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RIC-6087 6.3/623


Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

A number of pages in this book are worksheets. The publisher licenses the individual teacher who purchased this book to photocopy these pages to hand out to students in their own classes.

Published by R.I.C. Publications® 2012 Copyright© R.I.C. Publications® 2012 Revised edition 2013 ISBN 978-1-921750-71-7 RIC– 6087

Titles in this series: Australian Curriculum Mathematics resource book: Number and Algebra (Foundation) Australian Curriculum Mathematics resource book: Number and Algebra (Year 1) Australian Curriculum Mathematics resource book: Number and Algebra (Year 2) Australian Curriculum Mathematics resource book: Number and Algebra (Year 3) Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) Australian Curriculum Mathematics resource book: Number and Algebra (Year 5) Australian Curriculum Mathematics resource book: Number and Algebra (Year 6)

Except as allowed under the Copyright Act 1968, any other use (including digital and online uses and the creation of overhead transparencies or posters) or any use by or for other people (including by or for other teachers, students or institutions) is prohibited. If you want a licence to do anything outside the scope of the BLM licence above, please contact the Publisher.

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This information is provided to clarify the limits of this licence and its interaction with the Copyright Act. For your added protection in the case of copyright inspection, please complete the form below. Retain this form, the complete original document and the invoice or receipt as proof of purchase. Name of Purchaser:

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All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2013. For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

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Internet websites In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class teacher checks all URLs before allowing students to access them.

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: NUMBER AND ALGEBRA (YEAR 3) Foreword Australian Curriculum Mathematics resource book: Number and Algebra (Year 3) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the number and algebra content strands of the national maths curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and assessment activities, along with links to other curriculum areas.

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

Number and Place Value .................................................... 6–77 • N&PV – 1 Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051) – Teacher information ......................... 6 – Hands-on activities .......................... 7 – Links to other curriculum areas ........ 8

– Resource sheets ...............9–12 – Assessment ...................13–14 – Checklist ...............................19

• N&PV – 2

Recognise, model, respresent and order numbers to at least 10 000 (ACMNA052)

– Teacher information ....................... 68 – Hands-on activities ........................ 69 – Links to other curriculum areas ...... 69

– Resource sheets .............70–72 – Assessment ...................73–74 – Checklist ...............................75

Answers ..............................................................................76–77 Fractions and Decimals .....................................................78–93 • F&D – 1

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– Teacher information ....................... 28 – Hands-on activities ........................ 29 – Links to other curriculum areas ...... 30

– Resource sheets .............31–33 – Assessment ...................34–36 – Checklist ...............................37

• N&PV – 4

Recognise and explain the connection between addition and subtraction (ACMNA054)

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Model and represent unit fractions including ½, ¼,1⁄3, 1⁄5 and their multiples to a complete whole (ACMNA058) – Teacher information ....................... 78 – Hands-on activities ........................ 79 – Links to other curriculum areas ...... 80

– Resource sheets .............81–89 – Assessment ...................90–91 – Checklist ...............................92

Answers ....................................................................................93 Money and Financial Mathematics ..................................94–109 • M&FM – 1

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– Resource sheets .............19–23 – Assessment ...................24–26 – Checklist ...............................27

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059) – Teacher information ....................... 94 – Hands-on activities ........................ 95 – Links to other curriculum areas ...... 96

– Resource sheets ........... 97–105 – Assessment ............... 106–107 – Checklist .............................108

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– Teacher information ....................... 38 – Hands-on activities ........................ 39 – Links to other curriculum areas ...... 39

• N&PV – 5

Represent and solve problems involving multiplication using efficient mental and written strategies and approptiate digital technologies (ACMNA057)

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– Teacher information ....................... 16 – Hands-on activities ........................ 17 – Links to other curriculum areas ...... 18

• N&PV – 3

• N&PV – 7

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Format of this book................................................... iv – v

– Resource sheets .............40–43 – Assessment ..........................44 – Checklist ...............................45

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055) – Teacher information ....................... 46 – Hands-on activities ........................ 47 – Links to other curriculum areas ...... 47

– Resource sheets .............48–52 – Assessment ...................53–54 – Checklist ...............................55

Patterns and Algebra ....................................................110–127 • P&A – 1 Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060) – Teacher information ..................... 110 – Hands-on activities ...................... 111 – Links to other curriculum areas .... 112

– Resource sheets ......... 113–123 – Assessment ............... 124–125 – Checklist .............................126

Answers ..................................................................................127

• N&PV – 6 Recall multiplication facts of two, three, five an ten and related division facts (ACMNA056) – Teacher information ....................... 56 – Hands-on activities ........................ 57 – Links to other curriculum areas ...... 58

Answers ..................................................................................109

– Resource sheets .............59–64 – Assessment ...................65–66 – Checklist ...............................67

New wave Number and Algebra (Year 3) student workbook answers ........................................................128–136

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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FORMAT OF THIS BOOK This teacher resource book includes supporting materials for teaching and learning in all sections of the Number and Algebra content strand of Australian Curriculum Mathematics. It includes activities relating to all sub-strands: Number and Place Value, Fractions and Decimals, Money and Financial Mathematics, and Patterns and Algebra. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the Proficiency Strands have also been included. Each section supports a specific content description and follows a consistent format, containing the following information over several pages: • teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for • hands-on activities • links to other curriculum areas

• resource sheets • assessment sheets.

• a checklist

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Answers relating to the assessment pages are included on the final page of the section for each sub-strand (Number and Place Value, Fractions and Decimals, Money and Financial Mathematics, and Patterns and Algebra).

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(NOTE: The Foundation level includes only Number and Place Value, and Patterns and Algebra.) The length of each content description section varies.

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Teacher information includes background information relating to the content description, as well as related terms and desirable student vocabulary and other useful details which may assist the teacher.

Related terms includes vocabulary associated with the content description. Many of these relate to the glossary in the back of the official Australian Curriculum Mathematics document; additional related terms may also have been added.

What this means provides a layperson’s explanation of the content description.

the teacher would use—and expect the students to learn, understand and use—during mathematics lessons.

description.

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The proficiency strand(s) (Understanding, Fluency, Problem Solving or Reasoning) relevant to each content description are listed.

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© R. I . C.Publ i cat i ons Teaching points provides a listn of the main teaching •f owhich rr evi ew pur poseso l y • Student vocabulary includes words points relating to the content

What to look watchforforsuggests suggestsany any difficulties and misconceptions the students might encounter or develop.

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Hands-on activities includes descriptions or instructions for games or activities relating to the content descriptions or elaborations. Some of the hands-on activities are supported by resource sheets. Where applicable, these will be stated for easy reference.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


FORMAT OF THIS BOOK Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English (literacy), Information and Communication Technology (ICT), Health and Physical Education (ethical behaviour, personal and social competence) and Intercultural Understanding (History and Geography, the Arts, and Languages). This section may list many links or only a few. It may also provide links to relevant interactive websites appropriate for the age group.

r o e t s Bo r e p ok u S Resource sheets are provided to support teaching and learning activities for each content description. The resource sheets could be cards for games, charts, additional worksheets for class use, or other materials which the teacher might find useful to use or display in the classroom. For each resource sheet, the content description to which it relates is given.

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Cross-curricular links reinforce the knowledge that mathematics can be found within, and relate to, many other aspects of student learning and everyday life.

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© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Assessment pages are included. These support activities included in the corresponding workbook. Many of the questions on the assessment pages are in a format similar to that of the NAPLAN tests to familiarise students with the instructions and design of these tests.

o c . che e r o t r s super Each section has a checklist which teachers may find useful as a place to keep a record of the results of assessment activities, or their observations of hands-on activities.

Answers for assessment pages are provided on the final page of each sub-strand section.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 1

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)

TEACHER INFORMATION

RELATED TERMS Skip-counting

What this means

• Counting forwards or backwards in multiples of a specific number; e.g. 2, 4, 6, 8, 10 ... .

• Students learn to classify types of numbers—in this case, odd numbers—by certain criteria. Students will need to reason about the various patterns they find.

Numeral

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• A figure or symbol used to represent a number.

• A whole number that leaves a remainder of 1 when divided by 2; i.e. 1, 3, 5, 7 ... .

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Odd number

• On grid paper, students practise drawing rectangles of varying lengths that are two squares wide. • Later, direct them to draw rectangles made of a specific number of squares. They will discover they can only draw a rectangle when the number is even. There will always be a piece ‘sticking out’ when the number is odd.

Even number

What to look for

• A whole number that is exactly divisible by 2; i.e. 2, 4, 6, 8 ... .

• Watch for students who can only skip count starting from zero. Students should be able to count in twos from any starting point. See also New wave Number and Algebra (Year 3) student workbook (pages 2–12)

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Student vocabulary count number skip count forwards

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Sub-strand: Number and Place Value—N&PV – 1

HANDS-ON ACTIVITIES Pairs in the classroom

Blank grids

Students make pairs of objects in the classroom. If the number of objects paired has ‘no remainder’, that number is ‘even’. If there is an ‘odd-one-out’, that number is odd. Objects to ‘pair’ could include: a given number of counters, items in a pencil case, students in the class, or books on display. Students make lists of odd and even numbers they found and discuss the numbers included in each list.

Use blank grids (refer to pages 11 and 12) so students identify odd and even numbers in a different representation to consolidate their knowledge. The grids can be completed with 1–100 or 1–120 or with random starting numbers beginning with 99, 54, 203 and so on. Students can use the same method of shading the multiples of 2 to identify the odd and even numbers.

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Provide groups of students with grid paper to investigate odd and even numbers, following the first teaching point on page 6. The numbers 1 to 20 can be written on blank playing cards. In turn, students turn a card over and colour grid squares in two square-wide lots to match that number. If a complete rectangle is drawn, the number drawn will be even; if there is a square sticking out on its own, the number will be odd. Students should record results and begin to predict if a number will be odd or even before colouring the grid paper.

The teacher or a student thinks of a number, writes it secretly on a card which is then placed face down and gives a clue; e.g. ‘I am an odd number between 10 and 60’. Other students raise their hand and are randomly chosen to ask questions to try to guess the number, such as ‘Is the number less than 30?’, ‘Is the number between 15 and 25?’ Students keep track of what clues and information have been answered.

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What number am I?

Flip array board

As students count by 2s, each number on the array is flipped over so all numbers that are multiples of 2 are one colour and the other numbers are another colour. Ask students to identify what type of number the multiples of 2 end with and what the other numbers end with. This will help students make the connection that numbers that are multiples of 2 (or numbers that can be divided exactly by 2) are even and end with 0, 2, 4, 6 or 8. The other numbers are odd (have a remainder if divided by 2) and end with 1, 3, 5, 7 or 9.

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Does it make a rectangle?

Odd and even lucky dip

Students place objects such as buttons, counters, unit cubes, paperclips, interlocking cubes and attribute shapes in a cloth bag or box. They take out one or more handfuls of the items and sort them into pairs to identify if the number of items is odd or even, then record their results.

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1–120 grid or 121–240 grid Use a 1–120 grid or 121–240 grid (refer to pages 9 and 10) in a similar fashion to the flip array board. Students shade the numbers that are multiples of 2. In pairs or a small group, students can take turns to throw a dice on the chart, observe the number rolled and identify it as an odd or even number.

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Sub-strand: Number and Place Value—N&PV – 1

LINKS TO OTHER CURRICULUM AREAS English • Use the book Even Steven and Odd Todd by Kathryn Cristaldi to reinforce concepts about odd and even numbers. As the title suggests, Steven is a boy who likes only even numbers while Todd likes only odd numbers. When Todd comes to visit Steven, the two boys clash in a battle of wits to prove even or odd is better. There is a comprehensive range of suggested follow-up activities at the end of the book.

Communication and Information Technology • The following web pages have interactive games dealing with odd and even numbers:

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– <http://www.softschools.com/math/games/odd_even_number_game.jsp> – <http://www.oswego.org/ocsd-web/games/Ghostblasterseven/ghosteven.html> – <http://www.ezschool.com/Games/EvenOdd.html>

• Create a table using a word processing or desktop publishing program to make up number grids to use in activities such as those suggested on page 7.

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Health and Physical Education

• Discuss why it is easier to run on an even number of legs (two) than it is to run on an uneven number of legs (like a three-legged race). Hold a three-legged race and have students work out the best rhythm to use with a partner.

Geography

• Investigate how students’ houses in their streets are numbered. They will discover the even numbers are on one side and the odd numbers are on the other. Ask students why they think the numbers are set out this way.

Science

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• Hunt for ladybirds in the school grounds or at home and estimate or count the numbers of spots on their backs, stating whether the number is odd or even. • Investigate why animals’ limbs generally occur in even numbers; e.g. humans and apes have two pairs of arms and legs, animals like elephants and camels have four legs, arachnids (spiders) have eight legs; insects (like ladybirds) have six legs. A snail could be considered as having one ‘foot’ which it uses to slide, whereas the other animals need even numbers to balance while walking.

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Sub-strand: Number and Place Value—N&PV – 1

RESOURCE SHEET

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CONTENT DESCRIPTION: Investigate the conditions required for a number to be odd or even and identify odd and even numbers

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Sub-strand: Number and Place Value—N&PV – 1

RESOURCE SHEET 121 – 240 grid

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CONTENT DESCRIPTION: Investigate the conditions required for a number to be odd or even and identify odd and even numbers

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RESOURCE SHEET

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CONTENT DESCRIPTION: Investigate the conditions required for a number to be odd or even and identify odd and even numbers

Blank 100-square grid

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Sub-strand: Number and Place Value—N&PV – 1

RESOURCE SHEET

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Investigate the conditions required for a number to be odd or even and identify odd and even numbers

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Assessment 1

Sub-strand: Number and Place Value—N&PV – 1

NAME:

DATE:

1. Shade one bubble to show whether each collection is an odd or even amount.

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2. In (h), draw your own collection and shade whether it is an odd or even amount. (a) (b)

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Assessment 2

Sub-strand: Number and Place Value—N&PV – 1

NAME:

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1. (a) Fill in the missing numbers in the grid. 1

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(b) Count by 2s, shading each of those boxes yellow.

(c) Are the numbers in the boxes you coloured yellow odd or even? Shade one bubble. odd

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(a) 2, 4, 6, 7, 8 (b) 0, 2, 4, 6, 8

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2. Which set of numbers shows a pattern with all even numbers? Shade one bubble.

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(a) 0, 2, 4, 6, 8 (b) 0, 1, 3, 5, 7 (c) 1, 3, 5, 7, 9 (d) 2, 3, 5, 7, 9

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CONTENT DESCRIPTION: Investigate the conditions required for a number to be odd or even and identify odd and even numbers

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Checklist

Sub-strand: Number and Place Value—N&PV – 1

Understand that numbers ending in 1, 3, 5, 7 and 9 are odd

Understand that numbers ending in 0, 2, 4, 6 and 8 are even

Group collections of objects in twos to identify odd and even numbers

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STUDENT NAME

Skip count by twos to identify odd and even numbers

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)

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Sub-strand: Number and Place Value—N&PV – 2

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

RELATED TERMS

TEACHER INFORMATION

Numerical representations

What this means

• Numbers can be represented by using digits; (e.g. 5732) and words (e.g. five thousand, seven hundred and thirtytwo).

• Students develop a good understanding of numbers to 10 000. This means understanding place value to read, write, say and represent larger numbers.

Number line

Teaching points

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Counting on the century e.g. 3100, 3200, 3400, 3500 ... Counting off the decade e.g. 1745, 1755, 1765, 1775 ...

• Watch for students who say one thing but write another. For example, a student may say ‘two thousand, seven hundred and thirty-two’ but write it as 27 032. (A zero has been substituted where the word ‘and’ was used.)

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• Indicates the position of a numeral; e.g. the place value of 7 in the number 4765 is hundreds. Estimating

What to look for

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• Finding an answer that is close to the exact answer by rounding or using one’s own judgment to make the best guess.

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Student vocabulary represent numeral digit number line

See also New wave Number and Algebra (Year3 ) student workbook (pages 13–20)

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Place value

• Students need to link materials, symbols and words to represent numbers. • A variety of methods can be used for students to model numbers; e.g. joining two three-prong abacuses or using a number line. • Arrow or place value cards will assist students with understanding numbers as they are partitioned according to place value. • When reading and saying numbers, the word ‘and’ is used between the hundreds and the tens values; e.g. six thousand, nine hundred and forty-five. It is not used between other places.

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• A number line gives a pictorial representation of real numbers. Points are marked at equal distances along the line and various scales can be used to mark numbers on the points.

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order greater than less than equal to place value estimate

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Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 2

HANDS-ON ACTIVITIES Number line activities Provide students with number lines (Refer to page 20; two blank number lines have been included for students to make their own.). Students can estimate or show exactly (depending on the number and the number line’s scale) where a given two-, three- or four-digit number would be placed, or estimate or state exactly the number an arrow is pointing to. Examples:

Estimate the number each arrow is pointing to. 0

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Base 10 block activities

• Provide students with Base 10 blocks so they can represent numbers of up to four digits. Students can use two, three or four dice to generate two-, three- or four-digit numbers and represent the numbers with the Base 10 tools. A selection of numerals can be written on blank playing cards for the students to randomly turn over and make the number shown before placing it in front of their finished model, ready for checking. Place value mats can also be used to display their models (refer to pages 21 and 22). • Instead of Base 10 blocks, students use craft sticks or straws in ones, bundles of 10 (held with an elastic band) and bundles of 10 tens (100) to model and display numbers of two or three digits. Two three-prong abacuses can be joined to used to assist in modelling numbers in the thousands.

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

Card games

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Mark four sets of blank playing cards with the numbers 0 to 9. In pairs or a small group, students have turns flipping over three cards to make three-digit numbers (or four to make four-digit numbers) which they write on a sheet of paper. After each student has written a number, these can be read and spoken out loud, written as words and ordered from smallest to largest (or vice versa). Students could also identify the number that comes before and after each number they made or count by tens or hundreds forwards or backwards. The place value charts on pages 21 and 22 can be used to assist in this activity.

Number expanders

This video explains how number expanders can be used to teach place value:

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<http://www.youtube.com/watch?v=panymPI67S8>

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(Templates are provided on page 23.)

Arrow cards

Teacher-made or commercial sets of arrow cards will also assist in teaching place value.

Greater than >, less than < and equal to = activities

This video presents an idea for introducing the greater than, less than and equal to signs to students. <http://www.ehow.com/video_4429478_greater-than_-less-game.html>

Calculator numbers Write three- and four-digit numbers on blank playing cards. Students play this game in pairs. Student 1 places the cards in a pile facedown. Student 2 has a calculator. Student 1 picks up a card and, using words, tells Student 2 the number the digits represent. Student 2 makes this number on the calculator. Each student checks to see if the other is correct. Swap places after each turn.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 2

LINKS TO OTHER CURRICULUM AREAS English • Use the book Alfie the alligator: A teaching rhyme about comparing numbers by Sandy Turley, which introduces the greater than, less than and equal to signs when comparing numbers. • More or less, by Stuart J Murphy, is about Eddie, a boy who is blindfolded at an amusement booth at a fair and has to guess the age of a contestant in three guesses or fewer. If he cannot do this, the ledge on which he is sitting tilts so he falls into a pool. Use the concept of this book for students to ask questions to guess numbers up to 10 000.

Communication and Information Technology

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• The following web pages are interactive games dealing with this sub-strand: – <http://www.ezschool.com/Games/Compare.html> (using the greater than, less than and equal to signs to compare numbers) – <http://www.oup.com.au/__data/assets/file/0019/154045/Numberline.swf> (identifying where numbers are located on a number line) – <http://pbskids.org/cyberchase/math–games/number–sense/> (rearranging the order of digits in numbers to make larger numbers)

Geography

• Use the scale on maps to calculate the distances between the city/town in which students live to other cities/towns in their own state or territory and other states and territories. Order the distances from closest to furthest from their own. • Postcodes are allocated to sections of cities and in regional areas within each state or territory. Note how the numerals are not read as whole numbers, so are really a ‘label’; e.g. postcode 6021 is read as ‘six, zero, two, one’ and not ‘six thousand and twenty-one’.

