are 2 or more zeros can be more of a challenge. We have practised this at earlier levels so it should be a matter of reminders and review to fully grasp this skill. When the digit to the left is zero we go further to the left until we find a digit larger than zero. Follow the steps in the example box, changing each place individually until tens are created and regrouped to give us ones. Example 3 12 90 90 18 2 Th, 0 H, 0 T is the same as – 1 8 6 9 200 tens. 3 0 1 3 9 Regrouping changes this to 199 tens, 10 ones (Alternate grouping method from SB 4) SB 3.7 can be completed. Use with WB Unit 3, Ex 7–8

Adding and subtracting money (3.8) The students have not done decimals before but we cannot avoid money problems and these use the decimal point.

This exercise brings home to them that there is nothing to be wary of in this work. All that was spoken of in doing regular subtraction still applies. The point to remember is that the decimal point must be aligned and should appear in the answer as well. SB 3.8 can be completed. Use with WB Unit 3, Ex 9

Subtraction practice (3.9) SB 3.9 A and 3.9 B bring together all that was taught in this unit. These exercises can be completed when the correct level of competence is reached. Use with WB Unit 3, Ex 10 Problem solving Discuss the language used and whether any of the terms are similar to the ones we looked at earlier. Are there any new ways of asking the questions? SB 3.9 C can be completed. As an extension activity, the students could be encouraged to list the different phrases that have been used to ask them to subtract. Use with WB Unit 3, Ex 10, if it wasn’t used with 3.9 A and B.

Assessment 2 Unit 3 Check and summary will show whether key points on rounding, addition and subtraction have been grasped. Assessment 2 tests knowledge of sequencing, rounding, addition, subtraction and problem solving.

Bright Sparks Teacher’s Book 5 • Unit 3

Sample lesson plan UNIT 3 3.1 Estimation skills – Review: rounding numbers (Ex 3.1 B)

Objectives (for the specific lesson)

RESOURCES

• To assess retention of the concept of rounding

Number lines; cards with 3-, 4- and 5-digit numbers; blackboard or whiteboard.

• To reinforce previously taught concepts about rounding • To extend understanding of rounding larger numbers

Engaging the students’ interest / Connections

Hold up number cards one by one for the students to read the numbers and name the place values. Ask questions that help the students to verbalise the concepts, e.g. How many places are in the number? What is the largest place in the number? Number value and place value are very closely linked to these skills.

Teaching the lesson

Ask the students what they remember about rounding. Answers may be that rounded numbers show estimated values, that numbers rounded to tens, hundreds, etc. have zero at the end. I like to use the analogy that zero is round so numbers that are rounded end with zero. Students should also understand that if the number started with four digits and therefore has thousands, it will also have thousands when they have finished rounding it. This is important because quite often when presented with a four-digit number to be rounded to tens, many students will omit the hundreds and thousands from the answer. Reinforce the constancy of the number of digits before and after rounding. They may also remember the rule that when rounding we look to the right of the digit to be rounded to see if it is smaller than 5 or if it is 5 or more. This determines whether it is rounded to the higher or lower place. Place 200 and 300 on the board. Ask individuals to place a number such as 276 between these hundreds. Identify that, as we are rounding to the nearest hundred, the 7 tens tells us what to do next. Ask if this would be closer to 200 or 300? Give other students the opportunity to place other numbers between the hundreds. Again place them closer to the correct hundred based on the rule. Continue with numbers in the thousands that are to be rounded to the nearest hundred. This is designed to give practice keeping all of the original digits while we round to a smaller place. Try the number 3416. How do we round this to the nearest hundred? Remember of course that the thousands will not be affected, so we can immediately write the digit that is in the thousands place, so this is not forgotten. Next, we have to identify the hundreds in the number. Underline this digit and look to its right. The digit to the right is lower than 5 which means the hundreds do not

Unit 3 • Bright Sparks Teacher’s Book 5

change. Follow up by writing the digit in the hundreds place. Since we are rounding to the hundreds, there will be 0 tens and 0 ones. Do a few more of these with the class before assigning them SB 3.1 B. Show the class some examples working with money, so that they understand that it is the same concept. SB 3.1 C can also be done. WB Unit 3, Ex 2 provides follow up work which can be set as homework.

Differentiating for different learning styles

The use of the number line is an alternate method of ascertaining the closer ten, hundred or thousand. It shows practically why we round to the higher or lower place value, for the benefit of the conceptually-weaker students.

Assessment

Informally assess understanding through asking leading questions in a discussion of what was done and how it was done. The ability to clearly express what was done shows how well the concept is understood.

Summary of key points

When rounding we look at the digit to the right of the place being rounded. If this digit is 5 or more we round to the higher ten/hundred/thousand. If this digit is less than 5 we round to the lower ten/hundred/thousand. The total number of digits will be the same before and after rounding.

Extension activities

Ask individual students to explain the steps used to the class. They can also, in groups, write or draw the steps to help someone who has never been taught rounding before.

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Unit 3

UNIT 4 Decimals Types of numbers, Tenths, Place value: hundredths, Decimals and whole numbers, Rounding decimals, Value, Ordering and comparing decimals, Rounding and estimating decimals, Addition and subtraction of decimal numbers, Problem solving, Group project: A new computer, Unit 4 check and summary, Assessment 3

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Recognise decimal fractions up to hundredths • Read decimal numbers to hundredths • Write decimals in figures and words • Write whole numbers and decimals in words and figures • Round decimal numbers to a whole number • Compare and order decimal and mixed whole and decimal numbers • Add and subtract decimals and mixed whole and decimal numbers

RESOURCES Decimal charts; flash cards with decimal numbers.

Teaching the content of the unit In this unit, decimals will be introduced. The students will learn how to recognise a decimal number as well as to read and write decimals to the hundredths place. Place value of whole numbers will also be reinforced.

Unit 4 • Bright Sparks Teacher’s Book 5

Types of numbers (4.1) Read through the introductory text with the students. Relate decimal numbers to common fractions, showing that each represents a part of a whole. Discuss the decimal chart and fraction chart pictured on this page of the SB. Make the connection that each shows parts of a whole. Enrichment: Integers – Discuss and give some oral practice using negative numbers and show how the answers are obtained. Decimal numbers Reinforce the points made in the text, e.g. simple decimal fractions are all numbers that range between 0 and 1 on the number line. The decimal point and the zero that is placed before it are the key to understanding, as the zero reminds us that there is no whole number and the digit that follows the decimal point is a part of the whole. Draw the number line on the board and put in the nine marks for the tenths. Ask the students in turn to fill in

the correct decimal numbers i.e. 0.1, 0.2, etc. A CD-ROM exercise in Block A gives further practice and extension of negative numbers.

Tenths (4.2) Remind students of the points previously discussed. Write a decimal number on the board (possibly 0.2). Ask questions such as ‘What does the zero at the beginning of the number tell us? Why do we need a point? What type of number follows the point?’ We are looking at numbers divided into 10 equal parts. These are called tenths. Let us try to name each portion of the whole. If 1 part is shaded what would this be called? Answer should be one tenth. This is written as a decimal in figures as 0.1. If 2 parts are shaded what would this be called? Answer should be two tenths. This is written in figures as 0.2. Call out more if necessary, then ask the students to complete SB 4.2 A. We move now to decimals that also have whole numbers. Review the place value of whole numbers and show that we are combining information gathered about whole numbers and tenths to complete the next exercise. Make it clear that the decimal point is positioned to the right of the ones place and before the tenths place. Give instructions to help the students draw the decimal chart and tell them to complete SB 4.2 B. Use with WB Unit 4, Ex 1 Read some of the answers aloud with the students, modelling the correct method of naming decimal numbers for them. 0.5 is five tenths, 1.6 is one and six tenths. Try to always model correct naming of decimal numbers. When the students are able to read these easily, SB 4.2 C can also be completed. Use with WB Unit 4, Ex 2

Place value: hundredths (4.3) A whole can also be divided into one hundred equal parts. Refer to the diagram. This time there are 2 strips shaded blue

(these are tenths) but the third strip has only six parts shaded blue. This makes twenty-six out of one hundred or twentysix hundredths. The 2 complete tenths are placed in the tenths column. The 6 individual hundredths are placed in a new column to the right of the tenths column. In this way the hundredths column is introduced. As we move to the right of our place value chart, the units of measurement continue to become smaller and smaller. Use the flash cards to give the students more practice reading decimal numbers and have them say out loud the place values of certain digits. SB 4.3 A and 4.3 B can be completed. Use with WB Unit 4, Ex 3 and 4

Decimals and whole numbers (4.4) Review writing whole numbers in figures and words. This part of the unit extends this knowledge so that it is combined with the writing of decimals that has just been learnt. Practise a few examples together, remembering to place the decimal point after the whole number. SB 4.4 can be completed.

Rounding decimals (4.5) Rounding decimals to the nearest whole number is exactly the same as rounding money to the nearest dollar. (This was practised in Unit 3 and in SB 4.) With money, there is a decimal point separating the dollars from the cents and we look at the place after the decimal point to determine whether we round up or leave the dollars as they are. The same thing is done here. Be careful to remind the students that the digit in the hundredths place does not need to be considered when rounding to the nearest dollar. SB 4.5 can be completed. A CD-ROM exercise in Block D gives further practice of this concept. Use with WB Unit 4, Ex 5

Value (4.6) Review the value of whole numbers i.e. 34 = 30 + 4. Do some other oral examples Bright Sparks Teacher’s Book 5 • Unit 4

with the students of numbers to the hundreds of thousands. Extend this to the value of decimal parts of numbers. 26 hundredths is broken down to 2 tenths and 6 hundredths. When showing value, these are written as common fractions – two parts out of ten becomes 2/10 and six parts out of a hundred becomes 6/100. Practise some of these around the class before instructing the students to complete SB 4.6 A, 4.6 B and 4.6 C. It is worth noting that students must be given further practice in spotting the difference between 3/100 and 30/100. Reinforce this by giving them work comparing numbers of this type and by asking them to draw diagrams showing the different numbers. Point out to them that since hundredths is the second place after the decimal point, a place holder can be used to fill the tenths position, so that 3/100 is written as 03/100.

When adequate practice of this has been done in groups and as a class, SB 4.7 can be completed.

CD-ROM exercise in Block A gives further practice of this concept.

Estimating decimals

Use with WB Unit 4, Ex 6 and 7

Ordering and comparing decimals (4.7) (See also sample lesson plan below.) In the same way that whole numbers are compared by first checking the value of the largest place, decimal numbers can also be compared. Review comparing simple whole numbers such as 23 and 41. Four tens is greater than two tens which make 41 the larger number. Practise some other numbers including numbers to the hundreds. Gradually integrate some decimal numbers into the comparisons, first asking students to compare the whole number values, later the tenths, and then the hundredths, to determine order. This can be practised with 2 or more numbers. Writing the numbers in columns is particularly useful in the grasping of this concept, as the students can immediately see that the decimal points are lined up. It makes it easier to see which digits are to be compared with each other.

Unit 4 • Bright Sparks Teacher’s Book 5

A CD-ROM exercise in Block A gives further practice of this concept. Use with WB Unit 4, Ex 8

Rounding and estimating decimals (4.8) Rounding money was previously connected to rounding decimal numbers to the nearest whole number. Since we’re rounding to the nearest whole number, the digit after the decimal point determines the result. Another method that could be used is this – 50 cents is half of a dollar. If the cents in the number are 50 or more, add a dollar. If the cents in the number are 49 or less, keep the dollars as they are. Complete SB 4.8 A. Use with WB Unit 4, Ex 9 Using the method of rounding to the nearest whole number can be very helpful with the quick totalling or comparison of sums of money, distances, time or other numbers which have a decimal point. Students complete SB 4.8 B.

Addition and subtraction of decimal numbers (4.9) The most crucial thing to remember here is that numbers must be set down with decimal points aligned. This was important for place value, comparing and ordering and it is equally important for addition and subtraction. Zeros can be used as place holders to ensure that numbers are not misaligned. Remind the students that these exercises are mixed addition and subtraction and that they should check that they have copied the correct symbol. SB 4.9 A and 4.9 B can be completed. The Challenge can be attempted by those students who work quickly and accurately. Decimal addition and subtraction practice SB 4.9 C and 4.9 D can be used if further

practice is required or used for revision at a later time. CD-ROM exercises in Block B give further practice of this concept. Use with WB Unit 4, Ex 10

Problem solving (4.10) Read the information on the chart with the students. This chart involves comparing, ordering, addition and subtraction. Review all of the skills taught in this unit before instructing the students to complete SB 4.10. Use with WB Unit 4, Ex 10, if it wasn’t used after Ex 4.9 D, above.

Group project: A new computer (4.11) Organise the class into groups so that no one is left out. It would be preferable to have mixed-ability groups but there is a

case for grouping because of friendship. Whichever method of grouping is chosen, be attentive and make sure that no one is omitted from the groups. Instruct the class that everyone should participate and decisions should be made only after discussion. This can be followed up in an art/computer lesson with a poster being made to advertise the event or in the composition lesson with an (imaginary) account of what took place.

Assessment 3 Unit 4 Check and summary will show if key points on value, place value, rounding, comparing, addition and subtraction of decimals have been grasped. Assessment 3, Parts 1 and 2, tests writing numbers in words and figures, ordering, comparing, sequencing, rounding, addition, subtraction and problem solving. It also tests skills in working with whole numbers and decimals.

Sample lesson plan UNIT 4 4.7 Ordering and comparing decimals

Objectives (for the specific lesson)

RESOURCES

• To understand the role of the decimal point

Squared paper or square lined books for setting down the numbers in columns.

• To be able to recognise when one decimal number is greater than another • To be able to order a series of numbers according to size

Engaging the students’ interest / Connections

Use decimal number cards, showing diagrams and figures of consecutive numbers. Give the students the opportunity to lay them down in order. Read aloud together the list of numbers to confirm the order.

Bright Sparks Teacher’s Book 5 • Unit 4

To determine order, ask questions such as ‘Which symbol should be fitted between 2.1 and 2.2? Would it be greater than or less than? Which symbol should be fitted between 3.8 and 3.7?’ Ask the students to use their hands to show the correct symbol. Remind them that the open end of the symbol always faces the larger number. Recognition of decimal numbers is reviewed as well as the symbols for greater than and less than.

Teaching the lesson

Review the value of digits in whole numbers. The number 52 has 5 tens and 2 ones. If this has to be compared to 23, which has 2 tens and 3 ones, we can write them one under the other and compare. We need only look at the 5 tens and 2 tens to see which one is larger. We can state that 52 > 23. Do another example of this using whole numbers before looking at decimal numbers – this time use a smaller number first. Bear in mind that the instruction asks the students to use the greater than and less than symbols, so when the greater or lesser number is found the students also have to use the correct symbol. Comparing decimal numbers is the same as comparing whole numbers. If we compare 2.6 and 4.2 we would write these one under the other so that the position of each place is clear. When we compare the digits in the ones place, 4 is clearly larger than 2. We can see that 2.6 < 4.2. Do several examples with 2-digit decimal numbers so that the class grasps the procedure. Ask them to name the values out loud as they make decisions about which number is greater or smaller. Next, move on to numbers that have a different number of places e.g. 5.1 and 32.7. It is even more important to set the numbers down in columns as the number of places now differs – 5.1 has ones as its largest place. 32.7 has tens as the largest place. The students should be taught to write 0 in any unoccupied places. When 3 tens is compared to 0 tens, 3 is obviously greater, making 32.7 greater than 5.1. Allow the students to put what they have just learnt into practice by doing SB 4.7, 1–6, before showing them how to deal with ordering three numbers. The concept is the same with the last few questions but three numbers adds another degree of difficulty. Encourage the students to set the numbers down in columns once again and compare based on the instruction. Remind the students to be careful to copy the digits and decimal points in the right order. It is always a good idea to check for errors even when you are sure there are none. They are instructed to order from greatest to least, so look for the largest number first. Fill in zeros to fill unused places once again and compare each column of digits, starting with the largest place. If the digits in the largest place are the same, compare those in the place next to this. Find the largest number and use the same method to compare the ones that are left to find the next in order. There should only be one left at this point. Write these down in the order that they were found.

Differentiating for different learning styles

Writing the numbers in columns is a good tip for students who are not able to visualise sequences mentally.

Unit 4 • Bright Sparks Teacher’s Book 5

Assessment

Write an account of the steps taken in point form.

Summary of key points

Write the numbers in columns. Fill in zeros for any unoccupied places. Compare the digits in each column starting with the largest place value. The number that has a digit with a larger place value is the larger number. Check your work.

Extension activities

A CD-ROM exercise in Block A gives further practice of this concept. On subsequent visits to the library, the students should now be able to help put books into the correct order on the shelves.

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Unit 4

UNIT 5 Multiplication Multiples, Multiplication speed tests, Arrays, Square numbers, Square roots, Problem solving: Mental computation, Multiplying large numbers mentally, Multiplying 3-digit numbers, Multiplying large numbers, Multiplying by multiples of 10, Multiplying by 2-digit numbers, Problem solving, Multiplication practice, Unit 5 check and summary, Assessment 4

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Understand the use of arrays • Recognise square numbers • Find the square root of square numbers • Use their knowledge of multiplication tables to solve problems • Multiply larger numbers using columns and regrouping

RESOURCES Counters; number grids; crayons; markers.

Teaching the content of the unit The skills and practice of multiplication are provided in this unit. Different learning styles are accommodated.

Unit 5 • Bright Sparks Teacher’s Book 5

referenced back to the Student’s Book lesson. CD-ROM activities are noted by the relevant lessons below.

Multiples (5.1) Study the multiples chart with the students. Ask probing questions to stimulate their thoughts. Look for patterns made by the numbers. Discuss what can be noticed about the numbers in each row or column. Practise counting in the multiples that are detected. This should be done thoroughly. Multiplication practice The exercise on this page requires the students to write down as answers some of the points discussed on the previous page. Since full discussion has already taken place, SB 5.1 A can be completed. Use the multiples chart where necessary to help complete SB 5.1 B. A CD-ROM exercise in Block A gives further practice of this concept. Use with WB Unit 5, Ex 1 or use this with the speed tests below.

Multiplication speed tests (5.2) Oral work on multiplication tables should be practised in groups and as a class to ready the students for these speed tests. SB 5.2 Speed tests can be completed on a daily basis, possibly over the course of a week, as a preliminary to other multiplication work. Look for improvement

in accuracy and/or speed during the period of the tests. Use with WB Unit 5, Ex 1, if not used previously.

Arrays (5.3) Use counters or paper and colours to duplicate the arrays shown, as you discuss the content of this page. Discuss the points made and show the two different ways that the array can demonstrate the factors. Draw the arrays and create others to show other multiplication sentences. Use WB Unit 5, Ex 2 before SB Ex 5.3

Square numbers (5.4) Draw the arrays to complete the multiplication sentences. Look at and discuss the shapes made by the arrays. Allow the students some time to create arrays showing square numbers, following the examples on the page. A CD-ROM exercise in Block A gives further practice of this concept.

Square roots (5.5) Read and discuss the information on square roots. Spend some time familiarising the students with the method for recording a square number, i.e. 32, 42, and the term ‘square root’ and its symbol. Make use of the practical application and complete SB 5.5 A and 5.5 B. Use with WB Unit 5, Ex 3

Problem solving: Mental computation (5.6) Each of these problems can be solved mentally. They require knowledge of tables or the ability to use the tables chart or arrays to find the answer. Practise tables as a preliminary activity. Complete SB 5.6. Use with WB Unit 5, Ex 4

Multiplying large numbers mentally (5.7) Briefly review place value. This knowledge will be needed to multiply numbers of two digits and more. Remind students that, like addition and subtraction, the

multiplication process begins on the right with the smallest place. The digits are multiplied moving from the right to the left, with regrouping when answers have more than one digit. Do two together with the class before instructing them to complete SB 5.7.

Multiplying 3-digit numbers (5.8) Further places are included now so focus has to be maintained to complete each step. Again, do some together with the class before instructing them to complete the appropriate exercises. Encourage the students to use the steps as laid out in the Student Book. SB 5.8 can be completed. Use with WB Unit 5, Ex 5

Multiplying large numbers (5.9) The same points apply to 5.9 A, which can also be completed. SB 5.9 B requires the students to solve word problems using the same skills practised in the previous exercises. Remind them to set the working down with the number to be multiplied by in the ones column. Use with WB Unit 5, Ex 6–7

Multiplying by multiples of 10 (5.10) Review the commutative property, i.e. numbers can be added in any order and the result will be the same. Review the associative property, i.e. the grouping of factors can be changed and the result remains the same. Check the example shown on the page. Students complete SB 5.10 A and B. Play with the numbers. Encourage the students to break them down and rearrange them to work out the answers. Check that answers are correct before selecting different students to show the break down that worked for them. Use with WB Unit 5, Ex 8

Multiplying by 2-digit numbers (5.11) (See also sample lesson plan below.) Follow the steps as set out on the page. The steps are colour coded for ease of use. Bright Sparks Teacher’s Book 5 • Unit 5

It can be very useful to expand the number that is being multiplied by and multiply each part separately to reinforce the steps. Using the same numbers as in the book, this would look like this:

• Note that multiple numbers of some items are purchased, so separate working will be necessary for these items.

438 438 1314 × 3 × 20 + 8760 1314 8760 10074

Multiplication practice (5.13)

Create a few more examples to do with the students before instructing them to complete SB 5.11. Use with WB Unit 5, Ex 9

Problem solving (5.12) Use SB 5.12 as a special activity. • Explain that the puzzle is like a crossword but it uses numbers which makes it a ‘crossnumber’ puzzle. Only one digit may be placed in each square. • Students copy the list of items into an exercise book with the correct prices beside each item. • They use their knowledge of place value to set the prices down in columns.

Use with WB Unit 5, Ex 10

Having learnt the skills necessary for long multiplication, this page offers the opportunity for further practice. Students complete SB 5.13 A, 5.13 B and 5.13 C in turn. Use with WB Unit 5, Activity (after Ex 10 in the WB).

Assessment 4 Unit 5 Check and summary will show if key points about multiples, square numbers and long multiplication have been grasped. Assessment 4, Parts 1 and 2, seeks to test skills in place value, addition, subtraction and multiplication of larger numbers. Part 2 emphasises problem solving.

Sample lesson plan UNIT 5 5.11 Multiplying by 2-digit numbers

Objectives (for the specific lesson) • To grasp the connection between expanding numbers and long multiplication

RESOURCES Multiplication tables.

• To be able to master the many steps necessary for long multiplication

Engaging the students’ interest / Connections

Initiate an oral multiplication tables session. Recite tables and call out questions out of order to encourage deeper thought and hopefully better retention. This work will link to expanding numbers, multiplication tables and multiplying by multiples of 10. Addition skills are also needed.

Unit 5 • Bright Sparks Teacher’s Book 5

Teaching the lesson

Practise expanding numbers as a reminder of how numbers are broken into their different values. Do some examples of multiplying the same number by ones and tens, remembering that the first step in multiplying by a multiple of 10 is to write the zero in the ones place. This leaves us with the simpler task of multiplying by a 1 digit number. Knowledge of multiplication tables is crucial to success here, so in the week prior to this, a lot of oral and written multiplication work should have been practised to prepare the students. Much of this could have been set as homework. The first few problems should be done as a class to help cement the concept. Ask for volunteers to complete answers for each multiplication and ask the students where to write the individual digits. Multiply by ones first and make sure that the students multiply from the ones place and continue to the larger places. If digits are regrouped they should be crossed out after they are added in so that the mistake of adding them a second time is not made. Donâ&#x20AC;&#x2122;t forget any digits. Multiply them all in turn. Multiply by the tens. First place the zero in the ones column and multiply, again beginning in the ones column and moving to the left until each number is multiplied. Give the same advice about digits that are regrouped. Cross each one after it is added in. The final step is to add the two sets of answers together, being careful not to do what should be the simple step, poorly. This addition is the final answer. Look at the number to see if it seems to be about the right size. Check the working and go on to the next problem. SB 5.11 can then be done. WB Unit 5, Ex 9 can be set as homework when the correct level of competence is achieved.

Differentiating for different learning styles

When working through an example on the board as in the example for teaching this page, set the 3 steps down side by side rather than underneath each other. This way the students can focus more easily on each stage of the working as each part is shown separately. Permission to use multiplication tables can often speed this process as some students are able to learn the steps but have difficulty memorising the tables.

Assessment

Check the working process and answers to determine whether the concept was understood. Discuss what was done with the students as a means of further cementing the concept.

Summary of key points

Long multiplication is a multistep process. Each step must be handled with care and special attention paid to the addition at the end as this is where avoidable errors can often be made.

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Unit 5

UNIT 6 Division Factors, Divisibility, Division: review, Using opposites: multiplication and division, Division speed tests, Division with remainders: review, Dividing larger numbers, Problem solving, Division using zeros, Using long division and zeros, Division with money, Using a calculator, Dividing by 2-digit numbers, Problem solving, Long division practice, Unit 6 check and summary, Assessment 5

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Find factors of numbers • Recognise prime numbers

Factors (6.1)

• Know the difference between a prime and a composite number

(See also sample lesson plan below.)

• Use rules of divisibility to find factors • Use multiplication to check division facts • Divide large numbers using long division • Solve problems using division • Understand that the remainder can be treated in different ways

RESOURCES Calculators; charts.

