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RIC-6086 8/622


Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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 ISBN 978-1-921750-70-0 RIC– 6086

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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© Australian Curriculum, Assessment and Reporting Authority 2012. 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 the author(s). 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.

Supplier:

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Copyright Notice

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

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School Order# (if applicable):

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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.

View all pages online PO Box 332 Greenwood Western Australia 6924

Website: www.ricpublications.com.au Email: mail@ricgroup.com.au


AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: NUMBER AND ALGEBRA (YEAR 2) Foreword Australian Curriculum Mathematics resource book: Number and Algebra (Year 2) 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.

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Titles in this series are:

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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)

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• • • • • • •

Contents © R. I . C.Pu bl i cat i ons • N&PV – 5 Money and Financial Format of this book ................ iv – v .................... •f orr evi ew pur posesMathematics onl y • 114–131 Number and Place Value .......... 6–99 Teacher information ................................... 6 Hands-on activities ..................................... 7 Links to other curriculum areas ................... 8 Resource sheets ................................... 9–16 Assessment ....................................... 17–18 Checklist ................................................... 19

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– – – – – –

• N&PV – 2 – – – – – –

• N&PV – 3 – – – – – –

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Teacher information ................................. 20 Hands-on activities ................................... 21 Links to other curriculum areas ................. 22 Resource sheets ................................. 23–30 Assessment ....................................... 31–32 Checklist ................................................... 33

• N&PV – 6 – – – – – –

Teacher information ................................. 74 Hands-on activities ................................... 75 Links to other curriculum areas ................. 76 Resource sheets ................................. 77–82 Assessment ....................................... 83–84 Checklist ................................................... 85

• M&FM – 1 – – – – – –

Teacher information ............................... 114 Hands-on activities ................................. 115 Links to other curriculum areas ............... 116 Resource sheets ............................. 117–127 Assessment ................................... 128–129 Checklist ................................................. 130

Answers ......................................... 131

Patterns and Algebra ........ 132–161 • P&A – 1

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Teacher information ................................. 34 Hands-on activities ................................... 35 Links to other curriculum areas ................. 36 Resource sheets ................................. 37–42 Assessment ....................................... 43–44 Checklist ................................................... 45

• N&PV – 4 – – – – – –

Teacher information ................................. 58 Hands-on activities ............................ 59–60 Links to other curriculum areas ................. 60 Resource sheets ................................. 61–70 Assessment ....................................... 71–72 Checklist ................................................... 73

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• N&PV – 1

– – – – – –

Teacher information ................................. 46 Hands-on activities ............................ 47–48 Links to other curriculum areas ................. 48 Resource sheets ................................. 49–55 Assessment .............................................. 56 Checklist ................................................... 57

• N&PV – 7 – – – – – –

Teacher information ................................. 86 Hands-on activities ............................ 87–88 Links to other curriculum areas ................. 88 Resource sheets ................................. 89–94 Assessment ....................................... 95–96 Checklist ................................................... 97

Answers ..................................... 98–99

Fractions and Decimals ...... 100–113 • F&D – 1 – – – – – –

Teacher information ............................... 100 Hands-on activities ................................. 101 Links to other curriculum areas ............... 102 Resource sheets ............................. 103–109 Assessment ................................... 110–111 Checklist ................................................. 112

– – – – – –

Teacher information ............................... 132 Hands-on activities ................................. 133 Links to other curriculum areas ............... 134 Resource sheets ............................. 135–142 Assessment ................................... 143–144 Checklist ................................................. 145

• P&A – 2 – – – – – –

Teacher information ............................... 146 Hands-on activities ................................. 147 Links to other curriculum areas ............... 147 Resource sheets ............................. 148–155 Assessment .................................... 156–159 Checklist ................................................. 160

Answers ......................................... 161

Answers ......................................... 113

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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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 2)

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 2)

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

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences (ACMNA026) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What does it mean

Sequence • A set of things (usually numbers) that are in order, with one thing following after another in a certain arrangement. Rule

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• Counting forwards or backwards by a number other than 1.

• Students should be able to apply this knowledge to find other sequences in the 120 chart; e.g. count by fours forwards and backwards.

Teaching points

• Students should model skip counting with concrete mathematic manipulatives, such as using counters to show what is meant by skip counting by twos, threes, fives and tens.

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• A rule is the procedure that a count must follow. Skip counting

• Using a 1–120 chart, students should be able to start at a number and skip count by twos, threes, fives or tens forward to 120, then skip count backwards from 120.

• A variety of pen and paper tools can be used by students to see skip counting in action; e.g. colouring the different sequences on a 1–120-chart, showing different skip counting sequences on a number line. • Model how skip counting can be shown in a table: position

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• Focus on forward counting from any number and then skip counting backwards from any number. Model with a 1–120-grid and/or number line.

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Student vocabulary order sequence skip count

What to look for

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• Link skip counting to counting with 5c and 10c coins. Model this with play money.

• Watch for students who, when asked to count by twos, actually count by ones. • Watch for students who have problems counting with numbers greater than 100.

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forwards backwards

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

HANDS-ON ACTIVITIES Skip counting manipulatives Have students count pictures or objects arranged in groups. For example, draw ‘kangaroo tracks’ in the sand for students to count by twos (feet) or fours (toes). Give the students buttons with two or four holes and ask the students to count the number of holes in a collection. Count by threes using three-leaf clover or pictures of tricycles. Give the students counters and ask them to show a number sequence using the counters, such as that shown on this page.

Skip counting practice

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Number stories

Encourage the students to solve problems using skip counting; for example: • If there are 10 people on a bus, how many feet are there altogether? • If there are ten 2-car garages, how many cars can the garages hold?

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Practise skip counting in different ways; for example, use body percussion (click, click, click, CLAP, for counting by fours), arm movements (flick hands, flick hands, raise hands) or different sounds (whisper, whisper, whisper, whisper, SHOUT!) Count backwards as well as forwards, using the charts on pages 11 to 15. Teachers could make number cards using multiples of a certain number, and give these to students, who must then assemble themselves in a line in the correct order, holding their number card in front of them.