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History

• Students investigate how various cultures in the past used knotted strings to represent numbers in the ones, tens, hundreds and thousands place values. Note: Strings of prayer beads are used today by religions such as Islam, Buddhism and Christianity. A useful website is: – <http://web.me.com/paulscott.info/history/katherine/page2.htm>

Civics and Citizenship

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• Investigate how books are organised using the Dewey number system in the school and local civic library.

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10

1

2 tens

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

3 ones

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Sub-strand: Number and Place Value—N&PV – 2

RESOURCE SHEET Number line (0 to 10 000) 100

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

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Sub-strand: Number and Place Value—N&PV – 2

RESOURCE SHEET

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

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Number lines


Sub-strand: Number and Place Value—N&PV – 2

RESOURCE SHEET Place value chart

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

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

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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21


Sub-strand: Number and Place Value—N&PV – 2

RESOURCE SHEET Place value chart

Thousands

Hundreds

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Ones

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

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


Sub-strand: Number and Place Value—N&PV – 2

RESOURCE SHEET Number expander template

hundreds

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tens

hundreds

hundreds

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

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23


Assessment 1

Sub-strand: Number and Place Value—N&PV – 2

NAME:

DATE:

1. Which number do you think the arrow is pointing to on each number line? Shade one bubble. 0

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6745

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4000

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6000

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0

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4490

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8000

2. Estimate the number you think each arrow is pointing to. 0

9000

7000

8000

9000

10 000

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7000

r o e t s Bo r e p ok u S 8710 3005 7725

2000

(b) 1800

6000

9000

10 000

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1000

2000

3000

4000

5000

6000

7000

8000

9000

10 000

10 000

. t o 3. Draw an arrowe to show where each number should be placed. c . che e r o t r s super (c)

0

10 000

(a) 3700 0

10 000

(b) 6850

24

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

w ww

0

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(b)


Assessment 2

Sub-strand: Number and Place Value—N&PV – 2

NAME:

DATE:

1. What numeral does each of these groups of place value blocks show? Shade one bubble. 2365

(a)

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3245 3365

4482

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2266

(b)

4428 3328 4448

(b)

6000 + 700 + 90 + 1

(c) 600 + 70 + 90 + 10

(d)

6000 + 70 + 90 + 1

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(a) 60 + 70 + 90 + 10

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

© R. I . C.Publ i cat i ons 2. Which ofo these equals 6791? one bubble. •f rr evi e w Shade pur po sesonl y•

3. Shade the bubble that is equal to the amount in the box.

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(a)

50

(b)

600

(c)

4000

50 ones o c . ch e 6 tens 6 hundreds 60 hundreds r er o st s r u e p 40 tens 40 hundreds 400 ones 50 tens

5 hundreds

4. Expand these numbers. (a) 834 = (b) 706 = (c) 6668 = (d) 5930 = Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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25


Assessment 3

Sub-strand: Number and Place Value—N&PV – 2

NAME:

DATE:

1. Write these numbers as words. (a) 6993

(b) 9405

Teac he r 5444

544

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r o e t s B r e orepresent. 2. Shade the bubble thatp shows the number the words ok u (a) five thousand, Sfour hundred and forty-four 504

5044

8330

8030

(b) eight thousand and thirty 830

8003

© R. I . C.P ubl i ca t i ons (b) 8760 •f orr evi ew pur posesonl y•

3. Which numbers comes before and after these? (a)

4973

,

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,

,

,

,

,

,

,

,

5. Count backwards by hundreds. 8440, 8340,

,

,

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,

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,

3152, 3162,

,

o c . c e h 3672 (b) 4734 4821 (c) r 10 000 1000 (a) 5893 er o t s super 7. Order these numbers from largest to smallest.

6. Use the ‘greater than’ (>) or ‘less than’ (<) symbol with these numbers.

7192 8523 8. Make the largest and smallest numbers with each set of digits. 26

Largest (a)

6, 9, 2, 3

(b)

1, 0, 8, 6

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

7839 799

8990

Smallest

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

CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 10 000

4. Count forwards by tens.


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

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

ew i ev Pr

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

Orders sets of numbers up to 10 000, including use of > and < symbols Uses expanded notation to represent numbers to 10 000 Counts forwards and backwards by tens and hundreds, on and off the decade

Represents the word form of numbers up to 10 000 as digits

Represents numbers up to 10 000 in word form

Locates numbers up to five digits on different scaled number lines Models numbers up to 10 000 using place value materials and diagrams

STUDENT NAME

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Teac he r

Sub-strand: Number and Place Value—N&PV – 2

Checklist

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

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27


Sub-strand: Number and Place Value—N&PV – 3

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

TEACHER INFORMATION

RELATED TERMS Place value

What this means

• The position of a digit in a number determines its value; e.g. the place value of 7 in 4765 is hundreds; the value of 7 in 4765 is 700 (digit X place value). Partitioning

• Students can split numbers according to a numeral’s place value using both standard partitioning and non-standard partitioning.

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

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Regrouping

• For standard partitioning (which is used in algorithms), numbers are reorganised in multiples of ten; e.g. from tens to ones, from hundreds to tens and vice versa. (Regrouping is also known as ‘trading’ or ‘renaming’.) For example, in the subtraction 426 – 153, the 426 can be regrouped as 300 + 120 + 6; in the addition 245 + 393, 4 tens + 9 tens = 13 tens can be regrouped as 1 hundred + 3 tens

What to look for

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• Dividing a number into parts. In standard partitioning, a number is split into parts according to the value of the numerals; e.g. 347 = 300 + 40 + 7 • In non-standard partitioning, a number is split not according to place value but to simplify the equation it is in—i.e. taking some from one number to give to another; e.g. 9 + 8 is 10 + 7, so 59 + 38 is 60 + 37.

• The hundreds-tens-ones (HTO) pattern in reading numbers needs to be well understood. • A number expander is an ideal tool for emphasising these links.

• Some students will know that in the number, 1367 (for example), the digit in the tens place is six. However, they may not recognise that there are 136 tens in 1367. Make sure questions vary; e.g. ‘What digit is in the tens place?’ and ‘How many tens are in that number?’. • Some students will also think when a number is partitioned (nonstandard) it is not the same as when the number is presented as a whole.

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Rearrange

See also New wave Number and Algebra (Year3 ) student workbook (pages 21–25)

• To rearrange the order of a group of numbers. The numbers are rearranged to assist in calculations; e.g. 7 + 8 + 3 = 7 + 3 + 8 = 10 + 8 = 18

o c . che e r o t r s super Proficiency strand(s):

Student vocabulary partitioning

Understanding Fluency Problem solving Reasoning

regrouping/trading/renaming rearrange calculate order place value

28

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 3

HANDS-ON ACTIVITIES As this content description (N&PV – 3) and the previous content description (N&PV – 2) both require students to have an understanding of place value, many of the hands-on activities and related resource sheets for the last descriptor will apply to this section. Refer to the following activities: Base 10 activities, card games, number expanders and arrow cards. The number expanders are particularly useful in helping students understand both the place value and value of digits in numbers as explained in the ‘What to look for’ section on page 28.

Number of the day

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Students help to make the chart by creating several number expanders with the same number written on each. The expanders can then be attached to a display board or chart with the various place values shown. These representations can be made with place value blocks, bundles of craft sticks and so on by students who still prefer using concrete materials to ‘see’ the numbers.

hundreds

Representing numbers

3

tens

5

ones

In pairs, students use the charts on page 31 to gain understanding in representing numbers according to their place value. In the top chart, a three- or four-digit number is written in the first column by a student. It can be generated by throwing a 10-sided dice three or four times to make a three- or four-digit number. The other student uses symbols or tally marks to represent each digit in the number. Together, the students check to see if the symbols match the number. In the bottom chart, the opposite applies with the numbers generated represented in the columns with symbols by one student starting in the thousands column, the other student then uses these symbols to work out and record the number in the column on the right.

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

Random numbers

four-digit number thrown 4826

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Selected digit

Rearranging numbers

Place value

Expanded form

m . u

w ww

In pairs, students use one of the charts on page 32 to represent numbers according to their place value, their expanded form and their actual value. Numbers can be generated by throwing a ten-sided dice three or four times to make a threeor four-digit number. This number is written on the chart. One of the digits is then selected and circled or underlined. Its place value, expanded form and value can then be completed; for example: Value

o c . che e r o t r s super

4826

hundreds

8 x 100

800

Demonstrate how rearranging the order of numbers can make it easier to calculate an answer mentally or in a written algorithm. Give the students a word problem; e.g. ‘Our family went fishing in the river. Dad caught 15 fish, Mum caught 13 fish, my sister caught 17 fish and I caught 14 fish. How many did we catch?’ In order, the sum is 15 + 13 + 17 + 14. If the order is changed to 13 + 17 + 15 + 14, it is easier to work out (13 + 17 makes 30, add 15 to make 45, then count on 14 to make 59.) Students can make similar word problems and describe how they could change the order of the numbers to make calculation easier. Numbers to rearrange can be generated by rolling a dice three or four times or choosing labelled number cards. Students can record the numbers as they appear, then rearrange if necessary as an addition number sentence that is easier to solve. They can explain why they ordered them in this manner. Numbers can also be rearranged in the following manner: 15 + 9 + 12 + 13 =? –1

+1

14 + 10

+ 25 = 49

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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29


Sub-strand: Number and Place Value—N&PV – 3

LINKS TO OTHER CURRICULUM AREAS English • Using a procedural format, students write instructions on a chart or whiteboard on how to use the resource sheets on pages 31 and 32. • Read A place for zero: A math adventure by Angeline Sparagna LoPresti. As the title suggests, the book is about the importance of zero in our base 10 number system.

Communication and Information Technology

History

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

• Take photographs of concrete materials students have in their classroom that help them 1000 100 understand place value; e.g. place value blocks, interconnecting cubes. Students show the photos to their parents and grandparents or friends/neighbours of a similar age and ask if these materials were used when they were at primary school. If not, ask them to describe what concrete materials were used to help them understand place 1 4 value. Make sketches of diagrams hundreds thousands to share with the class. Discuss the similarities and differences in teaching practices between then and now. • The following activity was outlined on page 18 but also applies to this section. Students investigate how various cultures in the past used knotted strings to represent numbers in the ones, tens, hundreds and thousands place values. Note: Strings of prayer beads are used today by religions such as Islam, Buddhism and Christianity. A useful website is: <http://web.me.com/paulscott.info/history/ katherine/page2.htm>

10

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• The following websites include interactive games or videos dealing with this sub-strand: – <http://www.curriculumsupport.education.nsw.gov.au/countmein/children_arrow_card.html> (Students must identify the correct arrow cards to drag onto a given number. This activity revises place value and demonstrates the additive aspect of expanded notation to four digits.) – <http://www.youtube.com/watch?v=KVi3FFFGKKM> – <http://www.youtube.com/watch?v=F9-vU3QMeRg> (Demonstration of two partitioning methods to calculate addition.)

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Health and Physical Education

3 ones

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• Take note of scores achieved in each quarter (or half ) of a netball or football game (or similar) during a physical education lesson. Apply the rearranging method to mentally add these scores more easily.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 3

RESOURCE SHEET Representing numbers Use symbols to represent the number on the chart.

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Ones

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Thousands

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

Write the number represented by symbols on the chart.

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Number

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CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

Number

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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31


Sub strand: Number and Place Value—N&PV – 3

RESOURCE SHEET Random numbers

Place value

Expanded form

Value

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

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Place value

Expanded form

Value

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4-digit number Selected digit thrown

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

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3-digit number Selected digit thrown


Sub-strand: Number and Place Value—N&PV – 3

RESOURCE SHEET Mental calculation strategies for addition and subtraction

Rearranging

Numbers can be added mentally if put in a different order to make groups of tens. Example 1: 3 + 8 + 7 + 2

3 + 7 + 8 + 2 = 10 + 10 = 20

Example 2: 24 + 8 + 6

24 + 6 + 8 = 30 + 8 = 38

Bridging decades It can be easier to add numbers if numerals of similar place value add up to multiples of 5 or ten (or a hundred with larger numbers). Example 1: 6 + 8

r o e t s Bo r e p ok u S 6 + 4 + 4 = 10 + 4 = 14

Example 2: 29 + 17

29 + 11 + 6 = 40 + 6 = 46

Teac he r

Splitting numbers

40 + 20 + 3 + 5 = 60 + 3 + 5 = 68

Example 2: 56 – 34

50 – 30 + 6 – 4 = 20 + 2 = 22

Jumping

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Example 1: 43 + 25

With addition, start with one number, partition up another number, then add the tens and then the ones. Example 1: 34 + 25

34 + 20 + 5 = 54 + 5 = 59

Example 2: 166 + 33

166 + 30 + 3 = 196 + 3 = 199

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Counting on or back from the front With subtraction, partition one number, then subtract the tens and then the ones. Example 3: 34 – 25

34 – 20 – 5 = 14 – 5 = 9

Example 4: 166 – 33

166 –30 – 3 = 136 – 3 = 133

Example 1: 55 + 24

55, 65, 75 + 4 = 79

Example 2: 55 – 24

55, 45, 35 – 4 = 31

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This is similar to jumping, but the tens are added or subtracted by counting on or back to be followed by the ones.

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CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

Numbers can be split into tens and ones to be added or subtracted mentally.

Using number lines

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Mental strategies for addition and subtraction can be recorded on a number line. With practice, these steps can be visualised without drawing the number line. Example 1: 55 + 43 =

+10

55

65

26

-4 30

-10 34

-10 44

+10

75

Example 2: 64 – 38 = -4

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+10

+10

85

+3

95 98

-10

54

64

Compensation Compensation involves adjusting one number and compensating with another. Example 1: 18 + 27

20 (add 2) + 25 (take 2) = 45

Example 2: 54 + 39

53 (take 1) + 40 (add 1) = 93

Example 3: 54 – 39

55 – 40 = 15 (1 is added to both numbers)

Example 4: 62 – 34

60 – 32 = 28 (2 is subtracted from both numbers)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

33


Assessment 1

Sub-strand: Number and Place Value—N&PV – 3

NAME:

DATE:

1. State the place value of each digit underlined. Shade one bubble. (a) 587

ones

tens

hundreds

(b) 4766

thousands

tens

hundreds

(c) 9303

thousands

hundreds

tens

r o e t s Bo r e 6048 600 + 40 + 8 684 p ok u 3000 + 900 +S 70 + 2 3972 3792

2. These numbers have been written in expanded form. What number do they represent? Shade one bubble.

541

(c) 5000 + 40 + 1

397

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(b)

648

5441

5041

3. Shade the bubble under those boxes that represent the number 7402.

7

us ands

tho

4

© R0. I . C.Pu btens l i cat i ons 740 •f orr evi ew p ur pose sonl y• (b) (c) d reds

hun

2

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on es

thousands

(a)

ones

74 hundreds and 2 ones

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(d)

tens

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7000 + 400 + 2

hundreds

(e)

. t etens 3 thousands 30o ones 30 c . che e200 ones r o 2 hundreds r 20 hundreds st super

4. Shade the bubble that is equal to the number in bold print. (a) 300 (b) 2000 (c) 10 000

1000 tens

10 hundreds

100 tens

5. Write the missing numbers. (a) 700 + 40 + 5 = (c) 5000 + 34

(b) + 30 = 5630

(d)

+ 300 + 68 = 4368 8000 +

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

= 8007

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

CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

(a)


Assessment 2

Sub-strand: Number and Place Value—N&PV – 3

NAME:

DATE:

1. Rearrange the order of these addends to calculate the answers. =

(a) 3 + 44 + 6 = (b) 5 + 23 + 245 =

=

2. Follow the pattern to extend the number facts.

r o e t s Bo r 120 – 40 = e p ok u 600 + 500 = 1200 – 400 = S (b)

(a) 6 + 5 =

12 – 4 =

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6000 + 5000 =

3. Show the method you use to solve each addition or subtraction. (a)

317 + 48

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

(c)

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(b) 566 – 37

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CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

60 + 50 =

o c . che e r o t r s super 436 + 347

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

(d)

R.I.C. Publications®

762 – 238

www.ricpublications.com.au

35


Assessment 3

Sub-strand: Number and Place Value—N&PV – 3

NAME:

DATE:

Use a mental or written method to solve these word problems. Show or explain how you calculated the answer.

(c) 86 parents were expected at the (d) Josh is competing in a longschool assembly. 53 chairs had distance swimming event that is so far been put out for them. How 1500 m. If he has swum 1220 m many more were needed? so far, how many more metres has he to swim?

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(e) Aiden downloaded 36 song tracks, while Mia and Bailey each downloaded 29. How many songs did they download?

36

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

(f) The school bus is licensed to seat 64 students. If 38 are already seated, how many more can fit on?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

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

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(a) 134 people travelled by bus to the (b) There are 25 students in Mrs beach. 62 people travelled by car. Martin’s class, 29 students in Mr How many people spent time at Long’s class and 28 in Ms Hart’s the beach? class. How many students are in the three classrooms?


Checklist

Sub strand: Number and Place Value—N&PV – 3

Demonstrates mental and written methods to calculate answers to addition and subtraction word problems

Demonstrates regrouping in calculations involving subtraction

Demonstrates regrouping in calculations involving addition

Uses place value to partition numbers up to at least 10 000

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STUDENT NAME

Recognises the place value of digits in numbers up to at least 10 000

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

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

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

37


Sub-strand: Number and Place Value—N&PV – 4

Recognise and explain the connection between addition and subtraction (ACMNA054)

TEACHER INFORMATION

RELATED TERMS Commutative property of addition

What this means

• Numbers can be added in any order without affecting the result (sum); example: 2 + 7 = 7 + 2

• Addition and subtraction are inverse operations; i.e. one operation will undo another. This is also known as ‘backtracking’. For example: 3+6=9

r o e t s Bo r e p ok u S 6+3=9

• A number sentence that is equal in value either side of the equals sign; e.g. 7 + 6 = 13, 6 + 7 = 7 + 6.

9–6=3

Partitioning

• Dividing a number into parts.

9–3=6

Students should be aware that the order in which addition takes place doesn’t matter (the commutative property of addition) e.g. 6 + 3 = 9, 3 + 6 = 9. This is not the case for subtraction with whole numbers: e.g. 9 – 3 = 6 but 3 – 6 = – 3 and cannot be done.

Teaching points

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Equivalent number sentence

• Links between addition and subtraction should be made when learning basic facts. • Encourage students to write down everything that links to a particular fact. For example, if a student knows 5 + 4 = 9, then he/ she also knows: 4+5=9

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 9–5=4 9–4=5

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What to look for • Students who think that subtraction is commutative; e.g. 7 – 3 is not the same as 3 – 7, although some students would interpret the latter as 7 – 3 (the larger takes the smaller). • Students who do not understand the meaning of the equals sign (=). Some students see the equals sign as an indication to write an answer, rather than it meaning expressions on both sides of the sign must be equal. For example, some students will complete

o c . che e r o t r s super

the number sentence 4 + 5 = + 4 , as 4 + 5 = 9 + 4 (instead of 5 + 4). Some number sentences do require what we consider ) but it should still be noted that an ‘answer’; (e.g. 4 + 5 = expressions either side of the sign are still equal.

Student vocabulary

See also New wave Number and Algebra (Year 3) student workbook (pages 26–29)

addition subtraction number sentence equivalent equal fact family

38

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Sub-strand: Number and Place Value—N&PV – 4

HANDS-ON ACTIVITIES Colour-coded materials Use place value blocks or interconnecting cubes in three different colours to represent number sentences involving the relationship between addition and subtraction facts. For example, in related number sentences such as ... 3+6=9

... students should choose one colour for the number 3, another for the number 6 and another for the number 9. They arrange the material so each part of any of the number sentences can be identified.

6+3=9 9–3=6 9–6=3

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

Discuss both addition operations and both subtraction operations with the students and the relationship they can see between the two types of equations.

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Addition and subtraction basic facts charts

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Display basic facts charts like those on pages 40 to 42 for students to refer to. Having instant recall will assist students in making the connection between addition and subtraction easier. Photocopy the charts so students can complete the answers. When they are familiar with the charts, extend their knowledge by explaining that if they know a fact like 7 + 2 = 9 or 9 – 2 = 7, then they know 17 + 2 = 19 and 19 – 2 = 17. (Charts can be enlarged to A3.)