Teaching the content of the unit This unit deals with facts to do with division. It explores the use of division and multiplication as reverse operations.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit.

Unit 6 • Bright Sparks Teacher’s Book 5

Call out some composite numbers and find factors in this way: ask the students for numbers that multiply to make the called number, e.g. 12 – answers could be 3 x 4, 2 x 6, 1 x 12. Note these in a prominent place before calling another composite number. A factor is a number that can multiply with another number to give a chosen product. Call others and note them also. Eventually go through the sets of factors and work out other ways of setting down the answers. One would be to write them in order of size. Read and discuss the information about factors with the students. Practise setting down answers in ascending order with the students. Discuss the meaning of the terms prime number – having only 2 factors – the number itself and 1, and composite number – having more than 2 factors. Name some prime numbers and find the factors of these. All numbers have factors; some have only two. SB 6.1 can be completed: Use with WB Unit 6, Ex 1 Activity – Finding prime numbers The work on this page teaches how prime numbers can be found. Supply the students

with copies of the number square or have them draw and complete the numbering 1 to 100 in a square lined book. Work with them as they follow the instructions on the page. When they reach the last instruction they will find that the numbers left are prime numbers, and the numbers crossed (other than 1) are composite numbers. 1 is excluded from both sets as it has only one factor and therefore does not fit either criterion.

repeated subtraction, it is the opposite of multiplication, and it is the only mathematics operation in which working is not done from the right. Follow the explanation that begins this part of the unit, explaining the points as necessary. The final point shows three different ways that division can be set down. Discuss these before asking the students to complete SB 6.3.

A CD-ROM exercise in Block A gives further practice of this concept.

A CD-ROM exercise in Block D gives further practice of this concept.

Use with WB Unit 6, Ex 2

Divisibility (6.2) The fact that the multiples of the numbers 2, 5 and 10 follow exact rules and make patterns should be pointed out. Recite with the class the various numbers that make the patterns. The students may notice that some numbers appear in more than one pattern. Discuss this fact and name some of the numbers that do this. (This is the beginning of understanding common multiples.) Learn the rules that are noted and complete SB 6.2 A. Use with WB Unit 6, Ex 3 More divisibility patterns There are some special rules that have nothing to do with the pattern made by the numbers. The number 3 has an interesting characteristic. If the sum of digits in a number can be divided exactly by 3 the number is a multiple of 3. Think up a few numbers and challenge the class to check this rule. Instruct the class to complete SB 6.2 B. The number 9 has the same characteristic. This time the sum of the digits must be divisible by 9. Work out a few together with the class, then SB 6.2 C can be completed. A CD-ROM exercise in Block A gives further practice of this concept.

Division: review (6.3)

Use with WB Unit 6, Ex 4

Using opposites: multiplication and division (6.4) Review fact families/trios by asking multiplication and division facts using the same factors/divisors. Knowledge of multiplication tables and divisibility is used. Practise some oral ‘tables’ work also, wording questions to stimulate knowledge of the reverse operation. Allow the students to work with a partner to do the Partner Activity. Following this they can work on their own to complete SB 6.4. A CD-ROM exercise in Block B gives further practice of this concept. Use with WB Unit 6, Ex 5

Division speed tests (6.5) Oral work on multiplication and division tables should be practised in groups and as a class to ready the students for the speed tests in the SB and WB. Use with WB Unit 6, Ex 6 Speed tests can be completed on a daily basis, possibly over a few days. Look for improvement in accuracy and/or speed during the period of the tests.

Division with remainders review (6.6) The answers can be worked out purely by dividing and carrying or a new method can be learnt.

Discuss what the students remember about division. Some points are that it is Bright Sparks Teacher’s Book 5 • Unit 6

This is the long division method:

1 Divide the larger place first. 7 tens ÷ 3 = 2 tens The 2 goes above the 7. 2 Multiply 3 by 2 = 6. The 6 goes under the 7. 3 Subtract 6 from 7 = 1.

24 r 1 3 ) 73 6 13 12 01

4 Bring down the 3 ones next to the 1. This says 13. Start Over

1 Divide: 13 ÷ 3 = 4. The 4 goes above the 3. 2 Multiply 3 by 4 = 12. 12 goes under 13. 3 Subtract 12 from 13 = 1. There are no more digits to bring down so 1 is the remainder. Practise the chosen method with the class, verbalising the steps used. SB 6.6 can be completed. Use with WB Unit 6, Ex 7

Dividing larger numbers (6.7) Long division is the recommended method for these larger numbers. Repeat the four steps shown above until every digit is divided. If the final subtraction ends with 0, there is no remainder. Practise several of these with the class before instructing them to work on their own. SB 6.7 can be completed. A CD-ROM exercise in Block D gives further practice of this concept.

Problem solving (6.8) Multiplication and division have both been practised. These problems are a mixture of both operations. Discuss with the students what clues they can find to know which operation to choose. Remind them of the multiplication clue words and put together a division list. Clue words for division – share, how many ... can be ...? how much does each ...? Look carefully at the meaning of the words to see whether a larger number is required in the answer or a smaller one.

Unit 6 • Bright Sparks Teacher’s Book 5

This determines whether multiplication or division is chosen. Do SB 6.8. Use with WB Unit 6, Ex 8

Division using zeros (6.9) Sometimes in long division we bring down a digit and find that we still do not have a large enough number to divide. Here we reinforce that 0 is a number and it can be an answer to a mathematical question. Make sure that each time 0 is found to be the answer, it is recorded. Go through the example in the example box. Work out some of the answers to SB 6.9 as a class then allow the students to complete the exercise on their own. Use with WB Unit 6, Ex 9

Using long division and zeros (6.10) As the numbers increase in size the method remains the same. The students should be encouraged to use the zero to hold the place and to work until the very last digit is divided. SB 6.10 can be completed. Use with WB Unit 6, Ex 10

Division with money (6.11) This is like working with decimals. Remind the students that the decimal points should be aligned in the dividend and the quotient. The decimal point is not utilised for the rest of the working. The cost of one cannot be more than the cost of many, so always check that the answer is reasonable and that the decimal point was used. 6.11 can be completed. Use with WB Unit 6, Ex 11

Using a calculator (6.12) Follow the steps suggested on the page. The students can make up a few more problems to pose to a partner. They can take turns to use the calculators.

Dividing by 2-digit numbers (6.13) Use of rounding and division skills come together in division by larger numbers. The

steps are itemised in the example boxes. It may be helpful with some students to use zero to hold the place/s at the beginning of the answer, as students sometimes write the answer to the first step above the largest place. This can cause them to lose track. SB 6.13 A and 6.13 B can be done. Use with WB Unit 6, Ex 12

Problem solving (6.14) Reasoning is a superior skill. Knowing how to use an answer and what to retain and what to discard is crucial in the ability to connect learning. In these division problems the opportunity to test these skills is given. Discuss the answers. Some of them have remainders but they do not all require the answer to be expressed with that remainder. If buses are taking out a group of students and some students are left over do we leave them behind? If several students are to eat pizza but the pizzas don’t divide exactly into that number do we buy fewer pizzas or add one more? This is the type of reasoning offered in this exercise. Complete 6.14. Use with WB Unit 6, Ex 13

Long division practice (6.15) Further practice of the skills learnt earlier is offered. Complete 6.15 A and 6.15 B. Take some time to extend the students’ knowledge base by teaching the facts introduced in the exercise in the Enrichment: The order for more than one operation. The rules encompassed by the term BODMAS are introduced. Be clear with the students that Division and Multiplication have equal status, as do Addition and Subtraction. Therefore when completing a problem with multiple operations, these operations should be completed in the order that they appear. The challenge that follows WB Unit 6, Ex 13, gives some practice of this skill.

Assessment 5 Unit 6 check and summary will show if key points on factors, prime numbers, divisibility and long division have been grasped. Assessment 5, Parts 1 and 2, tests skills in factors, divisibility, multiplication and division. Part 2 incorporates higher thinking skills.

Sample lesson plan UNIT 6 6.1 Factors

Objectives (for the specific lesson)

RESOURCES

• to understand the meaning of the term ‘factors’

Paper; pencil; colours; multiplication tables.

• to be able to find pairs of numbers that give the product in question • to gain an awareness of prime numbers

Engaging the students’ interest / Connections

Ask the class to draw an array for the number 12. Check what was drawn. Hopefully all of the different combinations were used. If all of the pairs were not offered, ask

Bright Sparks Teacher’s Book 5 • Unit 6

them to draw a second array to see if the goal can be achieved. List the answers found and tell the class that this is the type of number we will be researching today. They are called factors. Division skills will also be practised, as well as a good knowledge of the multiplication tables and the use of arrays.

Teaching the lesson

Inform the class that every number has factors. Some have several factors; some have only two. Let’s look at the number 12 once more. Write12 at the top of the page and create two columns below this to set down its factors. The first factor of any number is always 1. Write this in the first column. This is multiplied by 12 itself to make 12. Write 12 in the second column.

12 1 × 12 2×6 3×4

If the number is an even number the next factor is 2. Write this under the 1 in the first column. Ask – What do we multiply by 2 to get 12? Write the answer to this in the second column. Next, see if 3 is a factor. We know a number is a factor if it can divide into the number without leaving a remainder. Yes, 3 is a factor so we find what is multiplied by 3 to make 12. Again, this goes in the second column. There are no numbers between 3 and 4 which means that there are no more pairs of factors that will combine to make 12. We have all of the factors of 12. These are always recorded in numerical order (1, 2, 3, 4, 6, 12). Choose another number and go through the process again. Invite the students to offer suggestions to help complete the chart. We can find which numbers are prime numbers because only one pair of factors will be found for these numbers – the number 1 and the number itself. Complete SB 6.1. WB Unit 6, Ex 1 can be set as homework.

Differentiating for different learning styles

Some students may need to have the multiplication tables available if they are not strong in memorising. In order to have the opportunity to learn the skill of finding factors, a compromise will have to be made so these students can find the answers.

Assessment

Informal assessment through discussion of what was done and how and why it was done can be used here.

Summary of key points in the lesson

A factor is a number that can be multiplied by another number to make a product.

Extension activities

Students can be encouraged to work on their own or in small groups to: • Start a factor chart which can be displayed to help the whole class. • Find a relationship between the largest factor and the one before it. What do they notice about even numbers? What do they notice about odd numbers?

Unit 6 • Bright Sparks Teacher’s Book 5

UNIT 7 Fractions Least (Lowest) Common Multiple, Greatest Common Factor (GCF)/Highest Common Factor, Prime factors, Common fractions (or proper fractions), Adding fractions, Decimals and fractions, Equivalent fractions, Reducing fractions to their simplest form, Estimating fractions, Improper fractions and mixed numbers, Equivalent fractions, Comparing fractions, Adding fractions, Subtracting fractions: review, Subtracting fractions with unlike denominators, Estimating and problem solving, Mixed numbers, Subtracting mixed numbers, Problem solving, Practice, Enrichment: Cross multiplication, Working with calculators, Unit 7 check and summary, Assessment 6

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Change mixed numbers to improper fractions • Change improper fractions to mixed numbers • Add fractions and mixed numbers with like and unlike denominators • Subtract fractions and mixed numbers with like and unlike denominators • Use HCF to reduce fractions to their lowest terms • Use LCM to make equivalent fractions • Use various strategies to solve fraction problems

RESOURCES Fraction charts; puzzles; calculators; fraction flashcards.

Teaching the content of the unit This unit teaches the facts necessary for addition and subtraction of common (proper) or mixed number fractions.

Least (Lowest) Common Multiple (7.1) Relate the students’ knowledge of multiplication tables to finding lists of multiples. Discuss the meaning of the word ‘common’. In mathematical terms it means belonging to two or more. List the multiples of any 2 numbers and look for multiples that are common to both. Continue listing and looking for common multiples. Discuss the meaning of least or lowest. Refer back to the original 2 numbers and multiples listed and select the one that is the least or lowest. Do this with groups of 3 numbers also. In this way, the students find the LCM. The key to doing this well is correctly finding multiples, so encourage the students to practise their tables (for homework) if they are not confident in their knowledge. SB 7.1 can be completed.

Bright Sparks Teacher’s Book 5 • Unit 7

A CD-ROM exercise in Block A gives further practice of this concept. Use with WB Unit 7, Ex 1

Greatest Common Factor (GCF) / Highest Common Factor (HCF) (7.2) Factors were studied in the division unit. A review of the meaning of the term factor should reveal that it is a number that is multiplied to give a multiple. Select two composite numbers, 20 or smaller, and list some factors. The examples on the page are 12 and 8. Look in this list for any factors that are common to both. Do other examples with the class; include finding factors of 3 numbers. Discuss the meaning of the words greatest and highest. In the lists just completed, look for the greatest or highest factor that they have in common. This is the GCF/HCF. SB 7.2 can be completed. Use with WB Unit 7, Ex 2

Prime factors (7.3) A factor tree looks just as it is described. It has branches with factors rather than leaves at the ends. They are fun to work out and the students get a chance to exercise their knowledge of multiplication and division facts. Start with any two factors of a number. Find factors of these two numbers. Continue drawing branches and finding factors until each limb ends with a prime number. These are the prime factors. These can be multiplied one by the other to build up to the original number. Have the students complete SB 7.3. The students can also be paired and asked to think of other numbers that their partner can factorise.

Common fractions (or proper fractions) (7.4) (See also sample lesson plan below.) Review the names of the parts of a common fraction, and what is shown by each. Use a picture that represents

Unit 7 â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

fractional parts of a whole. Also write the fraction represented in figures and question the students in this way: Which digit shows how many parts there are altogether? Which digit shows how many parts are coloured? What are the names of the different parts of a fraction? Do the same with pictures of parts of a set. SB 7.4 can be completed. Use with WB Unit 7, Ex 3

Adding fractions (7.5) Remind the students that when adding fractions, the numerators are added, but the number of parts in the fraction (the denominator) remains the same. An analogy previously used is this: we do not add cows to cows and get horses therefore it follows that we do not add thirds to thirds and get another unit. Do a few oral examples before instructing the students to complete SB 7.5.

Decimals and fractions (7.6) Here fractions are related to the decimals recently learnt. Ask the students what they remember about writing decimals. Review the names of the places and point out that the denominators 10 (ten) and 100 (hundred) speak for themselves in identifying the place value. SB 7.6 can be completed. CD-ROM exercises in Block F give further practice of this concept. Use with WB Unit 7, Ex 4

Equivalent fractions (7.7) Domino games matching blocks with the equivalent fractions shaded would be a good preliminary to this section. Focus initially on the size of the portion shaded and then on the different number of parts within the shape. Practise naming the equivalent fractions drawn in SB 7.7. The students can now complete this exercise and perhaps draw a few more of their own.

A CD-ROM exercise in Block D gives further practice of this concept. Use with WB Unit 7, Ex 5

Reducing fractions to their simplest form (7.8) Use structured play with equivalent fractions to prepare for the conceptual material in this section. Look at some of the fractions that have been made equivalent. Which do the students believe to be the simpler form? If we take simple to mean easy the answer should logically be the fractions with the smaller digits. For a fraction to be in its simplest form the numerator and the denominator must have no factors in common. If they are found to have a factor in common, each digit must be divided by this factor. Do some practice showing the students 2 numbers that have a factor in common e.g. 4 and 6. Can they spot the common factor? It is 2. Write the two numbers as a fraction and divide by this factor. 4÷2 = 2 6÷2 3 Try some others, and then allow them to complete SB 7.8 A and 7.8 B. Use with WB Unit 7, Ex 6

Estimating fractions (7.9) Study the information about estimating fractions and do some practice with some fractions that the students think up. This page plays an important role in helping the students look carefully at fractions to determine size. SB 7.9 can be completed. Use with WB Unit 7, Ex 7

Improper fractions and mixed numbers (7.10) Discuss and learn the three definitions given. To show students how to change an improper fraction to a mixed number, ask them to look at the diagram in the Challenge box representing the mixed number. The diagram shows 4 3 4 and 4 . Together it is more than a whole;

it is 4 . This is 1 whole and 3 more fourths. 3 Written as a fraction, this is 1 4 . Use some other examples to reinforce the concept. When the students understand this use of the diagram and can make up examples of their own, they can be shown the procedural steps needed to obtain the same result. 11 Example: 5 Step 1 Divide the numerator by the denominator.

2 r 1 5 ) 11

Step 2 Write the whole number.

Step 3 Work out the remainder and write it over the same denominator to the right of the whole number.

2 5

SB 7.11, 1a-e can be done.

Equivalent fractions (7.11) Look at the diagrams used on the previous page of the SB for Improper fractions and mixed numbers to see how this works in reverse. We can recognise that the diagram with the green squares shows 3 7 1 4 and also that this is the same as 4 . We 4 can also recognise that 1 9 is the same as 13 5 9 . Now look at 1 6 in section 7.11 of the SB. The diagram shows us how this looks as an improper fraction. Follow the stages outlined by the example to find a shorter method. SB 7.11 2a–e can be done. Ex. 7.20 B 1 and 2 offer further practice of this concept. A CD-ROM exercise in Block D gives further practice of this concept. Use with WB Unit 7, Ex 8

Comparing fractions (7.12) We have learnt one method in SB 7.9 to help us gain an approximation of which fraction is larger, but sometimes we need to be more exact in our thinking than this method allows. The traditional way Bright Sparks Teacher’s Book 5 • Unit 7

is to make both denominators the same by finding the Lowest (Least) Common Multiple. Review the work on finding the LCM and apply it to the work on this page. Remember that if one fraction already has the LCM as its denominator it does not need to be changed. Show both fractions with the same denominator and compare them to see which is smaller or larger. Complete SB 7.12. A CD-ROM exercise in Block D gives further practice of this concept. Use with WB Unit 7, Ex 9

Adding fractions (with unlike denominators) (7.13) This also involves finding the LCM of the denominators as it is not possible to add fractions with different denominators to each other. A point to take note of is this. If one of the denominators is a multiple of the other then this denominator is the LCM. It therefore follows that the fraction with this denominator does not need to be changed. Get students to do the Partner Activity before going on to SB 7.13 as individual work. Use with WB Unit 7, Ex 10

Subtracting fractions: review (7.14) Give the students some practice breaking whole numbers into fractions and expressing them as improper fractions. Discuss taking away a fraction from a whole number and how, logically, it makes 1 4 2 more sense to take away 4 from 4 , or 5 5 from 5 , etc. Give some practice subtracting simple fractions from 1 whole. Follow the working of the two examples in SB 7.14, reinforcing to the students that in order to subtract from a whole number larger than 1, regrouping of 1 whole is necessary. It is done in the same way as regrouping a ten if the problem was 34 – 16 = ? 1 is taken from the whole number and changed into a fraction with the same denominator as the fraction to

Unit 7 • Bright Sparks Teacher’s Book 5

be subtracted. Students do SB 7.14 A. Follow the steps drawn in the SB to subtract a whole number from a mixed number and do SB 7.14 B. Drawing the shapes and subtracting is a good way to grasp the concept of subtracting a mixed number from a whole number. Drawing combines the two stages just learnt. If the students are adept at subtracting a fraction from a whole number using regrouping, they should soon be able to perform this operation mechanically. SB 7.14 C, 7.14 D and 7.14 E can be done. Use with WB Unit 7, Ex 11–14

Subtracting fractions with unlike denominators (7.15) The review of subtracting fractions with the same denominators is offered as a review of the steps of subtraction. Once the students find these steps clear, they can approach the fractions in the Partner Activity. Working with a partner helps them to verbalise any difficulties. The first step is to make the fractions equivalent so that they can be subtracted. Review the methods for making fractions equivalent: 1) find the lowest multiple that both denominators have in common (the LCM), 2) ask yourself if both fractions need to be changed, 3) use the LCM to make the necessary change/s. When both fractions have the same denominator, subtract the numerators. Look at the answer to see if it is in its simplest form. Try out the method shown in the example box, which gives a more practical idea of the concept. Students do SB 7.15. Use with WB Unit 7, Ex 15

Estimating and problem solving (7.16) The problems on this page utilise many of the skills taught so far. Prepare the students to do this work by reviewing each

skill before attempting the page. Do SB 7.16. Use with WB Unit 7, Ex 16

Adding mixed numbers (7.17) Review what is already known. Fractions must have the same denominator before they can be added together. If the addition comes to an improper fraction it must be converted to a mixed number. If the digits in the fraction have a factor in common the fraction must be simplified (brought to its lowest terms). Discuss the points and use examples to make the explanations clearer. Read through the steps for the order of working with the students and do a few together before allowing the students to complete SB 7.17 on their own. Use with WB Unit 7, Ex 17

Subtracting mixed numbers (7.18) The various types of mixed number regrouping were itemised and taught separately. Review each method and give extra practice in any areas that need it. When the students are fully prepared, allow them to complete exercise SB 7.18 A. Working with mixed numbers Review how we know which operation is used to solve a problem. Read through the problems with the students, identifying the clues that we need to take note of. SB 7.18 B contains mainly subtraction problems. SB 7.18 C contains mixed problems. They can both be completed at this time. Use with WB Unit 7, Ex 18

Problem solving (7.19) Read through and discuss the suggested strategies. Perhaps you or the students can suggest others. See how well they work in solving the questions posed. A good strategy works every time; test yours with

different fractions and decide if they work. SB 7.19 can be done. Use with WB Unit 7, Ex 18, if this wasn’t used with section 7.18.

Practice (with fractions) (7.20) 7.20 A gives an opportunity to practise mixed fraction work and much of SB 7.20 B reinforces earlier teaching on improper and mixed number conversions. 7.20 1a–j and 2 a–j compliment SB 7.11. Use with WB Unit 7, Ex 19

Enrichment: Cross multiplication (7.21) This is a page introducing cross multiplication as a strategy that can be used to solve mathematical problems. Encourage the students to try the method and, using their knowledge of fact families/trios, challenge each other with more questions. There are some problems to be solved and/or discussed.

Working with calculators (7.22) The students are now encouraged to use the calculator to have more fun with Mathematics. Follow the instructions on the page in the SB. SB 7.22 can be completed using the calculator. Cross multiplication is recommended.

Assessment 6 Unit 7 Check and summary will show if key points about fractions have been grasped. Assessment 6, Parts 1 and 2, tests all fraction skills: finding LCM, finding GCF, writing fractions, equivalent fractions, comparing fractions, reducing fractions (including changing improper fractions to a mixed number), adding and subtracting fractions.

Bright Sparks Teacher’s Book 5 • Unit 7

Sample lesson plan UNIT 7 7.4 Common fractions (or proper fractions)

Objectives (for the specific lesson) • To aid understanding of fractions as part of a whole • To aid understanding of fractions as part of a set

RESOURCES Puzzles of geometric shapes divided equally into fractional parts; squared paper; rulers; colours.

• To be able to recognise the numerator as the specified section • To be able to recognise the denominator as the whole

Engaging the students’ interest / Connections

Share the squared paper and ask the students to draw a shape that is 4 squares across by 2 squares down. What is the name of this shape? Colour 3 of the smaller squares. Ask them to describe what part of the shape is shaded. They may say 3 parts out of 3 eight or they may say directly that it is 8 . Formally acknowledge that it is a fraction if this is not said directly. Ask them to draw another shape, 6 squares across by 2 squares down. Name this shape and shade 5 of these squares. Ask them to describe the shape, and write the fraction that represents it on the board for them to see. The students already know the term ‘fractions’ and they will now be reminded how the different parts are determined.

Teaching the lesson

Discuss what the students know already about fractions. The students need to recognise that these are not whole numbers but represent a part of the whole. Ask them if they remember the term ‘numerator’ and what the numerator tells us. The answer is: the number of parts counted. Ask them if they remember the term ‘denominator’ and what the denominator tells us. The answer is: the number of parts altogether in the whole. The discussion should develop into recognition that a number of items can also be categorised as fractions. When some of a group of items are selected, this becomes a part of a whole as well. Again, ask questions to encourage verbalisation of conceptual knowledge. Which digit represents the whole number of items? Which digit tells us the number of items being counted? Pose some imaginary situations similar to those in SB Exercise 7.4, 7–10. WB Unit 7, Ex 3 can be used for homework.

Differentiating for different learning styles

The students who have difficulty with the concepts may continue creating and recreating fractional parts for a longer period of time while the others complete the

Unit 7 • Bright Sparks Teacher’s Book 5

exercise. The more competent students can make up some similar problems to those in Exercise 7.4, 7–10, and can exchange them with a partner.

Assessment

Ask questions orally and encourage verbal explanations to determine understanding.

Summary of key points

Fractions can be parts of a whole. Fractions can be a certain portion of a set of items. The numerator tells us the number of identified parts. The denominator tells us how many there are in the whole.

Extension activities

Use the fraction puzzles and ask the students to count the pieces and complete each puzzle. Can they name the fraction when all of the pieces are in place? They can remove some pieces themselves and name each fraction as it is created. They can create some fraction problems of their own.

Bright Sparks Teacher’s Book 5 • Unit 7

UNIT 8 Geometry Lines, Angles, Measurement of angles, Triangles, Polygons, Naming plane (2D) shapes, Describing movement, Circles: review, Symmetry, Solid (3D) shapes: review, Making nets, Coordinates, Perimeter: review, Perimeter problem solving, Area and perimeter: review, Calculating area, More area problems, Enrichment: Area of irregular shapes, Area of triangles, Volume, Unit 8 check and summary, Assessment 7

OVERVIEW OF UNIT

RESOURCES

Objectives / Outcomes

Protractor; ruler; construction paper; hand mirrors; squared paper; patterned fabric; shape templates; shape charts; building blocks.