• Determine the number of eyes in your classroom (count by twos), and the number of fingers (count by fives) and toes (count by tens).

Sit down (skip counting game)

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

Ask the students to stand up. The teacher calls out a skip counting number sequence and intentionally misses out a number (e.g. 2, 4, 6, 10). The students need to listen for the skipped number and when they hear the gap in the sequence, they quickly sit down. The last to sit down leaves the game. Play until there is a winner.

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Make copies of the 1–120 chart on page 9. Working in small groups, each student has a pencil. Choose a target skipcounting sequence. One students at a time rolls the dice and skip counts the number of times rolled on the dice. For example, if skip counting by 5s and a four is rolled, the student moves to 20 on the chart. This can also be done backwards. The first student to reach the other end of the chart wins.

‘Beep’ (also called ‘Buzz’)

The students stand in a circle. Decide which counting sequence (twos, threes, fours or fives) will be the ‘beep’ numbers. One student starts the count from one, which continues around the circle. On the selected multiple, a student says ‘beep’ instead of the number. For example, if counting by fives, the count would be ‘1, 2, 3, 4, beep, 6, 7, 8, 9, beep, 11’ etc. When a student says ‘beep’, he or she sits down. The game continues until only one student is left standing. The game can also be played skip counting backwards.

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Count on

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Write numbers on cards and put them into a bag or box. Each student takes a number from the bag and then counts on from it, using a given number sequence. For example, if a student chooses the number 8 and must count on by fives, he or she says, ’8, 13, 18, 23, 28’ etc. Use larger numbers for students who can skip count backwards.

Circles and stamps Students play this game in pairs with a dice and rubber stamp. Each student rolls the dice twice. The first roll determines how many circles to draw and the second roll determines how many stamp marks to place in each circle. Skip count to see who has the most stamps.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

LINKS TO OTHER CURRICULUM AREAS English • Read books that include skip counting such as: – One is a snail, ten is a crab by April Pulley Sayre and Jeff Sayre – Two of everything by Lily Toy Hong – Mooove over!: A book about counting by twos by Karen Magnuson Beil. – How many feet in the bed? by Diane Johnston Hamm – Each orange had 8 slices: A counting book by Paul Giganti

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– Two ways to count to ten: A Liberian folktale by Ruby Dee – Spunky monkeys on parade by Stuart J Murphy – Arctic fives arrive by Elinor J Pinczes

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Information and Communication Technology

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• Watch a video of a frog jumping over every second number from 1 to 100 at <http://vimeo.com/7419963>

• Play games at <http://www.ngfl-cymru.org.uk/vtc/explore_num_seq/eng/Introduction/>, <http://ictgames.com/octopus. html> (finding 10 more than different numbers) or http://www.apples4theteacher.com/math/games/1000-numberchart-10.html (students can colour numbers on an interactive number chart). • Practise counting aloud by different skip counting sequences at <http://www.amblesideprimary.com/ambleweb/ mentalmaths/supersequencer.html>

Health and Physical Education

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• Play hopscotch (or a similar game involving jumping along a line of numbers), where the students hop or jump over every second number to practise skip counting by twos. • Learn a dance with repeating steps.

• Play games where a win or goal increases the score by two, four, five or 10 points. Students tally each goal or win, then count by the correct sequence to find out the final score.

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• Make a wall chart using the students’ hand prints. With paint, each student makes a print of his/her hand onto a long sheet of paper. When dry, number the hands to make a skip counting by fives chart for the classroom. The same can be done with feet to make a counting by 10s chart.

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• Look at artworks which contain repeated images or items that can be skip counted. For example, look at ‘Large dance troupe’ by John R Keyser. Talk about the way that the dancers are grouped by twos. Count the dancers by twos, their fingers by fives etc. (Visit <http///www.johnkeyser.com/html/dancerwallscultures.html>)

Languages

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• Practise skip counting in different languages.

Science • Find common features of plants or animals that come in pairs , threes or fours and count them using the correct skip counting sequence. For example, eyes and wings often come in pairs, legs can come in pairs or fours, leaves on a clover plant grow by threes.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET 1–120 chart

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CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

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or 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61 etc.

Patterns in number sequences on number lines

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CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

The digit in the tens place increases by one every second number. 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69

So 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 etc.

RESOURCE SHEET © Australian Curriculum, Assessment and Reporting Authority 2012

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Adding 5:

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or 4, 14, 24, 34, 44, 54, 64, 74 etc.

The digit in the tens place increases by one: 0, 10, 20, 30, 40, 50, 60, 70 etc.

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Adding 10:

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


RESOURCE SHEET Skip counting by twos

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To count by twos, either add 2 to the previous number, or count and skip every second number. If you start counting from 0 (or another even number) by twos, the numbers are all even numbers: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 etc. If you start counting from 1 (or another odd number) by twos, the numbers are all odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 etc. Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET Skip counting by threes

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

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


RESOURCE SHEET Skip counting by fives

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CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

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To count by fives, add 5 to the starting number and continue. If you start counting from 0 by fives then each number will end in either 5 or 0: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 etc. If you start counting for a different number, every second number ends with that same digit; for example: 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56 … Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET Skip counting by tens

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

10

© Australian Curriculum, Assessment and Reporting Authority 2012

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


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CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

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

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To count by fours, add 4 to the starting number and continue. If you start counting by fours from 0, the numbers are: 0, 4, 8, 12, 16, 20, 24, 28 … If you start counting by fours from 1 the numbers are: 1, 5, 9, 13, 17, 21, 25, 29 … If you start counting by fours from an odd number, then all the numbers are odd. If you start from an even number, all of the numbers are even. Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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Number lines

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© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

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


NAME:

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1. Use the number lines to show skip counting: (a) by twos, starting from 3. 1

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Assessment 1

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CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

(d) 55, 50, 45, 40, 35, (e) 92, 94, 96, 98, 100,

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(a) 5c

50c

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

30c (c) 5c

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NAME:

DATE:

1. Skip count to find out how many of each thing are in the four fish tanks.

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(a) If there are 10 fish in each tank, how many fish are there?