Domino addition and subtraction families

Play in pairs or a small group. Students take turns to select a domino from a selection placed face down. They then proceed to make related addition and subtraction number sentences.

6 +– 2 4

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

Triangle card game

Making up number sentences

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If the number 2 is covered, the missing number has to be 2. It cannot be 10 if the highest number is placed at the top.

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The triangular-shaped templates on page 43 can be used to show the connection between addition and subtraction. Teacher or students write three related numbers on each corner of a card as shown. The highest number is written on the top of the triangle. (This ensures only one number can be the answer in the game when one of the other numbers is covered over.) Repeat with other cards. Students play in pairs. All cards are placed face down. One student picks up a card and turns it so the numbers can be read correctly. He or she covers one number with a finger and shows the card to the other student, who must use addition or subtraction to work out the missing number. Note: Template can be enlarged to A3 and laminated.

Students can use modelling materials to compose number sentences of related addition and subtraction facts. Give them problems such as: ‘Write four different addition and subtraction number sentences using the numbers 5, 4 and 9’. Students answers would be 5 + 4 = 9, 4 + 5 = 9, 9 – 5 = 4, 9 – 4 = 5.

o c . che e r o t r s super L O C A

Provide number sentences with missing numbers; e.g. 4 + 17 +

= 42 or

= 9,

+ 5 = 9. More difficult examples such as

+ 25 = 42 could be worked out with a calculator.

INKS TO

THER

URRICULUM

REAS

English • Follow a theme such as ‘Travel’ to compose word problems with the students which they can solve using either addition or subtraction; for example: ‘The ferry ride to the island cost $32. Maddie counted out $24 from her wallet. How much more does she have to count out?’ (Students can add by counting on from 24 or subtract 24 from 32 to find the answer.)

Communication and Information Technology • The following website contains an interactive game dealing with this sub-strand:<http://www.ezschool.com/Games/ FactFamily1.html> (students make related addition and subtraction fact families).

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

39


Sub-strand: Number and Place Value—N&PV – 4

RESOURCE SHEET Addition basic facts chart

1 2

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1+5 1+6 1+7 1+8 r o e t s Bo r e p o7 2 + 8 2 + 1 2u + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 +k S 1+2

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© R. I . C.Publ i cat i ons 6 + 0• 6f +o 1r 6r +e 2v 6i + 3w6 + 4u 6r + 5o 6s +e 6s 6o + 7n 6y + 8•6 + 9 e p p l 6 5

8+8

. 9+8 te9 + 2 9 + 3 9 + 4 9 + 5 9 + 6 9 + 7 o c . che e r o r st super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

8 +9

9+9

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

CONTENT DESCRIPTION: Recognise and explain the connection between addition and subtraction

0

0

Teac he r

+


Sub-strand: Number and Place Value—N&PV – 4

RESOURCE SHEET Blank addition basic facts chart

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© R. I . C.Publ i cat i ons orr evi ew pur posesonl y• 6 •f 5

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CONTENT DESCRIPTION: Recognise and explain the connection between addition and subtraction

7

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2

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

41


Sub-strand: Number and Place Value—N&PV – 4

RESOURCE SHEET Subtraction basic facts charts

– 0 1 2 3

6 7 8

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© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 9–1

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o c . che e r o t r s super

6 7 8 9 42

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recognise and explain the connection between addition and subtraction

9–0

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9


Sub-strand: Number and Place Value—N&PV – 4

RESOURCE SHEET Triangle card game templates

+ –

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+ –

+ –

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t–e +.

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CONTENT DESCRIPTION: Recognise and explain the connection between addition and subtraction

© R. I . C.Publ i cat i ons –rr +r –pos •+f o evi ew pu esonl y+•–

+ o c . che e r o r st super + –

+ –

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

+ –

R.I.C. Publications®

www.ricpublications.com.au

43


Assessment 1

Sub-strand: Number and Place Value—N&PV – 4

NAME:

DATE:

1. Write four addition and subtraction number sentences represented by this diagram.

r o e t s Bo r e (b) p 10 – 3 = 7 (c) 10 + 3 = 13o (d) 10 = 7 + 3 u k S

2. Which number sentence is not part of the fact family? Shade a bubble.

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(a) 3 + 7 = 10

3. Fill in the missing numbers. (a) 2 +

=9

9–

=2

(b) 4 + 12 –

= 12 =8

(c)

+ 6 = 15 =9

15 –

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(a) 3

6=9

9

6=3

9 9=6

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4. Fill in the missing addition or subtraction signs. (b) 10

3 =13

13

3 =10

11

10

11

(c) 5

6 = 11

6=5

o 5=6 c . che e r o t 6 5 =11 r 10e =r 3s 13 sup 13 = 3

5. Write four related addition and subtraction facts using 3, 5 and 8.

44

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recognise and explain the connection between addition and subtraction

© R. I . C12.P l i cat i ons+ 9 = 15 – 4u =b • r evi ew p posesonl + 7f =o 9r + 8u =r 12 –y 6 =• 9

9–2=


Checklist

Sub-strand: Number and Place Value—N&PV – 4

Compiles related addition and subtraction facts from three given numbers

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

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STUDENT NAME

Identifies related addition and subtraction facts represented in diagrams Identifies missing numbers in related addition and subtraction number sentences Identifies missing addition and subtraction signs in number sentences

Recognise and explain the connection between addition and subtraction (ACMNA054)

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

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

45


Sub-strand: Number and Place Value—N&PV – 5

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

RELATED TERMS

TEACHER INFORMATION

Commutative property of addition

What this means • Students need to become fluent with basic addition and subtraction facts. Basic addition facts are 0 + 0 to 9 + 9. The basic addition facts need to be linked to their related subtraction facts. (See previous sub-strand N&PV – 4: pages 38 to 45.) Students can then combine their basic fact knowledge, and place value and partitioning knowledge to perform calculations. (See page 33 for mental strategies for addition and subtraction.)

• Numbers can be added in any order without affecting the result (sum); for example: 2 + 7 = 7 + 2. Place value

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

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Partitioning

• Dividing a number into parts. In standard partitioning, a number is split into parts according to the value of the places; e.g. 347 = 300 + 40 = 7 • In non-standard partitioning, a number is split into parts not according to place value; e.g. taking some from one number to give to another: 9 + 8 is 10 + 7, so 59 + 38 is 60 + 37.

• Review students’ fluency with basic addition and subtraction facts. • Check their understanding of place value and partitioning. Provide students with a two-digit addition calculation, let them calculate the answer and then enquire as to how they performed the calculation. Typically, their responses can be categorised as: – splitting one number, e.g. 28 + 37 becomes 28 + 30 + 7 – splitting both numbers, e.g. 28 + 37 becomes 20 + 30 + 8 + 7 – adjusting one number and compensating, e.g. 28 + 37 becomes 30 (add 2) + 35 (take 2).

© R. I . C .Publ i cat i ons What to look for •f orr evi ew pur posesonl y•

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• In addition, these are numbers added to find the sum or total. For example, in the number sentence 3 + 4 = 7, 3 and 4 are the addends. Subtrahend/Minuend

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• In subtraction, a subtrahend is subtracted from a minuend to find a difference. For example, in the number sentence 8 – 5 = 3, 8 is the minuend, and 5 is the subtrahend. Student vocabulary addition subtraction number sentence

• Students with poor basic fact knowledge or who struggle to partition numbers according to place value. • Performing adjusting and compensating operations can be more prone to error as students may adjust one number but not compensate correctly.

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Addends

Teaching points

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• The position of a digit in a number determines its value; e.g. the place value of 7 in 4765 is hundreds; the value of 7 in 4765 is 700 (digit times place value).

See also New wave Number and Algebra (Year 3) student workbook (pages 30–33)

o c . che e r o t r s super Proficiency strand(s): Understanding Fluency Problem solving Reasoning

equivalent equal basic facts fact family splitting numbers

46

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Sub-strand: Number and Place Value—N&PV – 5

HANDS-ON ACTIVITIES As this content description (N&PV – 5) requires understanding of place value and partitioning combined with basic fact knowledge to perform calculations, refer to the hands-on activities on pages 17 (N&PV – 2) and 29 (N&PV – 3) to revise and check students’ understanding in this area. The hands-on activities on page 39 (N&PV – 4) also provide ideas for connecting the relationship between addition and subtraction facts.

Addition and subtraction basic fact charts Display basic fact charts like those on pages 40 to 42 in the content description (N&PV – 4) or provide photocopies for students to complete. Pages 48 and 49 give multiple copies of charts that can be photocopied and given as personal charts for students to keep for referral.

Basic facts card games

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• Using the basic fact charts on pages 40 and 42 as a reference, make sets of facts on blank playing cards or small squares of thick card. Students can work in pairs to sort the facts into groups of doubles, into groups of facts adding or subtracting with zero, of ‘turn around’ facts like 4 + 3 and 3 + 4, and so on. This will help them identify some of the strategies outlined on page 50. • Use blank playing cards to make sets for games of ‘Snap’ or ‘Concentration’. Ensure there are pairs of facts included that equal the same number and also provide two sets of cards with the numbers 0 to 9 in each pack. • Five or six students sit in a circle. Basic fact cards are placed face down. In turn, students pick up a card and are allowed to keep it if their answer is correct. (Students can check each other’s answers.) Answers should be given within a couple of seconds of reading the card.

Basic fact bingo

Use multiple copies of the bingo template on page 51 to create a ‘basic fact bingo game’. Write addition, subtraction or a mixture of both facts on the cards. Have the numbers 0 to 9 written on counters (or similar) and placed in a container or face down. Teacher or a student picks up a counter and calls out the number. Students look at their bingo card (can be shared with a partner) and cover with a counter or cube any fact that has that number as the answer. First to cover all his/ her facts shouts ‘Bingo’. Winning cards can be checked by cross-checking with the numbers that have been called out. Note: The game can be played with a selection of the numbers from 0 to 9 on the students’ bingo cards, with the basic facts called out instead of the other way around.

© R. I . C.Publ i cat i ons Tic-tac-toe • f orr evi ew pur posesonl y•

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Write basic addition or subtraction facts on the tic-tac-toe templates on page 52. Play the game like normal tic-tac-toe except students have to answer the maths fact before drawing an X or a 0 over the fact.

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Classroom quizzes

Quizzes can be conducted in various ways. A student can be timed by another to see how quickly he or she can write the answers to a selection of basic facts written on a sheet or called out from a pack of cards. A ‘Beat the clock’ format could be used to see how many correct facts a student or small group can complete in a given time; e.g. 30 seconds. Two students can play against each other to see who is first to call out the answer to a fact or write it on the board.

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o c . che e r o t r s super LINKS TO OTHER CURRICULUM AREAS

Communication and Information Technology

• The following websites contain interactive games dealing with this sub-strand: – <http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html> – <http://www.fun4thebrain.com/addition/dinoDiscoAdd.html> – <http://www.kidsnumbers.com/add_it_up.php> – <http://www.kidsnumbers.com/subtraction_missing_number.php> – <http://www.kidsnumbers.com/subtraction-action.php>

Economics • Discuss the usefulness of knowing addition and related subtraction facts to cope with real-life situations such as shopping (without a calculator) and counting out change.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

47


Sub-strand: Number and Place Value—N&PV – 5

RESOURCE SHEET Addition basic facts charts 0

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

r o e t s Bo r e p ok u S 9

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Sub-strand: Number and Place Value—N&PV – 5

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CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

Subtraction basic facts charts

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Sub-strand: Number and Place Value—N&PV – 5

RESOURCE SHEET Strategies for memorising basic addition and subtraction facts The following strategies can be used by students to develop mental strategies for memorising basic addition and subtraction facts. They can then be applied for addition and subtraction of larger numbers. Use concrete material where necessary to help understanding.

The commutative property of addition

Adding with zero

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If zero is added to any number, the answer remains that number; e.g. 6 + 0 = 6. (These facts don’t need memorising.)

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Subtracting with zero

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If zero is subtracted from any number, the answer remains that number; e.g. 6 – 0 = 6. If any number is subtracted from itself, the answer is zero; e.g. 6 – 6 = 0. (These facts don’t need memorising.)

Adding and subtracting with one

If one is added to or subtracted from any number, the answer is one more or one less than that number; e.g. 8 + 1 = 9, 8 – 1 = 7. With subtraction, if the number to be subtracted is one less than the number it is taken away from, the answer is one; e.g. 6 – 5 = 1. (These are other easy facts that don’t need memorising.) If these four points are taken into account, the following single-digit addition and subtraction facts are those that need memorising.

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

Addition

Subtraction

4=2+2

4–2=2

14 = 5 + 9, 6 + 8, 7 + 7

5 – 2 = 3, 5 – 3 = 2

6 = 2 + 4, 3 + 3

15 = 6 + 9, 7 + 8

6 – 2 = 4, 6 – 3 = 3, 6 – 4 = 2

7 = 2 + 5, 3 + 4

16 = 7 + 9, 8 + 8

7 – 2 = 5, 7 – 3 = 4, 7 – 4 = 3, 7 – 5 = 2

8 = 2 + 6, 3 + 5, 4 + 4

17 = 8 + 9

8 – 2 = 6, 8 – 3 = 5, 8 – 4 = 4, 8 – 5 = 3, 8 – 6 = 2

9 = 2 + 7, 3 + 6, 4 + 5

18 = 9 + 9

9 – 2 = 7, 9 – 3 = 6, 9 – 4 = 5, 9 – 5 = 4, 9 – 6 = 3, 9 – 7 = 2

5=2+3

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10 = 2 + 8, 3 + 7, 4 + 6, 5 + 5

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11 = 2 + 9, 3 + 8, 4 + 7, 5 + 6 12 = 3 + 9, 4 + 8, 5 + 7, 6 + 6

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13 = 4 + 9, 5 + 8, 6 + 7

To help memorise subtraction facts, related addition facts can be used. To solve 8 – 5, it can be helpful to think that 5 + ? = 8. If 5 + 3 = 8, then 8 – 5 = 3.

o c . che e r o t r s super

Further strategies to apply when adding and subtracting include: Counting on and back

When adding or subtracting 1, 2 or 3 to or from a number, count on from the larger number or count back when subtracting; e.g. when adding 3 + 14, count on 3 from 14: 14 + 1 (15) + 1 (16) + 1 (17), so 3 + 14 = 17. Doubles or near doubles Doubles facts are easier to remember than other facts, so knowing 5 + 5 = 10 can help solve 5 + 6 (add one more) and 10 – 5. Bridging to ten When one addend in an addition is 7, 8 or 9, the other addend can be split to make a 10; e.g. to add 9 to 4, subtract 1 from the 4 and add it to the 9 to make 10, then add 3 (9 + 4 = 10 + 3 = 13).

50

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

This means that numbers can be added in any order without affecting the answer; e.g. 2 + 5 = 7 and 5 + 2 = 7. When referring to an addition fact chart, it becomes obvious many facts are the same except for their order. This reduces the number of facts that need to be memorised; i.e. if you know 2 + 5 then you also know 5 + 2. (This does not apply to subtraction.)


Sub-strand: Number and Place Value—N&PV – 5

RESOURCE SHEET

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CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

Bingo game templates

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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www.ricpublications.com.au

51


Sub-strand: Number and Place Value—N&PV – 5

RESOURCE SHEET

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o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

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

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Tic-tac-toe templates


Assessment 1

Sub-strand: Number and Place Value—N&PV – 5

NAME:

DATE:

1. Complete these addition facts. (a) 1 + 8 =

2. Complete these subtraction facts.

3. Complete these addition and subtraction facts.

(a) 5 – 2 = +3=8

(a)

r o e t s Bo (b) r e p (c) 9 – 3 = ok 0+7= u (c) S 6+6= (d) 8 – 1 =

(d)

(e) 3 + 9 = (f) 8 + 7 =

(b) 7 – 0 =

=9

9+

+5=8

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(c)

(e) 8 – 7 = (f) 4 – 2 =

(d) 7 =

+2

(e) 8 –

=4

(f) 6 = 6 –

9b – 8l = © R. I . C.(g) Pu i cat i ons(g) – 8 = 4 r evi ew(h)pu sesonl y• (h) • 9 +f 9o =r 5 –r 3p =o (g) 2 + 6 =

4+0=

(j)

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+ 3 = 12

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CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

(b) 4 + 5 =

9–1=

(j)

7+

(k) 18 – o c . che (l) 6 – 3 = e (l) 14 – r o t r s su r e p (m) 7 – 5 = (k) 8 – 4 =

(m) 5 = (n) 4 + 6 =

=9 =8 +1

(n) 8 – 6 = (n) 17 =

(o) 5 + 9 =

= 13

+8

(o) 9 – 2 = (o) 9 –

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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=5

53


Assessment 2

Sub-strand: Number and Place Value—N&PV – 5

NAME:

DATE:

1. Rearrange the order of these numbers, if necessary, to make it easier to add and find the total. Show what you did in the space. (b) 17 + 5 + 3 =

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r o e t s Bo r e p ok u (c) 4 + 11 + 6 + 4 = (d) 1 + 19 + 9 + 10 = S

2. Write the answer to each problem. Show how you worked each out in the space. (Look carefully to see whether you have to add or subtract.)

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

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(b) 56 – 9 =

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(d) 49 + 33 =

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

(a) 2 + 5 + 8 + 5 =


Checklist

Sub-strand: Number and Place Value—N&PV – 5

Demonstrates how to partition or split numbers to make calculations easier

Applies knowledge of basic facts to addition and subtraction of larger numbers

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STUDENT NAME

Demonstrates fluency with basic addition facts for single-digit numbers Demonstrates fluency with subtraction facts related to basic addition facts Demonstrates fluency with related addition and subtraction facts

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

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

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

55


Sub-strand: Number and Place Value—N&PV – 6

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

TEACHER INFORMATION

RELATED TERMS Commutative property of multiplication

What this means

• Numbers can be multiplied in any order without affecting the result (product). Example: 3 x 5 = 5 x 3 Multiplication terms

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

• To fully understand tables, students need to have developed an array concept of multiplication. Drawing rectangles on grid paper that match the dimensions of the particular fact will help; for example: 3 x 5

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• In multiplication, a multiplicand and a multiplier are multiplied to find a product; e.g. in 3 x 5, 3 is the multiplicand, 5 is the multiplier and 15 is the product. The term ‘factors’ is generally used for the multiplicand and multiplier; i.e. 3 and 5 are factors of 15.

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• Students need to learn their tables and the related division facts. Begin with the twos as these are related to the addition doubles.

Turning the rectangle (array) around will show the connection to 5 x 3:

Division terms

• In division, a dividend is divided by a divisor to find a quotient; e.g. in 8 ÷ 4, 8 is the dividend, 4 is the divisor and 2 is the quotient.

© R. I . C.Publ i cat i ons • An arrangement used to model • f orr evi ew pur posesonl y• multiplication with whole numbers. Array

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Students should note that 3 x 5 = 5 x 3 (i.e. the commutative property of multiplication). Links then need to be made to the associated division facts: 3 x 5 = 15

5 x 3 = 15

15 ÷ 3 = 5

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Arrays can be made by arranging a set of objects (such as counters) into columns and rows or by using grid paper or geoboards. Each column must have the same number as the other columns and likewise with each row.

15 ÷ 5 = 3

Establish this fact before embarking on any form of drill.

Note: Just as addition and subtraction are inverse operations (i.e. one operation will undo another), multiplication and division are inverse operations. This is also known as ‘backtracking’.

o c . che e r o t r s super What to look for

Student vocabulary multiplication division fact family

• Students who do not understand the commutative property of multiplication. • Students who say the division calculation the wrong way around. See also New wave Number and Algebra (Year 3) student workbook (pages 34–38)

multiplication grid array geoboard groups shape

56

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 6

HANDS-ON ACTIVITIES Geoboard arrays Provide geoboards, 1-cm grid paper and objects such as counters or cubes for students to make arrays in structured and non-structured activities with multiplication facts of 2, 3, 5 and 10. Refer to page 64 for grid paper templates.