At the end of this unit students should be able to: • Recognise different lines • Recognise different types of angles • Name angles in more than one way • Measure and calculate the size of angles • Recognise different types of triangles • Know the properties of ten plane shapes • Create repeating patterns using flips and slides • Name the parts of a circle • Recognise and draw lines of symmetry in a variety of objects

This unit teaches about lines, angles, 2 dimensional and 3 dimensional shapes. It also includes finding the perimeter, area and volume, as well as plotting and reading coordinates.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit.

• Find the perimeter of a variety of shapes

• Calculate area of rectangles and right angled triangles using a formula

Lines (8.1)

• Identify and describe 7 solid shapes • Read and plot coordinates on a grid

• Begin to understand how volume is calculated

Teaching the content of the unit

Unit 8 • Bright Sparks Teacher’s Book 5

Read and discuss the information given with the students. Talk about places where they can see examples of the different types of line, e.g. railway tracks, roads – parallel lines; electric or telegraph lines – line segment; road junction, ceiling beams – intersecting or perpendicular line; etc. Follow up on the discussion box. Think of other situations where the relationship

between a straight and a curved line can be proved. SB 8.1 can be done. CD-ROM exercises in Block C give further practice of this concept. Use with WB Unit 8, Ex 1

Angles (8.2) (See also sample lesson plan below.) Use the information about angles as a starting point for discussion. Follow the instructions to do the practical activity. The students can work in groups taking turns to make and name the types of angle. Naming angles The letters represent points on the rays. We name the angles by using these points. Three ways of doing this are shown. Draw some more representations of angles on the board or show posters of other examples that the students can practise naming. Do the Partner Activity. The students can also reuse their angle strips to make the angles shown. Naming types of angle refers to the words acute, obtuse, etc. Naming angles refers to the use of the letters at the points. Be very clear in how these phrases are used. SB 8.2 can be done. A CD-ROM exercise in Block C gives further practice of this concept. Use with WB Unit 8, Ex 2

Measurement of angles (8.3) Review the measurements and names of types of angles. Provide the students with some diagrams of angles and give them time to do some practical measuring (the angles should have arms slightly longer than a regular protractor). In order to find missing angles the students need to be very sure how many degrees there are in each type of angle. Constant reinforcement of this is necessary. Finding the degrees of a missing part of a straight line or right angle becomes child’s play when this knowledge is assured. This interfaces with basic subtraction skills already practised. Ask questions to

stimulate the thought process e.g. How can we find a missing number when we already know the total? The answer is by subtracting. Use the examples and work out the answer to these. First state what we know – A straight line measures 1800, the acute angle shown is 400, the difference between these two numbers is 1400. Is this a reasonable answer? Check this way: the missing angle is obtuse (more than 90 and less than 180) so 1400 is a suitable answer. State the known information before doing the calculation. Complete SB 8.3. Use with WB Unit 8, Ex 3

Triangles (8.4) Ask the students to give a definition of a triangle. Look at the many representations of triangles shown on the page. Discuss the differences and similarities in the shapes. Refer to the names of the types of triangle. With the students, think of a mnemonic that will keep them reminded of which name goes with each one. An example is isosceles – the pronunciation begins with ’eyes’. We have two eyes and an isosceles triangle has two sides as well as two angles that are the same. SB 8.4 can be done. A CD-ROM exercise in Block C gives further practice of this concept. Use with WB Unit 8, Ex 4

Polygons (8.5) Name the polygons that are shown on the page. The teacher should supply any names that are not known by the students. Describe the properties of each one and make comparisons. Define a quadrilateral and ask the students to draw their own quadrilateral. Discuss what they understand by the term ‘regular polygon’. Determine through discussion the qualities of an irregular shape. If we know that a regular shape has sides of the same length and angles Bright Sparks Teacher’s Book 5 • Unit 8

of the same measurement, we should also know that an irregular shape has sides and angles that differ. SB 8.5 can be completed. A CD-ROM exercise in Block C gives further practice of this concept.

Naming plane (2D) shapes (8.6) Use practical materials to demonstrate. Use a cut out square and turn it at different angles to show the students that it is the same shape. Look at the parallelogram and the rhombus, which have similarities. Make comparisons of the two shapes and determine why they are named differently. SB 8.6 can be done. Use with WB Unit 8, Ex 5

Describing movement (8.7) Follow the instructions in the Activity for flips and discuss the result. A flip shows a reflection of the subject. Explain that when we look into a mirror we see an image in reverse. Select two students of similar size and ask them to stand facing each other. Choose one of them to initiate movement. The other is to copy exactly (mirror) what they see the first one do. Ask questions: Which hand does child 1 raise? Which hand did child 2 raise to match this? In which direction did child 1 move? ... child 2 ...? Ask other questions relating to the actions chosen by child 1. Use with WB Unit 8, Ex 6 Read with the class the information about slides. A slide faces the same direction as the original pattern piece. Patterns can be made by sliding and drawing a shape in new locations. A slide is never lifted or turned over. Some students may have a family member or friend who sews. Ask them to bring in some pieces of patterned fabric so that they can be used to give a better idea of pattern making. The follow up Activity can be turned into an art lesson. They can use a geometric or other shape to create a pattern. This all stimulates the students’ visual awareness and the ability to see patterns in all aspects

Unit 8 • Bright Sparks Teacher’s Book 5

of life. Patterns can be made using flips also. A CD-ROM exercise in Block C gives further practice of this concept.

Circles: review (8.8) Discuss the parts of a circle. Ask the students to read the names and descriptions. Follow up on the discussion point and the suggested activity. Each child can draw their own circle (draw around a jar) and fill in the names of the parts in colours of their choosing. Do SB 8.8 A and 8.8 B. Use with WB Unit 8, Ex 7

Symmetry (8.9) Review line symmetry with the students – a method of determining if a diagram has line symmetry is stated on the page. Encourage working in pairs. Put the students into pairs to discuss and work out if the pictures show a line of symmetry. The line of symmetry should be drawn based on the view of the picture shown in the diagrams. Do the same for the numbers that are listed. Give the students tracing paper to trace SB 8.9 A and 8.9 B and fill in the line/s of symmetry. Use with WB Unit 8, Ex 8 Use the Enrichment exercise to reawaken awareness of the concept of rotational symmetry. A CD-ROM exercise in Block C gives further practice of this concept.

Solid (3D) shapes: review (8.10) Before the lesson, ask the students to collect 3-dimensional objects. A display of solid shapes should be mounted. Read through the suggested work on this page and encourage the students to use the mounted display and other examples that exist in the classroom. The solid shape may be a part of a larger object in some cases. Read and discuss the diagrams of solid shapes and the definitions beside them.

There are several names to be learnt, not only names of shapes but parts of shapes. Mathematics and Language Arts should be integrated, if possible, to accommodate learning the names, meanings and spellings. SB 8.10 can be done. A CD-ROM exercise in Block C gives an extension of this concept. Use with WB Unit 8, Ex 9

Making nets (8.11) Discuss the objects in the solid shape display and use the mathematical name for them as preparation to do SB 8.11. The students can be given copies of the nets from which to build the solid shapes. Further practice creating nets of solid shapes would be advisable also. Use with WB Unit 8, Ex 10

Coordinates (8.12) Maps are set out on grid lines. Maps in atlases and on the weather news show the imaginary lines which we know as grid lines. These are numbered going from left to right and from bottom to top. Look at the first grid. It is numbered 0 â&#x20AC;&#x201C; 7 in both directions. Coordinates on a grid are recorded in a particular way. The brackets and the comma both play their part. First we record the horizontal information, followed by the vertical information. There is an idea in the example box to help the students remember this order. Ask students to do the Partner Activity, then go through the answers with the class. Do the suggested Activity, also with partners, for further practice. A CD-ROM exercise in Block C gives further practice of this concept. Use with WB Unit 8, Ex 11

Perimeter: review (8.13) Remind the students that knowledge of the number of sides in the shape is vital before the perimeter can be worked out. The perimeter can be found by adding

the measurements of each side together. Review the qualities of regular polygons. Since each side measures the same, a shorter method can be used to find the answer. The length of one side can be multiplied by the number of sides in the shape. Instruct the students to complete SB 8.13 A and WB Unit 8, Ex 12 . A ruler is needed to do SB 8.13 B. Each side must be measured accurately and the measurements added together. Look at the questions in SB 8.13 C and in an interactive manner work towards the response that shapes 1, 2, 3 and 5 are all regular polygons. Encourage students to use the shorter method to find the perimeter. Assign SB 8.13 C.

Perimeter problem solving (8.14) A pictorial representation of each problem will provide a concrete picture of each shape. Do encourage the students to follow this instruction to help find the solutions. 6 and 7 reintroduce the concept of the missing number which has been used in much of the problem solving so far. Remind them to use what they know to help them find out what they do not yet know. The total is known (this is the biggest number), some sides are known; add the known sides and subtract this total from the perimeter. (See if they can remember this method with gentle prodding from you.) Assign SB 8.14. Use with WB Unit 8, Ex 13 More able students can complete the Challenge. A CD-ROM exercise in Block E gives further practice of this concept.

Area and perimeter: review (8.15) Explore how area differs from perimeter. Work out definitions with the students. Review the two methods of finding the area: counting squares or multiplying the length by the width. Complete SB 8.15. Use with WB Unit 8, Ex 14, which gives practice counting the squares. Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Unit 8

Calculating area (8.16) Remind the students that the length of a rectangle is multiplied by its width to find the area. 6 cm × 3 cm = 18 cm2 6 cm

3 cm

The answer is expressed in square measure. This is not to be confused with square numbers (62 = 6 × 6). In the answer 18 cm2, the 2 expresses that 18 squares of 1 cm × 1 cm in dimension can be used to cover the shape. Ask students to do SB 8.16 A. SB 8.16 B and 8.16 C Working with area, offer further practice of the same skill and can also be assigned. Use with WB Unit 8, Ex 15

More area problems (8.17) Make a connection with this and the work with fact families (trios). Make these points. Two factors and a multiple are needed to make a multiplication sentence. factor × factor = multiple The multiple is the largest number so it is the part of the equation that tells us the area. One factor is given and we have to work out the other. We can reverse this and divide the multiple by the factor that we know. The missing factor is the answer. Our knowledge of square numbers tells us that there is only 1 factor which is multiplied by itself to form the multiple. Assign SB 8.17. Use with WB Unit 8, Ex 16

Enrichment: Area of irregular shapes (8.18) The knowledge gained to find the area of

Unit 8 • Bright Sparks Teacher’s Book 5

rectangles can be transferred to find the area of irregular shapes. Example 1 shows an L-shaped figure. Break this down to look like 2 rectangles and find the area of each, then add the 2 answers together. We could also find the area of the large rectangle (ignoring the fact that a part is missing), then the area of the missing part and finally take one from the other. Example 2 shows 2 rectangles, one within the other, with the border shaded. Again we find the area of each rectangle but this time we want the area of the border only. Subtraction is used to find the answer. Use discussion to draw out why different operations were used. Follow up with the Partner Activity. A CD-ROM exercise in Block E gives an extension of this concept. Use with WB Unit 8, Ex 19

Area of triangles (8.19) To help with the concept formation, cut a rectangle diagonally in half, producing 2 right-angled triangles. Discuss what was done. Compare the size of the triangle and the rectangle. One is double the other in size. Lay the 2 right-angled triangles on top of the rectangle to reinforce this information. Give the dimensions of the rectangle and ask the students to work out the area. Next ask them for the area of the triangle. Allow them to express what they know and what they can deduce from what they know. If the triangle is half the size of the rectangle, logically the area is half that of the rectangle. Share the formula for the area of a triangle with the class. Remind them to always bear in mind the relationship between the size of the triangle and the size of the rectangle as they find the area. Display a large diagram depicting the 2 shapes side by side or with the triangle inlaid on the rectangle. Assign SB 8.19. Some students work better with 1 the alternate formula 2 base × height. This can be used if preferred.

A CD-ROM exercise in Block E gives further practice of this concept. Use with WB Unit 8, Ex 17

Volume (8.20) Review the properties of solid shapes. Demonstrate the use of building blocks to create a cuboid with a base that is 5 squares long and 4 squares wide. It should have a height of 3 squares. How can we find out how much space is occupied by this shape (this is also called the volume)? The blocks can be counted individually to find the answer but that could be a lengthy process. If we multiply 5 × 4 that only tells us the area of the base. There are 3 layers in all. We have to multiply this 3 times and add the totals together. Try each idea as it is suggested. Talk about the

solid shape again and look for a shorter way of determining the volume. Each layer has the same number of blocks: 5 × 4 = 20 blocks. 3 layers would mean we multiply 20 × 3 = 60. The result is that we multiplied the length by the width by the height. This is 5 × 4 × 3. The answer is expressed using cm3. SB 8.20 can be completed. A CD-ROM exercise in Block E gives further practice of this concept. Use with WB Unit 8, Ex 18

Assessment 7 Unit 8 Check and summary will show if key points on lines, angles, plane and solid shapes have been grasped. Assessment 7 tests the geometry skills taught in Unit 8.

Sample lesson plan UNIT 8 8.2 Angles – naming angles

Objectives (for the specific lesson) • To understand how angles are formed • To be able to recognise that angles have different shapes • To learn the names of the different types of angle

RESOURCES Strips of card about 20 cm × 4 cm (with holes pre-punched if fasteners are to be used); paper clips, fasteners or string.

• To learn how to use the letters that label rays to name angles

Engaging the students’ interest / Connections

Begin by doing a craft activity. Distribute the materials to make an angle – 2 pieces of card and a paper clip. Instruct the students to put the two pieces of card together in such a way as to look like the hands of a clock saying 3 o’clock. Fasten them with the paper clip. Continue instructions to move the hands around so that they create different shapes. They can move them closer together and further apart freely. The paper clip can be removed and replaced if necessary. Give them a few moments to ‘play’ with their angles.

Bright Sparks Teacher’s Book 5 • Unit 8

They should know the terms line, line segment, and ray. Which of these terms best describes the materials they are using? The answer is ray. These are something like the hands of a clock. Discuss this similarity and ask which times are suggested by some of the angles made.

Teaching the lesson

Move on to more directed activity. Ask the students to form a pointed angle. Tell them that this angle is called an acute angle. When something is acute it is sharp or pointed, like this angle. An example is an acute pain, that makes you feel that something pointed is pushed against you. Next ask them to form a more open angle. Ask them to stretch the pieces so they make a straight line. This one is called a straight angle. Ask them to show you other shapes that they have discovered. You should be able to identify a right angle, which you should name for them, and an obtuse angle. The word obtuse can be used to describe something that is not direct. Some students may make other acute or obtuse angles. This will give you the opportunity to define the different types of angle and show them that the right angle and the straight angle always look exactly the same. The direction that the rays face is the only thing that will change. Obtuse and acute angles can vary in width but do have specifics beyond which they cannot stray. Define the different angles clearly for the students. Use the definitions in SB 8.2 which offer practice naming angles. Each ray is named with a letter at each end of it. The point made by the connecting lines of the rays has only one letter. Begin and end with a letter from the open part of the angle; the letter at the vertex is used in the middle of these. An angle can also be named using only the letter at the vertex, with the angle sign in front of it. After completing this exercise, WB Unit 8, Ex 2 can be used for homework.

Differentiating for different learning styles

Have the quicker students draw the angles facing in as many different directions as they can.

Assessment

Verbal assessment can be used in the first instance. A more formal assessment would require you to create a worksheet with series of the different angles pointing in different directions. The students would have to name each angle or classify them under the different headings.

Summary of key points

Angles are formed when two rays meet. The rays may be facing any direction. The name of the angle is determined by the size of the space between the 2 rays. The letters used to name the ray are used in a different way to name the angle.

Extension activities

Identify objects around the room which show the various angles. Have students explore whether there any other parts of the body that can make the different angles. The elbow was already mentioned in the exercise. Can any other body parts do the same job?

Unit 8 â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

UNIT 9 More decimals Multiplying decimal numbers, Division by a whole number, Adding zeros to the dividend, Multiplying and dividing decimals by 10, 100, 1000, Enrichment: SI, the metric system, Metric conversions, Unit 9 check and summary

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Multiply decimal numbers by whole numbers and decimals • Divide decimals by a whole number • Multiply and divide multiples of 10 by moving the decimal point • Use knowledge of the metric steps to convert metric measurements

Multiplying decimal numbers (9.1) (See also sample lesson plan below.) Review place value of whole numbers, as well as that of the decimal places tenths and hundredths. Introduce the thousandths place, which is one place to the right of the hundredths place. Do some oral and flashcard work asking the students to identify the place of specific digits. Review the steps of long multiplication. 1) Work from right to left starting with the ones place. 2) Multiply by each place value in turn.

RESOURCES Metric conversion charts; flash cards of decimal numbers.

Teaching the content of the unit This unit teaches multiplication and division of decimal numbers. It makes use of money problems and metric conversions as a means to provide further practice of the skills.

3) When multiplying by the tens, put zero in the ones. 4) Add the 2 sets of figures to get the final answer. The difference with decimal numbers is that there are decimal points which seem to interrupt the flow of the multiplication. The decimal point plays no part during the multiplication process but at the end all digits that follow the decimal points should be counted (see the example box). If there are 3 places, count 3 places from the right and place the decimal point before that digit. Work out the first 2 problems of SB 9.1 A as a class before instructing the students to continue on their own. SB 9.1 B offers further practice of the same skill. CD-ROM exercises in Block B give further practice of this concept. Use with WB Unit 9, Ex 1–3 Bright Sparks Teacher’s Book 5 • Unit 9

Division by a whole number (9.2) Review division of larger numbers. 1) Start on the left and divide the first digit. 2) Multiply this answer by the divisor. 3) Subtract. 4) Bring down the next digit. In long division of decimal numbers the same steps are followed. The decimal point plays no part for the working below the dividend, but it must appear in the quotient. It is aligned with the position it holds in the dividend. Work out the first 2 problems of SB 9.2 with the class and assign the rest as individual work. Use with WB Unit 9, Ex 4

Adding zeros to the dividend (9.3) It is not correct with decimal numbers to have a remainder. To avoid this we use a zero to create a new decimal place in the dividend. Adding a zero after the decimal point does not change the value of the original number. Show examples of a few comparisons using decimal numbers with and without the extra zero. E.g. Which is more 3.9 or 3.90? ... 4.56 or 4.560? ... 723.1 or 723.100? Therefore when we have divided each digit of the dividend and still have a remainder we can use the zero to give us another digit to bring down. (This may also be a good time to help them apply the concept that after every whole number, the decimal point is implied. This means 9 = 9.0) Instruct the students to do SB 9.3. WB Unit 9, Ex 5 and 6 can be done in the same manner as the previous exercise. When there appears to be a remainder, add zero after the smallest place in the dividend and continue working. CD-ROM exercises in Block A and D give further practice of this concept.

Multiplying and dividing decimals by 10, 100, 1000 (9.4) Review multiplying by 10s (SB 4 and 5: Unit 5.10). Note that the answer always

Unit 9 â&#x20AC;˘ Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5

increases by 1 place. Each digit moves one place to the left. When the number is a decimal number the decimal point appears to move one place to the right. When we multiply by 100 the decimal point moves 2 places to the right and by 1000 it moves 3 places to the right. The decimal point moves a place to the right for every zero in the multiplier. Dividing by 10 has not been practised but it follows the same procedure. Since multiplication and division are reverse operations the reverse of what happened for multiplication will be true for division. The answer always decreases by 1 place. The decimal point moves one place to the left for every zero in the divisor. Instruct the class to complete SB 9.4 A and SB 9.4 B. SB 9.4 C is suggested as a timed exercise. It comprises mixed multiplication and division work. CD-ROM exercises in Block A and D give further practice of this concept. Use with WB Unit 9, Ex 7

Enrichment: SI, the metric system This is an informational part of the unit. Read and discuss the information. Assign the new words as a spelling and vocabulary exercise. Assign research to find out more about the system.

Metric conversions (9.6) Use discussion and memory aids to help the students learn the order of the steps on the metric ladder. Connecting this with what they know about multiplying and dividing by 10 should make the conversion task easier. An enlarged copy of the chart should be displayed to help the students until they learn each step. SB 9.6 A can be done. Use with WB Unit 9, Ex 8 An important point to remember is that regardless of whether the chart deals with grams, litres or metres the prefixes remain constant.

Using decimals in metric measurements

Assessment

The students’ skill in multiplying and dividing by multiples of 10 is given further practice with this exercise. Challenge them to learn the steps and complete SB 9.6 B at a later date, without referring to the chart.

Unit 9 Check and summary will show if key points on multiplying and dividing decimals have been grasped.

Use with WB Unit 9, Ex 9

Sample lesson plan UNIT 9 9.1 Multiplying decimals

Objectives (for the specific lesson)

RESOURCES

• To relate multiplying decimals to multiplying whole numbers

Pencils; paper.

• To understand what to do with the decimal point • To understand that the numbers do not need to be aligned

Engaging the students’ interest / Connections

Count around the class in multiples of 6, 7, 8 or 9. These tend to be the multiplication tables that are least known. Similarly do some spot calling of parts of the tables and make it feel more like a game so that students will be keen to take part. Knowledge of multiplication tables is key to success at this work.

Teaching the lesson

Review the long multiplication process, reminding the students about breaking the number to be multiplied by into its different values. Use the example in the SB and follow each stage of working. Next, as the example shows, put in some decimal points and work it out again. Even though these numbers have a decimal point between the digits, we ignore this and break the number into values as though they were tens and ones. The answer will be identical to the original answer. Point out to the students that it is only at this stage that the decimal point is used. Note that there are two decimal points in the problem. Count the places after each decimal point and add them together. In the example there are three places. Show the students that they are going to count three places from the smallest place (on the right) and place the decimal point before the third digit – in other words three places from the right. Reinforce the fact that the decimal point played no role in the early working. Yet it is important and must be used now.

Bright Sparks Teacher’s Book 5 • Unit 9

Emphasise to the students that they are following the same steps as multiplying whole numbers but there is one extra step. This is the step where we find out where to place the decimal point. Many of the numbers in the exercise have zero in the ones position. Remind them that we do not multiply by 0 as the answer is always the same – 0. It adds no value. If the number to be multiplied by is 0.8 we just multiply by 8. We must, however, count the places held by the zeros which follow the decimal point when determining the number of decimal places. SB 9.1 A and 9.1 B can be done. WB Unit 9, Ex 1–3 follow up on this concept.

Assessment

This is a very early stage in the learning process and too early for formal assessment. Ask students to verbalise the steps that they are using. Take note of how well they are able to perform the task set and arrive at the correct answer. Some may be able to continue on their own, others will need careful monitoring in order to reach the same standard.

Differentiating for different learning styles

Some students may find it works better if they count the decimal places and make a note of how many there are before multiplying. This could be set down beside the problem to be used later. This avoids the situation where they forget to count the decimal places.

Summary of key points

Decimal points do not play a part in the multiplication process. Decimal points are placed in the answer at the end of the working. Count the number of decimal places in both factors to know where to place the decimal point in the end answer.

Extension activities

There are CD-ROM exercises in Block B which give further practice of this concept.

Unit 9 • Bright Sparks Teacher’s Book 5

UNIT 10 Measurement Units of length, Longer lengths: review, Working with units of length, Practice with longer units of length, Mass, Converting between units of mass, Capacity: review, Converting between units of capacity, Mixed units, Problem solving: different units of measurement, Unit 10 check and summary

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Select the correct units when measuring length • Select the correct units when measuring mass • Select the correct units when measuring capacity • Convert to/from units in common use • Apply knowledge of conversion to solve measurement problems

for homework. Each WB exercise is cross referenced back to the Student’s Book lesson. CD-ROM activities are noted by the relevant lessons below.

Units of length (10.1) Review the names of the metric units that are most commonly used (millimetre, centimetre, metre and kilometre). Discuss which units are smaller and which are larger. Order them according to their size. Have the students demonstrate the length of a millimetre and a centimetre using their fingers. Check that the students are showing accurate representations of the measurements. SB 10.1 can be done. Use with WB Unit 10, Ex 1

RESOURCES

Longer lengths: review (10.2)

Scales; 30 cm rulers; metre rulers; empty ice cream and margarine containers; plastic cups; bottles.

Have the students stretch out their arms to demonstrate a metre. Give them a memorable description of a one kilometre distance – perhaps from school to ..... is 1 km (a place that they would know). Some of them may walk this distance to and from school each day. SB 10.2 can be done.

Teaching the content of the unit This unit explores measurement of length, mass and capacity, and gives further practice with metric conversions.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit. Practice exercises in the Workbook are noted as ‘WB’ and may be used in class or

Use with WB Unit 10, Ex 2 Relate all measurements to the students’ experiences to give them a frame of reference.

Working with units of length (10.3) The students can use the information in the hint box as they complete SB 10.3 A. Use with WB Unit 10, Ex 3

Bright Sparks Teacher’s Book 5 • Unit 10

SB 10.3 B can also be completed at this time. The conversions in the information box give quick references for conversion of metres to centimetres and vice versa. Focus some attention on breaking m into cm and 1 1 3 learning what fractions ( 4 , 2 , 4 ) of a m are worth in cm. The students can refer to the box as they complete SB 10.3 C, WB Unit 10, Ex 4 and 10.3 D. SB 10.3 E and WB Unit 10, Ex 5 provide practice in applying the knowledge gained as metres and centimetres are added and subtracted. A CD-ROM exercise in Block E gives further practice of this concept.