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(d) If there are two rocks in each tank, how many rocks are there? 2. Write the next three numbers in the sequences. Use the 1–120 grid to help you.

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r o e t s r ein each tank, Boo (b) If there are three p snails 9 12 u k how many snails are there? S (c) If there are five plants in each tank, how

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3. Start at any number on the number grid. Add 10 and colour that number. Keep adding 10 and colouring until the end of the chart. What do you notice about the numbers you coloured?

(f) 55, 57, 59, 61, , 18

,

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

© Australian Curriculum, Assessment and Reporting Authority 2012

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

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

CONTENT DESCRIPTION: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

Assessment 2


Checklist

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

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences (ACMNA026)

Recognises simple patterns in number sequences

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

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Teac he r

STUDENT NAME

Skip counts forwards and backwards by 2s to and from 120, from any starting point Skip counts forwards and backwards by 3s to and from 120 from any starting point Skip counts forwards and backwards by 5s to and from 120 from any starting point Skip counts forwards and backwards by 10s to and from 120 from any starting point

© Australian Curriculum, Assessment and Reporting Authority 2012

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o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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19


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

Recognise, model, represent and order numbers to at least 1000 (ACMNA027) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS Place value

What does this mean

• A positional system of notation in which the position of a digit determines its value. In the decimal (base ten) system, the value of the digits is based on the number ten.

• Students should be able to understand that there are different ways of representing numbers and identifying patterns beyond 100, up to (and just over) 1000.

• An order in which numbers increase in value.

• Students need to be able to state which number is larger and why, and be able to show this using manipulative materials such as craft sticks, MABs and money.

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Ascending

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• Students need to model numbers using craft sticks and MABs. They should be able to write these numbers from previous modelling with either manipulating materials or from pictures of manipulative materials.

Descending

• Students need to become familiar and fluent with writing numbers in a variety of contexts.

• An order in which numbers decrease in value.

• Students should be able to read, say, write and count any number up to 1000.

Teaching points

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

• To fully understand numbers beyond 100, students need to be able to count by ones, twos, fives and 10s for numbers up to 100 and over.

• Students need to be able to read, say, write and count numbers beyond 1000. • Students should be given the opportunity to use place value grids showing 1000s, 100s, 10s and ones.

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• They need opportunities to show larger numbers with bundles of 100 craft sticks, abacus and MABs. • They should be able to find these numbers on a 120–220 grid, a 320–420 grid.

• Students should be able to make connections among manipulatives, pictures/drawings and symbols

o c . che e r o t r s super

• They should be able to place numbers on number lines displaying numbers greater than 100 up to 1000

What to look for

• Those students who cannot count in the correct sequence. For example, look for the students who count 109 and then say 200 or those who start counting by tens once they reach the hundreds: 501,502,503,504,505, 506,507,508,509,510,520,530 …

Student vocabulary hundred

• Some students spell the numbers incorrectly; e.g. when they hear ‘one hundred and one’ they write 1001. Some students develop the thinking that every time they hear an ‘and‘ they put in a zero. Sometimes this works—’one hundred and seven’ is written 107—however, when they hear ‘one hundred and twenty-eight’ they write 1028

thousand place value

20

Proficiency strand(s): Understanding Problem solving

Fluency Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

HANDS-ON ACTIVITIES Ideas for using 101–1100 number charts (pages 24 to 28) • Randomly blank out numbers (or cover them with a counter) on the page. The students use the patterns in the charts, or the numbers before and after, to work out which number is hidden. • Teachers could say a number and ask the students to put their finger or a counter on that number as quickly as possible. • Teachers could cut one chart into strips and hand them out to individual students or groups of students to put together in order, or cut out a chart as a puzzle for students to reassemble. • Ask students to identify a number 10 before or 10 after another number. Ensure they use the patterns in the chart (rather than counting), moving up and down the columns, to find the answer. Similarly, ask them to find a number 100 before or after a certain number. Go through the charts as a class, adding 10 or 100 to any number and noticing which digit changes.

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

• Enlarge a number chart to A3. Students could throw a counter onto the chart (which is placed on the floor). They say that number, then make the number using base ten or MAB blocks.

Teac he r

Making bundles

Numbers in newspapers Provide the students with newspapers and ask them to find large numbers in the print (e.g. 100–1000 or above) and cut them out. In pairs or small groups, they can order the numbers (preferably about 10 numbers) from smallest to largest, or largest to smallest. After they have glued them in order on a sheet of paper, ask them to write which number would come 10, 50 or 100 after each number.

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Give the students ample opportunities to make and count bundles of manipulatives. Use matchsticks, craft sticks, straws, pipe-cleaners or sticks to make groups of 10 (bundling the objects together with rubber bands). Allow them to group ten bundles of 10 together to make and count 100s. Also count using different amounts of base ten or MAB blocks.

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

Tape measure

Measure each student in the classroom to the nearest centimetre. Students can put the numbers in order from lowest to highest or vice versa. Also lay out a tape measure on the floor and ask students to find a particular number that is called out.

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Three dice

Students take turns in small groups to roll three dice. They then use the numbers rolled to make as many different numbers as they can. Try playing a game where the student who correctly writes and reads the highest or lowest number possible wins. Students could also roll two or three dice, use the digits to record a number, then make this amount using MAB blocks, grouping them in hundreds, tens and ones.

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Playing card games

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Provide small groups of students with a pack of playing cards (without the picture cards, and with aces equalling 1). Place the cards face down in a pile between the players. Each player selects (or is dealt) three cards and arranges them to make the highest (or lowest) number possible. The player with the largest (or lowest) number wins the round.