Class arrays

Grid paper showing 5 x 2

Geoboard showing 5 x 2

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Students in the class are divided into groups with different numbers in each group; e.g. 6, 9, 10. One group comes to the front of the class and arranges themselves in an array.; e.g. six students could arrange themselves in two rows with three students in each. Students who are not part of that group have to work out the related multiplication and division sentences.

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Find the multiples

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Students use the 1–120 grid on page 9 and skip count to find the multiples of 2, 3, 5 and 10 as far as 2 x 10, 3 x 10 and so on. Use a different shade for each multiple. Those that have the same answer can be partly shaded with each appropriate colour.

Multiplication grids

A completed and a blank multiplication grid for facts of 2, 3, 5 and 10 have been provided on pages 60 and 61. The completed grid can be used as a personal reference for the students. With the blank grid, students can, over time, fill in the blanks with the facts they know. Point out to them that if they know 2 x 3 then they also know 3 x 2 so two sections can be filled in. Discuss with them that any number multiplied by 0 has the answer of 0, and any number multiplied by 1 has the multiplicand as the answer. These are facts that are easy to remember.

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

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– Use blank playing cards or similar to create cards for use in multiplication and division card games such as ‘Concentration’, ‘Snap’ or ‘Fish’. Write multiplication number sentences—such as 3 x 4 = 12 or 5 x 2 = 10—on 20 cards, and 20 related division facts—such as 12 ÷ 4 = 3 or 10 ÷ 5 = 2—on 20 other cards. – These cards can also be used to test known and unknown facts. In pairs, students test each other by picking a card to see if the other can immediately recall it. If so, it gets placed in a personal pile of known facts. If not, it goes into an unknown facts pile. Later, or on another day, students work on making the unknown facts in an array and practising immediate recall.

Triangle card game

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The triangular-shaped templates on page 59 can be used to show the connection between multiplication and division. Write three related numbers on each corner of a card as shown. The highest number is written on the top of the triangle (this ensures only one number can be the answer in the game when one of the other numbers is covered over). Repeat with other cards. Students can play in pairs. All cards are placed facedown. One student picks up a card and turns it so the numbers can be read correctly. He or she covers one number with a finger and shows the card to the other student who must use multiplication or division to work out the missing number. Note: The templates can be left blank for students to fill in multiplication and division fact families they recall.

12 x÷ 4 3

If the number 4 is covered, the missing number has to be 3. It cannot be 36 if the highest number is placed at the top.

Spinning facts Use the six- and ten-sided spinner templates on pages 62 and 63 to play chance games with multiplication facts of 0, 1, 2, 3, 5 and 10. As shown in the diagram, use either a pencil or a split pin and arrow to spin the spinner. Students can play in pairs. One student generates a multiplicand from the six-sided dice and a multiplier from the ten-sided dice; e.g. 3 x 10. The other student orally and/or in writing gives the answer. If necessary, a multiplication grid can be used to check the answers. After a set number of turns (e.g. five), students swap places.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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57


Sub-strand: Number and Place Value—N&PV – 6

LINKS TO OTHER CURRICULUM AREAS English Prepare an oral or written procedure for using a multiplication table or making an array to show 2 x 6 (or similar) on a geoboard or grid paper or with counters.

Communication and Information Technology The following websites are interactive games dealing with this sub-strand: – – – –

<http://www.fun4thebrain.com/multiplication/alienmunchmult.html> <http://www.fun4thebrain.com/Division/alienmunchdiv.html> <http://www.fun4thebrain.com/multiplication/herocostumecloset.html> <http://www.fun4thebrain.com/Division/superherocostumediv.html>

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Health and Physical Education

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Arrange numbers of students in arrays for different ball games; e.g. three teams of 2 x 8 for passball, two teams of 1 x 10 for tunnel ball.

Economics

Identify items that are packaged in arrays before they are sold; e.g. booklets of stamps, packages of stickers, eggs in cartons. Explain how each array is arranged; e.g. the eggs in the illustration are arranged in a 2 x 6 array.

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

The Arts

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Discuss the usefulness of knowing multiplication and related division facts to cope with real-life situations where you do not use a calculator, such as shopping, counting out change as a shop assistant and so on.

Observe examples of bricks or floor tiles that have been laid in arrays and make replicas of the patterns on grid paper.

Science

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View pictures on the internet or observe in the school grounds or local community plants that have been grown in arrays such as vegetables, flowers, fruit trees in orchards, grapes in vineyards and pine trees in plantations. Discuss why they are planted in arrays and not randomly.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET Triangle card game templates

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET Multiplication grid

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts

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Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET Blank multiplication grid

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts

5

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Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET Six-sided spinners

0

0

1 1

1

2

1 2

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0

10

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5

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts (Use in conjunction with page 63.)

0

5

5 3

10

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Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET Ten-sided spinners

2

2

3

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1

0

9

2 3

2

3

4

6

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 6

RESOURCE SHEET

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

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts

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Grid paper


Assessment 1

Sub-strand: Number and Place Value—N&PV – 6

NAME:

DATE:

1. Which number sentence is shown on each array? Shade one bubble. (a) 5 x 2

(b)

3x4

1x5

3x3

2x5

4x4

5x5

4x3

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2. Write the multiplication number sentence that is represented by each diagram.

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(a)

© R. I . C.Publ i cat i ons or evi ew oseso(c) nl y• = 6r (b) p 4 xu 5r =p x 3 = 18 (a) • 2 xf 20 =

x4

20 ÷ 5 =

3x2=

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x6

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=2

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts

3. Fill in the missing numbers.

x 6 = 18

o c . 4. Fill in the missing multiplication or division signs.e ch r er o t s super x 5 = 20

6÷3=

2=6

(b) 8

4=2

2

6 = 12

4

12

6=2

8

(a) 12

12 = 6

2

18 ÷

15

3=5

2=8

3

5 = 15

2=4

15

5=3

8=2

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

4 R.I.C. Publications®

(c)

=6

15 = 5 www.ricpublications.com.au

3 65


Assessment 2

Sub-strand: Number and Place Value—N&PV – 6

NAME:

DATE:

1. Complete these multiplication facts.

2. Complete these division facts.

(a) 10 x 3 =

(a) 10 ÷ 2 =

3. Complete these multiplication and division facts. (a) 1 x 6 =

(b) 8 ÷ 4 = r o e t s Bo r e p(c) 3 ÷ 3 = o (c) 14 ÷ 7 = u k S (d) 15 ÷ 3 = (b) 5 ÷ 1 =

(d) 3 x 3 =

(d) 5 x 5 =

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(c) 2 x 4 =

(e) 3 x 8 =

(e) 18 ÷ 2 =

(e) 5 x 9 =

(f) 5 x 6 =

(f) 6 ÷ 3 =

(f) 12 ÷ 3 =

(h)

(g) 9 ÷P 3u = b 20 ÷ 4 = © R. I . C. l i cat i o(g) ns orr evi ew p u poses(h) on y • (h) 20 ÷ 10 =r 10l x6= 10 x • 0 =f

(i)

3x6=

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(j)

5x4=

30 ÷ 3 =

(i)

(j)

16 ÷ 8 =

(j)

3x7= 15 ÷ 3 =

o c (l) 14 ÷ 7 = (l) . 3x8= che e r o t r s s r u e p (m) 10 ÷ 0 = (m) 0 x 6 = (k) 12 ÷ 4 =

(k) 18 ÷ 2 =

(n) 3 x 9 =

(n) 15 ÷ 5 =

(n) 12 ÷ 1 =

(o) 5 x 7 =

(o) 12 ÷ 6 =

(o) 5 x 8 =

(k) 2 x 8 = (l)

5x8=

(m) 10 x 7 =

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(g) 2 x 7 =

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Recall multiplication facts of two, three, five and ten and related division facts Note: Give students a time limit to complete each set; e.g. 1 minute.

(b) 1 x 7 =


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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

Demonstrates fluency with division facts related to multiplication facts of 2, 3, 5 and 10

Demonstrates fluency with multiplication facts of 2, 3, 5 and 10

Identifies missing multiplication and division signs in number sentences

Identifies missing numbers in related multiplication and division facts

Identifies related multiplication and division facts represented in arrays

STUDENT NAME

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Sub-strand: Number and Place Value—N&PV – 6

Checklist

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

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Sub-strand: Number and Place Value—N&PV – 7

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

TEACHER INFORMATION

RELATED TERMS Multiplication terms

What this means • Perform: – mental – written, and – calculator-assisted calculations involving multiplication. The problems can be presented in various forms, including as word problems.

Commutative property of multiplication

Teaching points

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• Numbers can be multiplied in any order without affecting the result (product); for example: 3 x 5 = 5 x 3. Distributive property of multiplication over addition

• Multiplication can be spread over addition. This is useful when multiplying larger numbers; e.g. 2 x 58 = (2 x 50) + (2 x 8)

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• In multiplication, a multiplicand and a multiplier are multiplied to find a product; e.g. in 3 x 5, 3 is the multiplicand, 5 is the multiplier and 15 is the product. The term ‘factors’ is generally used for the multiplicand and multiplier; e.g. 3 and 5 are factors of 15.

• There will come a point when students can no longer perform calculations in their head and need to write things down. It is at this point that an efficient written method of calculation is required. • All written calculations rely on: – fluency with basic number facts – place value (including place value partitioning) – renaming numbers (partitioning in a variety of ways) – a step-by-step procedure. (Refer to page 70 for suggestions.) • When tackling word problems, students will require exposure to words like ‘product’ that imply multiplication.

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Student vocabulary multiplication

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• Students’ written calculations typically encounter problems in one of the four areas outlined above. If a student is experiencing difficulty, check if he/she fully understands the different method of calculation. Note: Refer to the hands-on activities and Resource pages of previous content description sections for ideas to develop areas such as fluency with basic number facts (N&PV – 6), place value and partitioning (N&PV – 3) and so on, if students are experiencing difficulty in calculations. • When tackling word problems, a student’s mathematical vocabulary may be causing the problem. Note that just because a student uses a particular word, it does not mean the word is fully understood by him or her.

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See also New wave Number and Algebra (Year 3) student workbook (pages 39–45)

product multiplier lots of sets of groups of factor place value renaming/regrouping/trading calculator

68

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Number and Place Value—N&PV – 7

HANDS-ON ACTIVITIES Concrete materials Provide grid paper (see template on page 64) or counters to make arrays. Use geoboards and place value blocks for students who still prefer to use concrete materials to represent and solve multiplication number sentences and word problems.

Calculator practice This content description requires students to use a calculator to check the solutions to problems. Ensure students are familiar with how to use a calculator and the correct terminology associated with it. Play games to practise multiplication on the calculator. Generate one-, two- or three-digit numbers using dice or number cards to find a multiplicand and a multiplier. Students find the solution using the calculator. If among students someone has a different answer, work out why this could have occurred. (Generally, a wrong number was keyed in.)

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Multiplying two-digit and three-digit numbers by a one-digit number

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Use the templates on page 71 to have students solve multiplication problems using partitioning methods. The teacher can choose the numbers or they can be generated randomly with dice or number cards. Students could work in pairs or individually. Answers should be checked with a calculator. If problems result, assist students to work out why any answers were incorrect. (Refer to the ‘What to look for’ section in the teachers notes on page 68.)

Multiplication number stories

Students play games to create number stories for multiplication from given numbers and to solve multiplication problems in word form. As above, use dice or number cards to generate two- or three-digit numbers. Play in pairs or individually. One student turns over a card or throws dice. Together or separately they can compose and record a multiplication number story with that number as the answer. Students can also write a multiplication number story first, before giving it to another student who must calculate the answer.

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

Picture/Diagram

Number sentence

How did you work out the answer?

Thinkboard

A thinkboard can be an effective way for students to represent and solve number stories. An example of one is shown.

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LINKS TO OTHER CURRICULUM AREAS

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English

Write a procedure (including appropriate diagrams) for how to perform a multiplication operation on a calculator or how and when to use particular keys (such as the Clear or Clear Entry key).

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Create a reference chart with a picture of the calculator keys Year 3 students are likely to use and a brief explanation of what each means.

o c . che e r o t r s sthep r e There were 7 cheeky monkeys atu zoo. Each monkey wanted to

The Arts

Create artworks to illustrate multiplication number sentences composed by the students, as suggested by the last ‘handson’ activity above.

take 5 peanuts out of a container. How many peanuts would the zookeeper have to put in the container for this to happen?

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69


Sub-strand: Number and Place Value—N&PV – 7

RESOURCE SHEET Mental and written calculation strategies for multiplication The following methods can be used by students to develop mental strategies for calculating multiplication. Working out should be jotted down so students can keep track of their thought processes. Demonstrate appropriate strategies gradually to individuals or groups of students. Multiplication is repeated addition Applying this fact can assist in calculations; e.g. 4 x 20 means 20 + 20 +20 + 20 = 80. Commutative property of multiplication

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Use of place value

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Students apply their knowledge of place value to understand that a number sentence such as 3 x 30 means 3 x 3 tens (which is 9 tens, which equals 90). Students could use place value partitioning; e.g. 5 x 25 is (5 x 20) plus (5 x 5) which is 100 + 25 = 125.

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Building with known facts

If a student knows that 5 x 5 = 25 but can’t remember the answer to 5 x 7, then build on from the known fact; e.g. 5 x 7 is two more groups of five from 5 x 5, so if 5 x 5 = 25 then 5 x 7 is 25 + 10 = 35. Splitting up factors

Split up a factor to make calculation easier; e.g. 12 x 4 is (12 x 2) x 2, which is 24 x 2, which is 48. Compensating

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

Compensation methods can be used; e.g. 5 x 9 is 5 tens take 5 ones, so the answer is 50 – 5 = 45.

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Example 1. 3 x 47 3 x 47

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=

3 x (40 + 7)

Example 3. 3 x 47 =

3 x 40

+

H

3x7

=

120

+

21

141

3 x 47

T 2 2 4

0 0 1 1

x Ones

H 1 1

70

O 7 3 1 0 1

Example 4.

3 x 47

3 x 40 3x7

T 4 x 2 2 4

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=

1 1

Example 2.

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The use of an efficient method of written calculation is required when numbers become too large for students to calculate mentally. Below are some partitioning methods students can use for multiplication of two-digit by one-digit numbers and three-digit by one-digit numbers. Each allows students to show how the numbers are partitioned in the calculation. Columns and rows are clearly defined so the ‘ones’, ‘tens’ and ‘hundreds’ all line up in the calculation—the opposite being a common reason why students make errors in written algorithms. Once they are familiar with these types of written calculations, algorithms can be set out without the rows and columns.

3

Tens 4 3 x 40 = 120

Ones 7 3x7 = 21

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

120 + 21 141

This box is used to add up the sum of the partial products

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CONTENT DESCRIPTION: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technology

This means the order of the numbers when multiplying does not matter; e.g. 33 x 2 is the same as 2 x 33. It is easier to mentally calculate 2 x 33 = 66 than 33 x 2 = 66.


Sub-strand: Number and Place Value—N&PV – 7

RESOURCE SHEET 1 Blank templates for 1- x 2-digit and 1- x 3-digit written calculations 1- x 2-digit templates

Problem:

= r o e t s B r e oo = p u k S

+

=

+

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Problem:

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1- x 3-digit templates

Problem:

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CONTENT DESCRIPTION: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technology (Refer to page 70, Example 1, for how to use the templates.)

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=

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+

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+

=

Problem:

=

=

+

=

+

=

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Sub-strand: Number and Place Value—N&PV – 7

RESOURCE SHEET 2 Blank templates for 1- x 2-digit and 1- x 3-digit written calculations 1- x 2-digit

1- x 3-digit

Problem:

Problem:

O

Thous. Hund. Tens Ones

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1- x 2-digit

1- x 3-digit

Problem:

T

x

Thous. Hund. Tens

O

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1- x 2-digit

Tens

Ones

Problem:

Ones

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Problem:

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1- x 3-digit

Hundreds

Tens

Ones

Ones

Problem:

72

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technology (Refer to page 70, Examples 2, 3 and 4 for how to use the templates.)

T

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Assessment 1

Sub-strand: Number and Place Value—N&PV – 7

NAME:

DATE:

Show the method you used to calculate these multiplications. Use a calculator to check your answers. 1. 3 x 34 =

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Yes No

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2. 58 x 5 =

Calculator check: Were you correct? Yes

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3. 42 x 8

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Calculator check: Were you correct?

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CONTENT DESCRIPTION: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technology

Calculator check: Were you correct?

Yes

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No

Calculator check: Were you correct? Yes No

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Assessment 2

Sub-strand: Number and Place Value—N&PV – 7

NAME:

DATE:

1. Use a mental or written method to solve these word problems. Show how you calculated the answer.

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(c) Mr Hayshed, the farmer, owns 24 hens. Each hen lays 1 egg each day. How many eggs do his hens lay in 1 week?

(d) Year 3 was helping their teacher, Ms Rule, to arrange chairs in the assembly area. She wanted 9 rows with 15 chairs in each row. How many chairs were needed?

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2. Write a multiplication word problem for this number sentence: 32 x 4 =

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technology

(b) Three buses were needed to take students to the interschool carnival. If each bus holds 64 passengers, how many students went to the carnival?

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(a) Radio station 3ZZ is giving away 10 prizes. Each prize contains 15 DVDs. How many DVDs will the radio station give away altogether?


Checklist

Sub-strand: Number and Place Value—N&PV – 7

Uses a calculator to check answers to multiplication problems

Writes multiplication number sentences in word form

Writes multiplication word problems in numerical form

Uses written strategies for solving multiplication problems

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STUDENT NAME

Uses mental strategies for solving multiplication problems

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

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Answers

Sub-strand: Number and Place Value

N&PV – 1

(a) odd (b) even (c) even (d) odd (e) odd (f ) odd (g) even (h) Teacher check

5. 8440, 8340, 8240, 8140, 8040, 7940, 7840, 7740, 7640, 7540 6. (a) > (b) < (c) > 7. 8990, 8523, 7839, 7192, 799 8. (a) 9632, 2369 (b) 0186, 8610

Page 14 Assessment 2

N&PV – 3

Page 13 Assessment 1

1

2

3

4

5

6

7

8

9

10

Page 34 Assessment 1 1. 2. 3. 4. 5.

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 (b) Students should shade the grid as shown. 2

3

4

5

6

7

8

9

10

16

17

18

19

20

12

13

14

15

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

(c) even 2. (b) shows even number pattern 3. (c) shows odd number pattern

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1. (a) 4490 (b) 8710 2. (a) As the arrow on the marked number line is clearly pointing midway between 3000 and 4000, students should work out it is pointing at 3500. (b) As the arrow on the marked number line is pointing at 7250, students should estimate 50 above or below this number. (c) The arrow on the scaled but unmarked number line is pointing at 5800. Taking this into account, students should estimate 100 above or below this number. 3. Teacher check students’ estimates

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Page 25 Assessment 2

1. Students should rearrange in the following way to make calculations of additions to 10 easier. (a) 44 + 6 + 3 = 53 (b) 245 + 5 + 23= 273 2. (a) 6 + 5 = 11 60 + 50 = 110 600 + 500 = 1100 6000 + 5000 = 11 000 (b) 12 – 4 = 8 120 – 40 = 80 1200 – 400 = 800 3. Students should demonstrate a partitioning, regrouping and/or rearranging method to calculate the answers; e.g. 317 + 48 = 315 + 50 = 365 (a) 365 (b) 529 (c) 783 (d) 524 Page 36 Assessment 3 Teacher check the written or mental method students used to calculate the word problems. Teachers might observe that some students will not understand the word problem and add instead of subtract (or vice versa). (a) 196 (e) 94

(b) 82 (f ) 26

(c) 33

(d) 280 m

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(a) 3365 (b) 4428 (b) 6000 + 700 + 90 + 1 (a) 50 ones (b) 6 hundreds (c) 40 hundreds (a) 800 + 30 + 4 (b) 700 + 6 (c) 6000 + 600 + 60 + 8 (d) 5000 + 900 + 30

Page 26 Assessment 3 1. (a) six thousand, nine hundred and ninety-three (b) nine thousand, four hundred and five 2. (a) 5444 (b) 8030 3. (a) 4972, 4974 (b) 8759, 8761 4. 3152, 3162, 3172, 3182, 3192, 4002, 4012, 4022, 4032, 4042

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(d) 7

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Page 24 Assessment 1

1. 2. 3. 4.