Practice with longer units of length (10.4) The conversions are shown for kilometres to metres and vice versa. Focus some attention on breaking km to m and 1 1 3 learning what fractions ( 4 , 2 , 4 ) of a km are worth in metres. Oral work and discussion of the conversions will speed up concept conservation. The students can refer to the information box as they complete SB 10.4 A and B and WB Unit 10, Ex 6 . SB 10.4 C and WB Unit 10, Ex 7 give them practice applying the concept as m and km are added and subtracted.

Mass (10.5) Discuss the information in the Mathematical language box and become familiar with a new unit for measuring mass – the metric tonne – which has the mass of 1000 kilograms.

Converting between units of mass (10.6) Read with the students the conversions for grams to kilograms and vice versa. Discuss whether it would be possible for a child to lift an object weighing milligrams, grams, kilograms or tonnes, and why. Create lists of things that could be weighed using milligrams, grams, kilograms or tonnes as the unit of measurement. SB 10.5 A can be done.

Unit 10 • Bright Sparks Teacher’s Book 5

Focus some attention on breaking kg into grams and learning what fractions 1 1 3 ( 4 , 2 , 4 ) of a kg are worth in grams. SB10.5 B and can be done. A CD-ROM exercise in Block E gives further practice of this concept. Use with WB Unit 10, Ex 8 Review the method for making numbers 10,100 and 1000 times larger or smaller. (The decimal point is moved to the right or to the left the appropriate number of places.) Remind the students of these points: 1) When the unit of measurement is small, more units are needed and when the unit of measurement is large, fewer units are needed. 2) After the decimal point, zero can be added at the end without changing the value of the number. Complete SB 10.6 and WB Unit 10, Ex 9 by moving the decimal point.

Capacity: review (10.7) (See also sample lesson plan below.) The units of capacity in frequent use are litres and millilitres. Discuss and list some items that can be measured in ℓ – soft drinks, gasoline; and mℓ – shampoo, medicine. The conversion is 1ℓ = 1000 mℓ. Focus some attention on breaking ℓ into 1 1 3 mℓ and learning what fractions ( 4 , 2 , 4 ) of a ℓ are worth in mℓ. SB 10.7 A and 10. 7 B and WB Unit 10, Ex 10 can be done. The concept of converting litres and millilitres is strengthened as addition and subtraction are completed in SB 10.7 C. Use with WB Unit 10, Ex 11

Converting between units of capacity (10.8) More practice of converting ℓ – mℓ and mℓ – ℓ is offered in SB 10.8 and WB Unit 10, Ex 12 . Review all conversions in an oral session before asking the students to complete SB 10.9.

Mixed units (10.9)

Assessment

More revision of each type of conversion should be carried out, and the various methods discussed, before asking the students to attempt SB 10.10.

Unit 10 Check and summary will show if key points on measurement of length, mass and capacity have been grasped.

A CD-ROM exercise in Block E gives further practice of this concept.

Sample lesson plan UNIT 10 10.7 Capacity: review

Objectives (for the specific lesson)

RESOURCES

• To gain knowledge of the different units of measurement

Empty containers of varying sizes e.g. teaspoons, bottle tops, yogurt containers, ice cream containers, bowls, buckets; water.

• To be able readily to select the correct unit for measuring different quantities

Engaging the students’ interest / Connections

Bring a bucket of water to the class (or take the class to a more suitable area for a practical lesson with water). Organise a race between two groups of students. Give one group bottle tops and a 2 litre ice cream container; give the other group yogurt containers and a 2 litre ice cream container. The task is to see who can fill their 2 litre container faster. After they have finished, discuss the advantages/disadvantages of the selected containers. Hopefully the students engaged in water play in their early years which would have given them some experience from which to build.

Teaching the lesson

Ask the students if it was practical to use bottle tops to fill an ice cream container. Discuss this. Give them the opportunity to voice some reasons for their answer. Ask the class if they know the names of any units of measurement. Some of the objects that we used today may have measurements on them. Check whether the students know the names of any types of liquid measures. Check also whether they know which ones are larger units and which ones are smaller. Correct and/or supply any missing information before directing the class to focus on the litre and the millilitre. Explain that the prefix ‘mille’ or ‘milli’ describes a thousandth of a larger unit e.g. millennium is a thousand years. A millennium is larger than a year. A litre has a thousand millilitres. A litre is more than a millilitre. A millilitre is a very tiny measure of liquid therefore when ‘milli’ is placed before litre we are generally going to see a large number. It takes a large number of tiny units to equal a large unit. Read through the conversion box on the page and do some oral work. Ask very simple questions based on the conversions that can be seen, to build confidence e.g. How

Bright Sparks Teacher’s Book 5 • Unit 10

many mℓ in 2 ℓ? After that build to conversions that can be worked out from the ones 3 1 1 displayed e.g. How many mℓ in 4 ℓ? Which is more, 2 ℓ or 4 ℓ? The questions in SB 10.7 B are all based on the ℓ to mℓ conversions so it is given that each time a whole number is seen in the litre section, the mℓ conversion will be a number in the thousands. Be careful with 4. It’s a tricky one. Exercises 10.7 A and B can be done.

Differentiating for different learning styles

At the beginning of the lesson, select carefully and allow the students who would benefit from the more practical approach to participate more fully in the experiment.

Assessment

An activity such as putting <, > or = between some simple measures of mℓ and ℓ.

Summary of key points

Litres and millilitres are measures of liquids. Litres are 1000 times larger than millilitres. Use a unit size measure appropriate to what is being measured.

Extension activities

Ask the students to list items (measured in litres or millilitres) from an imaginary shopping trolley. Set the students the task of finding items that are about check items in their home or the supermarket.

Unit 10 • Bright Sparks Teacher’s Book 5

1 2

litre/500 millilitres. They can

UNIT 11 More fractions Multiplying fractions, Multiplying whole numbers and mixed numbers by fractions, Cancelling, Drawing a sketch, Dividing fractions, Mixed multiplication and division of fractions, Mixed problem solving, Teamwork: Measurement game, Unit 11 check and summary, Assessment 8

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Cancel, in order to multiply fractions by fractions • Multiply fractions by whole numbers • Multiply mixed numbers • Find reciprocals and divide common fractions • Divide whole and mixed numbers by fractions • Apply skills to solve multiplication and division problems

RESOURCES Squared paper.

lesson. CD-ROM activities are noted by the relevant lessons below.

Multiplying fractions (11.1) (See also sample lesson plan below.) Do practical work drawing and colouring 1 fractions to demonstrate finding 2 of 1 2 , as well as other combinations. Associate the word ‘of’ in these demonstrations with ‘multiplied by’. With fractions the terms are synonymous. Show the students an alternative (mechanical) way of finding the answer. The numerators can be multiplied by each other (1 × 1 = 1) and the denominators also (2 × 2 = 4) to get the same answer. Check these against the ones already drawn. A common mistake made when multiplying fractions is to multiply 1 by 1 and get 2. Be mindful as they perform this simple operation. If the answer has factors in common, reduce it to its simplest form (lowest terms). SB 11.1 can be done. Use with WB Unit 11, Ex 1

Teaching the content of the unit This unit focuses on multiplication and division of fractions

Multiplying whole numbers and mixed numbers by fractions (11.2) Review converting mixed numbers to improper fractions. Mixed numbers cannot be multiplied until they have been converted to improper fractions. A whole number e.g. 6 must also be converted to a fraction. This is done by using the whole number as the numerator and introducing the denominator 6 1. So whole number 6 becomes 1 . What we have done is state the number of whole items and that each whole item has only Bright Sparks Teacher’s Book 5 • Unit 11

1 part, hence the denominator 1. When the mixed number or the whole number has been converted in this manner, the multiplication process can begin. Remind the students that the numerators are multiplied by each other and the denominators by each other to achieve the answer. If the answer is an improper fraction it should be brought to its simplest form (lowest terms). The simplest form of an improper fraction is a mixed number or a whole number. Practise a few of these before instructing the students to complete SB 11.2. A CD-ROM exercise in Block F gives further practice of finding a fraction of a whole (the Challenge concept on this page of the SB). Use with WB Unit 11, Ex 2

not given. We must read to find out how many parts are contained in the whole. Discuss the fraction words used which help to show this. Four-fifths suggests 5 parts, nine-tenths suggests 10 parts, etc. When this is ascertained draw a sketch (diagram) to represent the whole. Shade the parts known and follow the directions in the example to the conclusion. SB 11.4 can be done. Use with WB Unit 11, Ex 4

Dividing fractions (11.5) What are we doing when we divide by 1 fractions e.g. 3 ÷ 2 ? We are asking how many halves there are in 3 items. Draw a diagram showing 3 circles. Split each one into halves. Based on the diagram, the answer is 6.

Cancelling (11.3) Cancelling is a method of simplifying fractions (bringing fractions to their lowest terms) before multiplying. Look at the fractions to be multiplied. Find a numerator and a denominator that have a factor in common. Divide by this factor. Look again to see if there are any other common factors and divide by these also. When all numbers with common factors have been cancelled, the numbers left can be multiplied. Use coloured pencils for cancelling so that each pair cancelled is represented by a different colour. It makes this work easier to check. Three fractions can be multiplied using the same method. Any one numerator can be cancelled with any one denominator. Give the students the opportunity to practise these skills as a class activity and in the Partner Activity before allowing them to do SB 11.3 and WB Unit 11, Ex 3 on their own. Encourage use of diagrams and discussion to aid understanding.

Strategy – drawing a sketch (11.4) Drawing a sketch is always a valid method to help visualisation of mathematical concepts. For these problems the whole is

Unit 11 • Bright Sparks Teacher’s Book 5

We can show 3 × 1 has the same result, using the method of multiplying by the reciprocal.

3×2=6=6 1 1 1

1 2

has been inverted (flipped, turned upside down) and the division sign changed to multiplication. 1

Dividing 3 by 2 has the same effect as 2 multiplying 3 by 1 . Using 2 fractions in our model we can 3 1 show 4 ÷ 4

How many quarters are there in three quarters? (3) This can be set out like this: 3 41 × 41 1 Cancel the 4s and we’re left with 3 over 1

which is the whole number 3. 3 1 Dividing 4 by 4 has the same effect as 3 4 multiplying 4 by 1 . 2 1

is the reciprocal of 2 . 1 of 4 .

4 1

is the reciprocal

Dividing fractions therefore has a step that we have not used before. The reciprocal of the divisor is found and the division sign changed to multiplication. Take some time to practise finding reciprocals. To complete the working, continue as we would for a multiplication problem. SB 11.5 can be done. Use with WB Unit 11, Ex 5

Mixed multiplication and division of fractions (11.6) Review the different concepts taught to ensure confidence as students work, then allow the students to complete SB 11.6 A and 11.6 B. Use with WB Unit 11, Ex 6

Mixed problem solving (11.7) Explore the language of multiplication and division with the students. Discuss the mathematical language and the different types of answer required. ‘How many’ on its own suggests a multiple effect; ‘How many ... left’ suggests subtraction.

Teamwork: Measurement game (11.8) Put the students into groups to play this game.

Assessment 8 Unit 11 Check and summary will show if key points on multiplication and division of fractions have been grasped. Assessment 8, Parts 1 and 2, tests skills in multiplication and division of decimal and common fractions, as well as problems involving metric conversions. The Activity Fraction game is an opportunity to reinforce concepts without doing repetitive written work.

Sample lesson plan UNIT 11 11.1 Multiplying fractions

Objectives (for the specific lesson)

RESOURCES

• To understand that multiplying fractions means finding a fraction of a fraction

Paper cut into rectangles; colours.

• To understand that, unlike multiplication of whole numbers, these answers are actually smaller than the original numbers being multiplied

Engaging the students’ interest / Connections

Give out paper to the students so that they can do the practical folding activity. Follow the instructions on the page. Give instructions to fold and shade another 1 1 example of multiplying fractions, perhaps 3 of 2 . Discuss with the class what the

Bright Sparks Teacher’s Book 5 • Unit 11

results show. Note that the part that is shaded as well as dotted is smaller than the original fraction. Ask if this is common when multiplying. We have always been taught that the multiplication process produces a larger number. Point out that the denominator actually shows a larger number. Discuss the fact that, in fractions, a larger denominator represents that more parts are available. The more parts there are the smaller each part will be. The students need to have the knowledge that a fraction is part of a number. A fraction is written with a numerator and a denominator. Fraction answers are always presented in their lowest terms.

Teaching the lesson

Now that the students have seen the process in practical terms, they can be shown the mathematical algorithm. Be sure to go at the students’ speed and not move on until they show readiness. To multiply fractions we multiply the numerators, then the denominators. Essentially we multiply the digits across the top followed by the digits across the bottom. Seeing the final answer and being able to relate it to the practical representation will aid understanding. Before they start this exercise, students should be reminded to reduce their answers to the lowest terms when the numerator and denominator have factors in common. SB 11.1 can be completed. WB Unit 11, Ex 1 can be given as follow up or homework.

Differentiating for different learning styles

Some students may wish to carry on folding and shading until they feel more comfortable. They should be allowed to continue.

Assessment

Correct the exercise and look for inconsistencies. Something to look out for is students being over confident and making the thoughtless error of multiplying 1 × 1 and getting 2. Encourage the students to do a self-assessment and tell you if there is anything that they are unsure of.

Summary of key points

Multiply numerator by numerator, denominator by denominator when multiplying fractions. Always bring answers to their lowest terms.

Extension activities

Some of the students may need to be challenged further and could be given a few examples of multiplying three fractions. They can also be reminded about reducing where the numerator and the denominator have factors in common as they complete the work.

Unit 11 • Bright Sparks Teacher’s Book 5

UNIT 12 Percentages, ratio and proportion Percent, Percent and decimals, Percent, decimals and fractions, Finding the percent of an amount, Problem solving, Comparing fractions, Practice with percent, Activity: Dominoes game, Discount, Problem solving, Wages and salaries, Simple interest, Ratio, Simplifying ratios, Proportion, Working with scale, Problem solving: fractions, ratio and percent, Unit 12 check and summary, Assessment 9

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Convert decimals to percentages and vice versa • Convert certain fractions to percentages and vice versa • Calculate discount and final selling price • Calculate interest and final selling price • Use these skills to solve problems • Compare numbers using ratio • Compare numbers using proportion • Use scale to calculate real measure

RESOURCES Rulers; homemade dominoes game (instructions are included).

Teaching the content of the unit This unit shows the relationship between fractions, decimals and percentages. It also teaches how to use ratio and proportion as methods of comparing.

Plan of operation The following are suggestions which may be helpful as you create lessons for this unit.

Percent (12.1) (See also sample lesson plan below.) Introduce the term ‘percentage’. In the same way that there are 100 cents in a dollar and that 100 runs make a century, the cent in percentage refers to 100. 17% represents 17 out of 100. The symbol looks like an artistic impression of 100. Look at the stroke and the zeros on either side of it. The students should practise writing the symbol, then they can use the symbol to write the correct number as a percent as they do SB 12.1. A CD-ROM exercise in Block F gives further practice of this concept. Use with WB Unit 12, Ex 1

Percent and decimals (12.2) A decimal number with places to the hundredths also shows a fraction out of a hundred. Converting decimals to percents involves making the hundredths a whole number (multiply by 100) and using the percentage symbol. To change percentages to decimals the reverse is done (divide by 100). It is worth reviewing with the students that a decimal recorded only to the tenths place can have zero added to it without the

Bright Sparks Teacher’s Book 5 • Unit 12

value being affected. SB 12.2 A and 12.2 B can be done. Use with WB Unit 12, Ex 2 and 3

Percents, decimals and fractions (12.3) Review equivalent fractions, factors and converting decimals to fractions. Refer to Units 4 and 7. These concepts all come together as percentages are studied. SB 12.3 A, 12.3 B as well as WB Unit 12, Ex 4 and 5 can be completed. A CD-ROM exercise in Block F gives further practice of this concept.

Finding the percentage of an amount (12.4) Two methods are shown but it is advisable to teach one and practise it then teach the other as extension work. Discuss the terminology – if the problem requires us to find a percentage of an amount then multiplication by that amount is necessary. Practise a few with the class and allow them to complete SB 12.4. CD-ROM exercises in Block F give further practice of this concept. Use with WB Unit 12, Ex 6

Problem solving (12.5) Read and discuss the problems with the class. Review the terms used and how they guide us to perform the correct action. Students need to be able to recognise when the requirement is: a percentage of an amount; how much more is required to reach a certain percentage; or the value of the percentage (i.e. the actual number of items). SB 12.5 can be completed.

Comparing fractions / changing fractions to a percentage (12.6) The concept of converting fractions to percentages is further developed. Previously fractions were changed to percentages after being made equivalent with a denominator of 100. Now we will use an algorithm to get the same result.

Unit 12 • Bright Sparks Teacher’s Book 5

A score from a test is normally written as a fraction in the first instance. This shows the individual’s score out of the maximum possible. E.g. 15 out of 25 is 15 25 . This fraction can be multiplied by 100% to show the percentage received. (100% = 100 1 ) We multiply by 100% to find percents. SB 12.6 and WB Unit 12, Ex 7 can be done.

Practice with percentages (12.7) Use this exercise to practise further the different concepts taught. Encourage the students to read the problems carefully to ascertain what is being asked. SB 12.7 A and 12.7 B can be completed. A CD-ROM exercise in Block F gives further practice of this concept. Use with WB Unit 12, Ex 8

Activity: Dominoes game (12.8) Follow the instructions and make the domino cards. Groups of students can take turns to play the game. Alternatively several sets of the game can be made as a craft activity and everyone can play at the same time.

Discount (12.9) Working out discount is a matter of finding a percentage of an amount. If the cost price is $40 and discount is 10%, find 10% of $40. The students should be able to achieve good results doing this. In order to find the new cost after discount, another step must be undertaken – the discount should be subtracted from the original price. SB 12.9 and WB Unit 12, Ex 9 can be done. An alternative way of doing this is to subtract the 10% from the whole (100%) which leaves 90%. Then calculate 90% of $40, and this is the final answer. Do not teach both methods at the same time but use the one that seems appropriate.

Problem solving (12.10) These problems offer practice working out discount. A measure of discernment is needed to know when to find the percentage, when to add figures together

and when to subtract. Discuss the terms used and how to interpret their meaning. SB 12.10 and WB Unit 12, Ex 10 can be done.

Wages and salary (12.11) Give the students the opportunity to research the meaning of the terms wages and salary. This and the other research project can be set for homework. The conversion of calendar terms to days, weeks and months should be reviewed: how many days, weeks in a fortnight? ... days, weeks in a month? ... days, weeks and months in a year? etc. Follow this up by working out the answers to SB 12.11. Use with WB Unit 12, Ex 11

Simple interest (12.12) Discuss the meanings of the terms introduced in the language box. Encourage the students to think of a way to calculate the interest and the total now in the bank account. Teach the same method used for finding discount but this time the figures are added together. There is the added difficulty of finding amounts with .5 %. Make each part of the fraction 10 times larger – move the decimal point 1 place to the right. This means that the numbers being worked with become whole numbers. The increased difficulty is that the denominator becomes 1000, but it can be cancelled in the same manner. SB 12.12 and WB Unit 12, Ex 12 can be done. To use the alternative method here would mean adding the percentage of interest to 100%. If the interest was 4% as in the discussion box, we would find 104% of the figure. Move the decimal point one place to the right as before to work out fractional percentages.

Ratio (12.13) A method of comparing numbers is to use ratio. Data can be broken down by examining the attributes of the items and listing, in the same order, the attribute and the number of items which share it. Read and discuss the information in the

example box. Look at the order of the colours named and then at the ratio given. Ask the students: Which number refers to white cars? Which number refers to red cars? Practise writing ratios in the three ways shown. Discuss the information in the discussion box and try to work out the answer. Students complete SB 12.13 and WB Unit 12, Ex 13 . A CD-ROM exercise in Block F gives further practice of this concept.

Simplifying ratios (12.14) Simplifying means the same here as in fraction work. In order to simplify a ratio, a common factor is found, and used to divide each number. When the figures in the ratio have no factors in common, it is in its simplest form. Review finding and listing factors of pairs of numbers and look for common factors. Students complete SB 12.14 A. Use with WB Unit 12, Ex 14

Working with a total See the example box featured on the page. Once we know how many parts there are in the ratio, we can use division to work out how much each part is worth. Follow the steps in the box. SB 12.14 B and WB Unit 12, Ex 16 can be done.

Proportion (12.15) In any equation work the standard rule is this: whatever is done to one side must be done to the other also. Show the students how this is true using the cross multiplication or equivalent fraction models in the example box.

Practical use of proportion The students may use the method of their choice to solve the problems in SB 12.15. Use with WB Unit 12, Ex 15 and 17

Working with scale (12.16) Scale is another representation of the use of ratio. Impress on the students the Bright Sparks Teacher’s Book 5 • Unit 12

importance of using the key (legend) as this will identify how many times larger the real object is. 1:3 tells that the measurement in the drawing has to be multiplied by 3. The students should use their rulers to measure and work out the actual measurements of the house as asked in SB 12.16 and WB Unit 12, Ex 18 .

Problem solving: fractions, ratios and percentages (12.17) Practice using the skills in fractions, ratio and percentages is offered. Questions should be read with care and word clues checked in

order to achieve good results. SB 12.17 and WB Unit 12, Ex 19 and 20 can be done.

Assessment 9 Unit 12 Check and summary will show if key points on percentage, ratio and proportion have been grasped. Assessment 9 tests knowledge of percentages, fraction and decimal conversions as well as problem solving with percentages, ratio and proportion.

Sample lesson plan UNIT 12 12.1 Percentages

Objectives (for the specific lesson)

RESOURCES

• To recognise that a percentage is a fraction out of 100

Squared paper cut into 10 × 10 squares; posters or sheets showing 100 squares with different portions coloured.

• To be able to express fractional parts as percentages

Engaging the students’ interest / Connections

The ability to count in tens is reviewed. Count in tens to 100. Practise this from different starting points. Show the students one of the hundred squares and count the portions that are coloured. Encourage them to count in multiples of ten and count individually only when part of the column is coloured. The students already know how to recognise fractions as parts of a whole. They can also recognise that the digits which follow the decimal points are part of a whole. This previous knowledge is linked to what is taught in this lesson.

Teaching the lesson

Introduce the other hundred squares one by one and ask for volunteers to identify the number of small squares coloured and express this out of 100. Write on the board a fraction with a denominator of 100 and explain that this fraction can be demonstrated on a number square. Challenge the students to tell you how. Share the blank 10 × 10 squares and ask individuals to show, by colouring, the representation that is displayed. They can turn to the other side of the paper and complete one more if necessary. Either several students can be asked to complete the same fraction or different fractions can be set at the same time to different groups of students.

Unit 12 • Bright Sparks Teacher’s Book 5

Use the other methods of recording fractions in some of the questioning. Keep a record of the fractions asked so that accuracy can be determined. Continue this until they have had enough practice to be able to complete exercise SB 12.1. WB Unit 12, Ex 1 can be set as homework.

Differentiating for different learning styles

There may be a case for placing a zero in front of a single digit numerator above 100 so that it can be seen as a 2 digit number.

Assessment

Informally assess understanding through asking leading questions in a discussion of what was done and how it was done.

Summary of key points

Percentages are proportions out of 100.

Extension activities

There is an exercise in Block F of the CD-ROM which gives further practice of this concept.

Bright Sparks Teacherâ&#x20AC;&#x2122;s Book 5 â&#x20AC;˘ Unit 12

UNIT 13 Measurement – time Review, Enrichment: 24 hour system, Calculating elapsed time

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Display competence in a variety of calendar conversions • Tell the time in the 24-hour system • Convert from 12-hour to 24-hour time and vice versa • Calculate elapsed time from a.m. to p.m. • Add times in the 12-hour and 24hour system • Subtract times in the 12-hour and 24hour system

RESOURCES Analogue clock; digital clock or watch.

Teaching the content of the unit This unit deals with telling the time in the 12- and 24-hour systems and gives practice with other calendar conversions.

Unit 13 • Bright Sparks Teacher’s Book 5

lesson. CD-ROM activities are noted by the relevant lessons below.

Review (13.1) (See also sample lesson plan below.) Do an oral review of the time facts listed on the page, as well as any others you feel relevant. Discuss the point noted when doing metric conversions – when the unit is small, more units are needed, when the unit is large, fewer are needed. A quick oral quiz of some calendar conversions will warm up the students’ mental skills before they complete SB 13.1. Use with WB Unit 13, Ex 1 and 2

Enrichment: 24-hour system (13.2) Read the statements in the enrichment box with the class and discuss the points made. Discuss any advantages or disadvantages that may exist with either system. Some may be: the same time appears only once in a day; starting from zero could be confusing. The Partner Activity can be done and checked before SB 13.2 and WB Unit 13, Ex 3 are set.