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For a different card game, remove the picture cards, aces and tens. Provide each student in a small group with a table (one column, up to 10 rows), with the number 1000 in the top row and 200 in the bottom row. Students take turns to turn over three cards from the pile, and use them to create a number to fill in the empty rows between. The student chooses where to write the number so it fits in between the other numbers in the table. The winner is the first student to correctly fill their table with numbers.

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Read my mind! One student chooses a number between a range (e.g. 600 to 700) and says ‘I am thinking of a three-digit number, one of my digits is 8. Can you read my mind?’ The other students try to guess what the number is.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

LINKS TO OTHER CURRICULUM AREAS English • Read Sir Cumference and all the king’s tens: A math adventure by Cindy Neuschwander, The King’s commissioners by Aileen Friedman, and Earth Day – Hooray! by Stuart J Murphy. • Sing ‘The grand old Duke of York’ and discuss how armies might group or arrange large numbers of soldiers in order to count them. Practise counting groups of soldiers using squads (10 soldiers) and companies (100 soldiers). How many companies did the Grand old Duke of York have?

Information and Communication Technology

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• Once the students have practised making and counting groups of 100 with manipulative items, they can take photos of them with a digital camera. After the images are uploaded onto a computer, they can paste multiple copies of the 10 and 100 bunches to create worksheets for other students to count.

Teac he r

• Play games (such as ordering numbers less than 1000) at <http://www.ezschool.com/Games/Order.html >, <http://www. wmnet.org.uk/resources/gordon/Higher%20And%20Lower%20-%20Reveal%20and%20Order%20v6.swf> or select the ‘Ascending 1-1000’ game at <http://www.mathsisfun.com/numbers/ordering-game.php>

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• Students can practise representing numbers with place value blocks at <http://www.learningbox.com/Base10/BaseTen. html> • Students can count collections of hundreds, tens and ones and write the number it makes at <http://www.hbschool. com/activity/numbers_to_1000/>

Health and Physical Education • Place written large numbers into hoops. The students must jump across an area containing the hoops from largest to smallest or smallest to largest. • Lay out on the ground a selection of numbers written in large print on cards (for example, 100, 150, 200, 250, 300 and 350). Call out a number between the lowest and highest numbers to one student at a time. That student must run up to the numbers and stand where the number would belong. For example, if the number is 117, the student would stand between 100 and 150. Once at the right spot, he/she can return to the starting point. The aim is to do this as quickly as possible. Instead of calling out the numbers, the teacher could write the numbers on small cards to encourage students to read numbers.

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History and Geography

• Find a local historical site. Represent how old the site is using MAB blocks or bunches of sticks.

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• Our present-day symbol for zero comes from India. Find out about other influences from India in our culture.

The Arts

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• Make patterns on number charts (pages 24-28) by colouring certain patterns of numbers.

Science

• Humans have 10 fingers and 10 toes. Find other animals that have the same number of limbs, toes or fingers.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET ‘Who’s the boss?’ Students play in groups of four. Each student has one number grid (game board). One student starts by saying a number from his/her board and covering it with a counter (or crossing it off with a pencil). The next student has to find and say a number from his/her board that is higher than the first student’s number. When there are no higher numbers to call, the person who last said the highest number becomes ‘the boss’ and starts a new round by calling a number from his/her game board. The winner is the first player to have covered (or crossed off ) all the numbers on his/her game board.

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

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RESOURCE SHEET 301–500 chart

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650 660 670

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

CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

Teac he r

501

© Australian Curriculum, Assessment and Reporting Authority 2012

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


RESOURCE SHEET 701–900 chart

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

r o e t s 735 736 B 737 738 r e o p o u S743 744 745 746 747 k748

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

833 834 835 836 837 838 . te o 842 843 844 845 846 847 . 848 c che e r o 852 853 854 855 856 r st857 858 su r pe 862

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RESOURCE SHEET 901–1100

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r o e t s 935 936 937 Bo938 939 r e p o u 943 S 944 945 946 947 948k949

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o 1049 c . che e r o 1054 1055 1056 1057 1058 1059 t r s super

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

1050 1060

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

CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

© R. I . C.Publ i cat i ons 992 993 994 995 996 997 998 999 1000 •f orr evi ew pur posesonl y•

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1021

950

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940

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


RESOURCE SHEET Matching cards for snap, go fish or concentration (enlarge, laminate and cut)

two hundred and forty-two

340

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

113

one thousand

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

© R. I . C.Publ i cat i ons •f orr evi e w pur posesonl y•402 245

o c . che e r o t r s super five hundred and one

three hundred and one

one hundred

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RESOURCE SHEET Place value grids Enlarge the grids. Students place MAB blocks or craft stick bundles into the place value grids. They can then say the number they have created, create a number given to them, or give a number to another student to read or find on a number grid (pages 24–28). If no blocks are available, use the pictures below.

Tens

Ones

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Teac he r

Hundreds

© Australian Curriculum, Assessment and Reporting Authority 2012

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

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30

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

Hundreds

m . u

© R. I . C.Pub l i cat i ons Ones Tens •f orr evi ew pur posesonl y•

Thousands


© Australian Curriculum, Assessment and Reporting Authority 2012

Assessment 1

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

NAME:

DATE:

1. Write the correct digits for each number word. (a) three hundred and twenty-seven (b) five hundred and thirty-five (c) seven hundred and six

r o e t s Bo r e p o u k one thousand, one hundred and eleven S

(d) one thousand

(e) one hundred and fifty-two

Teac he r

(f)

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2. Write these numbers in order from lowest to highest. (a) 324, 456, 239, 701 (b) 408, 232, 199, 210

(c) 990, 465, 781,1001

© R. I . C.Publ i cat i ons 3. How many blocks are shown each picture? the • f or r ev i e w pinu r po sesShade onl ybubble. •

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CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

(d) 211, 112, 200, 149

(a)

(d)

. te o 1160 1006 303 333 330 152 125 150 . 1600 c che (b) (c) e r o r st super

402 422 420

(e)

257 572 275

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(f)

319 139 193

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

NAME:

DATE:

1. Write the number to show how many blocks there are.

= 100

= 10

=1

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Teac he r

(a)

= 1000

© Australian Curriculum, Assessment and Reporting Authority 2012

Assessment 2

(e) (f) © R. I . C.Publ i cat i ons 2. Write the numbers in order from highest to lowest. •f orr evi ew pur posesonl y• (d)

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3. Which arrangement of the digits makes the largest number? Shade the bubble. 4 0 (a)

(d) 32

7

401 104 410 9

5

2

926 962 692

(b)

892 982 928 3

6 (e)

8

(c)

7

5

853 385 835

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

753 573 735

(f)

1

4 714 471 741

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

CONTENT DESCRIPTION: Recognise, model, represent and order numbers to at least 1000

(a) 128, 921, 137, 738


Checklist

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

Recognise, model, represent and order numbers to at least 1000 (ACMNA027)

Identifies number patterns beyond 100

Orders numbers to 1000

Writes numbers to 1000

Models numbers to 1000

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

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Teac he r

STUDENT NAME

Reads numbers to 1000

© Australian Curriculum, Assessment and Reporting Authority 2012

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m . u

© 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 2)

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33


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

Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What does it mean

Partition • To break any whole number into whole number parts. Place value

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

• Students should be able to do this by modelling, using Unifix™ blocks, bundles of craft sticks, place value blocks, a 1–120-chart or an abacus • Students need to be able to read, say and write the grouping or the partitioning for different collections beyond 100.

Teaching points

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• A positional system of notation in which the position of a digit determines its value. In the decimal system, the value of the digits is based on the number 10.

Teac he r

• Students should be able to rearrange collections beyond 100 by grouping or partitioning the numbers in a variety of ways; e.g. 520 could be seen as 500 plus 20, or 250 plus 270.

• To fully understand this, students needs to be given the opportunity to break any number into different parts. This is commonly known as the part-part-whole strategy.

• Students should understand that any number can be broken into a number of different part-part-whole arrangements. Initially they should work with smaller numbers (numbers under 20) and then numbers up to 100.

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

• This involves seeing combinations of any number up to 100. This includes knowing that 100 is also 50 + 50, 75 + 25 or 65 + 35. Using a variety of manipulatives to show this gives students a way of modelling and writing the combinations

What to look for

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Student vocabulary group rearrange abacus

m . u

• Students who do not understand that numbers can be displayed in a great variety of ways.

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

place value partition digit

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

HANDS-ON ACTIVITIES Introducing tens, ones and one hundreds Allow students to make a group of 10 ones (use pipe-cleaners, craft sticks, matchsticks, sticks, Unifix™ cubes, Lego® bricks etc) and bundle them together (for example with a pipe-cleaner or a rubber band). Write the number ‘10’ on the board and discuss how the digit 1 shows that there is 1 one group of ten and 0 ones. Ask students to place two more items next to the group and write ‘12’ on the board. Discuss how there is still just one group of ten, but now there are 2 ones. Indicate, the position of the 1 in the number 12. Ask students to put 10 tens into a group and bundle. Write the number ‘100’ on the board and point out the position of the 1 in the number. Ask the students to make 3 tens, 4, ones etc. until they understand the concept. When you combine 100 tens, you get a group of 1000. When you combine 10 hundreds, you also get a group of 1000.

Paper plates

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

Hand out paper plates with large numbers written on them. The students can make the number using MAB blocks, in different ways (‘50’ can be 50 ones, single cubes, ‘five tens’, a combination of ones cubes and tens lengths).

Teac he r

Highest number

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To use the game, students work in small groups with pack of cards (picture cards removed), each with a blank place value grid. The students choose one card at a time from a central, facedown pile. They place the card in one of the place value positions on their sheet. They choose another card and must put it into another position (positions cannot be changed). The player who, when all four cards have been placed on the grid, has the highest number, is the winner. Students can be asked what each digit represents in its place.

Exchanging at the bank

Provide students with four dice and a quantity of MAB blocks. Students work in pairs or small groups, with one playing the role of the banker while the others are customers. The customers take turns to roll four dice. They take that number of ‘ones’ cubes and count them in front of the banker, putting them into groups of 10. The banker exchanges each pile of ones for one tens. Once students have mastered exchanging ones for tens, introduce a hundreds block and exchange tens for hundreds.

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

m . u

Similarly, put out three containers or cartons. Label one container ‘Ones’, another ‘Tens’ and the last ‘Hundreds’. Provide the students with numerous craft sticks in three colours. Students roll a dice and put that number of sticks (or other manipulatives) of one colour into the ones container. When they have ten ones, they can exchange for a different coloured craft stick to put into the tens, and so on.

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Bead strings

Make bead strings with 100 beads, grouped by colour in groups of 10. Slide and count the beads in different ways, such as by tens or partitioning in various ways.

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Place value bingo (page 39)

Copy and cut the individual cards. Students write a three-digit number on a sheet of paper. The teacher or a student takes and reads the cards one at a time at random. Students cross out or cover the digit if they have it in the correct place in their number. The first student to cover or cross out all their digits correctly is the winner.

Place value on an abacus (page 40)

Once the students have practised using an abacus to show numbers, cut out the abacus pictures, words and number strips. The students can put them back into the correct groups of three. Or give the students a ready-made number on an abacus, which they then have to make with place value blocks.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Play games, such as making numbers on an abacus, at <http://www.ictgames.com/arrowCards_revised_v5.html>. Click in the correct digit (in the ones, tens or hundreds place) at <http://www.free-training-tutorial.com/place-value/clickthedigit. html> • At <http://www.bbc.co.uk/schools/starship/maths/games/place_the_penguin/big_sound/full.shtml> students place a penguin on a number chart in the 100s, tens or ones place. • Use an online abacus to make numbers at <http://www.ictgames.com/abacusInteger.html> or <http://www.bgfl.org/ bgfl/custom/resources_ftp/client_ftp/ks2/maths/bead/index.htm>. The website <http://www.familylearning.org.uk/place_ value_games.html> has a list of other online games.