(c) 1000 tens (c) 600

Page 35 Assessment 2

11

N&PV – 2

(c) 9 thousands (c) 5041

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(a) 8 tens (b) 7 hundreds (a) 648 (b) 3972 (c), (d) and (e) represent 7402 (a) 30 tens (b) 20 hundreds (a) 745 (b) 4000

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N&PV – 4

Page 44 Assessment 1

1. 5 + 4 = 9, 4 + 5 = 9, 9 – 4 = 5, 9 – 5 = 4 2. (c) 10 + 3 = 13 3. (a) 2 + 7 = 9, 9 – 7 = 2, 9 – 2 = 7, 2 + 7 = 9 (b) 4 + 8 = 12, 12 – 4 = 8, 12 – 4 = 8, 4 + 8 = 12 (c) 9 + 6 = 15, 15 – 6 = 9, 6 + 9 = 15, 15 – 6 = 9 4. (a) 3 + 6 = 9, 9 – 6 = 3, 9 – 3 = 6, 9 = 6 + 3 (b) 10 + 3 = 13, 13 – 3 = 10, 13 = 3 + 10, 13 – 10 = 3 (c) 5 + 6 = 11, 11 – 6 = 5, 11 – 5 = 6, 6 + 5 = 11 5. 3 + 5, 5 + 3, 8 – 5 = 3, 8 – 3 = 5

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Answers

Sub-strand: Number and Place Value

Page 66 Assessment 2

N&PV – 5 Page 53 Assessment 1 1. (a) 9 (h) 18 (o) 14 2. (a) 3 (h) 2 (o) 7 3. (a) 5 (h) 9 (o) 4

(b) 9 (c) 7 (d) 12 (e) 12 (f ) 15 (g) 8 (i) 4 (j) 17 (k) 11 (l) 15 (m) 16 (n) 10 (b) 7 (c) 6 (d) 7 (e) 1 (f ) 2 (g) 1 (i) 0 (j) 8 (k) 4 (l) 3 (m) 2 (n) 2 (b) 0 (c) 3 (d) 5 (e) 4 (f ) 0 (g) 12 (i) 2 (j) 6 (k) 9 (l) 6 (m) 4 (n) 9

Page 54 Assessment 2

1. (a) (h) (o) 2. (a) (h) (o) 3. (a) (h) (n)

30 0 35 5 2 2 6 60 12

(b) 7 (c) 8 (d) 9 (e) 24 (f ) 30 (g) 14 (i) 18 (j) 20 (k) 16 (l) 40 (m) 70 (n) 27 (b) 5 (c) 1 (d) 5 (e) 9 (f ) 2 (i) 10 (j) 2 (k) 3 (l) 2 (m) 0

(g) 3 (n) 3

(b) 2 (c) 2 (d) 25 (e) 45 (f ) 4 (i) 21 (j) 5 (k) 9 (l) 24 (m) 0 (o) 40

(g) 5

N&PV – 7

r o e t s Bo r e p ok u S Page 73 Assessment 1

1. (a) change 2 + 5 + 8 + 5 to 5 + 5 + 8 + 2 = 10 + 8 + 2 = 18 + 2 = 20 (b) change 17 + 5 + 3 to 17 + 3 + 5 = 20 + 5 = 25 (c) change 4 + 11 + 6 + 4 to 4 + 6 + 11 + 4 = 10 + 11 + 4 = 21 + 4 = 25 (d) change 1 + 19 + 9 + 10 to 19 + 1 + 10 + 9 = 20 + 10 + 9 = 30 + 9 = 39 2. Students should show how they calculated the answer. It could be through regrouping a formal algorithm and showing where they regrouped the tens and ones— splitting one or both numbers or adjusting one number and compensating. (Refer to page 46 for examples of these types of partitioning.) Examples of methods that could be used:

1. 102

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Students should demonstrate how they calculated the number sentences by showing a mental or written strategy in the space under each number sentence. (Refer to page 70 for examples.) They can attempt to correct their calculation if they find it is incorrect after checking with the calculator. 2. 290

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Some students will not change the order of the numbers in any sum. This is acceptable as long as the answer is correct. They may simply rely on a sound knowledge of basic facts to obtain the answer. Many students will rearrange the numbers to bridge to ten, count on, add doubles first and so on. Possible rearrangements could be:

3. 336

Page 74 Assessment 2

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1. Students should demonstrate how they solved the word problems by showing a mental or written strategy in the space. (a) 150 (b) 192 (c) 168 (d) 135 2. Teacher check

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(a) 28 + 37 = 20 + 30 + 8 + 7 = 50 + 8 + 7 = 50 + 15 = 65 (b) 56 – 9 becomes 56 – 10, which equals 46. As 10 and not 9 has been subtracted, add 1 to compensate. (c) 64 – 18 becomes 64 – 20, which equals 44. As 20 and not 18 has been subtracted, add 2 to compensate. (d) 49 + 33 becomes 50 + 33, which equals 83. As 50 and not 49 has been added, subtract 1 to compensate.

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1. (a) 5 x 2 (b) 4 x 3 2. (a) 3 x 5 (b) 4 x 2 3. (a) 2 x 3 = 6, 6 ÷ 3 = 2, 3 x 2 = 6, 6 ÷ 3 = 2 (b) 4 x 5 = 20, 20 = 5 x 4, 20 ÷ 5 = 4, 4 x 5 = 20 (c) 6 x 3 = 18, 18 = 3 x 6, 3 x 6 = 18, 18 ÷ 3 = 6 4. (a) 12 ÷ 2 = 6, 2 x 6 = 12, 12 ÷ 6 = 2, 12 = 6 x 2 (b) 8 ÷ 4 = 2, 4 x 2 = 8, 8 ÷ 2 = 4, 8 = 2 x 4 (c) 15 ÷ 3 = 5, 3 x 5 = 15, 15 ÷ 5 = 3, 15 = 5 x 3

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Sub-strand: Fractions and Decimals—F&D – 1

Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole (ACMNA058)

TEACHER INFORMATION

RELATED TERMS Fractions

What this means

• A fraction is a part of a whole number; e.g. 1⁄3, ¾. The numerator (number above the line) shows how many parts are in focus. The denominator (number below the line) shows how many parts the whole number is divided into. Unit fractions

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

• To fully understand the fractions ½, ¼, 1⁄3 and 1⁄5, students need to use a variety of models including folding and cutting 2-D shapes and paper strips into ½, 1⁄3, ¼ and 1⁄5. • Students need to be shown strategies for folding 1⁄3 and 1⁄5. • Show these fractions and make statements such as ½ and ½ equals a whole by joining the pieces back together. • Show ½, 1⁄3, ¼, 1⁄5 on a fraction wall and make statements such as ‘2⁄5 and 3⁄5 equal one whole’. • Students need to be able to write these statements with symbols.

What to look for

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• Unit fractions are those with a numerator of 1; e.g. ½, 1⁄3, ¼, 1⁄5.

• Students need to know the unit fractions of ½, ¼, 1⁄3, 1⁄5. • They see how each of these fractions make one whole; e.g. ½ and ½ equals one whole.

• Students who think of fractions as whole numbers. • As folding paper for ½ and ¼ is far simpler than folding for 1⁄3 and 1⁄5, students are often frustrated with folding activities more complicated than ¼— when there seems to be too many fold lines on the paper model. • Students who have difficulty folding circles.

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Student vocabulary fraction half/halves third/thirds

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quarter(s)/fourth(s) fifth/fifths whole equal parts share divide

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Sub-strand: Fractions and Decimals—F&D – 1

HANDS-ON ACTIVITIES Paper folding to represent fractions • Distribute same-sized sheets of paper to individual or pairs of students. They mark one sheet as ‘Whole’. A second sheet is folded in half, with each half marked ‘½’. A third sheet is folded in half the same way and half again to make quarters, with each quarter marked ‘¼’. The marked sections can be shaded different colours so they can be identified more easily. Students compare the number of parts and the sizes of the different fractions. Extend the activity by folding same-size sheets into thirds or fifths and so on and compare with the halves and quarters. • Students experiment with folding paper in different ways to make halves, quarters, thirds, fifths and so on, ensuring the fractions are equal in size. • Cut out the halves, quarters, thirds and so on that have been made from the activities above and sort the fractions from the largest to the smallest.

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Fractions on a number line

Fraction wall

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• The resource sheet on page 83 can be used as a reference to show students how to locate unit fractions on a number line. Blank number lines are provided on page 84 for students to locate the fractions themselves. They will need rulers to measure the length between the ‘0’ and ‘1’ points to divide each line into half, quarters etc.

A ‘fraction wall’ reference chart is provided on page 81 (and a blank fraction wall on page 82) for students to compare the number of parts and their sizes of different unit fractions. Students can make their own 3-D fraction wall by folding a number of the same-sized strips of paper into halves, thirds, quarters and so on and placing them under an unfolded strip that represents a whole.

Use of manipulative materials

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Materials such as pattern blocks, Cuisenaire™ rods, magnetic or wooden fraction cakes, and coloured interconnecting cubes are readily available in most schools. Students can use these manipulative materials to demonstrate how a whole can be divided into different fractions.

Example: Connect eight interconnecting cubes of the same colour. Place four lots of two cubes in a different colour alongside to show quarters.

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Identifying fractions in collections

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Use collections such as buttons, counters or plastic eggs in an egg carton to find different fractions of a collection. Ensure students understand that the collection is the ‘whole’ or ‘1’.

Dividing objects into fractions

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Provide a variety of objects for students to work out how to divide or cut each into halves, thirds, quarters etc. (Students may suggest measuring with a ruler or with scales, so have these available.) Emphasise that each part must be equal. Objects to use could include lengths of string, wool or streamers; fruit; modelling clay; symmetrical pictures; paper 2-D shapes; and/or cups of water.

Card games with fractions

1. Use the sorting fractions cards on pages 85 and 86 to help identify different ways unit fractions can be represented; i.e. words, fraction notation, shading part of a shape, circling part of a collection. Photocopy onto stiff card and laminate for durability. Games such as ‘Concentration’, ‘Snap’ or ‘Fish’ can be played, where students have to match pairs of cards that represent the same fraction. 2. Use the matching fractions cards on pages 87 and 88 to help students identify written fractions with the matching shaded area(s) of various shapes. Photocopy onto stiff card and laminate for durability. Games such as ‘Concentration’, ‘Snap’ or ‘Fish’ can be played, where students have to match pairs of cards that represent the same fraction.

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Sub-strand: Fractions and Decimals—F&D – 1

LINKS TO OTHER CURRICULUM AREAS English • The following list is a selection of books that could be useful to teach fraction concepts: – Full house by Dayle Ann Dodds – Apple fractions by Jerry Pallotta – Fraction action by Loreen Leedy. • Explain the word origin of ‘fraction’ to the students. It comes from the Latin word ‘fractus’ meaning ‘to break’. • Discuss how fractions can be expressed in different ways in languages other than English. The fraction ‘1⁄3’ is expressed as ‘one-third’ in English (with the numerator identified first and denominator second) but in Japanese it is expressed as ‘three parts, one of them’ (with the denominator identified first and numerator second).

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Communication and Information Technology

The following web pages are interactive games dealing with odd and even numbers:

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– <http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw42848> (Deciding whether pizzas have been cut up into equal parts.) – <http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw45005> (Matching pizza toppings with a written fraction.) – <http://www.sheppardsoftware.com/mathgames/fractions/fracTut1.htm> (Identifying the denominator and numerator.) – <http://www.sheppardsoftware.com/mathgames/fractions/memory_fractions1.htm> – <http://www.sheppardsoftware.com/mathgames/fractions/fractionSet.htm> (Students see how many fractions they can match to pictorial representations in a given time.) – <http://www.primarygames.com/fractions/start.htm> (Identifying the fraction of pizza left on a plate.)

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Health and Physical Education

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• Create healthy fruit and vegetable platters in health and physical education lessons. Decide how to peel and/or cut up fruit evenly into halves, quarters, eighths and so on to share with the class.

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• Share items made in cooking activities evenly with the class; e.g. work out how many scones or pikelets are needed in each batch, work out how to cut up a healthy pizza into a number of equal parts according to the number of children. • Lay a rope on a grassed area or draw a number line on a bitumen area. Students help to mark the line in quarters. In turn, they jump, leap or hop as indicated by the teacher, counting the fraction they move to as they go; e.g. ¼, 2⁄4, ¾, 4⁄4(1). Repeat with thirds, fifths, sixths and so on.

The Arts • Create a giant fraction wall following the resource sheet on page 82. Students paint large strips of art paper a different colour for each fraction. Use black paint or thick black marking pens to divide and label each fraction appropriately. Attach to a display board or suitable place in the classroom.

Science • Polar bear math: Learning about fractions from Klondike and Snow by Edward R Emberley is based on the life of two polar bear cubs that were hand reared by zookeepers at an American zoo. One side of the page shows photographs and gives facts about the cubs being reared, while the other side uses fractions to show things that happened to the cubs.

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Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Fraction wall

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¼

¼

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

¼

1⁄3

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1⁄10

1⁄12

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RESOURCE SHEET

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

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Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Fractions on number lines

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

1

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8⁄12

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7⁄8

9⁄10

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RESOURCE SHEET

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

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Blank number lines


Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Sorting fractions – 1

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

½

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Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Sorting fractions – 2

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one. tetenth

1⁄10

1⁄12 86

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

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oneeighth

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Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Fraction match – 1

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

1⁄6

1⁄3

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5⁄10

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

3⁄12 R.I.C. Publications®

6⁄8 6⁄12

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Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

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Fraction match – 2


Sub-strand: Fractions and Decimals—F&D – 1

RESOURCE SHEET Fraction chart

whole

1 halves

1⁄3

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¼

¼

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¼

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

quarters

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1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 1⁄12 Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Assessment 1

Sub-strand: Fractions and Decimals—F&D – 1

NAME:

DATE:

1. Which diagram does not show ½? Shade one bubble. (a)

(b)

(c)

(d)

2. Place each fraction on the number line: ¼, 2⁄4, ¾.

r o e t s Bo r e p ok u Sfractions make 1 whole? Shade one bubble. 3. How many of these halves

2

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(b) 1 whole =

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(c) 1 whole =

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4. Colour the fraction shown.

5. Write the fraction shown.

(a)

(c)

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

(a) 1 whole =

1

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Assessment 2

Sub-strand: Fractions and Decimals—F&D – 1

NAME:

DATE: 2. Which fraction is the largest? Shade one bubble.

1. Draw lines to cut this pizza into quarters.

(a) ½ (b) ¼ (c) 1⁄3

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© R. I . C.Publ i cat i ons 4. Colour the fraction shown. •f orr evi ew pur poseso nl y• (a) half (b) one-quarter (c) 2⁄4

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CONTENT DESCRIPTION: Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole

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r o e t s Bo r e p ok one bubble. 3. Which fractionu of these objects has been shaded? Shade S

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Checklist

Sub-strand: Fractions and Decimals— F&D – 1

Orders unit fractions according to size

Identifies unit fractions in collections

Writes unit fractions in fraction notation

Identifies unit fractions in partitioned shapes

Locates unit fractions on a number line

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STUDENT NAME

Understands that fractional parts must be equal

Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole (ACMNA058)

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Answers

Sub-strand: Fractions and Decimals

F&D – 1 Page 90 Assessment 1 1. (c) 2. Teacher check 3. (a) 2 halves (b) 4 quarters (c) 3 thirds 4. Teacher check 5. (a) 2⁄3 (b) 2⁄4 or ½ (c) 2⁄5 (d) ½

1. Teacher check 2. ½ 3. (a) ¾ (b) 3⁄5 (c) 1⁄3 4. Teacher check

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Page 91 Assessment 2

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Sub-strand: Money and Financial Mathematics—M&FM – 1

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

RELATED TERMS

TEACHER INFORMATION

Money

What this means

• A form or denomination of banknotes and coins used as currency. Currency

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• The act of giving cash as payment for something.

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• The form of money a country uses as a medium of exchange; e.g. Australian dollar, Japanese yen. Tendering cash

• Students need to be able to recognise the relationship between dollars and cents. • Students should be able to represent money in multiple ways using Australian coins and notes; i.e. a given amount can be made using a variety of notes and coins. • Students should be able to show and state what coins would be needed to buy certain everyday products. • Given a certain amount of money, students should be able to work out the change using manipulatives; i.e. using play money and stating how much change they should receive.

Transaction

Teaching points

• An exchange or transfer of funds such as between a customer and a cashier in a shop or a customer and an ATM.

• Set up place value-type situations so that students are manipulating and exchanging money as appropriate. Link this to the concept of addition and subtraction of money. • Students should practise different ways a sum of money can be represented; e.g. how many ways could you make $2.50, $9.75, $12.50 or $14.50? • Students should be given a certain amount of play money to purchase everyday items and work out the change to be received by using the money or by calculating it on a calculator, using written forms or calculating it mentally.

Rounding rules

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• • A price ending in 1c or 2c is rounded

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down to the nearest 10c. • A price ending in 3c or 4c is rounded up to the nearest 5c. • A price ending in 6c or 7c is rounded down to the nearest 5c. • A price ending in 8c or 9c is rounded up to the nearest 10c.

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Student vocabulary money cash

What to look for • Students who do not understand the value of the different coins in the Australian currency. • Students who do not understand there are 100 cents in a dollar, and, therefore, cannot regroup the different coins to form a dollar. • Students who have difficulty with skip counting in multiples of 5 and 10. • Students who have difficulty with adding or subtracting 10 or 5 to/ from a quantity.

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The price of an item in a shop needs to be rounded to the nearest 5c as there are no 1c to 5c coins to make up the amount (cash purchases only).

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See also New wave Number and Algebra (Year 3) student workbook (pages 50–62)

cents dollars coins notes currency change rounding value

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Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Money and Financial Mathematics—M&FM – 1

HANDS-ON ACTIVITIES Money for hands-on activities Templates of Australian notes and coins have been provided on pages 101 and 102. They can be photocopied onto card and laminated for durability. Commercially bought plastic coins and paper money can be used. Provide opportunities for students to study both sides of actual notes and coins (with careful supervision) so they can identify all the features. Using a website such as <http://www.australian-information-stories.com/australian-money.html> helps provide information about the features on our notes and coins for the teacher to relate to students, or for capable students to read themselves.

Representing money values

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Use the coin equivalence charts on pages 97 to 100 as references for students. In pairs, students can work out ways other than those shown on the charts to make up 50c, $1, $2 and so on. They should use play money to show these ways and share findings with the class. (Note: The one hundred dollar note has not been included.)

On blank playing cards or small sheets of paper, write monetary amounts appropriate to your students’ level of understanding. Students should work in pairs; they will need the cards, play money and a large sheet of paper or a clear tabletop area to place the money on. The cards are placed facedown. One student chooses a card and places it in the middle of the sheet/tabletop. Together, the students ascertain two to four ways of representing that money value using different denominations. When finished, it can be checked by the teacher before the other student chooses another card with a different amount.

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Money value game

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How much change? – 1

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Enlarge, colour and cut out the game cards on page 103. (Laminate for durability.) The prices end in 5c or 10c, so rounding to work out change is not required. Students can work individually or in pairs with teacher guidance to work out the change required, or students’ change can be checked after they have independently tried to work it out. (A calculator, or written and/or mental methods can be used.) For the activity, students need the cards and play money. The cards are placed facedown, and students are told the maximum of what they can ‘spend’ by the teacher; e.g. $5, $6.50, $10. Students each choose a card, read the price tag and work out the change they should receive, then make this amount with the play money. Extend so students choose two cards and have to add the prices before calculating the change.

How much change? – 2

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Enlarge, colour and cut out the game cards on page 104. (Laminate for durability.) Many supermarkets price their items not to the nearest 5c or 10c; (e.g. $1.48, $3.59) so the prices require shop rounding before working out the change. This will need to be discussed and practised with the students. Refer to the rules for rounding in the teacher information on page 94 and/or use the reference chart on page 105 for students to refer to. Students can work individually or in pairs to work out the change required after rounding, which can be checked after they have independently tried to work it out. (A calculator, or written and/or mental methods could be used.) For the activity, students need the cards and play money. Cards are placed facedown. Prices are decided by the teacher; e.g. $10, $15, $22. Students choose a card, read the price tag, apply shop rounding, work out the change they should receive and make this amount with the play money. After practice, have students choose two cards and have to add the prices before working out the change.