Calculating elapsed time (13.3) There are two methods for calculating elapsed time. One is the counting on method and the other direct subtraction. The students can try both and work with the one that suits them best. If time regrouping (renaming) has to be done, the key point is to remember that they are regrouping from 60 and not 10 as there are 60 minutes in an hour. Convert 1 hour = 60 minutes when renaming. Do a few

examples with the students and instruct them to do SB 13.3 A. Use with WB Unit 13, Ex 4 and 5

More time problems

is to be done to solve the problems. The choice of operation in this exercise is addition or subtraction. You could evaluate what needs to be done by listing the clue words under the appropriate operation.

In the 12-hour time system the number indicating the time repeats itself – a.m. or p.m. clarifies the time of day. If someone travelled from 9 a.m. until 2.30 p.m. and we want to know how long the journey lasted, we can see an issue with the smaller number (the finishing time) needing to be the one from which we subtract. This makes the subtraction a little more complicated. Break it down as described to reach the answer.

Addition

Subtraction

At what time did she finish?

How long is it from ... to ...?

.... would we arrive?

How much faster?

Another method that works well is converting the afternoon time to the 24hour system. A straightforward subtraction can then be undertaken. SB 13.3 B has a variety of time problems. Read carefully to see what is required in the answer.

Before students do SB 13.3 D, review time facts and the different bases needed to complete calculation of weeks and days, hours and minutes, minutes and seconds and years and months. Then SB 13.3 D and WB Unit 13, Ex 7 can be done.

SB 13.3 C – Calculating time – discuss the key words that help in determining what

A CD-ROM exercise in Block F gives an extension of this concept.

Discuss why these actions are correct. SB 13.3 C and WB Unit 13, Ex 6 can then be done. CD-ROM exercises in Block E give practice with elapsed time and ordering events by time.

Sample lesson plan UNIT 13 13.1 Review

Objectives (for the specific lesson)

RESOURCES

• To consolidate knowledge on time conversions

Large clock; individual clocks (manufactured or homemade).

• To consolidate skills in reading analogue clock times • To reinforce skills in displaying analogue clock times

Engaging the students’ interest / Connections

Use the large clock to display clock times for the students to read. Move the hands in a clockwise direction to each new time. Next, engage the students by asking each child that gets a time correct to display a time of their own. Check that the hour hand is moved between the numbers on the clock face into the correct position to show how many minutes have passed.

Bright Sparks Teacher’s Book 5 • Unit 13

Check students’ knowledge of times on the hour, half hour, quarter hour, as well as minutes past and to the hour. Students also need to be able to remember time conversions, e.g. how many: minutes in an hour, days in a year, etc. Multiplication and division skills will also be engaged.

Teaching the lesson

A very interactive lesson is required as teaching and review will be incorporated into one session. First read together the conversions that are printed in the time facts. In order to be sure that these are known, do a quiz type session where questions are asked requiring answers as printed in the time facts. Include some questions that require multiples of the answers given (how many months in 2 years) and divisions also (how many weeks in half of a month). Check that the vocabulary is familiar to each child. Do they know the words millennium and fortnight? Explain their meanings or ask students to define these words. A number of different clocks are pictured on the page. Ask questions about what these clocks have in common as well as questions about how they differ. For instance one of them is a 24-hour clock. Where might these clocks be more commonly seen? Discuss the different types of numerals that are used on clocks and their equivalent numbers. The review exercise – SB 13.1 can be done. WB Unit 13, Ex 1 and 2 can be used for homework to follow up on the exercise.

Differentiating for different learning styles

Some students will be very knowledgeable and confident and wish to answer all of the questions but you will need to draw answers from the less confident students as well. Select students who do not volunteer from time to time and ask them questions that they already know the answers to. This will help to build their confidence. Ask questions of the more able students that will push them to deeper thinking. Gifted students need to be challenged to keep their interest.

Assessment

Oral time testing would be a suitable method, as this is mainly review work.

Summary of key points

These conversions are not uniform and need to be learnt thoroughly. The hour hand of the clock must be carefully positioned in relation to the distance travelled by the minute hand.

Extension activities

Students can be given the task of researching 24-hour clock usage. This would include the number system used to show 24-hour times.

Unit 13 • Bright Sparks Teacher’s Book 5

UNIT 14 Statistics, data and probability Finding the mean, Working with the total, Interpreting data and drawing graphs, Making graphs/frequency charts, Enrichment: Interpreting data with a line graph, Circle graphs (pie charts), Interpreting the circle graph, Using percentages in circle graphs, Probability, Enrichment: Introduction to sets, Enrichment: Types of set, Displaying data in Venn diagrams, Practice with sets, Unit 13 and Unit 14 check and summary, Assessment 10

OVERVIEW OF UNIT Objectives / Outcomes At the end of this unit students should be able to: • Find the mean of 2 or more numbers • Interpret data in bar graphs, pie charts and line graphs • Collect data and create a graph • Interpret data in a Venn diagram • Display data in a Venn diagram

Finding the mean (14.1) (See also sample lesson plan below.) The mean is the average score of 2 or more sets of data. It is a two-step process which is found by adding together the scores and dividing this answer by the total number of scores. Prepare some sets of data for which, when they are added together and divided, the quotient will be a whole number. Do these with the class as a preliminary exercise before instructing them to do SB 14.1. Use with WB Unit 14, Ex 1

RESOURCES Buttons; beads; charts.

Teaching the content of the unit This unit teaches how to collect, handle and interpret data.

Working with the total (14.2) The students have been taught several times that division and multiplication are reverse operations and that addition and subtraction are also. An extension of finding the mean is to work backwards from the mean to find out the total. Experience doing reverse operations is crucial to mastering this concept. The total was divided to find the mean therefore the mean must be multiplied to find the total. This is extended even further to finding a missing score when the total and the mean are known. Encourage them to discuss their actions with their partner as they do the questions in the Discussion box. Check this work for accuracy and instruct the class to complete SB 14.2. Use with WB Unit 14, Ex 2 Bright Sparks Teacher’s Book 5 • Unit 14

Interpreting data and drawing graphs (14.3) Bar graphs should be familiar to the students. This particular graph is numbered in multiples of 5 so a measure of estimation is necessary to read data that falls between the calibrated marks. Discuss what is shown by each axis and the necessity to name them. Discuss also the mathematical language used and how best to go about finding the answers, then instruct the students to complete SB 14.3. A CD-ROM exercise in Block F gives further practice of this concept. Use with WB Unit 14, Ex 3

Interpreting the circle graph (14.7) Review decimal, fraction and percentage conversions. The students can use their knowledge of fractions and decimals to answer the questions about the circle graph in SB 14.7.

Using percentages in circle graphs (14.8) Review the conversion of percents to whole numbers. Do SB 14.8 and WB Unit 14, Ex 4 .

Making graphs / frequency charts (14.4)

Probability (14.9)

The students can follow the instructions given to draw their own graph with the information as set out. Check that the information is correctly recorded. Students can make up some questions of their own to accompany their graph.

Follow the instructions and use plenty of discussion to help the reasoning process. Think up other ways of testing probability, e.g. tossing a coin to see how many times you get heads. Some things can be subject to probability, others cannot. Discuss this and make a chart categorising the responses. Students complete SB 14.9.

Group Activity Next comes creating a graph from the beginning. This involves deciding on the type of information to be gathered, how it is to be calibrated, how many students are to be used in the study, etc.

Enrichment: Interpreting data with a line graph (14.5) Discuss the different components of the graph – the purpose of the dots and the line that connects them, the numbers on the vertical axis and the days of the week on the horizontal axis. Answer the questions on the line graph in SB 14.5. CD-ROM exercises in Block E and F give further practice of reading graphs.

Circle graphs (pie charts) (14.6) Read and discuss the information about the circle graph/pie chart. It can be seen that the size of the sector (piece of the circle) is proportionate to the size of the data represented. Look for the Highest

Common Factor of the numbers to be represented in the circle chart in SB 14.6. This will tell you how many pieces of the pie are needed.

Unit 14 • Bright Sparks Teacher’s Book 5

WB Unit 14, Ex 5 accompanies this exercise. A CD-ROM exercise in Block F gives further practice of this concept.

Enrichment: Introduction to sets (14.10) This is more of a re-introduction as set work is primarily started in the early school years. Discuss the information on the page.

Enrichment: Types of sets (14.11) The information supplied needs to be discussed and examples shown in a practical way. Beads, buttons or other small objects can be used. Attributes of colour, shape and size can be discussed. Where possible, the students can be used to demonstrate the categories named: i.e. students with dogs, students under a certain height. True-to-life results illustrate a point in a more memorable way. The terms and symbols for: intersection, union,

empty set, subset, should be learnt. Charts demonstrating their meanings should be displayed. SB 14.11 can be done.

Displaying data in Venn diagrams (14.12) Read and discuss the example and the way it is displayed. Break the class into groups to do the follow up Group Activity.

Practice with sets (14.13) Three different ways of setting down data are shown. Discuss this to be sure the students see the differences and understand how to use the information. Do SB 14.13 and WB Unit 14, Ex 6 .

Assessment 10 Unit 13 and 14 Check and summary will show if key points on time and statistics have been grasped. Assessment 10 tests time and calendar conversions in Part 1. Conversions of the 12-hour to 24-hour system and statistics are tested in Part 2. The three final assessments are separated into Parts A and B with Part A offering practice at multiple choice. They each contain a good cross section of questions covering all concepts studied in SB5. There are seven mixed review exercises which complete WB5.

Sample lesson plan UNIT 14 14.1 Finding the mean

Objectives (for the specific lesson) • To understand the meaning of the terms average and mean • To be able to find the mean of 2 or more numbers • To use knowledge of different ways to use remainders

Engaging the students’ interest / Connections

Split the class into groups of 4 or 6. Give each group a word to research and describe to the class in any way they choose (drawing, story, etc.). There is only one word but the students won’t be told that they are looking for the same word. The word is ‘average’. Give them a few minutes to research and think up a presentation. Call ‘time’ and look at the presentations. Students’ addition and division skills must be tapped into for this lesson. We are also going to employ the decision-making skills related to retaining remainders as such, or adding zero after the decimal point to continue division, and bring the answer to a decimal place.

Teaching the lesson

Discuss the presentations and what we have learnt about the meaning of the word (‘average’). Talk about different situations when the word average is used and what it conveys. In everyday terms we think of it as an ordinary standard. If something is

Bright Sparks Teacher’s Book 5 • Unit 14

average it is of medium grade. Introduce the word ‘mean’ and explain that it is the mathematical term for average. The mean of a set of numbers is found by adding the sets of information together and dividing them by the number of sets. As a preliminary to doing SB 14.1, prepare some simple sets of numbers that when added and divided come to a whole number. Practise these together with the class to give them time to understand the technique. Next, give them some numbers that would leave a remainder of 2 out of 4, or 3 out of 6. Remind them that there are instances when a remainder cannot be left. This is true of finding a mean; a mean cannot be 3 and 2 left over. Ask if they can they remember what is done in those cases. Remind them that we include the decimal point and add a zero after it. This way, we have another digit to ‘bring down’ and divide again. A decimal becomes a part of the answer. SB 14.1 can now be completed. WB Unit 14, Ex 1 can be set for homework if SB 14.1 is adequately done.

Differentiating for different learning styles

For slow learners, keep the numbers simple and avoid introducing the type of question that will require adding a decimal point. It would be best for them to grasp the basic step first. The quicker students can be given some problems where the mean and the number of scores is known and they have to find out the total score.

Assessment

Go around the room giving students a chance to explain their working and give their answer. Verbally expressing what they have done will reinforce the concept as well as showing what they have understood of the process.

Summary of key points

The mean is found by adding the sets of information together and dividing this total by the number of sets.

Extension activities

The students can be set to create problems and test other members of the class to see if they can solve them.

Unit 14 • Bright Sparks Teacher’s Book 5

Answers to Student’s Book 5 UNIT 1: Number 1.1 Place value 1.1 A 1 One hundred 2 Ten thousand 3 Ten 4 One thousand 5 One hundred thousand 6 Five hundred 7 Seventy 8 Nine hundred 9

Four hundred thousand

10 Sixty thousand 11 Twenty 12 Six hundred and fifty

5 9 thousands 3 hundreds 9 tens 0 ones 6 1 million 6 hundred thousands 0 ten thousands 3 thousands 9 hundreds 4 tens 7 ones 7 2 thousands 0 hundreds 6 tens 1 ones 8 1 hundred thousands 0 ten thousands 9 thousands 4 hundreds 5 tens 7 ones 9 2 ten thousands 0 thousands 8 hundreds 9 tens 0 ones 10 7 ten thousands 1 thousands 6 hundreds 3 tens 4 ones 11 Forty-five thousand, seven hundred and eighty 12 Nine thousand, eight hundred 13 Twenty-four thousand, five hundred and one

13 Five thousand nine hundred

14 Fourteen thousand, four hundred and ninety-nine

14 Twenty-five thousand

15 Nine hundred and sixty-five

15 One hundred and fifty thousand

16 Eighteen thousand and twenty

1.1 B

17 One hundred thousand

Tens

Hundreds

18 Ninety-nine thousand, one hundred and nine

Tens

19 One thousand, two hundred

Hundred thousands

Hundreds

20 One million, nine hundred thousand and one

Tens

1.1 D

Ten thousands

32 050

74 184

Ones

813

89 012

Thousands

9 401

1 100 000

10 Hundreds

63 528

856 916

Challenge:

90 600

10 1 050 015

100 000

1.2 Value

1 000 000

1.2 A

1.1 C

Tens

7 Ones

1 3 hundreds 5 tens 7 ones

Thousands

8 Thousands

2 8 thousands 9 hundreds 0 tens 3 ones

Ones

3 2 thousands 5 hundreds 4 tens 0 ones

Ten thousands 10 Hundreds

4 5 ten thousands 1 thousands 0 hundreds 8 tens 9 ones

Tens

11 Ones

Hundreds

12 Hundreds

Ten thousands

Bright Sparks Teacher’s Book 5 • Answers

13 Ten thousands 15 Tens

Challenge:

14 Thousands

15 hundreds

1.2 B

7532

600 + 90 + 1

10 840

80 + 9

6270

4000 + 80

1.3 D

300 + 5

9624

60 400

90 000 + 1000 + 10 + 2

8325

50 739

8000 + 700 + 70

49 484

40 001

500 + 70 + 8

3622

9 9060

90 000 + 5000 + 300 + 20 + 4

51 400

10 7084

30 + 2

1.3 E

10 2000 + 500 + 60 + 1

4000 + 90

1.3 Expanded form

5000 + 40

1.3 A Examples are given, either form of expansion can be used

20 000 + 5000 + 900 + 80 + 7

90 000 + 600 + 50 + 7

(3 × 1000) + (8 × 100) + (2 × 10) + (1 × 1)

10 000 + 5000 + 800

70 000 + 70

(4 × 10 000) + (5 × 1000) + (7 × 100) +

5000 + 600

(9 × 10) + (8 × 1)

2000 + 300 +70

6 × 100 + 7 × 10 + 3 × 1

90 000 + 5

1 × 10 000 + 2 × 1000 + 4 × 100 + 6 × 1

10 40 000 + 500 + 60

1000 + 500 + 70 + 3

11 (5 × 1000) + (5 × 10)

6 000 + 50 + 3

12 (4 × 100) + (6 × 10) + (7 × 1)

10 000 + 900 + 80

13 (8 × 10 000) + (7 × 1000) + (1 × 1)

(6 × 10 000) + (5 × 1000) + (8 × 1)

90 000 + 9 000 + 300 + 30

14 (1 × 10 000) + (3 × 1000) + (4 × 10) + (5 × 1)

10 20 000 + 20 + 2

15 (1 × 1000) + (1 × 100)

1.3 B

16 (6 × 10 000) + (2 × 10)

4245

84 000

621

7 9260

18 (8 × 100) + (9 × 10) + (9 × 1)

9 329

8 508

19 (4 × 1000) + (4 × 1)

13 105

9 3007

20 560

10 70 501

20 (3 × 10 000) + (5 × 1000) + (1 × 10) + (2 × 1)

1.3 C

1 10 ones

8 hundreds

2 11 ones

3 hundreds

3 19 tens

7 thousands

4 14 tens

12 hundreds

5 4 tens

10 11 tens

Answers • Bright Sparks Teacher’s Book 5

17 (9 × 1000) + (7 × 100) + (5 × 10)

1.4 More expanded numbers with regrouping 1.4 A

2 a nine hundred and two b eight thousand, one hundred and five

2 4 × 100

c two thousand, four hundred and forty-six

3 14

d twenty-one

4 17 × 100

e forty thousand, five hundred and twelve

(2 × 10)

1.4 B 1 16 × 10

4 (4 × 1000)

2 15 × 1

3 80

6 12 × 1

Challenge: a 67 × 10 b 62 × 1 c 20 × 100

1.5 Forming numbers Partner Activity a

largest – 8734, smallest – 3478

smallest/smallest odd – 2369, smallest even – 2396, largest odd – 9623, largest/largest even – 9632

1.5 1

Greatest – 6541

Smallest – 1456

Largest odd – 6541

Largest even – 6514

Smallest odd – 1465

Smallest even – 1456

Assessment 1 Part 1 1 a hundreds b tens c thousands d tens e ten thousands f

ones

g hundreds h ten thousands i

ten thousands

hundred thousands

nine thousand and six

g eighteen thousand, four hundred h sixty-two thousand, three hundred and ninety-seven i

five hundred and eleven

one hundred thousand and two

3 a 97

f 14 511

b 416

g 45 607

h 29 501

9300

d 6417

100 000

e 200 020

62 005

157

8643

Part 2 1 a 50

f 300

b 8

g 0

c 900

h 90 000

d 9

10 000

e 2000

7000

2 a 953

f 20 985

b 546

g 5030

c 8632

h 4002

d 15 261

16 050

e 46 100

55 210

3 a 5636 b 42 502 c 24 700 d 2676 e 13 764 4

Choose this or one of the other formats

a 600 + 80 b 1000 + 500 + 60 + 2 Bright Sparks Teacher’s Book 5 • Answers

c 7000 + 800 + 40

2.2 B

d 60 000 + 4000 + 300 + 70 + 8

5, 16, 37, 41, 92

5 a 1 ten

f (5 × 10)

18, 34, 52, 69, 76

b 17 tens

g (6 × 100)

315, 345, 362, 390, 397

h 16

1096, 3062, 4091, 6024, 8014

11, 15, 19, 169, 773, 1978

e 7 thousands

81, 67, 57, 19, 3

8430

98, 66, 52, 49, 44

4569

779, 778, 764, 732, 722

Challenge:

9021, 7016, 6083, 4029, 1055

10 3415, 990, 576, 34, 9

Unit 2: Patterns, sequence and order

2.1 Ordering numbers

12 ones

d 15 tens

3 × 100

2.1

4 3 , 9, 16, 47

12 980, 984, 989, 991, 992 13 7, 7.1, 7.4, 7.5, 27.7 1 2,

2, 2 2 , 3, 3 2

32, 875, 911, 1265

15 twenty, two thousand, twenty thousand, two million

800, 801, 813, 825

9008, 9100, 9789, 9900

2.3 Problem solving

12, 45, 597, 650

3567, 6821, 7590, 8890

327, 2678, 5499, 12 000

5670, 12 570, 24 500, 90 046

9560, 9561, 9565, 9569

6335, 6452, 6689, 6721

10 62, 2451, 9788, 89 746 Challenge: Ascend is to climb or go up; descend is to go down.

2.2 Counting and ordering 2.2 A 1

50, 51, 52, 53, 54

237, 238, 239, 240, 241

2000, 2001, 2002, 2003, 2004

89 910, 89 911, 89 912, 89 913, 89 914

84, 83, 82, 81, 80

2108, 2107, 2106, 2105, 2104

299, 298, 297, 296, 295

8, 10, 12, 14, 16

58, 56, 54, 52, 50

10 275, 270, 265, 260, 255

1 2,

Answers • Bright Sparks Teacher’s Book 5

2.3 1

42 steps

23 visitors

54 sandwiches 7

7 metres

8 62¢

66 students

59 butterflies

10 19 students

89 items 23 bottles

Challenge: 74 minutes /1 hour and 14 minutes

2.4 Patterns 2.4 A 1

100 106

4 70 60

39 37

5 60 72

36 42

2.4 B 1

65 71

5 48 96

44 33

6 2 1

45 63

7 350 300

11 13

Challenge: 1 1 4, 2,

1, 2

2.4 C

11 15

sun sun sun triangle

12 a efg b 8 c 20 d 20

arc

Unit 1 and Unit 2 check and summary

678 789

D 378 207

4 4

D ten thousands 7

D 63 024

2 squares vertically

A 56 306

A 62 479

triangle with right angle at top right triangle with right angle at top right

B 7

C 8532

arrow up; arrow down

C 19

10 B 41

4×4

or 1

C 1 500 000

2.4 D

Unit 3: Operations – addition and subtraction

arrow down arrow left arrow right

3.1 Estimation skills

heptagon octagon

3.1 A

100¢

200 + 100 = 300

60¢

900 + 100 + 1000 = 2000

$60

2000 + 400 = 2400

80 + 20 + 160 + 40 = 300

8000 + 2000 + 10 + 100 = 10110

3.1 B

100

8 000

10 VII

20 000

14 000

10 90 000

11 4

91 000

11 40 000

12 1 3

4 000

12 30 000

Challenge:

560

13 4700

8540

14 19 000

12 060

15 1800

2.5 Revision

1010

2.5

3.1 C

98 421

C $46

A $160

18 212

D $248

B $5039

first, second, third, fourth, fifth

C $4801

8000

Challenge:

67, 479, 3209, 19 450, 54 700

a $10 b $1 c $145 d $0

56 209

3.2 Properties of addition

(9 × 10 000) + (8 × 1 000) + (3 × 10) +

3.2

(5 × 1) is one form

6 12

7 11

8 7

10 14

9 17

10 15

Bright Sparks Teacher’s Book 5 • Answers

11 20

19 9

17 123 190

19 5844 credits

12 19

20 11

18 $7899.75

20 13 185 students

13 21

21 60

3.5 Subtraction practice

14 20

22 49

3.5 A

15 18

23 95

6 623

16 14

24 80

7 216

17 11

25 100

615

8 69

18 13

509

9 47

3.3 Addition with regrouping

202

10 93

3.3 A

3.5 B

5 110

827

9 427

868

6 1302

676

10 190

261

7 1270

153

11 54 cakes

1044

8 1727

12 26 years

191

13 $38

3.3 B 1

851

9 9488

14 126

4093

10 9348

270

15 267

11 155

11 617

318

10 421

12 9999

3.6 Subtracting large numbers

15 671

13 675 km

3.6 A

1415

14 4136 people

41 380

84 955

5491

15 37 600 feet

394 082

1961

7593

70 908

3.4 Adding large numbers

3.6 B

3.4 A

174 135

7 280 km

3265

23 992

9 086

172 210

64 687

86 782

95 583

486 km

53 186

89 501

220 342

380 700

96 602

92 200

104 328

10 71 128 km

108 964

10 88 003

3.4 B

3.7 Regrouping with zeros 3.7

583 439

9 $2376.58

2119

980 990

10 $35 630.95

640

8498

887 354

11 57 532

8357

12 560

889 099

12 681 982

1510

8537 types were extinct

224 036

13 818 680

13 312

10 15 567 species

700 337

14 13 925

257 216

15 $1609.85

$479.19

16 902 383

Answers • Bright Sparks Teacher’s Book 5

3.8 Adding and subtracting money

3.8

f triangle pointing up, 2 triangles together forming diamond

$145.75

$14.01

g 3 red stars

$3800.35

$653.07

$9261.50

$385.46

20 60

$9.53

$301.88

70 10

$3.29

10 $285.50

40 50

50 80

90 30

C 9800

A 12 600

B 48 000

B 50 000

B 4000

C 5000

3.9 Subtraction practice 3.9 A 1

5060

1838

30 296

4078

65 041

3057

15 750

$111.25

117

10 $7.59

3.9 B 1

770 188

83 876

41 088

302 085

189

$2610.10

288 317

$390.87

19 209

10 $5204.20

3.9 C 1

4280 airline credits

890

265 m

1250 litres

15 minutes

$1.25

16 760

837 km

$21 200

10 2715 km

Unit 3 check and summary 1

C 4000

D 216

B 9

A 204 888

B 6400

D 24 685

A 240 000

A $702

C 299 939

10 C $4150

Assessment 2

Part 2 1 a 78

1773

b 127

23 512

c 149

k 32 093

d 294

e 378

m 71 015

f 9383

n $52.41

g 9314

o $389.35

1882

h 7888 2

$104

3 a $1187 4

$197

3 360 km

26 900 people

$139.45

2 642 m

109 years

b $853

10 $25 748.40

Part 1

Unit 4: Decimals

1 a 48, 96

4.2 Tenths

b 89, 91

4.2 A

c 21, 18

0.1

4 0.7

d S, E

0.4

0.9

0.6

0.3

e 4,

1 42

Bright Sparks Teacher’s Book 5 • Answers

0.2

8 0.5

4.2 B hundreds

1 2 3 4 5 6 7 8

11.3

103.6

tens

ones

tenths

64.3

. . . . . . . .