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

Health and Physical Education

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152

100s

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• Play ‘abacus run’. Make an ‘abacus’ by placing three cones or other markers in a line, labelled (left to right) ‘Hundreds’, ‘Tens’ and ‘Ones’. Students line up behind a parallel line next to a collection of beanbags. Write various three-digit numbers on cards. Give one student at a time a card. Each must, one beanbag at a time, put the right number of beanbags next to the appropriate cones. For example, if given the number 271, the student would place one beanbag on the hundreds cone, seven on the tens and one on the ones. Alternatively, the abacus could be three baskets, and the students must throw the correct number of beanbags into the right baskets.

10s

1s

• Play ‘place value tag’. The students run, jump or skip in a defined area. Two students are ‘it’ and try to tag the other students. Once a student has been tagged, he or she must stand still. In order to move again, the student must answer a place value question the teacher (or a selected student) asks. Teachers can ask a question or show a card with one number highlighted. If the student can say what place value that number is worth (e.g. the 4 in 542 is four tens), they can move again.

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

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History

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• Draw three large rectangles on the ground with chalk or rope to make a place value grid. Label the columns (left to right) hundreds, tens and ones. Put students into groups of 10. Call out different numbers in which the digits add up to 10, such as 325, 154 or 244. The students must run out and the correct number stand in the sections of the place value grid.

• Find out more about the history of the abacus.

The Arts

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• Students can make their own beads from hard-drying dough or clay and paint. They can use them to create strings of 100 beads (10 white, 10 red etc).

• Students can make their own abacus. Each student will need four tongue depressors, 36 large beads, four bamboo skewers and wood glue. Lay one tongue depressor down and glue the four wooden skewers evenly along it. Glue another tongue depressor on top of the first one and the skewers. When dry, thread nine beads onto each skewer. Cover the other end of the skewers with tongue depressors, and glue. Use the abacus to count and represent numbers.

36

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

o c . che e r o t r s super

2 groups of 100

This is called the hundreds This is called the tens place. place.

The third digit tells us how many groups of tens there are in the number. This number has a ‘7’ in the tens place. So there are seven tens in addition to the one thousand and two hundreds.

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

R.I.C. Publications®

9 groups of 1

This is called the ones place.

The last digit tells us how many ones there are in the number. This number has a ‘9’ in the ones place, so there are nine ones.

www.ricpublications.com.au

There can only be up to nine groups in any place value. For example, you can’t have 10 ones in the ones place; a group of 10 ones (one group of ten) belongs in the tens place.

place. This means the 9 is a smaller number than the 2 because nine ones equals 9 and two hundreds equals 200.

m 7 groups of 10 . u Even though 9 is a ‘bigger’ number than 2, in the number 1279 the 9 is in the ones place and the 2 is in the hundreds

1 group of 1000

This is called the thousands place.

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The second digit tells us how many sets of one hundred are in the number. This number has a ‘2’ in the hundreds place. So there are two hundreds in addition to the one thousand.

© Australian Curriculum, Assessment and Reporting Authority 2012

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

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The first digit tells us how many groups of one thousand are in the number. This number has a ‘1’ in the thousands place. So there is 1 group of 1000.

Where a digit sit in a number tells us about its value.

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Teac 1279 her

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

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

RESOURCE SHEET

Explanation of the value of digits in their places

37


Partitioning numbers

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15 groups of 10 people

6 groups of 25 people

2 groups of 75 people

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Teac he r

Groups can be arranged to make them easier to count. One hundred and fifty people can be grouped (partitioned) in different ways; for example: • 1 group of 100 and 5 groups of 10 people

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m . u

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

. te6 ways to group the blocks. Write them o Take 100 blocks. Find below. c . c e her r 1. o t s s r u e p 2. 3. 4. 5. 6. Try the same with larger collections (e.g. 250, 310). 38

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

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


RESOURCE SHEET Place value bingo

0

1

2

3

4

ones

ones

ones

ones

ones

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Teac he r

9

ones

ones

ones

ones

ones

0

1

2

3

4

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

6

7

8

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CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

5

r o e t s Bo r e p o8k 6 7 u S

tens

tens

tens

tens 1

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9

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

o c 2 3 4. ch e r er o t s super

tens 5

hundreds hundreds hundreds hundreds hundreds 6

7

8

9

hundreds hundreds hundreds hundreds Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

R.I.C. Publications®

Place value bingo!

www.ricpublications.com.au

39


RESOURCE SHEET Place value on an abacus

The abacus is an ancient calculating tool. It is used to count and show numbers. It has three columns (bars). Each column has a different place value. On each column, beads can be placed.

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

This column shows how many groups of tens there are.

This column shows how many groups of ones there are.

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

T

O

O

H

T

O

50 + 3

200 + 1

100 + 20 + 4

2 hundreds and 1 ones

1 hundreds, 2 tens and 4 ones

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528

430

612

500 + 20 + 8

400 + 30

600 + 10 + 3

5 hundreds, 2 tens and 8 ones

4 hundreds and 3 tens

6 hundreds, 1 tens and 2 ones

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

This column shows how many groups of hundreds there are.

T

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Teac he r

H

© Australian Curriculum, Assessment and Reporting Authority 2012

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


Canteen order

The canteen lady needs to order food for the school canteen. Work out how many and what size bags she needs to order for the next week. Canteen How Number of items in a Number of each pack item many pack to order needed?

r o e t s Bo r e p ok u S 100 Pack

Muffins

L

ones

102 juicy

COOL

L

COO

L

COO

10 Pack

COO

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Apples

400

100 Pack

10 Pack

Icy poles

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juicy

juicy

juicy

ones

75

Muffins

Muffins © R. I . C .Publ i cat i ons ones • f o r r e v i e w p u r p o sesonl y• Yoghurt Pack

Loaves of bread

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Ham slices

83

m . u

95

tubs

Pack

ones

© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

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CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

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

o c . che e 350 r o t r s super

Cheese slices

290

Bread rolls

220

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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Arrow cards

Copy each different set onto card of a different colour (e.g ones yellow, tens orange, and hundreds green). Call out a number and students can make the number then describe the place value of the different digits.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

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


DATE:

1. Write the digits made by the groups shown. (a) 5 hundreds, 4 tens, 8 ones: (b) 3 hundreds, 0 tens, 1 ones: (c) 7 hundreds, 3 tens, 0 ones:

r o e t s Bo r e p ok u S (b)

(d) 1 hundreds, 7 tens, 9 ones:

2. Which number does each abacus show? Shade a bubble to show your answer.

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3. Shade a bubble to show your answer.