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Classroom shop Setting up a classroom shop enables students to practise simple operations involving money and giving change in a meaningful situation. There are some helpful teacher tips in the R.I.C. Publications handbook Money matters (by Paul Swan and Linda Marshall). There is also a money game, Money, Money, Money by Richard Korbosky.

Catalogue shopping Collect a variety of food and retail catalogues for students to select items from, round the prices (if necessary) and give change from set amounts. They could also be given a set amount from which to work out how many items they could buy with it.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Money and Financial Mathematics—M&FM – 1

LINKS TO OTHER CURRICULUM AREAS English

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Communication and Information Technology

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• The following list is a selection of books that could be useful to teach the concepts of use of money and finance. (While some selections involve currencies such as the American dollar, the concepts behind the story can be adapted to Australian currency.) Possible resources include: – Alexander, who used to be rich last Sunday by Judith Viorst (The story of what happens to the dollar Alexander received from his grandparents.) – Money makes the world go round –Vol. 2 by Greg Smith (Three children travel back in time from the year 3050 to present-day Australia to learn about money concepts.) – Small change by Rob Lewis (This story is about a family of human-like shrews. Alice finds a small coin and gives it to her younger brother, Sam, as Alice and her older brother, Pete, consider it too small to be of value.) – My rows and piles of coins by Tololwa M Mollel (A young Tanzanian boy tries to save money to buy a bicycle so he can help his mother carry heavy loads to market.) – Matthew and the midnight money van by Allen Morgan (Matthew helps the midnight money van man clean up pennies that have fallen on the ground, so he can earn money to buy his mother a Mother’s Day gift. There is a version on the internet at <http://www.youtube.com/watch?v=qBmvB1GAvog>.) • Write a report about one of the native Australian animals that feature on our coins or one of the famous Australians who feature on our banknotes.

• The following webpages contain interactive games involving activities with Australian currency: – <http://www.rosettaprimary.tased.edu.au/mathsobjects/waysOfmaking.htm> (Students click on coins, the total of which is automatically calculated.) – <http://www.rosettaprimary.tased.edu.au/mathsobjects/piggybank.htm> (Identifying coins needed to make a given amount of money.) – <http://www.funbrain.com/cgi-bin/cr.cgi> (Identifying coins needed to give the correct change for a set price.)

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

• In small groups, create different designs for Australian notes and coins that feature other famous people or native animals, or different categories such as famous landmarks, foods, plants etc.

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• Visit a mint or go on a web-based virtual tour of a website to find out about how our coins are made. • Find images of currencies used in other countries; e.g. Bali – Indonesian rupiah, Japan – yen, England – pound. Students could also bring samples from home (left over from a holiday/business trip) so others can view. Compare with Australian dollars and cents.

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• Animals unique to Australia feature on our coins: platypus, echidna, kangaroo, emu and lyrebird. Investigate facts about each animal: classification, appearance, covering, behaviour, diet, habitat and so on. Compare and contrast the similarities among them. Students or teacher could create a quiz by by means of which animals have to be sorted into categories; e.g. Which animals feed their young milk? Which animals can’t fly?

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RESOURCE SHEET Coin equivalence charts – 1

10c $0.10

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How many other ways can you make 50c? Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

www.ricpublications.com.au

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Sub-strand: Money and Financial Mathematics—M&FM – 1

RESOURCE SHEET Coin equivalence charts – 2

$1 $1.00

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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RESOURCE SHEET Notes and coins equivalence charts – 1

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How many other ways can you make $10? Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

R.I.C. Publications®

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Sub-strand: Money and Financial Mathematics—M&FM – 1

RESOURCE SHEET Notes and coins equivalence charts – 2

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$50 $50.00

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How many other ways can you make $50? 100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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Sub-strand: Money and Financial Mathematics—M&FM – 1

RESOURCE SHEET Coin templates

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CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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www.ricpublications.com.au

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Sub-strand: Money and Financial Mathematics—M&FM – 1

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

CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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Note templates


Sub-strand: Money and Financial Mathematics—M&FM – 1

RESOURCE SHEET

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CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

Game cards for giving change – 1 (Theme: School canteen)

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Sub-strand: Money and Financial Mathematics—M&FM – 1

RESOURCE SHEET Game cards for giving change – 2 (Theme: Items in a supermarket)

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

CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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RESOURCE SHEET Rules for rounding prices

Rounding prices When purchased, an item with a price ending in 1c or 2c is rounded down to the nearest 10c. Examples:

41c rounds to 40c

$2.62 rounds to $2.60

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When purchased, an item with a price ending in 3c or 4c is rounded up to the nearest 5c.

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When purchased, an item with a price ending in 6c or 7c is rounded down to the nearest 5c. Examples:

46c rounds to 45c

$2.67 rounds to $2.65

When purchased, an item with a price ending in 8c or 9c is rounded up to the 10c value.

© R. I . C.Publ i cat i ons Examples: 48c rounds to 50c $2.69 rounds to $2.70 •f orr evi ew pur posesonl y•

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How would these items’ prices be rounded when purchased?

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CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

Examples:

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Assessment 1

Sub-strand: Money and Financial Mathematics—M&FM – 1

NAME:

DATE:

1. Which collection shows one way of making $12.50? Shade one bubble.

(a)

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2. Draw coins and banknotes to show two ways to make $18.50. (a)

(b)

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CONTENT DESCRIPTION: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

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Assessment 2

Sub-strand: Money and Financial Mathematics—M&FM – 1

NAME:

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1. A mini-pizza costs $4.75. How much change from $10 would you get? Shade one bubble. (a) $5.50

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$5.25

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$4.75

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$0.25

2. Round each of these prices to the nearest five or ten cents. Write the new price on the line under the picture.

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3. Isobel has these coins:

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4. You have $10. How much change would you get if you spent: (a) $8.70?

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$7.35?

(c) $5.20?

(d)

$2.85?

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Checklist

Sub-strand: Money and Financial Mathematics— M&FM – 1

Demonstrates how to round prices to the nearest five- or ten- cent value

Works out the change required for simple transactions to the nearest five cents and 10 cents

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STUDENT NAME

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Represents money values in different ways

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Answers

Sub-strand: Money and Financial Mathematics

M&FM – 1 Page 106 Assessment 1 1. (b) 2. Teacher check 3. $5, $5, $5, $2, $2, $1 Page 107 Assessment 2

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1. (b) 2. (a) $2.80 (b) $1.65 (c) $4.45 (d) $3.90 3. (d) 4. (a) $1.30 (b) $2.65 (c) $4.80 (d) $7.15

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Patterns and Algebra—P&A – 1

Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060)

TEACHER INFORMATION

RELATED TERMS What this means

Number pattern

• A sequence of numbers arranged according to a specific rule. Repeating number pattern

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• A list of numbers that increase or decrease in size as the rule is followed; 5, 10, 15, 20, 25, 30 ... Routine growing pattern

• A list of numbers that increase or decrease in size with a constant difference; e.g. 1, 4, 7, 10, 13, 16 ... Non-routine growing pattern

Teaching points

• Students need to be given the opportunity to describe patterns using 2-D shapes. They need to be able to continue the pattern, whether it is a repeating pattern or a growing pattern. • They need to be able to use a table to describe what is happening, replicate it with a manipulative material, then state the rule. Examples: Position

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Student vocabulary number pattern repeating pattern growing pattern

copy/continue/describe forwards/backwards rule skip counting add subtract take away

– What is happening in the pattern? – State the rule in your own words.

– What is happening in the pattern? – State the rule in your own words. • Students need to be able to describe a rule from an instruction (such as ‘Start at 5 and add 3 each time’), show the pattern with materials and describe in a table. • Students need to be able to look at a number pattern (such as 3, 5, 7, 9, 11), explain what is happening in the number pattern and state the rule in their own words.

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• Counting forwards or backwards in multiples of a specific number; e.g. 2, 4, 6, 8, 10 ...

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• A set of random numbers that form a unit that is repeated; 2, 3, 2, 3, 2, 3 ... Growing number pattern

• Students need to understand what it means to describe a pattern, what it means to continue a pattern and what it means to create a pattern. • The emphasis of this descriptor is on patterns involving addition and subtraction. • Students need to be able to describe a number pattern they are presented with and state what is actually happening in the pattern. (This is the rule.) • Students need to describe a rule for a number pattern, then create the number pattern.

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• Some students have trouble seeing the pattern because they have problems with skip counting and either subtraction or addition. • Some students may confuse the positional value of a number in a pattern with the number itself; e.g. if the number 5 comes third in a pattern, the number is confused with 5. In such occurrences, it may be better to use manipulatives to show amounts. See also New wave Number and Algebra (Year 3) student workbook (pages 63–74)

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Patterns and Algebra—P&A – 1

HANDS-ON ACTIVITIES Skip counting in groups Divide a group of students or the whole class into two groups. Provide a number chart; e.g. a 1-100 chart, 1-120 chart or a 0-99 chart. Students practise skip counting by, for example, threes while following your pointer. The two groups take turns to state the next number in the pattern. Ask them if they can work out the pattern. Try other multiples with or without a pointer but with the chart on view for students to refer to if necessary. Don’t always start at the beginning of the chart; start at 9, 22 or 39. Skip count backwards as well as forwards.

Skip counting with a calculator

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Students use the constant function on a calculator to skip count by various multiples, starting from zero and also from other numbers. They read and record the numbers displayed on the screen and describe the pattern orally and in written form. (Use the pattern identification table on page 113.) A calculator can also be used to subtract various multiples.

Describing number patterns

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Give students a sequence of numbers (e.g. 3, 5, 7, 9, 11) or provide a description of a number pattern (e.g. ‘Start at 3. Count by 2s until you reach 11’). They make a model with manipulatives such as counters or unit cubes. They describe the pattern, work out what the next one or two numbers in the sequence will be and show that with the manipulatives. The pattern identification table on page 113 can be used with this activity, with the teacher filling in the table for students.

Creating own number patterns Students use manipulatives such as unit cubes or counters to create their own number patterns. They use the pattern identification table on page 113 to record the pattern and explain in their own words what is happening.

© R. I . C.Publ i cat i ons Toothpicks/Straws number patterns •f orr evi ew pur posesonl y•

Use toothpicks or plastic straws cut into approximately 3 cm-long lengths to copy, model, describe, continue and create number patterns. For example, students can copy this design and describe how they made it.

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Number grids

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They write and explain a rule in their own words and compare with a classmate’s. Both rules may be worded differently but still be correct.

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Use the various number grids provided on pages 115 to 117 for students to describe and continue the number pattern that has been coloured in by the teacher, another student or one they create to give to another student to describe and continue. The numbers in the pattern should be lightly coloured so they are still visible. Use numbers other than 0 or 1 to start numbering on the blank grids on pages 114 and 118. Card 5

Card 12

Rule:

Rule:

Start at 1. Add 1. Then add 2. Repeat the pattern until you reach 16.

Start at 0. Add 1. Then add 3. Repeat the pattern until you reach 20.

Card 16

Card 2

Pattern:

Pattern:

93, 95, 97, 99, 101 ...

16, 14, 12, 10, 8 ...

Guess my rule/Guess my pattern

Enlarge, laminate for durability and cut out the number pattern cards on pages 119 and 120. Students use one set of the cards at a time. They place the cards face down and choose one. According to the pack they are using, they work out the rule stated on the card and create the number pattern in numerals or work out the pattern from the numbers on the card and describe the rule in writing. (A thinkboard can be an effective way for students to work out the pattern.) Teacher should check their answers. (Answers are provided on page 127.)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Sub-strand: Patterns and Algebra—P&A – 1

LINKS TO OTHER CURRICULUM AREAS English

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Communication and Information Technology • These two websites provide interactive labelled 1-100 grids to create number patterns: – <http://www.apples4theteacher.com/math/games/100-number-chart-one.html> – <http://www.primarygames.co.uk/pg2/splat/splatsq100.html>. • This website provides a blank 1-100 grid for students to create their own number patterns: – <http://www.hellam.net/maths2000/100square.html>.

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• The following two books, suitable for this age group, are about the number pattern known as the Fibonacci sequence, discovered by Leonardo Fibonacci in the early 13th century. The sequence is 1, 1, 2, 3, 5, 8, 13 …, while the rule is ‘the next number in the sequence is the sum of the previous two numbers’. Fibonacci discovered that this number sequence occurs in the way things can grow in nature; e.g. in how rabbits multiply, the way in which a nautilus shell grows and how daisy petals form. To explain, read: – Growing patterns by Sarah C Campbell (Contains photographs and information about the Fibonacci number pattern in nature.) – Rabbits, rabbits everywhere: A Fibonacci tale by Ann McCallum (A girl has to work out the pattern in which rabbits multiply to stop them from eating the vegetables in Chee’s garden.)

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The Arts

History

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• Provide students with tessellating patterns and ask them to work out a method of colouring the patterns according to a number sequence; e.g. 2 squares coloured red, 1 square coloured yellow, repeat. Tessellations have been provided on pages 121 to 123. The following website includes blank and coloured tessellating patterns with options to print: <http://gwydir.demon.co.uk/jo/tess/grids.htm>. • Identify patterns of movement when learning simple dance moves, such as the ballroom dance ‘The barn dance’ and the bush dance ‘Heel ‘n’ toe polka’. Use the internet to find the steps to these two dances. A useful resource for these and other ballroom and bush dances is the education handbook Phys ed ‘n’ kids by Phil Peirce (R.I.C. Publications).

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• Learn about Leonardo Fibonacci and how he discovered the Fibonacci number sequence by studying rabbit populations. The book Blockhead: The life of Fibonacci, by Joseph D’Agnese, is suitable for this age group. Fibonacci is widely considered the greatest Western mathematician of the Middle Ages.

Science

• When a tree trunk is cut and a cross-section viewed, ‘rings’ can be seen. The total number of rings defines the age of the tree and the pattern of spaces between each ring demonstrates its year-by-year growth pattern; i.e. thick spaces between rings indicate a good growing season (sufficient rainfall etc.). Investigate this with the students.

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Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET Pattern identification tables

Position Pattern

Position

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Pattern

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

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Sub-strand: Patterns and Algebra—P&A – 1

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1–120 grid

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RESOURCE SHEET

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

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

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Blank 1–120 grid


Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET Number pattern cards – 1 Card 1

Card 2

Card 3

Card 4

Rule:

Rule:

Rule:

Rule:

Start at 2. Add 2 each time until you reach 30.

Start at 1. Add 2 each time until you reach 29.

Start at 3. Add 3 each time until you reach 36.

Start at 26. Subtract 2 each time until you reach 0.

Card 5

Card 6

Card 7

Card 8

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Add 1. Then add 2. Repeat the pattern until you reach 16.

10 each time until you reach 250.

Card 9

Card 10

Card 11

Subtract 10 each 5 each time until time until you you reach 60. reach 20.

time until you reach 21.

you reach 36.

Card 13

Card 14

Card 15

Rule: Start at 112. Subtract 1 until you reach 97.

Rule:

Rule:

Card 12

Rule: Rule: © R. I . C.Publ i ca t i ons Rule: Start at 75. Start at 49. Start at 14. Add 2 Start at 0. •5f orr e vi ew2 each pur p os es onl yAdd •1. Then Subtract each Subtract each time until time until you reach 25.

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add 3. Repeat the pattern until you reach 20.

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Rule:

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

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r o e t s Bo r e p o u k Rule: Rule: Rule: Rule: S Start at 1. Start at 110. Add Start at 120. Start at 15. Add

Card 16

Rule:

o c . che e r o t r s super Start at 189. Add 1 until you reach 202.

Start at 24. Start at 15. Add 3 Subtract 2. Then each time until subtract 1. Repeat you reach 39. the pattern until you reach 12.

Card 17

Card 18

Card 19

Card 20

Rule:

Rule:

Rule:

Rule:

Start at 20. Add 20 each time until you reach 180.

Start at 160. Subtract 20 each time until you reach 40.

Start at 5. Add 5. Then add 1. Repeat the pattern until you reach 34.

Start at 4. Add 3 each time until you reach 34.

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Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET Number pattern cards – 2 Card 1

Card 2

Card 3

Card 4

Pattern:

Pattern:

Pattern:

Pattern:

1, 3, 5, 7, 9, 11 ...

16, 14, 12, 10, 8 ...

15, 20, 25, 30 ...

68, 67, 66, 65 ...

Card 7

Card 8

4, 7, 10, 13, 16 ...

60, 55, 50, 45 ...

1, 2, 4, 5, 7, 8, 10 ...

15, 14, 12, 11, 9 ...

Card 9

Card 10

Card 11

Card 12

Card 14

Card 15

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Pattern:

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Card 6

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Card 13

Pattern:

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© Pattern: R. I . C.PubPattern: l i cat i onsPattern: 32, 42, 52, 62 110, 100, 90, 2,u 6,r 8,p 12, 14, 18s ... o 6, 9,l 12, 15, •...f or r e vi e80 w... p o se n y •18 ... Pattern:

Card 16

. te3, 6, 7, 10, 11, 14 ... 60, 50, 45, 35, 30 ... 93, 95,o97, 99, 101 ... c . che e r o r st super Pattern:

Pattern:

Card 17

Card 18

Card 19

Card 20

Pattern:

Pattern:

Pattern:

Pattern:

21, 23, 25, 27, 29 ...

20, 18, 16, 14 ...

0, 4, 8, 12, 16 ...

2, 4, 3, 5, 4, 6, 5 ...

6, 10, 14, 18, 22 ...

120

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

Pattern:

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

Card 5

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


Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

Tessellating patterns – 1

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Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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

CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

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

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Tessellating patterns – 2


Sub-strand: Patterns and Algebra—P&A – 1

RESOURCE SHEET

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

Tessellating patterns – 3

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Assessment 1

Sub-strand: Patterns and Algebra—P&A – 1

NAME:

DATE:

1. Look at the pattern below.

Which picture would come next in the pattern? Shade one bubble.

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(a)

2. Draw the next picture for each pattern. (a)

(b)

(c)

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(b) Write your own rule for your pattern. Pattern:

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Rule:

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3. (a) Use circles to make your own number pattern.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

r o e t s Bo r e (b) (c) (d)o p u k S


Assessment 2

Sub-strand: Patterns and Algebra—P&A – 1

NAME:

DATE:

1. (a) Look at the number pattern shown in the table. Position

1

2

3

4

5

Pattern 16 14 12 10

8

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Rule (a) Start at 25. Count by 5s to 70.

Pattern

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

(b) Start at 6. Add 2. Then add 1. Repeat until you reach 26.

3. Look at each number pattern and write the rule. Rule

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Pattern (a) 27, 24, 21, 18, 15, 12, 9, 6

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CONTENT DESCRIPTION: Describe, continue and create number patterns resulting from performing addition or subtraction

2. Read each rule and complete the number pattern.

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(b) Describe what is happening in the pattern.

o c . che e r o t r s super 4. Make your own number pattern and write the rule.