5 6 4 3 9 6 7 4

600.15

0.26

2 8 4 2 1 0

0 1 1 9 4 8 3 2

1 3 5 9

10 250.02

4.4 Decimals and whole numbers 4.4 1

18.4

103.28

31.7

4.2 C

562.87

Four tenths

40.11

Six tenths

Two hundred, and fifteen hundredths

Two tenths

Fifty-six and three tenths

Seven tenths

Eighty-nine and four hundredths

Five tenths

Sixty-two and four tenths

One and one tenth

10 One hundred and fifty-four and

Three and eight tenths

Five and three tenths

4.5 Rounding decimals

Twelve and nine tenths

4.5

twenty-six hundredths

4.3 Place value: hundredths

4.3 A

433

105

300

511

606

210

10 990

hundreds

tens

ones

tenths

hundredths

1 2 2 0 4 2 1 0 7 0

5 1 1 9 4 8 3 2 0 5

. . . . . . . . . .

4 6 1 3 9 6 7 4 2 8

5 4 8 2 1 3 7 6 5 2

1 2 3 4 5 6 7 8 9 10

6 8

4.6 Value 4.6 A 1

2 10

4 100

11 1000

9 10

300

14 30

4.3 B

0.32

8 100 9 10

4.7

4.6 B

12.9

0.56

3 0.45

0.59

0.8

4 0.4

3 5 9 7 6

Answers • Bright Sparks Teacher’s Book 5

3 10 2 100 4 100

5 0.04

8 0.2

114.90

12 $18.43

6 0.5

9 0.62

396.88

13 $37.05

7 0.09

10 0.02

12 006

14 6 800.15

10 $11.16

15 $1582.73

4.6 C 1

34.02

39 990.09

11 $410.76

101.06

18 004.09

Challenge:

397.13

32 465.02

2.52 seconds

3571.82

1780.04

41.65 seconds

9004.06

10 6400.24

89.8 seconds/1 min. 29.8 secs.

4.7 Ordering and comparing decimals

4.9 C

4.7

48.8

9 4105.11

48.7 4.87 0.51

710.8

10 6889.93

10.04 0.48 0.41

64.86

11 775.36

26.4 2.67 2.65

9426.1

12 3102.75

10 523.3 52.3 52.03

612.29

13 789.13

126.72

14 9075.88

2174.11

15 7721.25

2700.99

4.8 Rounding and estimating decimals 4.8 A 1

$56

$239

$487

$56

$106

$210

$9847

$1099

$1200

10 $6725

4.9 D 1

328.9

6 408.1

$3400.18

7 5785.45

1150.17

8 142.36

2626.56

9 $6501.45

653.85

10 $6426.55

4.8 B

4.10 Problem solving

$20

Lily

37 seconds

Jamaal

$115

9.0

Yes, it is just under $10

6.55

9.52

7.25

Jamaal

7.25 7.25 7.9 8.5 9.5 9.52 0.75

4.9 Addition and subtraction of decimal numbers 4.9 A 1

9.6

5507.24

124.1

5 $59.27

840.1

6 $10.97

10 0.7

Unit 4 check and summary

4.9 B 1

177.92

4 3544.58

A $3

A 103.17

556.76

5 $331.95

D tens

3 10

C 1246.08

$7.16

6 $62.16

Bright Sparks Teacher’s Book 5 • Answers

A <

B 1 115.26

10 a $46

D 498.86

10 B 8.75 seconds

b $135

Assessment 3

11 a 50

Part 1

1 a 11 420

12 115.87, 115.96, 345.12, 492.9

b fifty-four thousand, six hundred and two

13 No, he needs 95¢ more.

c 30 000

15 54.7 seconds

82 441, 17 490, 8997, 1749

65 083

1379

5 a

14 0.15 seconds

Unit 5: Multiplication 5.1 Multiples

b 20¢

5.1 A

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

Answers may vary.

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

8, 16, 24, 32, 40

9, 18, 27, 36, 45

11 7

12 49

13 121

14 72

a 380 or 400 b 1200 or 1230 c 3000 or 3100 9

5800

10 25 000 11 11 040 km 12 30 000 feet 13 $276 14 1357 lunches 15 $62 610 Part 2

4 100

10 12

15 6

5.1 B 6x 7x 8x 9x

0 0 0 0

6 7 8 9

12 14 16 18

71 909

18 21 24 27

19 209

24 28 32 36

$9.50

30 35 40 45

7 a 1550 bottles

36 42 48 54

b 1599 bottles

42 49 56 63

8 a 12.7

48 56 64 72

54 63 72 81

60 70 80 90

9 a 670

66 77 88 99

b 1584

72 84 96 108

213

10 816

1179

b One hundred and thirty and fortyone hundredths

Answers • Bright Sparks Teacher’s Book 5

5.2 Multiplication speed tests

Other arrays may be:

5.2

Test 1

Test 3

20 8 50

24 11 77

18 15 54

12 30 96

24 10 49

21 48 99

14 55 48

25 12 64

16 27 72

2 × 12

Test 5 12 × 2

10 36 45 63

Test 2

Test 4

Test 6

144

7 84 55

120

1 × 24 and 24 × 1 can also be shown.

132

121

10 35

5.3 Arrays 1 6×4

5.3 1

4×6

5 × 2 = 10

Partner Activity:

The product is 12. The shape is a rectangle.

6 × 3 = 18

4 × 4 = 16

Bright Sparks Teacher’s Book 5 • Answers

7 × 5 = 35

2 × 7 = 14

10 1 × 11 = 11

5.4 Square numbers 5

8 × 4 = 32

Look at the arrays you drew in Exercise arrays you drew in Exercise 5.3. Which of the arrays are square? 3: 4 × 4, 6: 3 × 3, and 8: 10 × 10 are squares. Challenge:

3×3=9

9 × 2 = 18

Every time ‘=’ is pressed on the calculator, the number is multiplied again. For example, if ‘6 × 6 =’ is entered, the result 36 is shown. If ‘=’ is pressed again, the number 216 is shown (6 × 36). If ‘=’ is pressed again, 1296 is shown (6 × 216). (This may not work with all calculators. The calculator will continue to multiply by the first number entered – i.e. if ‘2 × 6 =’ is entered and ‘=’ is pressed again and again, it will continue to multiply by 2, not by 6.)

5.5 Square roots 5.5 A

3×3

9 squares

7×7

49 squares

8×8

64 squares

10 × 10 = 100

Answers • Bright Sparks Teacher’s Book 5

5.8 Multiplying 3-digit numbers

9×9

5.8

808

1186

81 squares

1569

474

1152

1350

660

2532

756

Challenge: 5

√9 = 3

√4 = 2

$16.55

√64 = 8

√144 =12

√100 = 10

5.9 Multiplying large numbers 5.9 A

5.5 B 1

Yes, it is possible. There can be 11 teams of 11 children. Explanations will vary. As 121 is a square number, it must be divisible into equal amounts – in this case, 11 lots of 11.

5070

14 130

7248

48 176

44 632

63 138

50 968

11 505

20 493

10 45 408

12 (This assumes that egg boxes usually hold 12 eggs.)

5.9 B 1

7950 trees

2100 flowers

600 ladybugs

7500 branches

5.6 Problem solving: Mental computation

3600 pests

5.6

5.10 Multiplying by multiples of 10

8 jacks

40 pencil holders

15 jacks

10 64 large shells

1200

6 games

11 56 small shells

800

70 days

12 48 buns

500

2100

60 points

13 24 soft drinks

600

2500

$72.00

14 30 prizes

400

10 1200

48 grass baskets 15 15 games

5.10 B

20 glass jars

16 000

600 000

Challenge:

18 000

250 000

60 cones

14 000

350 000

5.7 Multiplying large numbers mentally

32 000

240 000

5.7

200 000

10 2 400 000

5.10 A

159

6 165

5.11 Multiplying by 2-digit numbers

7 138

5.11

8 416

676

5 1680

136

9 420

1525

6 4148

288

10 272

170

7 $9130

1012

$20 800

Bright Sparks Teacher’s Book 5 • Answers

4155

13 22 570

$13 060

14 800 kg

10 3204

14 28 244

13 545

15 $3600.00

11 9990

15 $81 420

3780

12 4155

Unit 5 check and summary

5.12 Problem solving

B 24

C (4 ÷ 2) + (35 × 2)

5.12

C 25

B 9204

1 a 125

B 120 + 15

D 2 × $12 × 100

b 75

D 10 074

A 43 670

c 150

A 280 000

10 D 7 × 32

d 15

Assessment 4

Part 1

e 750

1 a 70

Tia

$30 $45

$25 $75

$60 $40

b hundredths

$75 $40

$50 $20

3 a four hundred and seventy-one, and three tenths

$40

Total $280

Tanya

b 400 2

c 10 2 a thousands

b twenty-six and fifty-eight hundredths

$220

5.13 Multiplication practice 5.13 A 1

800

120 000

1500

16 000

1200

35 000

4900

16 000

18 000

10 120 000

5.13 B 1

756

6 375

1056

7 1435

924

8 504

946

9 899

850

10 5146

5.13 C

2925

15 795

10 104

10 9984

26 432

11 $50.25

9976

12 $43.00

$4575

13 800 metres

Answers • Bright Sparks Teacher’s Book 5

4 a

87 642

b 6230.5 c 312.26 5 a

about 4400

b about 3100 or 3000 6 a $46.00 b $219.00 7

8743

8 a 4958 b 14 022 c 4108 d 4825 e 1791 f 650 g 18 432 h 133 000

2400

14 000

Part 2

Divisible by 2

Not divisible by 2

9: 9, 18, 27, 36, 45

1156

4683

7: 7, 14, 21, 28, 35

118

2861

372

Arrays showing 3 × 8, 8 × 3, 4 × 6, 6 × 4, 2 × 12, 12 × 2, 1 × 24, 24 × 1

9954

5 zeros

30 × 12 = 360 exercise books

9 × 31 = 279 students

460 × $4 = $1840.00

98 × 3 = 294 pieces of chicken

68 × 15 = 1020 passengers

6: 6, 12, 18, 24, 30

8: 8, 16, 24, 32, 40

5: 5, 10, 15, 20, 25

10 14 × 24 = 336 bottles 11 The same. Reasons given will vary. e.g. 14 = 2 × 7 and 24 = 2 × 12, so the sum could be written as 2 × 7 × 12 and 2 × 12 × 7, which are the same. 12 12 × 46 = 552 seats 13 a

5 × 4 = 20 runners

b 20 × 200 = 4000 metres

Unit 6: Division 6.1 Factors 6.1 1

10: (1, 2, 5, 10)

15: (1, 3, 5, 15)

16: (1, 2, 4, 8, 16)

24: (1, 2, 3, 4, 6, 8, 12, 24)

30: (1, 2, 3, 5, 6, 10, 15, 30)

8: (1, 2, 4, 8)

9: (1, 3, 9)

21: (1, 3, 7, 21)

35: (1, 5, 7, 35)

10 50: (1, 2, 5, 10, 25, 50)

6.2 Divisibility 6.2 A

Even numbers are divisible by 2. Odd numbers aren’t. 2

35 – 5

370 – 5, 10

400 – 5, 10 805 – 5

9550 – 5, 10

15 – 5

25 600 – 5, 10

150 – 5, 10 625 – 5

200 – 5, 10 7340 – 5, 10 3580 – 5, 10

1445 – 5

6285 – 5

16 795 – 5

6.2 B Number Sum of digits Divisible by 3

1 2 3 4 5 6 7 8 9 10

25 625 1581 474 273 8013 1011 6425 5110 4296

7 13 15 15 12 12 3 17 7 21

no no yes yes yes yes yes no no yes

Number

Sum of digits Divisible by 9

64 775 120 801 1800 216 5544 2793 3402 69

10 19 3 9 9 9 18 21 9 15

6.2 C

1 2 3 4 5 6 7 8 9 10

no no no yes yes yes yes no yes no

Bright Sparks Teacher’s Book 5 • Answers

6.3 Division: review

6.5 Division speed tests

6.3

6.5

11 12

Test 1

Test 3

12 11

13 9

14 9

15 9

16 12

17 4

18 12

19 11

20 8

10 8

6.4 Using opposites: multiplication and division

10 7

10 110

Test 2

Test 4

Partner Activity:

6 × 8 = 48

10 × 5 = 50

8 × 6 = 48

5 × 10 = 50

48 ÷ 6 = 8

50 ÷ 5 = 10

48 ÷ 8 = 6

50 ÷ 10 = 5

9 × 12 = 108

12 × 9 = 108

108 ÷ 9 = 12

10 10

108 ÷ 12 = 9

Challenge:

6.4

3 × 25 = 75

6 × 25 = 150

11 9

100 ÷ 25 = 4

200 ÷ 25 = 8

12 6

125 ÷ 25 = 5

50 ÷ 25 = 2

13 7

6.6 Division with remainders: review

14 30

6.6

15 12

9 r1

11 11 r2

16 8 tents

8 r3

12 11 r1

17 40 people

6 r3

13 10 r2

18 10 Cub Scouts

10 r1

14 6 r2

19 32 boys

12 r3

15 5 r5

10 4

20 12 boys

4 r3

16 4 r4

12 r4

17 11 r2

12 r4

18 4 r7

6 r6

19 7 r7

10 4 r9

10 40

Answers • Bright Sparks Teacher’s Book 5

20 12 r1

21 4 oranges left over.

938 r2

18 527

22 He filled 6 bags.

911 r2

7070

23 He had 29 coconuts.

912 r2

10 375 children

24 a 7 boxes b 6 eggs left over

Challenge:

6.7 Dividing larger numbers

491 times

6.7

6.11 Division with money

26 r2

11 8 r2

6.11

46 r6

12 45 r1

$89.15

73 r4

13 13

$29.20

10 504

14 26

$281.40

11 $6.25

61 r1

15 75

$3.38

12 $1.20

73 r6

16 12 r2

$94.50

13 426

78 r3

17 68

944

14 $5.40

75 r1

18 80

4995 r5

15 412 times

92 r6

19 24 hours

1455

20 78

6.13 Dividing by 2-digit numbers

10 79 r3 Challenge:

2418

6.13 A

5 12

6.8 Problem solving 6.8

34 r33

4r 9

$2.50

109 lampshades 6

45 paintings

180

22¢

18 necklaces

38 hats

6.13 B

73 pots

41 carvings

$1440

12 boxes

$900

10 94 wind chimes

6.9 Division using zeros

24 rows

6.9

10 66 beads

107 r3

6.14 Problem solving

104

109

10 104 r2

6.14

103

11 102 plates

1 a

102

12 102 kites

b $10.00

104 r5

13 76 kites

104 r2

14 409

201 r1

15 302 $5 notes

102 r3

5 kites

6 pizzas. He would only have 40 slices if he bought 5 pizzas.

3 a

94 bags

b 2 cakes left

6.10 Using long division and zeros 6.10 1

933 r3

3837

847 r2

9617

12 kennels

12 students were observers

57 dancers

16 bags Bright Sparks Teacher’s Book 5 • Answers

6.15 Long division practice

6.15 A

101

333 r4

179

10 353 r2

$5.66

11 23

10 181

12 38

11 111 tickets

13 151 r6

12 32 people

1201

14 205

13 805

$2.08

15 20 r6

14 216 children

160 r2

15 27 Part 2

6.15 B

1 a 11

10 214

b 7

e 12

c 10

2 a 108

e $3.50

b 9459 r1

$16.84

c 760

36 r12

d 10 748

h 48

456

312

393 r8

212

11 204

12 360

1877 r20

13 307

124

14 509

245

15 658

336

Unit 6 check and summary 1

B false

C 37

B 20

B 4

C 103

B 132

D $57.18

D 23 r2

10 A 9

24 days

960 litres

No, 4 children would be left

Yes, one will have fewer

$2.40

Challenge: 573 868

456

Part 1

600

b 84: (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84)

Unit 7: Fractions

c 48: (1, 2, 3, 4, 6, 8, 12, 16, 24, 48)

7.1 Least (Lowest) Common Multiple

2, 3, 5, 7

7.1

5: 5, 10, 15, 20, 25

All even numbers are divisible by 2.

9: 9, 18, 27, 36, 45

12: 12, 24, 36, 48, 60

18 books

60: (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)

2004

Assessment 5 1 a

Divisible by 3

Divisible by 5

Divisible by 9

2 a

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

45 1425 222

635 45 1425

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Answers • Bright Sparks Teacher’s Book 5

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

3 9

3 20

15 33

3 a 6

7 a 9 or

b 10

8 a 20

c 30

2 3

9 a 33

d 12

7.2 Greatest Common Factor (GCF) / Highest Common Factor (HCF)

4 12

1 3

7.5 Adding fractions 7.5

7.2 1 a

10: (1, 2, 5, 10)

b 20: (1, 2, 4, 5, 10, 20) c 36: ( 1, 2, 3, 4, 6, 9, 12, 18, 36) d 60: (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)

4 5

11 15

9 10

3 4

7 9

7.6 Decimals and fractions

2 a

15: (1, 3, 5, 15)

7.6

18: (1, 2, 3, 6, 9, 18)

1 a 0. 5

0.7

b 21: (1, 3, 7, 21)

c 0.19

0.72

e 0. 47

30: (1, 2, 3, 5, 6, 10, 15, 30)

c 16: ( 1, 2, 4, 8, 16)

2 a 10

8 10

a 4

c 100

64 100

28: (1, 2, 4, 7, 14, 28)

e 100

b 3

7.7 Equivalent fractions

c 8

7.7

6 bracelets

9 plates with 3 tarts + 2 cupcakes. Another possible answer 3 plates with 9 tarts + 6 cupcakes.

7.3 Prime factors 7.3 1 a

1 2

= 4

3 5

6 10

1 3

= 6

1 2

2 4

2 3

= 6

2 3

4 6

1 1

= 2

1 2

5 10

7.8 Reducing fractions to their simplest form

40: 2 × 2 × 2 × 5

b 56: 2 × 2 × 2 × 7

7.8 A

c 48: 2 × 2 × 2 × 2 × 3

1 2

2 3

b 42: 2 × 3 × 7

1 4

4 5

c HCF/GCF = 6

4 5

4 9

3 4

1 3

1 2

2 a

72: 2 × 2 × 2 × 3 × 3

d LCM = 504

7.4 Common fractions (or proper fractions) 7.4 1

1 4

2 4

4 7

5 6

2 5

2 6

1 2

1 3

7.8 B 1

3 4

1 3

1 4

1 5

Bright Sparks Teacher’s Book 5 • Answers

1 3

4 7

1 2

3 7

7.14 Subtracting fractions: review 7.14 A

7.9 Estimating fractions 7.9

7.14 B

1 2

10 1

2 10

b 13

31 8

11 3

b 4

1 5

22 4 5

6 3 10 or 5 4 1 8 or 2

7.14 D

c 2 4 2 a 4

7.14 C

7.11 1 a 1 6

1 2

4 2

7.11 Equivalent fractions

1 2 3

1 3 1 5 4 2 6 or 3

c 8

7.14 E

7.12 Comparing fractions

8 16 or 8 4

7.12

1 10 or 1 5

3 5 4, 6

1 1 1 12 , 9 , 4

1 2 9, 3

1 6 7 6 , 12 , 8

3 3 5, 4

6 3 5 12 , 5 , 6

Partner Activity:

7.15 Subtracting fractions with unlike denominators Partner Activity:

4 5

1 12

4 10

13 15

11 12

1 15

1 20

3 20

10 24

7 12

7.13 Adding fractions 7.13 1

3 1 20

33 40

11 14

7 10

3 8

2 5

5 12

7.15 1

7 20

17 40

7 15

1 14

39 40

1 14

1 9

35 36

3 10

7 12

1 8

1 22

Challenge: 7 18

100

Answers • Bright Sparks Teacher’s Book 5

7.16 Estimating and problem solving

7.19 Problem solving

7.16

7.19

1 a 3 cups of food

2 b 3

About 2 tins of pie

About 4 cups of coconut mixture

7.17 Adding mixed numbers 7.17

5 2 kg

1 4

1 2

7.20 Practice 7.20 A 1

4 24

5 6

10 5 8

4 12

10 7 10

7.20 B

7.18 Subtracting mixed numbers 7.18 A

g 1 2

h 2 2

i 6 3

j 5 6

d 45

e 39

5 8

2 a 3

10 2 8

2 3 cups of lime juice

2 2 kg of cherries

4 8 kg of flour

5 3 litres of gasoline

1 1 2

7.18 C m ribbon 1

b No, only 1 2 m is left 7

less – 14 8

more –

3 3 (3 6 )

33 +

7 8

1 1

22 5

9 2

46 9

21 2

d 5

143 10

81 11

e 8 3

1 6

2 15

of the vegetable patch ( 3 m)

Challenge:

1 1 a 5 4

c 5

7.18 B

f 1 4 (1 12 )

b 25

1 a 1 4 (1 8 )

c 1 6

1 53

is greater

6 3 cups of sugar

7.21 Enrichment: Cross multiplication Partner work: 1

8 12

10 6 15 4 15

3 4

7.21 1

10 × 3 = 30

5 × 6 = 30

Jan can make 6 tarts. Bright Sparks Teacher’s Book 5 • Answers

101

12 a

e 18

f 22

g 12

6 4

4 × 9 = 36 6 × 6 = 36 9 boxes will last 6 months.

b 5

10 6

d 9

9 ?

4 5

= 15 10 × 15 = 150 6 × 25 = 150 He can carve 25 animals in 15 days.

1 1 1

c 8 8

13 a 4 b 14

29 17 c 3 8

5 8 4

7.22 Working with calculators

15 2 7

7.22

16 3

144

Part 2

13.12

1 a =

b >

f >

c >

g =

d <

h >

3 2 a 3 8

9 24

Unit 7 check and summary 1

A 24

10 15

C 3

4 5

B 8

B 5

C 0.4

10 C 1 3

1 8

b 14 3

3 7

2 3

carton

11 24

cups

More (2 2 bags)

1 6

c 12: (1, 2, 3, 4, 6, 12)

1 53

10 1 8 metres of ribbon

2 5

Assessment 6 1

6, 12, 18, 24, 30, 36

2 a 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 b 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 3 a 28 b 24 4 a 12: (1, 2, 3, 4, 6, 12) b 50: (1, 2, 5, 10, 25, 50)

15: (1, 3, 5, 15)

of the cord 3

d 8

Unit 8: Geometry

9 20

8.1 Lines

17 100

8.1

1 2

1 a perpendicular line

2 5

10 a 11

b point 1 2 10 3 , 6 , 30 ,

etc. b 4

3 5

c line segment d parallel lines e line f

102

Answers • Bright Sparks Teacher’s Book 5

intersecting lines

2 a AB, XY, etc.

• it has straight sides

b AB–PO, AB–RS, XY–PO, XY–RS, etc.

• it is a closed shape

c MP, MA, NX, NO, GS, GY, FB, FR, etc.

• all sides are equal length

d M, N, F, G

• it has eight sides

Challenge:

• it has eight angles

Right angles formed by NE, ES, SW, NW.

• all angles have equal measurement

Straight angles formed by NS and WE. Partner Activity:

3 Regular hexagon • it is flat

right

d right

• it has straight sides

obtuse

e acute

• it is a closed shape

straight

f obtuse

• all sides are equal length • it has six sides

8.2 Angles 1

ABC, CBA

LKM, MKL

• it has six angles

FED, DEF

PRQ, QRP

• all angles have equal measurement

GJH, HJG

STU, UTS

8.3 Measurement of angles 1

q = 450

w = 300

r = 1000

p = 350

z = 400

t = 250

8.4 Triangles 1

z = 500 scalene

4 y = 200 isosceles

x = 600 equilateral 5

v = 450 right 6 t = 1150 scalene

w = 900 right

8.5 Polygons Name of shapes: square, rectangle, trapezium, parallelogram, triangle, pentagon, hexagon, octagon 8.5 1 Square • it is flat

4 Equilateral triangle • it is flat • it has straight sides • it is a closed shape • it has three sides • all sides are equal length • it has three angles • all angles have equal measurement 5 Regular pentagon • it is flat • it has straight sides • it is a closed shape • it has five sides • all sides are equal length • it has five angles • all angles have equal measurement Challenge: Regular nonagon

• it has straight sides

• it is flat

• it is a closed shape

• it has straight sides

• it has four sides

• it is a closed shape

• all sides are equal length

• it has nine sides

• it has four angles

• all sides are equal length

• each angle is a right angle

• it has nine angles

2 Regular octagon

• all angles have equal measurement

• it is flat Bright Sparks Teacher’s Book 5 • Answers

103

8.6 Naming plane (2D) shapes 8.6 1 a regular octagon b square

8.9 A

c rhombus

Teachers to check student drawings and lines of symmetry.

d rectangle e hexagon f

circle

g equilateral triangle h pentagon i

parallelogram

square

circle

octagon

rhombus

pentagon

quadrilateral

Numbers: 0 1 3 8 (The number 1 can be folded in such a way here, but cannot always be, according to how it is written. This may also apply to 3 and 8.)

2 lines of symmetry

1 line of symmetry

4 lines of symmetry

2 lines of symmetry

1 line of symmetry

4 lines of symmetry

8.9 B a

Teachers to check mirror image drawings.

8.8 Circles: review

Teachers to check mirror image

8.8 A

drawings.