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(a) How many tens in this collection? 3 10 30

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© Australian Curriculum, Assessment and Reporting Authority 2012

NAME:

(a)

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

Assessment 1

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

o c . c e herin this collection? r (b) How many hundreds o t s su er 40 400 4 p (c) How many ones in this collection? 12 4 3 (d) How many tens in this collection? 900 90 9

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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NAME:

DATE:

1. Which is more? Write the answer. (a) 3 tens

or

2 tens and 9 ones?

(b) 2 tens and 9 ones

or

8 tens and 1 one?

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2. Partition each number. For example: 729 is

7

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(c) 6 tens and 2 ones

+

(a) 352 is

+

+

(b) 598 is

+

+

(d) 230 is

+

+

(e) 471 is

+

+

9

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3. Draw dots on the abacuses to represent the numbers.

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(d) 44

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(b) 364

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H

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(c) 109

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(e) 407

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

H

T

O

(f) 228 R.I.C. Publications® www.ricpublications.com.au

© Australian Curriculum, Assessment and Reporting Authority 2012

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

CONTENT DESCRIPTION: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

Assessment 2


Checklist

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

Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Understands that threedigit numbers are made of hundreds, tens and ones

Models and represents numbers on an abacus

Partitions collections to 1000

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Teac he r

STUDENT NAME

Groups collections up to 1000

© Australian Curriculum, Assessment and Reporting Authority 2012

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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45


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

Explore the connection between addition and subtraction (ACMNA029) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION

Commutativity

What does this mean

• When two numbers are added, the sum is the same regardless of the order of the addends; for example: 4 + 2 = 2 + 4

• Students need to become fluent with partitioning numbers to understand the connection between addition and subtraction. They need to see that 9 + 5 is equal to 5 + 9 and that 14 – 5 is 9 and 14 – 9 is 5. This knowledge should be extended into arrangements of 100 – 20.

Addend

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• This content description focuses on the importance of commutativity and that subtraction is the reverse of addition. • Students become familiar with the process of counting on to identify the missing element in an additive problem.

Teaching points

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• Any of the numbers that are added together in an equation; for example, in 2 + 3 = 5, the 2 and the 3 are addends.

• Students should be given the opportunity to break up any number up to 100 by using a variety of manipulative materials and then writing the corresponding addition and subtraction number sentences. • Students should also be given the opportunity to solve word problems which involve addition and subtraction. The important concept here is to work out the parts within the whole of the word problem.

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

• Students should be given the opportunity to solve number sentences that have missing elements and in which counting on could be used as a strategy for solution; e.g. 7 + ? = 10 or 6 + ? = 10.

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Student vocabulary part whole add

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What to look for • Students who see two numbers in a problem and automatically think they should be added.

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

sum plus equals addition subtraction minus (–)

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

HANDS-ON ACTIVITIES Rewind! Students can act out number problems, such as one child having 12 marbles then winning another 14 so he has 26. Students then ‘rewind’ the act to show how the same story can be a numeric subtraction problem; there were 26, 14 went away, and 12 were left. The students watching can work out and record both equations.

Dice games • Students roll two 10-sided dice and write as many facts as they can using the two numbers rolled. For example, 10 and 4 can be 10 + 4 = 14, 4 + 10 = 14 and 10 – 4 = 6.

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

• Students can roll two dice and try to find an addition or subtraction operation. For example, if they roll a 3 and a 9, they could write 3 + 6 = 9 or 9 – 6 = 3. • Roll two 10-sided dice. Add the two numbers together. Students have to work out how many more they would need to make 30, 40 or 50.

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• As an individual activity, students roll two six-sided dice, add the two numbers and record the result on a sheet of paper. Roll the dice again and add the sum to the numbers already recorded. The game continues until the student gets as close to 100 as possible. They can then answer questions such as, ‘Do you have more or less than 100? How many more/less?’ • Roll a 10-sided dice to get a number. Students then try to work out how many more they need to add to that number to read another number set by the teacher. Students could use a number line to count on to find the missing addend.

Partitioning practice

whole

Give students collections of (initially) 20 manipulatives, then later 100. (Coins, buttons, counters, tokens, building blocks, stacking cubes etc. could be used.) Ask them to break the collection into two different parts in as many ways as they can. They record their partitions. Compile the results on a large class chart. The teacher could also state a certain number and ask the students how many more they would need from that number to make 100. (Do this with other numbers, too.)

part

10

part

6

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Lots of problems

Give students the three digits of an addition problem (e.g. 7, 3, 4) and ask them to write as many different number sentences as they can using the numbers from the set. They should use both addition and subtraction; for example: 4 + 3 = 7, 3 + 4 = 7, 7 – 4 = 3, 7 – 3 = 4, 7 = 4 + 3, 7 = 3 + 4, 3 = 7 – 4, 4 = 7 – 3.

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Three-leaf number fact families (page 49–51)

Students can work in pairs, or teachers can use these with small groups. Copy and cut (laminate if desired) the individual cards. Cover one leaf and show the ‘clover’ to the students, who must work out the number that is covered. The last clovers have been left intentionally blank for teachers or students to create their own number families.