(b) 10, 15, 25, 30, 40, 45, 55, 60, 70

Pattern: Rule:

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STUDENT NAME

126

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

States rule for repeating and growing addition and subtraction number patterns

Creates and writes a rule for own addition or subtraction number pattern

Describes and continues an addition or subtraction number pattern represented in numerals

Describes and continues an addition or subtraction number pattern represented in words

Uses a table to describe what is happening in an addition or subtraction number pattern

Uses 2-D material to create and describe an addition or subtraction number pattern

Uses 2-D material to continue an addition or subtraction number pattern

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Checklist Sub-strand: Patterns and Algebra— P&A – 1

Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060)

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Answers

Sub-strand: Patterns and Algebra

P&A – 1 Page 124 Assessment 1 1. (d) 2. (a) Students should draw 7 connected squares in a row. (b) Students should draw an arrangement of 12 small circles. (c) Students should draw an arrangement of 9 connected squares. 3. Teacher check Page 125 Assessment 2

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

Answers for Resource sheet: Number pattern cards – 1 (page 119) Card 1: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 Card 2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 Card 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 Card 4: 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0 Card 5: 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16 Card 6: 110, 120, 130, 140 , 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250 Card 7: 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20 Card 8: 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 Card 9: 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25 Card 10: 49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21 Card 11: 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36 Card 12: 0, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20 Card 13: 112,111, 110, 100, 99, 98, 97 Card 14: 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202 Card 15: 24, 22, 21, 19, 18, 16, 15, 13, 12 Card 16: 15, 18, 21, 24, 27, 30, 33, 36, 39 Card 17: 20, 40, 60, 80, 100, 120, 130, 140, 150, 160, 170, 180 Card 18: 160, 140, 120, 100, 80, 60 , 40 Card 19: 5, 10, 11, 16, 17, 22, 23, 28, 29, 34 Card 20: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34

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1. Teacher check the students’ answers. Example: The pattern starts at 16 and 2 is subtracted each time until 8 is reached. 2. (a) 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 (b) 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26 3. (a) Teacher check the students’ answers. Example: Start at 27 and subtract 3 until you reach 6. (b) Teacher check the students’ answers. Example: Start at 10. Add 5. Then add 10. Repeat until you reach 70. 4. Teacher check

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Answers for Resource sheet: Number pattern cards – 2 (page 120) Note: Students wording will vary Card 1: Start at 1. Add 2 each time. Card 3: Start at 15. Add 5 each time. Card 5: Start at 4. Add 3 each time. Card 7: Start at 1. Add 1. Then add 2. Repeat. Card 9: Start at 32. Add 10 each time. Card 11: Start at 2. Add 4 each time. Card 13: Start at 6. Add 4 each time. Card 15: Start at 60. Subtract 10. Then subtract 5. Repeat. Card 17: Start at 21. Add 2 each time. Card 19: Start at 0. Add 4 each time.

Card 2: Start at 16. Subtract 2 each time. Card 4: Start at 68. Subtract 1 each time. Card 6: Start at 60. Subtract 5 each time. Card 8: Start at 15. Subtract 1. Then subtract 2. Repeat. Card 10: Start at 110. Subtract 10 each time. Card 12: Start at 6. Add 3 each time. Card 14: Start at 3. Add 3. Then add 1. Repeat. Card 16: Start at 93. Add 2 each time. Card 18: Start at 20. Subtract 2 each time. Card 20: Start at 2. Add 2. Then subtract 1. Repeat.

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NEW WAVE NUMBER AND ALGEBRA (YEAR 3) STUDENT WORKBOOK ANSWERS N&PV – 1 Page 2

Page 5

1. 6 shoes – even 12 eggs – even 24 tentacles – even 6 babies – even 18 drinks – even 30 drinks – even 20 sides – even 9 sides – odd 25 fingers – odd 25 sides – odd Page 6 The Australian Grand Prix

A battle between odd and even orange yellow

KEY

pink

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purple stripes

dark green stripes 2

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2. 2, 4, 6, 8, 10, 12, 14, 16, 18 3. yellow = 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50 pink = 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80 4. 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80 5. 33, 35, 37, 39, 41, 43, 45, 47 ,49, 51, 53, 55, 57, 59, 61 6. 63, 65, 67, 69, 71, 73, 75, 77, 79 7. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

2. Odd – 31, 75, 81, 87, 93, 105, 109, 115, 117, 137, 151, 167, 213, 219, 231, 239, 251 3. Even – 48, 52, 58, 92, 98, 100, 122, 124, 136, 142, 162, 180, 182, 192, 206, 210, 228, 314 4. Teacher check

Page 7

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Decide and draw

Circle like a shark

1. 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67 2. 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50 3. 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98 4. 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105 5. 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147 6. 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150

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

46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68

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47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69

88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110 Count and decide

1. 9 – odd 14 – even 15 – odd 6 – even 14 – even 26 – even

128

16 – even 12 – even 18 – even 16 – even 21 – odd 24 – even

3. (a) 1117 (c) 1111 4.

(b) (d)

1118 1112

1082 1084 1086 1088 Green 1090 1092 1094 Orange 1096 1098 1100 1102 1104 Purple 1106 1108 1110 1112 1114 1116 1118

63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85

1081 1083 1085 1087 1089 1091 1093 1095 1097 1099 1101 1103 1105 1107 1109 1111 1113 1115 1117

112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134

Grey

101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

Grey

68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90

Green

79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101

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(b) 148

112 114 116 118 120 122 124 126 128 130 132 134 Orange 136 138 140 142 Purple 144 146 148

1. (a) 149 2.

Odds make it count

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113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149

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Page 12

Page 9 Roll and create Teacher check

1.

Digits provided Largest 2, 1, 6, 5 4, 2, 7, 9 9, 0, 2, 7 1, 5, 6, 1 2, 4, 9, 5 9, 3, 7, 8 5, 5, 0, 1 3, 7, 1, 9 8, 8, 2, 9 3, 6, 2, 7

6521 9742 9720 6511 9542 9873 5510 9731 9882 7632

1256 2479 0279 1156 2459 3789 0155 1379 2889 2367

1 693 945

5

2

odd

2 394 884

2

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even

4 938 173

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9 583 772

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5 922 847

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2 394 842

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3 884 663

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odd

3 746 460

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2 774 390

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even

8 499 227

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7 882 092

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3 882 116

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2 936 884

2

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Largest

Smallest

3, 5, 1, 9

9531✔

3159✘

2, 7, 1, 8

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1278✔

3, 6, 9, 2

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3269✘

1, 5, 7, 2

7521✔

1257✔

3, 9, 5, 8

5893✘

3589✔

N&PV – 2

4, 7, 9, 1

4971✘

1479✔

Page 13

5, 5, 0, 3

5530✔

3055✘

Expand these numbers

1. 8000 + 500 + 60 + 2 7000 + 100 + 20 + 3 9000 + 900 + 70 + 5 9000 + 70 + 3 1000 + 700 + 70 + 6 3000 + 300 + 40 + 4 9000 + 700 + 30 + 4 1000 + 90 + 8 3000 + 900 + 40 + 5

6000 + 700 + 70 8000 + 200 + 20 + 3 9000 + 900 + 80 + 7 1000 + 200 + 30 + 4 3000 + 40 8000 + 900 + 70 + 1 5000 + 500 + 70 + 8 6000 + 700 + 80 + 2

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 6, 1, 1, 9

9116✘

1169✔

5, 7, 9, 2

9725✘

5279✘

6, 5, 4, 8

8645✘

4568✔

Big and small – 2

Digits provided

Largest

Smallest

9873

3789

4, 4, 7, 6

7644

4467

2, 5, 2, 0

5220

0225

1, 6, 8, 7

8761

1678

4, 6, 9, 6

9664

4669

3, 3, 7, 1

7331

1337

8774

4778

9110

0119

8750

0578

9743

3479

Digits provided

Largest

Smallest

7, 2, 8, 3

8273✘

3278✔

6, 9, 3, 9

9936✘

3699✔

1, 1, 8, 7

8711✔

1187✘

3, 5, 6, 6

6653✔

3566✔

9, 3, 5, 1

9513✘

1359✔

8, 3, 9, 2

9328✘

2398✘

4, 7, 0, 8

8074✘

0478✔

5, 1, 2, 9

9521✔

1259✔

4, 5, 9, 6

9645✘

5469✘

9, 1, 1, 0

9011✘

1019✘

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4, 7, 8, 7 1, 1, 0, 9 5, 0, 7, 8 3, 4, 7, 9

2.

Smallest

Odd-numbered Even-numbered Odd digits digit or even?

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Digits provided

Digits provided

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1.

1.

Big and small – 1

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Big numbers, but are they odd?

Expand these, but watch the zeros

1. 6000 + 700 + 70 1000 + 80 + 3 2000 + 90 + 9 6000 + 700 + 3 5000 + 100 + 1 4000 + 80 + 7 3000 + 50 + 5 800 + 70 + 7 900 + 10 + 2 4000 + 900 + 2 6000 + 600 + 6 2000 + 900 + 10 3000 + 400 + 40 7000 + 30 + 3 2000 + 90 + 1 3000 + 700 + 6 2000 + 900 + 8

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Match these numbers

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Oh dear, these are mixed up

1. (a) 2319 (b) 4852 (c) 6511 (d) 8209 (e) 9028 (f ) 9191 (g) 5946 (h) 1324 (i) 7036 (j) 3980 (k) 6207 (l) 5225 (m) 3773 (n) 8585 2. 1324, 2319, 3773, 3980, 4852, 5225, 5946, 6207, 6511, 7036, 8209, 8585, 9028, 9191

Page 20

One less – and one more

1668, 1670 8098, 8100 2668, 2670 1000, 1002 3000, 3002 4079, 4081 8106, 8108 3908, 3910 2002, 2004 5108, 5110

7010, 7012 1598, 1600 1100, 1102 4001, 4003 9010, 9012 5100, 5102 8098, 8100 5018, 5020 2948, 2950 8700, 8702

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

Order these close numbers

1. (a) 4010, 4050, 4080, 4100, 4110 (b) 6050, 6090, 6250, 6400, 6550 (c) 7070, 7100, 7370, 7700, 7770 (d) 5010, 5100, 5150, 5500, 5550 (e) 3050, 3100, 3300, 3400, 3450 (f ) 9050, 9100, 9350, 9500, 9800 1. (a)–(f ) Teacher checks numbers have been placed correctly on number lines. Page 18

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

1. (a) 100, 101, 110, 111, 121 (b) 200, 202, 210, 212, 222 (c) 303, 310, 311, 313, 323 (d) 400, 404, 414, 420, 424 (e) 500, 501, 505, 511, 515 (f ) 600, 606, 611, 616, 620 1. (a)–(f ) Teacher checks numbers have been placed correctly on number lines. Page 17

2313, 2413, 2513, 2613, 2713, 2813 6870, 6970, 7070, 7170, 7270, 7370 1374, 1474, 1574, 1674, 1774, 1874 8053, 8153, 8253, 8353, 8453, 8553 4678, 4778, 4878, 4978, 5078, 5178 8076, 8176, 8276, 8376, 8476, 8576

ew i ev Pr

Teac he r

1. 1943 – One thousand, nine hundred and forty-three 7034 – Seven thousand and thirty-four 8181 – Eight thousand, one hundred and eighty-one 6069 – Six thousand, and sixty-nine 1439 – One thousand, four hundred and thirty-nine 8819 – Eight thousand, eight hundred and nineteen 2354 – Two thousand, three hundred and fifty-four 2543 – Two thousand, five hundred and forty-three 8118 – Eight thousand, one hundred and eighteen 3199 – Three thousand, one hundred and ninety-nine 6096 – Six thousand, and ninety-six 5506 – Five thousand, five hundred and six 3919 – Three thousand, nine hundred and nineteen 2544 – Two thousand, five hundred and forty-four 7043 – Seven thousand, and forty-three 1349 – One thousand, three hundred and forty-nine 2445 – Two thousand, four hundred and forty-five 8991 – Eight thousand, nine hundred and ninety-one 8811 – Eight thousand, eight hundred and eleven 5605 – Five thousand, six hundred and five 2. 11, 19, 8, 16, 12, 6, 13, 20, 14, 9, 4, 1, 17, 3, 2, 7, 10, 15, 18, 5

2. (a) (b) (c) (d) (e) (f )

N&PV – 3 Page 21

What’s up with 5?

Number

Value of 5

3568

500 or 5 hundreds

7582

500 or 5 hundreds

m . u

Page 15

Number

Value of 5

4566

500 or 5 hundreds

8534

500 or 5 hundreds

o c . che e r o t r s super

Words and numbers Eight thousand, seven hundred and ninety-one Three thousand, and sixty-nine Two thousand, nine hundred and forty-seven Eight thousand, six hundred and one Two thousand, seven hundred and sixteen Nine thousand, eight hundred and seven Four thousand, eight hundred and seventeen Eight thousand, eight hundred and ninety-one

456

50 or 5 tens

513

500 or 5 hundreds

751

50 or 5 tens

579

500 or 5 hundreds

9533

500 or 5 hundreds

1560

500 or 5 hundreds

5804

5000 or 5 thousands

5007

5000 or 5 thousands

3560

500 or 5 hundreds

8356

50 or 5 tens

2315

5 or 5 units

9935

5 or 5 units

Extended form

Number

Extended form

Number

5000 + 400 + 20 + 9

5429

4000 + 500 + 70 + 7

4577

2000 + 100 + 50 + 6

2156

5000 + 300 + 30

5330

7000 + 600 + 50 + 8

7658

2000 + 50 + 4

2054

3000 + 500 + 10 + 9

3519

3000 + 5

4000 + 900 + 20 + 5

4925

1000 + 500 + 8

3005 1508

5000 + 100 + 70 + 1

5171

9000 + 500 + 9

9509

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Extended form

Number

Extended form

Number

20 + 500 + 3 + 1000

1523

9 + 3000 + 50 + 300

3359

7 + 50 + 600 + 4000

4657

1000 + 6 + 20 + 500

1526

100 + 5 + 9000 + 20

9125

700 + 70 + 5 + 9000

9775

600 + 2 + 50 + 5000

6652

50 + 8000 + 6 + 100

500 + 8 + 90 + 5000

5598

800 + 40 + 1000 + 5

8156 1845

500+ 4 + 60 + 1000

1564

400 + 5000 + 7 + 90

5497

Place value using wishball

Teacher check Page 23 45 195 70 75

2. 4. 6. 8.

1. 3. 5. 7.

1. 3. 5. 7.

A big day at the beach

78 152 91 108

Page 25

2. 4. 6. 8.

Page 26

2. 4. 6. 8.

Page 29

2159 m 1769 m 617 m 787 m

1. A 12, 12, 28, 28 B 18, 33, 33, 18 C 33, 29, 29, 33 D 18, 44, 44, 18 E 16, 19, 19, 16 F 23, 28, 28, 23 G 45, 17, 17, 45 H 39, 13, 12, 39 I 46, 16, 16, 46 2. C, D, G, I

Total is 80 Total is 102 Total is 124 Total is 124 Total is 70 Total is 120 Total is 124 Total is 104 Total is 124

Four sums from three numbers!

4 + 6 = 10, 6 + 4 = 10, 10 – 6 = 4, 10 – 4 = 6 9 + 6 = 15, 6 + 9 = 15, 15 – 9 = 6, 15 – 6 = 9 7 + 8 = 15, 8 + 7 = 15, 15 – 7 = 8, 15 – 8 = 7 19 + 5 = 24, 5 + 19 = 24, 24 – 5 = 19, 24 – 19 = 5 11 + 12 = 23, 12 + 11 = 23, 23 – 11 = 12, 23 – 12 = 11 6. 8 + 4 = 12, 4 + 8 = 12, 12 – 8 = 4, 12 – 4 = 8 Page 27

Bigger numbers but still connected

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

w ww

1. 2. 3. 4. 5.

330 224 216 324

Can you walk a golf course?

4491 m 681 m 3222 m 2777 m

N&PV – 4

260 80 92 203

ew i ev Pr

Page 24

4 + 4 + 4 + 6 = 18 6 + 4 + 4 + 4 = 18 4 + 6 + 4 + 4 = 18 4 + 4 + 6 + 4 = 18 18 – 4 – 4 – 4 – 6 = 0 18 – 6 – 4 – 4 – 4 = 0 18 – 4 – 6 – 4 – 4 = 0 18 – 4 – 4 – 6 – 4 = 0 7 + 4 + 4 + 4 + 4 = 23 4 + 7 + 4 + 4 + 4 = 23 4 + 4 + 7 + 4 + 4 = 23 4 + 4 + 4 + 7 + 4 = 23 23 – 4 – 4 – 4 – 4 – 7 = 0 23 – 4 – 4 – 7 – 4 – 4 = 0 23 – 4 – 7 – 4 – 4 – 4 = 0 23 – 7 – 4 – 4 – 4 – 4 = 0

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

A big day at school

Teac he r

1. 3. 5. 7.

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

Number sentences

. te

Page 30

Split the numbers

1. (b) 60 + 9 + 30 + 3 = 102 (c) 20 + 1 + 50 + 3 = 74 (d) 80 + 7 + 10 + 6 = 103 (e) 30 + 6 + 10 + 9 = 55 (f ) 80 + 6 + 30 + 5 = 121 g) 50 + 5 + 30 + 7 = 92 h) 20 + 9 + 70 + 4 = 103 (i) 10 + 8 + 60 + 7 = 85 (j) 30 + 3 + 80 + 6 = 119 (k) 20 + 3 + 40 + 2 = 65 (l) 40 + 6 + 90 + 9 = 145 (m) 50 + 9 + 30 + 7 = 96 (n) 10 + 7 + 40 + 8 = 65

o c . che e r o t r s super

These numbers are the best of friends

1. A 9, 9, 5, 5 B 9, 8, 8, 9 C 11, 7, 7, 11 D 12, 7, 7, 12 E 6, 6, 5, 5 F 4, 9, 9, 4 G 5, 11, 11, 5 H 8, 7, 7, 8 I 12, 12, 9, 9 2. I, D, C

N&PV – 5

m . u

Page 22

Page 28

Total is 28 Total is 34 Total is 36 Total is 38 Total is 22 Total is 24 Total is 32 Total is 30 Total is 42

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Page 31 1. (b) (d) (f ) (h) (j) (l) (n) Page 32

Make the second line

N&PV – 6

20 + 17 = 37 (c) 20 + 20 = 40 30 + 29 = 59 (e) 14 + 11 = 25 20 + 20 = 40 (g) 20 + 12 = 32 30 + 30 = 60 (i) 22 + 28 = 50 20 + 44 = 64 (k) 20 + 30 = 50 16 + 32 = 48 (m) 24 + 7 = 31 20 + 27 = 47 My knowledge of subtraction (h) 76 + (30 – 3) = 106 – 3 = 103 (i) 136 + (40 – 1) = 176 – 1 = 175 (j) 112 + (30 – 2) = 142 – 2 = 140 (k) 144 + (50 – 2) = 194 – 2 = 192 (l) 116 + (40 – 2) = 156 – 2 = 154 (m) 151 + (30 – 3) = 181 – 3 = 178

Teac he r

1.

Mistakes on this grid x

0

1

2

3

5

1

0

0

0

0

0

0

2

0

1

5

6

11

22

3

0

3

6

8

15

30

4

0

4

9

10

20

40

5

0

5

10

20

25

40

6

0

6

12

16

30

60

7

0

7

16

21

40

70

8

0

9

16

27

40

85

9

8

9

18

27

45

81

10

10

10

20

30

50

109

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

10

2. Yes, 19 errors

Page 35

More mistakes on this grid

x

0

1

2

3

1

1

0

0

0

2

0

3

4

6

3

0

3

7

9

4

0

4

8

14

5

0

5

10

15

6

0

6

12

18

7

0

8

14

24

8

1

8

18

24

9

0

11

18

10

0

10

22

ew i ev Pr

1. (a) 53 + (20 – 2) = 73 – 2 = 71 (b) 39 + (20 – 2) = 59 – 2 = 57 (c) 48 + (20 – 3) = 68 – 3 = 65 (d) 73 + (30 – 2) = 103 – 2 = 101 (e) 83 + (30 – 1) = 113 – 1 = 112 (f ) 62 + (30 – 1) = 92 – 1 = 91 (g) 94 + (40 – 3) = 134 – 3 = 131

Page 34

5

10

0

0

12

22

15

30

20

40

35

40

30

65

35

70

44

80

29

45

90

30

60

100

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

132

15 11 13 12 12 16 3 10 13 5 10 17 14 7 13 8 2 13 13 18

w ww

1.

Take time to take on 20 15 18 25 20 21 19 25 17 20 22 14 17 17 22 21 25 15 18 20 24

11 14 3 8 15 2 6 21 8 18 9 11 4 6 8 4 12 7 15 16

. te

A different kind of speed test

Speed test 1 10 9 7 9 30 70 15 24 27 12 0 30 9 18 21 24 3 30

Speed test 2 30 24 30 12 9 50 3 40 27 24 21 10 15 30 18 80 60 0

Speed test 3 90 30 30 18 80 15 24 21 12 9 27 90 100 0 12 40 9 110

m . u

Page 33

Page 36

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


Page 37

The answer is there!