1 a circumference

8.10 Solid (3D) shapes: review

b radius

8.10

c diameter

Teachers to check drawings a – j.

radius

cone

f pyramid

diameter

cylinder

g cuboid

8.8 B

cuboid

h cylinder

circumference – B

prism

cylinder

diameter – AD

sphere

cube or cuboid

radius – OE, AO, OD

parallel lines – HI–JK

intersecting lines – HI & ML or JK & ML

right angle – N

Shape

a b

8.9 Symmetry

Discuss:

104

yes

10 no

Answers • Bright Sparks Teacher’s Book 5

d e

faces

sphere 1 curved cylinder 2 flat, 1 curved cone 1 flat, 1 curved pyramid 4 flat cuboid 6 flat

edges vertices

0 2

0 0

6 12

4 8

8.11 Making nets

8.15 Area and perimeter: review

8.11

8.15

Shapes are: cuboid triangular prism

12 cm2

16 cm2

9 cm2

8 cm2

cylinder cube

7 cm2

11 cm2

8.12 Coordinates

11 cm2

10 cm2

Partner Activity:

8.16 Calculating area

•

A (5,7)

8.16 A

•

B (6,2)

70 m2

•

C (2,5)

• •

1440 mm2

60 mm

75 cm2

D (5,4)

36 cm2

144 cm2

E (2,3)

60 km2

56 km2

8.13 Perimeter: review

4800 cm2

10 54 m2

8.13 A

8.16 B

42 cm

19 m

10 cm2

25 cm

18 m

800 mm2

10 8 cm2

24 m

34 m

300 m2

11 40 m2

24 m

28 m

90 cm2

12 60 mm2

64 cm2

13 49 cm2

160 mm2

14 112 cm2

250 mm2

15 144 cm2

9 cm2

8.13 B 1

8 cm

13 cm

12 cm

6 2 cm

8.13 C

77 m2

24 cm

8.16 C

15 cm

128 mm

54 squares

32 m2

16 cm

23 m

40 m2

9 m2

16 m

x = 12 cm

28 m2

6 cm

10 y = 11 m

Challenge:

8.14 Perimeter problem solving

1 km2

68 m

12 cm

8.17 More area problems

5 cm

8.17

14 m

x = 10 m

4 cm

Challenge:

4 m

15 m

24 cm

6 m

30 cm

8 mm

10 3 m

6 cm

Challenge: 30 cm

Bright Sparks Teacher’s Book 5 • Answers

105

8.18 Enrichment: Area of irregular shapes

8.20 Volume

Partner Activity:

8.20

Example 1 Another way is to find the area of the completed large rectangle and then subtract the area of the missing part.

1000 cm3

270 000 cm3

1920 cm3

36 m3

300 cm3

Area of the completed large rectangle: 5 cm × 4 cm = 20 cm2

Unit 8 check and summary

Area of the missing square: 2 cm × 2 cm = 4 cm2

D right angle

B intersecting lines 7 D sphere

Subtract area of missing square from area of large rectangle: 20 cm2 – 4 cm2 = 16 cm2

C 1800

8 B 6

B square

9 A cylinder

Area of shape = 16 cm

C diameter

10 C triangle

Using method of finding area of each rectangle:

Assessment 7

Top rectangle = 3 cm × 2 cm = 6 cm Bottom rectangle = 5 cm × 2 cm = 10 cm Area of whole shape = 6 cm + 10 cm = 16 cm or Left-hand rectangle = 3 cm × 4 cm = 12 cm Right-hand rectangle = 2 cm × 2 cm = 4 cm Area of whole shape = 12 cm + 4 cm = 16 cm

Part 1 1 a point

d right angle

b parallel lines

e obtuse angle

c perpendicular lines 2 a acute

c right

b obtuse 3 a 500

b 1100

4 a t = 550

b r = 900

5 a regular hexagon

Example 2 Area of large rectangle: 8 cm × 5 cm = 40 cm2

b square

Area of small rectangle: 6 cm × 3 cm = 18 cm2

d regular octagon

Area of shaded part: 40 cm – 18 cm = 22 cm2

f parallelogram

c regular pentagon

e rectangle

6 circle

8.19 Area of triangles 8.19

106

6 A symmetry

1 a 6 cm2

f 210 m2

b 312.5 cm2

g 28 m2

c 462 cm2

h 21 cm2

d 200 m2

50 m2

e 2 m2

15 cm2

300 cm2

She can make 2 fins by cutting the rectangle diagonally into halves.

Answers • Bright Sparks Teacher’s Book 5

radius

circumference

diameter

Teachers to check mirror image drawings.

Teachers to check student drawings and lines of symmetry. 1 line of symmetry should be shown down the centre.

9 a cube

cone

b cylinder

cuboid (or cube)

10 a 12 b 6 c 8 Part 2 1 a 28 cm

30 cm

2 a 9 cm

6 cm

8 cm

3 a 56 cm

24 cm

30 cm

4 a x = 9 m b

w = 8 cm

5 a 25 m

150 m

24 cm

28 m

9 a 8 cm2

Challenge: $2.75 9.1 B 1

0.06

136.05

204.1

0.51

0.054

0.0045

4.158

3224

102.9

10 8.992

11 $8.37 12 $10.88 13 $6.75 14 0.3 ℓ 15 $4275.70 Challenge:

9 cm2

10 a 105 mm2 b

96 m2

18 m2

0.624 ℓ

4.368 ℓ

11 66 squares

9.2 Division by a whole number

12 390 tiles

9.2

13 400 cm2

1.62

14 660 cm2

0.386

10 30.5

15 8 cm

3.2

11 3.49

16 6 m

0.096

12 0.258

17 12 cm2

$5.00

13 31.2

18 48 m3

0.145

14 12.285

19 Yes. Explanations will vary. Total number of cubes is 9. This is a square number, so a cube with sides of 3 blocks each can be made.

1.6

15 0.541

0.022

20 45 000 cm3

1.1

9.3 Adding zeros to the dividend 9.3 1

1.26

6.225

3.65

5.455

9.1 Multiplying decimal numbers

14.5

510.5

9.1 A

32.41

$700.50

16.24

10 1.018

Unit 9: More decimals

51.25

37.5

$16.25

Challenge:

0.16

10 $249.00

102.4

11 $26.46

8.88

12 4.165

37.2

13 668.7

319.8

14 26.88

$8.43

Bright Sparks Teacher’s Book 5 • Answers

107

9.4 Multiplying and dividing decimals by 10, 100, 1000

Unit 9 check and summary 1

D 62.5

B 7.8329

9.4 A

C 45

right

135

64 490

B 0.68

left

973.4

554

A 32.41

D 0.165

9961.2

3200

D 5673.6

10 A 0.11

628

32 790

6284

10 775 346

9.4 B

10.1 Units of length

8.62

0.288

10.1

4.614

0.0865

1 a mm

42.53

0.9884

b cm

e cm

0.35

0.08 686

0.7525

10 0.984 753

9.4 C

c mm 2 a 6.5 cm

4.7 cm

b 65 mm

47 mm

3 a–f Teachers please check.

5.3

0.905

4426

1.8

10.2 Longer lengths: review

9541

6970

10.2

0.78

3096.2

42.433

10 0.0648

9.6 Metric conversions

10.3 Working with units of length

9.6 A 1

260 mm

11 2 km

5 m

12 32 000 mℓ

1800 cm

13 400 000 mℓ

18 000 mm

14 15 ℓ

64 m

15 6700 cm

8 m

16 90 cm

19 000 g

17 5.4 kg

9 g

18 7 g

47 000 mg

19 20 m

10 8 000 mg

20 265 000 mℓ

9.6 B

108

Unit 10: Measurement

0.66 cm

2147 mℓ

897 mm

3.891 kg

0.1644 m

724 500 mg

365 g

10 82 000 g

4 mℓ

11 97.144 cm

0.034 m

12 3 600 000 cm

Answers • Bright Sparks Teacher’s Book 5

10.3 A 1

7000 m

5 km

12 000 m

8.5 km

6500 m

2.45 km

4360 m

4.001 km

15 230 m

10 2.2 km

10.3 B 1

10 cm

10.3 C 1

50 cm

300 cm

75 cm

350 cm

100 cm

375 cm

200 cm

500 cm

250 cm

10 1000 cm

10.6 Converting between units of mass

10.3 D 1

100 cm

250 cm

10.6

1 2 3 4

175 cm

7000 mg

11 35 000 kg

3000 kg

12 525 g

m m

10.3 E

62 000 g

13 228 mg

25 cm

55 cm

8.712 kg

14 0.412 g

25 cm

125 cm

9 t

15 125 kg

1 m

150 cm

6 kg

16 0.89 kg

1.25 m

150 cm

25 g

17 175 000 g

89 cm

10 7 m

18 kg

18 432 mg

10.4 Practice with longer units of length

0.095 t

19 560 mg

10.4 A

10 16 000 kg

20 680 kg

1500 m

3250 m

750 m

4750 m

1250 m

0.75 km ( 4 km)

mℓ

4000 m

1.5 km

ℓ

2500 m

10 1.25 km

ℓ

ℓ mℓ

10.4 B

10.7 A

ℓ

3 4 km

mℓ

10 mℓ

4500 m

10.7 B

1 2 3 4

1 4 km

10.7 Capacity: review

10.4 C

3000 mℓ

350 mℓ

500 mℓ

3 (4

1 2

3ℓ 300 mℓ

ℓ

500 m

750 m

0.75 ℓ

1000 m

3 km

0.0035 ℓ

1 km

4500 mℓ

10 3600 mℓ

10.5 Mass

ℓ)

10.7 C

10.5 A

500 mℓ 1 (2

1ℓ

600 mℓ

g or kg

tonnes

0.5 ℓ

500 mℓ

tonnes

10.8 Converting between units of capacity

10 kg

10.5 B 1

2000 g

1500 g 1 (4

kg)

ℓ)

10.8 1

15 000 mℓ

672 mℓ

4000 g

148 000 mℓ

10 4554 mℓ

2 kg

9000 mℓ

11 7 mℓ

1 1 2 kg 1 4 kg

6 ℓ

12 980 mℓ

13 ℓ

13 400 mℓ

4.1 ℓ

0.25 kg

1.25 kg

3500 g

10 800 g

14 3200 mℓ 1 (4

0.25 ℓ

125 mℓ

ℓ)

15 0.025 ℓ 16 0.066 ℓ

Bright Sparks Teacher’s Book 5 • Answers

109

17 2944 mℓ

19 0.054 ℓ

18 6832 mℓ

20 0.00485 ℓ

11.2

10.9 Mixed units

6 7

3 5 1 42

7 9

3 8

10.9 1

0.035 g

1.042 m

0.000 687 kg

460 mm

8000 g

6200 cm

2500 mℓ

0.084 ℓ

10 140 000 mℓ

10.10 Problem solving: different units of measurement

3 1

10 6

Challenge: 20 $75

11.3 Cancelling

10.10 1

8 times

250 mℓ

Partner Activity:

0.342 kg

0.03 ℓ

1.35 m (135 cm)

5 times

425 cm

1.026 kg

50 pieces of chalk

10 650 g

Challenge: 1.03 cm

Unit 10 check and summary 1

A 50

D 250

C 1000

A metre

D kilograms

B pumpkin

B litre

A litres

10 A metre

Unit 11: More fractions 11.1 Multiplying fractions 11.1 1

1 15

1 8

2×1 1 = 3 21 3 1 1

5×4 1 = 8 5 2 2 1

c 1 1 9×5 1 = 210 91 2 d 1 1 7×6 1 = 212 142 4 11.3 1 2 3 4 5

5 7 3 5 4 9 1 5 3 5 1 16

1 4 3 7

11 $18.00

5 9

4 15

2 9

3 8

1 8

3 20

7 32

Teachers please check.

1 12

2 5

Activity:

110

11.2 Multiplying whole numbers and mixed numbers by fractions

There are 12 parts altogether.

3 parts are shaded twice.

1 3

3 4

3 12

which is 4 .

Answers • Bright Sparks Teacher’s Book 5

1 5

Challenge:

11.4 Drawing a sketch 11.4 1

$12.00

$20.00

42 marbles

80 ℓ

$30.00

120 children

11.5 Dividing fractions

Unit 11 check and summary

11.5

C 8

A $40

C $10

D 3

3 10

A 2 5 metres

D 40 m

A 3

3 34

5 6

24 slices

10 40 slices

Challenge:

11.6 Mixed multiplication and division of fractions 11.6 A 2 3

1 6

3 10

3 4

3 16

2 25

10 15

1 27

10 B 1 2

Assessment 8 Part 1 b 845 c 8.874 d $31.93 e $39.00 f

2.72

g 0.36 h $1.24

1 14

4 29

6 7

5 36

1 3

5 12

0.368

3.984

k 0.69

11.6 B 1

$9.00

$3.33

4 a 357.9 b 262

52 121

c $12 750 d 8.3492 e 2.204

Challenge:

11.7 Mixed problem solving

ℓ

11.7

Teachers to check.

a b

1 8

16 pieces

1 11 4

72 cupcakes

9 coconuts

Part 2

1 28

1 4 hours

0.75 ℓ

14 000 g

2.8 g

500 cm

3090 mg

32 cups

4 2 m

Challenge: 1

$13.50

1 a 163.4

5 pizzas

10 Teachers to check.

Bright Sparks Teacher’s Book 5 • Answers

111

8 km

12.2 Percent and decimals

0.25 km

12.2 A

3500 cm

14%

0.20

10 0.000 524 kg

85%

0.40

11 Less

92%

0.06

12 4

64%

0.05

13 2

19%

10 0.18

14 29 cm

12.2 B

15 72 cm

1 a 0.25

d 0.84

Part 3

b 0.78

e 0.39

1 12

2 15

2 a 30%

d 11%

3 7

b 3%

e 10%

1 2

3 10

2 25

4 5

c 0.12

c 80% 0.29

15%

Challenge: 1

10%

100

3 6.25

12.3 Percents, decimals and fractions 12.3 A

10 1 5

Unit 12: Percent, ratio and proportion

12.1 Percent 1

43%

11 15%

13%

12 58%

29%

13 3%

14 16%

98%

15 75%

96%

16 21%

66%

17 32%

52%

18 87%

11%

19 13%

10 7%

3 4 5

12.1

112

20 9%

Answers • Bright Sparks Teacher’s Book 5

1 10 1 5 7 10 1 4 1 2

3 4 2 5

9 10

3 5 31 50

12.3 B 1

0.30 = 30%

0.75 = 75%

0.25 = 25%

0.90 = 90%

0.80 = 80%

0.25 = 25%

0.70 = 70%

0.40 = 40%

0.30 = 30%

10 0.85 = 85%

12.4 Finding the percent of an amount 12.4 1

7 students

24 children

$40

$120

$3.50

10 4 passed

12.5 Problem solving

12.7 B

12.5 1

12 children

40%

7 cookies

55%

70%

50%

7 a 30 songs b 60% 8

10%

12%

Fraction

Decimal

Percent

1 2

0.5

50%

3 4

0.75

75%

1 10

0.1

10%

3 5

0.6

60%

1 5

0.2

20%

12.9 Discount

10 76%

12.9

Challenge:

Discount $8

$22.50

38%

Sale price $72

$144

12.6 Comparing fractions

Discount $9

$31.50

Sale price $51

$12.30

Discount $10

$153

Sale price $30

10 $57

Discount $6

Sale price $114

12.6 1

40%

25%

10%

48%

7.5% or

12.10 Problem solving 1 72%

12.10

12.7 Practice with percent 12.7 A 1 a 40%

32%

b 20%

40%

c 30 sweets 9

$16.00

$24

$448

Yes, $48 needed 6

$7.20

$32

$18.

$32

more, 20% is $6

12.11 Wages and salaries

2 a 18%

10 25%

12.11

b 36%

11 $90.00

$31 200

less

17%

12 $50.00

$31 200

$340

0.07

13 20%

12.12 Simple interest

100%

14 40%

12.12

150

15 $100.00

1 a $120

$10 400

b $4120

Less

$3244.73

$720

12.13 Ratio 12.13 1

3 : 2

4 : 9

3 2 4 9

3 to 2 4 to 9

Bright Sparks Teacher’s Book 5 • Answers

113

5 : 4

2:5

5:7

4:1

7:4

7:3

2:3

5 4 2 5 5 7 4 1 7 4 7 3 2 3 3 1

10 3 : 1

5 to 4 2 to 5 5 to 7 4 to 1 7 to 4 7 to 3 2 to 3 3 to 1

12.14 Simplifying ratios

12.16 1

7 2 m

2 bathrooms

36 m 18 m

1 42 1 42

9 m

1 10 2

10 6 m

12.17 Problem solving: fractions, ratios and percents 12.17

12.14 A 1

1 : 3

3:1

1 : 3

10 1 : 5

1 : 3

11 2 : 1

3 : 2

12 2 : 3

4 : 3

13 1 : 4

5 : 1

14 5 : 1

1 : 4

15 1 : 8

1:2

3 : 2 ( 2 , 3 to 2)

$44

3 a 75% b 48% 4 a 6 red dresses b 34 black dresses 3

c 3 : 17 ( 17 , 3 to 17) 1

5 a 4 b 2:1

12.14 B

c 40 items

1 a 2 : 3, 3 , 2 to 3

Challenge:

b 6 shells c 9 shells 3

2 a 3 : 1, 1 , 3 to 1 c 3 dogs 1

3 a 1 : 5, 5 , 1 to 5 b $10 and $50 4 a 16 girls b 12 boys

2 : 1, 1 , 2 to 1

4 eggs

3 : 1, 1 , 3 to 1

4 cups

2 : 1, 1 , 2 to 1

9 cups

48 cookies

6 eggs

Challenge: 1

1 cup

$5520

D 53%

C $36

B 0.86

D4:7

C 70%

B $30

3 5

A 9

10 D 12

Part 1

12.15

1 : 3 ( 3 , 1 to 3)

75%

Assessment 9

12.15 Proportion

Unit 12 check and summary

b 9 dogs

114

12.16 Working with scale

Answers • Bright Sparks Teacher’s Book 5

Any 2 squares should be shaded.

12% 56

3 a 100 b 80% c 35% 4 a 12%

d 3%

b 0.78

e 125%

c 45%

11 6 goats

Matching answers are side by side

12 a 80 fish b $700 13 170 tickets

0.2

1 5

25%

1 4

10%

0.1

3 4

0.75

0.15

15%

13.1

50%

1 6 weeks

1 2

14 192 people 15 $325.00

Unit 13: Measurement – time 13.1 Review

2 730 days

100%

0.05

5 100

4 2 minutes

90%

0.9

5 28 days

0.4

2 5

3 2 days

6 90 minutes 7

18 000 seconds

$45

8 11 weeks

9 3 years

25%

10 48 months

10%

11 2.15, quarter past two

10 40%

12 4.45, quarter to five

Part 2

13 7.04, four minutes past seven

92%

14 11.35, twenty-five minutes to twelve

$3.40

15 8.25, twenty-five minutes past eight

3 a 117 students

Partner Activity:

b 40%

00:30

20%

09:15

5 a $60

14:45

b $161.25

22:26

c i $36.80

13.2 Enrichment: 24-hour system

ii $55.20

13.2

d $75.00 6 a 1 : 3

two to five

b 3 : 2

3 17

c 3 : 4 7

10 straw roses

4:3

1 a 02:30

d 00:15

b 19:20

e 11:42

c 23:59 2 a 3.55 a.m.

b 11.32 a.m. e

12.29 a.m. 5.17 p.m.

c 2.30 p.m.

10 $10 Bright Sparks Teacher’s Book 5 • Answers

115

13.3 Calculating elapsed time

5 a 970 tickets

2170 tickets

13.3 A

b 1200 tickets

310 tickets

1 a 2 hrs 20 mins c

1 hr 51 mins

210

b 1 hr 45 mins 2 a 6 hrs 5 mins

b 4 hrs 45 mins d 3

12 hrs 23 mins 11 hrs 5 mins

6.05 p.m.

8.16 a.m.

4.03 p.m.

14.3 Interpreting data and drawing graphs The numbers on the vertical axis mean the number of cones sold.

3.27 p.m.

13.3 B 1

Challenge:

9 hrs 45 mins

1 22

hrs

13.3 C 1

5.10 p.m.

3 hrs 30 mins

2.02 p.m.

26 seconds

1 hr 46 mins

3 hrs 20 mins

2 hrs 40 mins

9.30 p.m.

13.3 D 1

12 wks 4 days

0 hrs 50 mins

2 wks 6 days

37 mins 5 secs

15 wks 6 days

63 yrs 4 months

1 wk 5 days

25 wks 4 days

31 hrs 15 mins

10 1 yr 103 days

Unit 14: Statistics, data and probability 14.1 Finding the mean

The high and low bars tell us the flavours that were sold. 14.3 1

Chocolate

Mint

Mint, vanilla

Strawberry, chocolate

18 cherry cones

13 vanilla cones

9 mint cones

Numbered singly

Yes, only 98 cones were used

10 Peanut, mint, strawberry IT Challenge : Teachers please check.

14.4 Making graphs / frequency charts 14.4 Teachers please check chart.

14.5 Enrichment: Interpreting data with a line graph

14.1 1

71 runs

$28

14.5

$551

$19.50

200

12 km

11.4 kg

600 visitors

92.3%

Thursday

14.2 Working with the total

4 a Sunday

Discuss:

b Most people do not work this day

3 135

Wednesday, Thursday

37.5

4 640

6 a 500 people b Vertical axis is calibrated in 200s

14.2 1

3 4474

Tuesday, Friday

4 $425

850

460 visitors

10 Answers will vary

116

Answers • Bright Sparks Teacher’s Book 5

14.6 Circle graphs (pie charts)

14.9 Probability

Discuss:

14.9

30 children

9–10 age group

5–6 and 7–8

Very likely – half of the time; reasons will differ, e.g. because 2 even numbers make an even number and 2 odd numbers make an even number.

Very unlikely/impossible, there is no zero so the lowest number is two ones.

Possible, reasons will differ, e.g. there are two 6s, one on each die.

14.6 Favourite pets 8

dog

cat

32 16

bird

14.11 Enrichment: Types of sets

fish

14.11 1 a (2, 4, 6, 8)

14.7 Interpreting the circle graph 14.7 2 3

Pink

Blue

Green and white

Pink

90 students play volleyball

0.15

180 students play netball

c (1, 2, 3, 5, 7, 11, 13, 15) d (3, 5) 3 a red, yellow, blue. Set letters will vary b answers will vary

Challenge: 1

c answers will vary d answers will vary

14.13 Practice with sets 14.13 1 a 5 b 4

Key

green blue white pink yellow

2 a (1, 3, 5, 15) b (2, 3, 5, 7, 11, 13)

3 10 1 5

b (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12)

cricket football netball table tennis volleyball

No, the total percentage of students is accounted for.

14.8 Using percentages in circle graphs 14.8 1

30 children

90 children

70 children

35%

11 and 12

60 students

170 students

92%

c It consists of all the members of both sets. There are no members in common. d The sets occupy separate spaces and there is no intersection between them. 2 a 29 children

13 children

b 5 children

11 children

c 16 children

8 children

3 a 37 children

5 children

b 8 children

14 children

d 5 children

Bright Sparks Teacher’s Book 5 • Answers

117

Unit 13 and Unit 14 check and summary 1

D 180

D 21

B 52

B 18

C 11.30 p.m.

C 25%

B 4.38

A 4.15

10 A 16

2 5

Assessment 10 Part 1 1 a 45 minutes b 2 hrs 45 mins 2

6.38 a.m.

3 a 14

f 48

b 300

g 150

c 3

h 730

d 36

i 4 2

j 5

7 wks 3 days

4 a 4.10, 16:10

9.30, 21:30

b 5.52, 17:52

3.40, 15:40

8.20 a.m. 18:25

2 a 12:15

Part 2 1 a Korea

d 11 elephants

b USA

e 8 elephants

c 7 elephants

162 cm

b 55 mins

12 A $640

D 1892

13 C 24 children

C 6

14 D 11

B 16

15 B 1

D 108

16 C

C $35

17 B 20 cm2

C 3478

18 C

B $163.50

19 D $21

10 A 36

7 8

5 12

3 5

20 A 25 litres

Part B 1

Thousands

8 10

Six thousand, one hundred and eighty

4 a 268 050

37 486

5 a 8000

b 9

7 a 6000

76 500

8 a 3478

8743

$171.60

13 50 r6 14 $238 15 a 12

132

b 12

16 a 9

1 4 b 1 15 12 d

17 $12.50

6 a 10%

d 12 students

b 20%

e 44 students

c pink

118

A 22 412

12 Yes, one number is doubled, the other halved

c 1.30 a.m.

6 bottles

b 1, 3, 6

b 10.05 p.m.

11 B 300 chairs

11 a 6, 36

3 a 2.50 p.m.

$4.00

B 70

10 Pablo

c 19:10

b 00:15

2 a 9.05 p.m.

Part A Multiple choice

Challenge: 1

Final assessment 1

Answers • Bright Sparks Teacher’s Book 5

1 4

19 a >

20 a obtuse

right

b acute

21 a (isosceles) triangle

b (regular) hexagon

10 B 12

16 A 15 mangoes

c cube

11 C 48

17 B 8

12 B 126

18 D 12 hrs 5 mins

22 a 3 faces

0 vertices

D 67

7 15 5 9

15 C 4%

b 2 edges

13 A

23 cuboid

14 C

24 a x = 6 m

Part B

b perimeter = 40 cm

Ten thousands

25 144 m

One million, nine thousand, and seven

26 g 27 a 33 mm

5000 g

b 1.2 ℓ

19 C $51 20 C

13 20

3 a 93 240

47 286

4 a 30 000

b 8

e 19

28 a 3.68

d 2.49

c 7

b $42.98

e 5300

5 a 4.5

c 14.57

f 0.859041

6 a 1770

$572

29 a 50%

d 9%

b 80 000

b 84%

e 0.25

7 a 8651

1568

c 12%

b 8516

30 90%

$75.67

31 38%

About $35

32 28 sheep

10 801 000 is greater

33 $135

11 a 1, 2, 8

34 a 72 hrs

240 mins

b 1, 64

b 4 hrs

730 days

12 20 (twice 10)

35 10

13 No, 32 pictures will be left

36 6 hrs 15 mins

14 18

37 9.21 p.m.