Teac he r

Speed test 2 5 2 10 5 6 5 3 3 3 5 5 5 10 3 3 5 6 2

3 x 4 = 12 15 ÷ 3 = 5 21 ÷ 3 = 7 20 ÷ 5 = 4 9 x 5 = 40 18 ÷ 3 = 9 15 ÷ 3 = 5 7 x 3 = 20 5 x 5 = 30 20 ÷ 4 = 5 3 x 4 = 12 25 ÷ 5 = 5 2 x 5 = 10

3 x 3 = 9 24 ÷ 3 = 8 3 x 4 = 12 6 x 5 = 40 21 ÷ 3 = 7 27 ÷ 3 = 7 7 x 2 = 14

4 x 4 = 16 16 ÷ 2 = 7 12 ÷ 3 = 4 16 ÷ 2 = 7 16 ÷ 2 = 7 7 x 5 = 40 7 x 5 = 40 16 ÷ 2 = 7 7 x 5 =40 16 ÷ 2 = 7 3 x 5 = 15 45 ÷ 5 = 8 8 x 5 = 40

6 x 5 = 30 35 ÷ 5 = 3 10 ÷ 2 = 4 8 x 5 = 42 12 ÷ 2 = 7 24 ÷ 2 = 8 21 ÷ 3 = 5 0 x 5 = 5 33 ÷ 3 = 9 14 ÷ 2 = 5 14 ÷ 2 = 5 40 ÷ 5 = 7 4 x 3 = 12

3 x 4 = 12 7 x 10 = 70 3 x 3 = 9 27 ÷ 3 = 8 10 x 5 = 40 5 x 5 = 25 24 ÷ 3 = 9 8 x 5 = 45 15 ÷ 5 = 7 8 x 2 = 16 40 ÷ 5 = 6 12 ÷ 2 = 9 0 x 5 = 0

7 x 5 = 21 8 x 3 =25 14 ÷ 2 = 5 4 x 4 = 16 3 x 4 = 12 3 x 10 = 30 9 x 2 = 18 6 x 3 = 18 2 x 5 = 10 9 x 2 = 17 25 ÷ 5 = 6 12 ÷ 3 = 5 1 x 5 = 6

6 x 2 = 12

2x4=8 4x2=8 3 x 5 = 15 8 x 10 = 80 4 x 5 = 20 7 x 5 = 35 50 ÷ 5 = 9 6 x 3 = 18 5 x 3 = 15

8 x 3 = 24 10 ÷ 2 = 6 4 x 5 = 20 27 ÷ 3 = 9 9 x 3 = 27 24 ÷ 2 = 9 9 x 4 = 36 6 x 2 = 12 6 x 10 = 60 1 x 3 = 3

4 x 4 = 16

7 x 5 = 35

0x5=0

0x3=0

5 x 5 = 25

4 x 3 = 12

1x5=5

6 x 3 = 18

3 x 10 = 30

9 x 3 = 27

0 x 10 = 0

9 x 11 = 99

3 x 5 = 15

7 x 5 = 35

9 x 5 = 45

7 x 2 = 15

8 x 11 = 80

8 x 2 = 16

5 x 4 = 21

5 x 10 = 59

3 x 10 = 33

7 x 3 = 22

4 x 3 = 12

10 x 2 = 21

9 x 5 = 50

3 x 4 = 11

4 x 5 = 23

8 x 5 = 40

4 x 4 = 17

5 x 11 = 50

5 x 3 = 15

2 x 5 = 10

8 x 3 = 24

3 x 5 = 15

1x3=3

9 x 2 = 18

10 x 10 = 100

7 x 2 = 12

1x3=3

10 x 2 = 20

9 x 5 = 45

2 x 10 = 20

8 x 5 = 42

9 x 10 = 90

2 x 5 = 10

6 x 10 = 60

6 x 5 = 30

5 x 5 = 35

8 x 5 = 40

4 x 5 = 20

4x2=8

6 x 3 = 18

9 x 5 = 55

3x2=6

1 x 10 = 10

10 x 1 = 11

0x3=0

5 x 3 = 15

2x3=6

3 x 5 = 14 4 x 3 = 14

2 x 5 = 11

0x8=0

7 x 3 = 21

10 x 5 = 50

10 x 3 = 30

9 x 10 = 99

7 x 10 = 70

0 x 10 = 10

2x3=6

6 x 2 = 12

6 x 4 = 25

3 x 3 = 10

5x2=9

8 x 3 = 24

7 x 3 = 21

3 x 5 = 15

6 x 3 = 19

3x3=9

8 x 10 = 80

10 x 3 = 30

7 x 5 = 35

7 x 5 = 40

5 x 2 = 10

7 x 2 = 14

6 x 5 = 30

2x2=4

6 x 2 = 11

1x5=5

8 x 5 = 40

4 x 10 = 40

3x3=9

7 x 10 = 70

5 x 10 = 50

9 x 3 = 27

10 x 5 = 50

7 x 3 = 21

9 x 5 = 45

6 x 3 = 18

1x2=2

6 x 11 = 66

5 x 5 = 25

0x5=0

4 x 5 = 20

5 x 5 = 25

Page 40

A busy day at school

4x2=8 6 x 2 = 12 9 x 5 = 45

1. 2. 3. 4. 5. 6. 7.

64 153 72 172 195 945 mins = 15 hours 45 mins 126

Page 41 1. 2. 3. 4. 5. 6. 7.

m . u

. te

5 x 5 = 25 7 x 5 = 36 9 x 3 = 27 15 ÷ 3 = 7 12 ÷ 3 = 4 7 x 5 = 35

2x3=6

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 8 x 5 = 32 5 x 5 = 25

5 x 5 = 25 21 ÷ 7 = 3 24 ÷ 3 = 8 7 x 2 = 40 45 ÷ 5 = 8 24 ÷ 3 = 8 30 ÷ 5 = 6 45 ÷ 5 = 9 7 x 5 = 40 35 ÷ 5 = 6 27 ÷ 3 = 9 24 ÷ 4 = 6 5 x 3 = 15

We better face the facts

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

Take me to your leader

w ww

12 ÷ 2 = 6 3 x 4 = 12 7 x 5 = 40 16 ÷ 2 = 7 21 ÷ 3 = 7 9 ÷ 3 = 3 5 x 5 = 25 20 ÷ 5 = 4 18 ÷ 3 = 6 7 x 3 = 22 7 x 5 = 40 3 x 4 = 12 5 x 5 = 25

Page 38

Page 39

Speed test 3 5 5 5 3 4 3 2 3 3 5 3 2 3 3 3 5 10 5

ew i ev Pr

Speed test 1 6 3 5 3 5 3 10 5 5 5 3 3 5 5 3 3 3 5

N&PV – 7

A busy day at the farm

126 184 156 152 374 609 132

o c . che e r o t r s super Page 42

1. (a) (b) (c) (d) (e) (f )

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

Big equations call for big grids

3 x (50 + 8) = 3 x 50 + 3 x 8 = 150 + 24 = 174 4 x (60 + 3) = 4 x 60 + 4 x 3 = 240 + 12 = 252 5 x (40 + 9) = 5 x 40 + 5 x 9 = 200 + 45 = 245 6 x (50 + 7) = 6 x 50 + 6 x 7 = 300 + 42 = 342 3 x (90 + 2) = 3 x 90 + 3 x 2 = 270 + 6 = 276 4 x (30 + 9) = 4 x 30 + 3 x 9 = 120 + 36 = 156

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133


1. (a)

More grids to use!

3 x 94

Page 46

x ones (b)

3

Tens

Ones

9

4

270

3 x 90

3x4

+ 12

= 270

= 12

282

ones

Tens

Ones

5

7

250

5x7

+ 35

= 35

285

5 x 50

5

= 250

4 x 39 Tens

x

3

Teac he r

(d)

4 x 30

4

1. (a) (b) (c) (d) (e) (f )

Tens

A 9 20 3 6 4 7 10 13 10 3 7 9 10 6 3 17 9 16 8 5

134

B 5 6 9 4 5 2 9 10 7 9 4 6 11 10 4 17 7 5 14 9

Ones 9

120

4x9

+ 36

= 36

156

5

Ones

9

3

450

5 x 90

5x3

+ 15

= 450

= 15

465

152 135 219 336 460 511

Plot these fractions

Page 49

What fraction is coloured here?

1. (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) (k)

5, 2⁄7 3, 1⁄4 1, 4⁄5 3, ½ 7, 0 1, 4⁄5 5, 0 3, ½ 2, 3⁄5 5, 1⁄6 2, 2⁄3

M&FM – 1

D 5 7 3 10 8 6 8 7 9 10 7 5 9 6 11 5 5 9 3 7

E 7 9 5 7 9 8 8 10 1 9 5 8 7 14 3 7 4 7 9 7

. te

Page 50

11 ways to make $1.10?

Teacher check Page 51 Can you read my mind? – I have 3 coins

We better face the facts – again

C 6 6 6 12 8 9 6 3 6 9 9 4 13 9 6 4 8 5 17 11

Teacher check

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

Calculator or pen?

w ww

Page 45

I just want my fair share

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

= 120

x

Page 44

Page 47

Teacher check

5 x 93

ones

Teacher check

ew i ev Pr

ones

Colour these fractions

Page 48

5 x 57 x

(c)

F&D – 1

1. Trick 1 – $2, $2, 20c 2. Trick 2 – $1, 50c, 5c 3. Trick 3 – $2, $2, $2 4. Trick 4 – $2, 10c, 5c 5. Trick 5 – 50c, 20c, 20c 6. Trick 6 – $1, 50c, 50c 7. Trick 7 – $1, 10c, 5c 8. Trick 8 – 50c, 50c, 50c 9. Trick 9 – $2, 50c, 5c 10. Trick 10 – $1, 10c, 10c or 50c, 50c, 20c 11. Trick 11 – 20c, 20c, 20c or 50c, 5c, 5c 12. Trick 12 – $1, 50c, 20c 13. Trick 13 – $2, $1, 10c 14. Trick 14 – $2, 20c, 5c Page 52 Change please!

m . u

Page 43

o c . che e r o t r s super

1. (a) Change from $5: $1.55, $3.05, $0.95, $2.65, $4.15 $0.30, $3.40, $2.60, $1.70, $4.10 (b) Change from $10: $5.45, $3.95, $6.45, $1.65, $8.05 $5.50, $2.80, $3.60, $1.20, $0.90 (c) Change from $20: $8.50, $16.50, $12.50, $2.40, $5.60 $11.50, $3.50, $17.50, $2.90, $16.30

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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


(d) Change from $50: $39.50, $27.50, $10.50, $5.50, $45.50 $24, $32, $5, $17, $39 Page 53 Dollars and cents

Dollars

cents

Dollars

cents

$1.21

121

$11.01

1101c

$0.66

66c

$2.88

288

$4.07

407

$4.04

404c

$1.33

133c

$7.07

707

$2.10

210

$5.51

551c

$2.02

202c

$13.02

1302

$5.09

509

$9.08

908c

$3.19

319c

$4.07

407

$1.89

189

$2.44

244c

$4.77

477c

$11.55

1155

$3.13

313

$3.30

330c

$8.01

801c

$9.19

919

$4.91

491

$4.17

417c

Page 54

Magic bags of money

Teacher check Page 58

More than one way to make a dollar

Teacher check Page 59 1. (b) (c) (d) (e) (f ) 2. (b) (c) (d) (e) (f ) 3. (b) (c) (d) (e) (f )

Six coin totals 20c, 30c, 40c, 50c, 60c, 70c 40c, 60c, 80c, $1, $1.20, $1.40 $1, $1.50, $2, $2.50, $3, $3.50 $2, $3, $4, $5, $6, $7 $4, $6, $8, $10, $12, $14 $1.20, $2.20, $2.30, $3.30, $3.40, $4.40 90c, $1.40, $1.60, $2.10, $2.30, $2.80 $1.05, $1.10, $1.60, $1.65, $2.15, $2.20 $2.20, $2.40, $3.40, $3.60, $4.60, $4.80 $4.50, $5, $7, $7.50, $9.50, $10 $2.70, $3.20, $5.20, $5.30, $5.80, $7.80 $3.40, $4.40, $6.40, $6.60, $7.60 , $9.60 $3.10, $3.20, $5.20, $5.70, $5.80, $7.80 $2.60, $2.70, $3.20, $4.20, $4.30, $4.80 $4.15, $4.25, $4.30, $6.30, $6.40, $6.45

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

Four coins - can you guess?

1. Trick 1 $1, 20c, 10c, 5c Trick 2 $2, 50c, 10c, 10c Trick 3 $2, $1, 50c, 20c Trick 4 50c, 50c, 50c, 20c Trick 5 $2, $2, $2, 5c Trick 6 $1, 20c, 20c, 5c Trick 7 $2, 10c, 10c, 10c Trick 8 50c, 50c, 50c, 10c Trick 9 $2, $2, $1, $1 Trick 10 50c, 50c, 50c, 5c 2. Answers will vary. Teacher check Page 55 How many coins in a note?

Page 60 1. 2. 3. 4.

Six ways Sam

ew i ev Pr

Teac he r

1.

Page 57

$1, 50c, $1, $2, 10c, $2 $1, $2, 50c, $2, $2, $1 50c, $1, 10c, 50c, $2, 50c 20c, $2, $1, $2, 20c, $1

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 1. (a) (c) (e) 2. (a) (c) 3. (a) (c) (e) Page 62

The great who am I?

10c (b) 20c 5c (d) $1 50c 10c, $2 (b) 20c, $1 $2, 5c (d) $1, 10c 20c (b) $2 5c (d) 50c 10c (f ) $1 Three coins and a note

m . u

w ww

. te

1. 20 x 50c coins 2. 10 x 50c coins 3. 15 x $2 coins 4. 20 x 50c coins – 5 x $2 coins Page 56 I need change please

Page 61

o c . che e r o t r s super

1. (a) Change from $4: $0.85, $1.45, $1.95, $0.65, $0.15 $1.30, $0.35, $1.10, $0.50, $0.80 (b) Change from $8: $3.25, $1.75, $0.45, $1.65, $1.05 $1.45, $0.75, $1.90, $0.20, $0.55 (c) Change from $25: $3.50, $1.50, $2.20, $1.85, $0.60 $3.65, $4.50, $3.10, $1.20, $2 (d) Change from $30: $9.50, $0.60, $7.85, $2.50, $5.70 $3.90, $7.60, $4.25, $6.40, $8.20

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

1. (a) Change from 50c : 45c, 10c, 35c, nil, 25c 15c, 30c, 40c, 20c, 5c (b) Change from $1: 55c, 30c, 65c, 20c, 45c 60c, 15c, 25c, 50c, 35c (c) Change from $2: 50c, $1.05, 75c, 40c, 15c $1.55, 90c, nil, 30c, 55c (d) Change from $5: $2.65, 85c, $2.40, 45c, $2.15 $1.25, $3.20, $3.85, $1.70, $2.05

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135


2. Teacher check Page 70 Know the rule! Where did we get to?

P&A – 1 Page 63

Hold that pattern

1. (a) (b) (c) (d) Page 64

Add 2 Subtract 5 Add 3 Subtract 4 Hold that pattern again!

1. (a) (b) (c) (d) Page 65

Add 5, minus 1 – 74, 73, 78 Add 3, add 4 – 34, 38, 41 Add 5, add 10 – 56, 66, 71 Add 6, minus 3 – 90, 87, 93 Shapes that build or shrink

1. 45, 40, 38, 33, 31, 26, 24, 19, 17, 12, 10 – reached 10 33, 30, 26, 23, 19, 16, 12, 9, 5 – reached 5 61, 57, 52, 48, 43, 39, 34, 30, 25 – reached 25 73, 68, 67, 62, 61, 56, 55, 50, 49 – reached 49 58, 55, 50, 47, 42, 39, 34, 31, 26 – reached 26 92, 90, 87, 85, 82, 80, 77, 75, 72, 70, 67 – reached 67 Page 72 Know the rule! How many moves? – 1

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

1. – 4, –1 + 10, + 9 + 10, + 3 + 9, + 2 + 8, + 4 –6 + 2, + 3 + 10, + 5 – 10, – 1 + 2, + 4, + 6 2. Teacher check Page 68 Watch the pattern and make it grow!

1. 5, 10, 12, 17, 19, 24, 26 – 4 moves 7, 10, 15, 18, 23, 26, 31, 34 – 5 moves 12, 16, 19, 23, 26, 30, 33, 37 – 5 moves 4, 11, 12, 19, 20, 27 – 3 moves 8, 11, 15, 18, 22, 25 – 3 moves 7, 12, 14, 19, 21, 26 – 3 moves Page 73 Know the rule! How many moves? – 2

ew i ev Pr

1. (a) 10 stars (b) 12 rectangles (c) 7 hexagons (d) 2 triangles (e) 1 cup (f ) 8 crosses (g) 4 diamonds Page 66 And the rule is? 1. + 5, – 4, + 5, + 10, – 2, – 3, + 11, + 5, + 4, – 3 Page 67 Ahh – I see the patterns!

Teac he r

1. 5, 8, 12, 15, 19, 22, 26, 29, 33 – reached 33 11, 15, 20, 24, 29, 33, 38, 42, 47, 51, 56 – reached 56 13, 18, 19, 24, 25, 30, 31, 36, 37 – reached 37 18, 21, 26, 29, 34, 37, 42, 45, 50, 53, 58, 61, 66 – reached 66 11, 13, 16, 18, 21, 23, 26, 28, 31 – reached 31 Page 71 Know the rule! This time take away

1. 75, 70, 68, 63, 61, 56 – 3 moves 57, 54, 49, 46, 41, 38 – 3 moves 42, 38, 35, 31, 28, 24 – 3 moves 94, 87, 86, 79, 78, 71 – 3 moves 68, 65, 61, 58, 54, 51, 47 – 4 moves 54, 49, 47, 42, 40, 35, 33 – 4 moves Page 74 Who wins the race?

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

Page 69

. te

Read the rules and lets go

1. 37, 41, 45, 49, 53, 57 95, 92, 89, 86, 83, 80 19, 23, 26, 30, 33, 37 54, 59, 62, 67, 70, 75 96, 91, 86, 81, 76, 71 69, 72, 75, 78, 81, 84 48, 58, 62, 72, 76, 86 69, 71, 72, 75, 77, 78 54, 59, 63, 68, 72, 77 46, 44, 41, 39, 36, 34

136

1. (a)

Yes

21 + 5, – 2

26

24

29

m . u

Next 5 22, 19, 16, 13, 10 68, 70, 74, 76, 80 31, 26, 36, 31, 41 34, 37, 39, 42, 44 87, 86, 90, 89, 93 55, 50, 60, 55, 65 79, 73, 70, 64, 61 32, 36, 42, 44, 48 97, 95, 104, 102, 111 68, 64, 72, 68, 76

w ww

Rule –3 + 4, + 2 + 10, – 5 + 2, + 3 + 4, –1 + 10, – 5 – 3, – 6 + 2, + 4, + 6 + 9, – 2 + 8, – 4

27

32

30

35

27 + 4, – 1

31

30

34

33

37

36

40

Yes

1

2

3

4

5

6

7

winner

43 + 5, – 2

48

46

51

49

54

52

57

53 + 6, – 1

59

58

64

63

69

68

74

Yes

Rule

1

2

3

10 + 4, – 1

14

13

17

16 + 3, – 1

19

18

21

(b)

4

5

6

1

2

3

winner

16

20

19

23

20

23

22

25 7

winner

o c . che e r o t r s super Rule

7

4

5

6

(c)

Rule

(d) Rule 101 – 4, – 1

1

2

3

4

5

6

7

winner

97

96

92

91

87

86

82

Yes

109 103 102

96

95

89

116 – 6, – 1 110

(e) Rule

1

2

3

4

5

6

7

55 + 8, – 2

63

61

69

67

75

73

81

59 + 7, – 1

66

65

72

71

78

77

84

winner

Yes

Teacher check predictions

Australian Curriculum Mathematics resource book: Number and Algebra (Year 3)

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Number and Algebra (Australian Curriculum): Year 3 - Ages 8-9