15 a 84

b 7

5 8

1 45

b the shop with off, it is % discount

19 a <

20 a 80%

75%

Final assessment 2

b 96%

86%

45 yrs

38 a 5%

Wednesday

b 100% 39 a 20

16 24 b

17 a 5

40 a $5 1 3

1 33 3

Part A Multiple choice 1

D hundredths

B $14.25

A 6203

C 64

C 297 600

A 192 tins

A 7

D $3225

18 2 8 pizzas

21 12% 22 $56 23 50 marbles 24 40 mangoes 25 a 84 hrs b 5 mins Bright Sparks Teacher’s Book 5 • Answers

119

26 9

15 a 12

27 3.13 p.m.

b 11

28 a 15 books

16 a 12

b 20 c

19 20

21 a >

22 a right

right

cuboid

b 129 books

17 a

c about 26 (25.8) books

b 14

29 54

Final assessment 3 Part A

18 $60

30 $210

Multiple choice

D 1 103 611

11 C 55

D 643 008

12 B 6

A 600

13 C $2792

C 5

14 B

D 32

15 B sphere

B $909

16 C 3888.45

D $494

17 A 0.194

D 7

18 A 240 rolls

C 320 passengers 19 D 99

10 A $0.84

3 20

20 A 36 shells

3 4

20 1 8 m of ribbon

b obtuse 23 a cylinder b rectangle 24 a 1 flat face

c 1 edge

b 1 curved face

d 0 vertices

25 a 82 cm

390 cm2

26 Teachers to check student drawings and lines of symmetry. There should be 2 lines of symmetry. 27 1000 cm3

Part B

28 tonnes

Hundred thousands

29 a 1000 kg

0.250 ℓ

9000

b 6.98 m

870 000 m

Sixteen thousand and fifty-one

30 1015 m b

72.2

25%

4 a 507 900

97 066

31 a $9.594

5 a 8

32 10 ℓ of milk

b 1

33 a

100

17 20

b 80%

7 a 9 000 000

160 000

c 63%

8 a 2349

2394

34 a

b 9432

35 $38

36 $84

$210

5 9

e 72% b

7 100

10 10.99, 19.09, 19.1, 100.9

37 a 90 mins

c 2 2 days

11 a 7, 28

b 4 mins

b 1, 7

7, 23

38 12 hrs 35 mins

12 32 (twice 16)

39 1 hr 32 mins

13 $30 030

40 64

14 60

120

13 20

Answers • Bright Sparks Teacher’s Book 5

1095 days

Answers to Workbook 5 Unit 1: Number 1 Place value 1

forty

seven thousand

three hundred thousand

eight hundred

two hundred thousand

fifty thousand

two thousand seven hundred, or twenty-seven hundred

8 9

Challenge: a

2M 5HT 6TT 7Th 3H 0T 0O

2B 0HM 0TM 4M 5HT 6TT 0Th 2H 2T 0O

4 Place value 1

704

2200

4920

14 000

fifty-nine thousand

613

two hundred and sixty thousand

1010

85 000

35 992

10 one million

2 Place value

10 786 102

tens

hundreds

ones

thousands

tens

5 Value

ten thousands

600

2000

hundreds

700

ten thousands

10 000

10 hundred thousands

1000

10 000

10 8000

3 Place value

Challenge: a

111 112

999 999

1 999 999

2 H 3T 4O

6 Value

2Th 0H 6 T 8O

30 000

3 Th 7H 0T 4O

500

900

5TT 5Th 4H 2T 1O

50 000

20 000

6Th 4H 7T 0O

600 000

6000

2 TT 7Th 3H 0T 8O

3000

10 400

1Th 8H 1T 0O

7 Value

6Th 6H 5T 4O

200 + 60 + 4

9TT 0Th 7H 4T 0O

30 + 2

10 6TT 2Th 8 H 7T 5O

9000 + 40 + 4

200 + 90

70 000 + 1 000 + 400 + 20 + 3 Bright Sparks Teacher’s Book 5 • Answers

121

9000 + 70

300 + 20 + 4

12 More expanded numbers with regrouping

90 000 + 2000 + 900 + 50 + 8

51 400

7084

700 000 + 50 000 + 300 + 60 + 1

60 400

314 230

10 200 000 + 6000 + 600 + 3

50 739

74 000

8 Expanded form

40 001

240 065

9060

10 806 525

1000 + 600 + 20 + 8

80 000 + 9000 + 700 + 50 + 4

400 + 60 + 8

30 000 + 1000 + 800 + 90

40 000 + 4000 + 300 + 20

3000 + 600 + 50

40 000 + 700 + 60

50 000 + 2000 + 4

20 000 + 9000 + 600 + 60

10 70 000 + 70 + 4 4 040 404

2 020 202 020

9 Expanded form

122

7643

6 3476

3467

7 9821

7643

8 1298

7634

9 1289

3467

10 9812

Unit 2: Patterns, sequence and order 1 Counting and ordering

Challenge: a

13 Forming numbers

680, 681, 682, 683, 684

2899, 2900, 2901, 2902, 2903

54 509, 54 510, 54 511, 54 512, 54 513

900, 899, 898, 897, 896

2318

60 300

4541, 4540, 4539, 4538, 4537

479

7580

12, 15, 18, 21, 24

6293

203

88, 86, 84, 82, 80

41 506

5060

335, 340, 345, 350, 355

39 040

10 97 020

5, 5 2 , 6, 6 2 , 7

10 Expanded numbers with regrouping

10 4.5, 5, 5.5, 6, 6.5

6 H

4 Th

2 Counting and ordering

4 H

57, 258, 721, 7255

14 ones

709 ones

601, 602, 616, 635

2 H

46 Th

5600, 603, 5608, 5639

10 H

10 30 TT

19, 90, 909, 910

11 Expanded numbers with regrouping

6407, 6460, 6465, 6467

58 340

3643, 13 641, 13 643, 30 643

20 609

2746, 2845, 27 450, 27 500

9046

570, 5700, 5754, 51 754

16 213

6324, 62 000, 63 024, 63 224

7256

10 803, 8030, 80 030, 83 030

Answers • Bright Sparks Teacher’s Book 5

3 Counting and ordering 1

92, 89, 28, 9

64, 60, 56, 18, 16

280, 265, 251, 234, 214

2008, 1298, 1090, 1078, 983

11870, 10979, 970, 93, 89

Challenge: a

4 949 594

4 949 497

81 38, 40, 44

21, 19, 17

20, 35, 40

400, 370, 360

81, 99, 108

56, 48, 40

10, 12, 13

72, 77, 83

80, 160, 320

69¢

$43

29 000

140 000

3430

18 400

3 Addition practice

10 8, 4, 2

749

6020

1158

4399

2825

13 349

7088

530

1234

10 883

Challenge:

5 Patterns 1

1 Pre-check

2 Rounding numbers and money

4 Patterns 1

Unit 3: Operations: addition and subtraction

a) ~14 100

53, 53, 6

$1.25, $1.50, $1.75

80¢, 85¢, 90¢

90¢, 80¢, 70¢

0.8, 0.9, 1

2, 1.5, 1

IX, X, XI

100, 10, 1

0.01, 0.001, 0.0001

b) ~65 000

4 Addition with regrouping 1

7426 credits

7863 tickets

457 people

5527 sacks

14 737 sheets of paper

5 Adding large numbers

10 678, 789, 900

6 Revision 1

432

125

10 24

38 691

38 408

72 192

$798.67

$1947.08

$12 811.00

$45 098.64

15 575

Bright Sparks Teacher’s Book 5 • Answers

123

70 693

10 76 597

Unit 4: Decimals 1 Place value: tenths

6 Subtracting large numbers 1

$33

211

8580 km

$571.50

1773

7 Regrouping with zeros 1

1564

962

5297

12 360

20 070

8 Regrouping with zeros

Hundreds Tens Ones

1 2 3 4 5 6 7 8 9 10

5 2 6 9 6 5 4 0 2 0

4 3 1 2 9

. . . . . . . . . .

2 8 0 7 1 0 5 0 2 9

3 7 2 4 6 5 9 1 6

2 Place value: tenths 1

Twenty-three, and five tenths

Eighty-four, and two tenths

Three hundred and sixteen, and four tenths

2020

Seventy-five, and three tenths

3620

Six hundred and sixty, and six tenths

26 893

3 Place value: hundredths

298

2352

17 569

9 Adding and subtracting money 1

$302.79

$23 720.65

$546.21

$755.34

$603.55

10 Subtraction practice

124

. Tenths

946 920

66 291

200 607

6020 kg

$9.75

Answers • Bright Sparks Teacher’s Book 5

Hundreds

Tens

Ones

2 3 9

0 0 0 5 5 1 8 9 4 4

0 6 0 7 0 6 5 0 0 3

1 2 3 4 5 6 7 8 9 10

1 2 3 9

. Tenths

. . . . . . . . . .

4 Place value: hundredths 1

3.2

21.08

18.5

50.9

1.42

900.7

67.3

9.07

21.18

10 396.37

2 1 0 4 9 0 1 5 0 2

Hundredths

5 8 6

5 2 7

5 Rounding decimals 1

5 10

300

706

9 100

20 000

580

10 300

6 Value

Unit 5: Multiplication 1 Check A B C 1 42

1 48

1 132

2 96

2 35

2 121

3 56

3 25

3 108

4 40

4 28

0.21

0.4

5 54

5 42

5 70

0.6

0.11

6 45

6 108 6 54

0.36

0.1

7 49

7 63

7 81

0.8

0.01

8 72

8 48

8 36

0.09

10 0.82

9 66

9 60

9 36

10 77

10 72

10 110

7 Value 1

12.4

51 860.19

2 Arrays

230.8

26 102.38

30 cups

621.98

71 808.9

27 rolls

3267.18

22 579.01

96 tins

400.05

10 13 290.28

48 books

8 Ordering and comparing decimals

$4.80

0.3 > 0.03

30.6 > 3.06

72 objects

7.62 > 7.6

95.09 > 90.59

7 6 × 9 = 54

125.9 > 120.9

8 9 × 6 = 54

Challenge:

253.6, 487.98, 3292.01, 3292.1

10 Teachers please check array.

9672.1, 9672.15, 90672.15, 906721.5

Challenge:

9 Rounding money 1

$453

$100

$2990

$35.00

$1.00

10 Adding and subtracting decimals 1

171.37

$288.03

3324.66

7 $1940.90

$247.55

8 2119.03

$63.25

4800.34

10 $6907.78

2810.14

11 Problem solving 1 a $33.95

yes, he has $105.90

a 12.2 sec

$6.05

Teachers please check array.

Answers will vary. Multiplication can be done any way round – i.e. 9 × 6 = 6 × 9 = 54

3 Square numbers / Square roots 1

121

4 Multiplying 2-digit numbers 1

104

432

90¢

405

$8.10

343

140

438

10 The same

16.2 sec Bright Sparks Teacher’s Book 5 • Answers

125

5 Multiplying 3-digit numbers

Activity:

546

$23.50

Across Down

768

4016

616

1456

$64.08

2046

5782

356

d 696

3801

10 $327

100

e 4050

6 Multiplying large numbers

905

g 500

10 935

76 552

400

18 148

380 538

15 884

106 205

Unit 6: Division

7 Multiplying large numbers 1

$348

2190 tuberoses

750 ginger lilies

2304 vases

8 Multiplying by multiples of 10 1

21 000

24 000

120 000

560 000

14 000

32 000

420 000

10 200 000

1 Factors 1

1, 2, 4, 5, 10, 20

1, 3, 5, 15

1, 2, 3, 6, 9, 18

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

2 Prime numbers 1

Crossed: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

90 000

Crossed: 6, 9, 12, 15, 18, 21, 24, 27, 30

1 200 000

Crossed: 10, 15, 20, 25, 30

Circled: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 prime numbers

9 Multiplying by 2-digit numbers 1

1904

3 Divisibility

2730

4340

18, 200, 5360, 580, 32 400, 26, 400, 16, 92, 300, 132 210, 76, 180

7620

1925

18, 81 945, 32 400, 7221, 33, 75, 300, 57, 13 2210, 180

$437.40

41 325

200, 5360, 580, 32 400, 400, 16, 92, 300, 76, 180

$317.07

32 832

200, 5360, 580, 81 945, 32 400, 625, 385, 400, 75, 300, 132 210, 180

18, 81 945, 32 400, 132 210, 180

10 $294.50

126

Challenge:

10 Problem solving

192 pencils

87 books

4 Basic division

232 students

$127.50

832 passengers

Answers • Bright Sparks Teacher’s Book 5

b 2

6 6

7 11

8 9

9 7

5 Using opposites: multiplying and dividing

11 Division with money 1

$48

6 11

$65

7 11

$2056

8 9

4 a 380

9 20

b $1900

10 8

12 Dividing by 2-digit numbers

6 Division speed tests

6 $1.30

6 8

205

7 $3.80

7 9

16 rows

8 7

$20.41

$203

9 27

26 r 2

$10 150

10 84

13 Understanding remainders

7 Division with remainders

No, 2 students will be left.

16 r 1

11 r 2

$12 more

9 r 2

11 r 2

Yes (6 trays will hold 108 flies)

4 r 1

9r3

Challenge:

7 a 5 boxes

8 egg boxes

5 eggs

8 a 20 bundles b 2 balloons

Unit 7: Fractions

8 Dividing larger numbers

1 Least (Lowest) Common Multiple 1

9 660

10 57 hot dogs

2 Greatest Common Factor (GCF) / Highest Common Factor (HCF)

150

7 $14

77 r 1

8 $38

58 r 2

12 r 4

9 Division using zeros

403

7 $204

102

105

9 $309

1 a 9

103

10 303 days

b 9

106

105

82 slices of pizza

3 Fraction of a set 5 4

2 a 31 12

10 Using long division and zeros

b 31 11 22

438

2456 r 2

3 a 15 ( 30 )

552

258 r 4

b 15 ( 30 )

669 r 1

Answers will vary. Bright Sparks Teacher’s Book 5 • Answers

127

4 Decimals and fractions

9 Comparing fractions

0.3

5 >

0.9

6 >

0.76

6 2 5 18 , 3 , 6

0.87

0.31

7 4 5 14 , 20 , 30

0.25

8 10

9 10

53 100

44 100

(or

10 Simple fraction addition 4 5)

(or

1 2

7 8

1 2 or

3 6

15 10

7 10

13 14 1

6 1 10 or

5 Equivalent fractions

4 4 8

2 parts shaded in each shape

5 8 3

8 parts shaded in each shape

6 1 8

6 parts shaded in each shape

2 9

5 1 7

12 Whole numbers subtracted from mixed numbers 1

2 3

1 2

5 8

3 4

1 2

4 3 10

1 3

3 4

1 2

5 5 2

6 1 8

7 Estimating 1

1 2

7 1

1 2

8 0

1 2

11 10

11 Fractions subtracted from whole numbers

11 25 )

6 Simplifying

1 2

9 10

1 3

2 9

8 Improper fractions and mixed numbers

128

13 Mixed numbers subtracted from whole numbers 1

1 3

14 Subtracting fractions with the same denominator 1

1 5

2 10

1 4

1 6

2 8

15 Subtracting fractions with unlike denominators 1

1 5

1 2

2 15

1 4

1 10

10 3

11 4

16 Estimating and problem solving

1 12

33 5

1 4 ℓ milk

29 10

15 desktops

9 2

35 6

Rainbow cake, check the sketches

Answers • Bright Sparks Teacher’s Book 5

17 Adding mixed numbers 1

1 52

6 10

8 10

4 Triangles

1 4 8 2

1 a isosceles b 40º 2 a scalene

5 19 6

3 a equilateral b 60º

5 Flat shapes (2D)

18 Subtracting mixed numbers

regular hexagon 6

circle

7 parallelogram

square

tins of paint

rectangle

9 rhombus

rhombus

10 regular hexagon

6 1 6

1 14

3 7 3 4

3 65

3 8 3 4

1 4

10 72 wedges

more (15 12 )

19 Strategies for problem solving 3

5 4 cartons

7 5 10

3–

3 10

= 2 10

20 Practice with fractions 3 12

6 4 12

7 1 8

4 69

4 8 9 7

9 5 3

regular octagon

Teachers to check students’ mirror image drawings.

regular pentagon

6 Describing movement

cakes

b 35º

7 Circles 1 and 2

circumference centre point

63 8

diameter

Unit 8: Geometry 1 Lines

radius

FG HK

AE FG or AE HK or AE ML or HK ML

B, C, D, J

BC, CD, DJ, CJ

2 Angles

8 Lines of symmetry Teachers to check students’ lines of symmetry: 1

2 lines

5 lines

obtuse

5 right

1 line

acute

6 acute

2 lines

obtuse

7 obtuse

3 lines

straight

8 right

4 lines

3 Measurement of angle

1 line

1 a = 40º

b = 20º

2 lines (shape is a rhombus)

2 x = 30º

q = 110º

1 line

3 t = 45º

z = 15º

10 Check students’ drawings of a square with the 4 lines of symmetry. Bright Sparks Teacher’s Book 5 • Answers

129

9 Solid (3D) shapes

Check students’ drawings for specified number of squares.

6 faces, 12 edges, 8 vertices (cuboid)

3 faces, 2 edges, 0 vertices (cylinder)

15 Calculating area

1 face, 0 edges, 0 vertices (sphere)

1 70 m2

4 faces, 6 edges, 4 vertices ( triangular pyramid)

2 3000 m2

Teachers to check students’ drawings. Name of shape: cone

4 a 64 squares

1 flat face 1 curved face 1 edge 0 vertices

3 360 cm2 b Check students’ drawings. c 64 cm2 5 a 30 m2 6

$750

12 cm2

Challenge:

10 Nets of solid shapes

3 cm2

triangular prism

Check students’ drawings.

16 More area problems 1 9 m2

11 Enrichment: Coordinates on a grid

2 2 km2

(2,3)

3 171 cm2

(8,3)

4 1296 m2

Check students’ work.

5 a 180 tiles

Check students’ work.

b Check students’ drawings.

Check students’ work.

c 180

Check students’ work.

12 Perimeter: review

Challenge:

48 cm

122 cm

17 cm

17 Right-angled triangles

24 m

1 a 120

48 m

b 63

56 cm

2 a Check students’ drawings.

13 Perimeter problem solving

b 10 cm2

96 m

3 a Check students’ drawings.

6 cm

b 5 cm2

38 m

50 cm2

48 cm

less (48 cm2)

72 m

18 Volume

14 Review of area

12 m3

Check students’ drawings for specified number of squares.

Teachers to check students’ drawings.

Volume = 125 cm3

Check students’ drawings for specified number of squares.

528 m3

130

Answers • Bright Sparks Teacher’s Book 5

324 000 cm3

4 Dividing decimal numbers by a whole number

Challenge:

4.5

10 000 cm3

14.2

19 Enrichment: Paths and borders, compound shapes

$40.00

0.24

Square = 25 m2

25.3

Triangle = 10 m2

5 Adding zeros to the dividend

Total = 35 m

28.12

Small square = 16 cm

0.95

Large rectangle = 48 cm2

19.06

Total = 80 cm2

$60.30

Outside area = 36 ft2

12.42

Inside area = 16 ft2

Area of border = 36 ft2 – 16 ft2 = 20 ft2

6 Problem solving: dividing decimal numbers

2 2

Unit 9: More decimals 1 Multiplying a decimal number by a whole number 1

6 1659.1

471.2

7 $24.90

1123.2

8 $715.50

333.2

9 $80.00

99.2

2 Multiplying decimal numbers by decimal numbers 1

258.26

6 0.072

$37.14

7 0.0012

31.372

8 0.048

0.025

9 0.088

0.056

3 Problem solving 1

$66.15

$74.25

1.5 mℓ

182.88 cm

84.8 ounces

400 g

1.6 ft

15 4 km

7 Multiplying and dividing decimals by 10, 100, 1000 1

8850.1

6 0.46

739

7 0.8636

7495

8 0.9884

43 890

9 0.09797

886 457

10 1.095864

8 Metric conversions 1

25 000

6 45

7000

23 000

8 2.6

9 9

6.5

10 0.028

382 000

9 Metric conversions with decimal numbers 1

0.36

6 278

25.4

7 51

0.2756

8 375

875

9 0.00394

3442

10 7499

Bright Sparks Teacher’s Book 5 • Answers

131

Unit 10: Measurement

8 Mass

1 Length

3000 g

2.25 or 2 4

8500

6 2 kg

1.5 kg

Teachers please check measurement of lines.

2 Longer lengths 1

4 km

Mama

5 m

3 Working with units of length

9 Converting between units of mass 1

1.716 kg

650 g or 0.65 kg 7

220

8 78

790

9 8000

0.336

10 3

53 260

6.2

31 250

7700

10 Capacity

0.875

2500 mℓ

3 2 or 3.5

4250

1 2

0.2

4 Working with units of length 1

100

250

2.75 or 2 4

6 4 21 000

ℓ or 0.5 ℓ

11 Capacity 3

5 Working with units of length 1

750

2750

1300

3.25 or 3 4

350 cm or 3.5 m or 3 2 m

325 cm or 3.25 m or 3 4 m

25 cm or

100 cm or 1 m

12 Converting between units of capacity

200 cm or 2 m

375

0.472

2600

0.05463

1 4

6 Practice with longer units of length 1

3500

1.75 or 1 4

5000

0.25 or

2.5 or

1 4 1 22

7 Practice with longer units of length

132

Unit 11: More fractions 1 Multiplying fractions 1

Check students’ answers. 6

25 48

1 6

4 15

50 003 m or 50.003 km

1750 m or 1.75 km

24 500 m or 24.5 km

1 8

21 32

6400 m or 6.4 km

3 20

1 8

6500 m or 6.5 km

1 30

8 15

Answers • Bright Sparks Teacher’s Book 5

2 Multiplying fractions and whole numbers / mixed numbers 1

4 2 4

2 25

1 5 3 2

3 Cancelling 1

1 21

2 5

1 2

3 20

4 Sketching strategy for problem solving 1

$40

4 $72

$36

48 eggs

400 ml

Challenge: $40

5 Dividing fractions 12

1 4

1 2

Unit 12: Percent, ratio and proportion 1 Writing percents

Challenge:

6 5

7 46

8 17

Check students’ shading. 9 62

10 3

2 Percents and decimals 1

25%

6 80%

96%

7 8%

81%

8 50%

75%

9 44%

30%

3 Percents and decimals

6 Multiplying and dividing fractions practice 1

5 12

6 15

1 12

7 28

2 5

8 28

0.36

6 0.6

0.89

7 0.06

0.23

8 0.02

0.95

9 0.09

0.5

10 0.2

4 Percents, decimals, fractions 3 5

50%

0.25

7 0.3

3 4

1 10

9 1 8

20%

4 5

10 1000

0.4

10 0.2

7 Multiplying and dividing fractions practice

5 Percents, decimals, fractions 1

0.7 70%

6 3

3 5 60%

2 3

19 20 0.95

0.8 80%

13 20 65%

3 10

1 15

2 3

8 25

9 36

2 9

10 1

Bright Sparks Teacher’s Book 5 • Answers

133

6 Finding a percent of an amount

13 Ratio

3 : 5, 5 , 3 to 5

$100

2 : 9, 9 , 2 to 9

$290

6 : 5, 5 , 6 to 5

$73

4 : 3, 3 , 4 to 3

$170

7 : 4, 4 , 7 to 4

2 6 4 7

7 Changing fractions to percents

14 Simplifying ratios

1 : 5

17 : 1

10%

1 : 3

4:1

20%

4 : 1

4:5

76%

9 : 20

9:1

24%

16 : 23

10 9 : 16

8 Practice

15 Proportion

1 a 213 2 4

40%

1 3 a 3

1 a 94% 2

30%

$87.04

5 a 40%

47 : 3

3 a 4 : 5 b The Brownies washed 16 cars.

60%

c The Cubs washed 20 cars.

9 Discount

16 Ratio problem solving

Amount saved Sale price

1 a 3 : 5

$108 $252

b $150

$33 $132

2 a 5 : 7

$47 $423

b First boy = $100, Second boy = $140

$150 $450

3 a 15 girls

$180 $60

17 Practical use of proportion

10 Discount problem solving

2:1

Lua’s

12 : 2

1 egg

$49.75

1 2

Challenge:

3 cups

Find 10%, then half of 10%. Add the two answers together.

18 Working with scale 1

11 Wages and salaries problem solving

$52 000

$53 460

12 Simple interest problem solving

134

$520

3% + $5000 = $5150 (4% added to $4500 = $4680)

Answers • Bright Sparks Teacher’s Book 5

cup

$250

18 boys

19 Ratio / percent / fraction problem solving

3 Enrichment: 24-hour clock 1