‘Make a number problem’ game (pages 52–53)

Give pairs or small groups of students two ten-sided dice: one numbered 1 to 10 and the other numbered 11 to 20 (or create dice using the templates on page 53). They roll the two dice, then make an addition or subtraction problem to match one of the numbers on their number board (three different boards on page 52). They then cover that number with a counter. The first student to cover a row or column wins.

‘Add to check’ Students make a tower of connecting blocks. They break off a certain number, then write or tell the corresponding subtraction sentence. They then put the tower back together to check their answer.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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47


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

HANDS-ON ACTIVITIES (CONT.) How many are missing?

Paper, scissors, rock

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Students work in pairs with a collection of manipulatives. One student counts out a set of, for example, 55 items. The other student records the total. The first student then takes some of the items while the other looks away (or closes his/her eyes) and puts them into a box or a paper bag. The first students then asks ‘How many are missing?’ The other student looks at the collection and works out the problem using either an addition or subtraction equation. Once he/she has an answer, the items are tipped out and counted to check. Students change roles and repeat the process.

Students play in pairs. After saying ‘paper, scissors, rock’ (or ‘one, two, three’), with one hand in a fist, swing it down on the count, and show a number of fingers on those hands both students raise. The players add the number of fingers together and record the score on a piece of paper. They have another turn and keep adding for 5 rounds. The students can record their different totals on a sheet of paper and discuss the scores, or add up a total score.

Balancing to find the answer

Equations are sums that are balanced (the same) on either side of the equals sign (=). Demonstrate this using a balance scale, and even-weighted small blocks or counters (or other small manipulatives). Ask students to place counters on the scales to represent a certain equation, such as 8 + ?= 17 or 17= ?+ 8. They place eight blocks in the left pan and 17 in the right pan. They then solve the equation by adding blocks one at a time and counting as they go. Ensure the students record their equations. Students could try to mentally work out the problem first, then check it using the scales.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• LINKS TO OTHER CURRICULUM AREAS

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English

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• Read Math-terpieces: The art of problem-solving by Greg Tang. Find the solutions to the puzzles by using different maths skills, such as subtracting in order to add.

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Information and Communication Technology

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• Allow the students to design and create their own ‘fact family’ questions, or word problem worksheets for classmates to solve using word processing and desktop publishing software. • Play games such as at making the number 10 in different ways at <http://www.ictgames.com/save_the_whale_v4.html>, or counting on to identify missing elements in problems to 20 at < http://www.ictgames.com/funkymum20.html> • Students can practise making fact families at <http://www.ezschool.com/Games/FactFamily1.html>

Health and Physical Education

• Give each student a black marker and a sheet of A4-size card on which a number is written. Students skip or walk etc. in a defined area. When the teacher calls ‘Stop!’ the two students closest to each other make three different equations using their numbers. They each write the equations on the back of their sheet of card.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET Three-leaf number fact families (3 to 13) (Cover one corner up with and work out the missing number by adding on or subtracting.)

0

5 – + 6 – +

3

5

3

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4

5 – +

0

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1

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6 – +

2 r 3 0 6 o e t s B r e oo p 6 7 7 u – – S3 + 3 0 + 7 1 +–k6 1

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

4

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4

2

4 – +

12 – + 13 – +

6

10

13

3

1

12 – + 13 – +

9

12

4

2

12 – + 13 – +

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

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10 – + 11 – + 12 – + 12 – + 13 – +

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RESOURCE SHEET Three-leaf number fact families (13 to 19) (Cover one corner up with and work out the missing number by adding on or subtracting.)

5

2

7

8

4

9 50

16 – + 16 – +

10

17 – + 17 – + 18 – + 18 – +

14 – +

6 – +

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2

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5 t 9r 6 8 7 7 o e s B r e oo p 15 15 15 15 k –u – – – S + + + + 1 14 2 13 3 12 4 11 4

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

18 – + 19 – +

11

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3

18 – + 19 – +

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

CONTENT DESCRIPTION: Explore the connection between addition and subtraction

15 – +

11

6

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3

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8

13 – +

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© Australian Curriculum, Assessment and Reporting Authority 2012

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


RESOURCE SHEET Three-leaf number fact families (19 to 22) (Cover one corner up with and work out the missing number by adding on or subtracting.)

4

9

3

8

20 – +

16

11

5

20 – +

14

6

19 – +

13

7

20 – +

19 – +

12

20 – +

1 r 19 2 18 o e t s B r e oo p 20 20 20 u – – S5 + 15 6 + 14 7 +–k 13 0

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20 – +

20

10

0

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8

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

20 – +

10

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15

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20

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R.I.C. Publications®

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CONTENT DESCRIPTION: © Australian Explore the Curriculum, connection Assessment betweenand addition Reporting andAuthority subtraction 2012

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

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RESOURCE SHEET ‘Make a number problem’ dice game – add or subtract (playing boards)

15

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1

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4

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p u S 3 14

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My number sentences:

1

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My number sentences:

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2

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

CONTENT DESCRIPTION: Explore the connection between addition and subtraction

19

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My number sentences:

© Australian Curriculum, Assessment and Reporting Authority 2012

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


RESOURCE SHEET

Teac he r

‘Sum answers’ game – add or subtract (10-sided dice to make)

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CONTENT DESCRIPTION: © Australian Explore the Curriculum, connection Assessment betweenand addition Reporting andAuthority subtraction 2012

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

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

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

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET Word problems (solve using counting on)

Story

Pictures

Number sentence

A new console game costs $42. Tim has $31. How much more money does he need?

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Teac he r

r o e t s Bo r e Harry has 20 plants, p o u k but needs 44 to fill S the garden. How

© Australian Curriculum, Assessment and Reporting Authority 2012

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

many more does he need? In the class of 24 students, 15 had dogs as pets. The rest had cats. How many students had cats as pets?

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Sarah has 17 jellybeans. Josie has 14 more than Sarah. How many jellybeans does Josie have?

o c . che e r o t r s super

Mrs Stanley made 45 cupcakes. She put icing on 24 of them. How many more did she have to ice? 54

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

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Alex had 25 collector cards. Albie gave him some more and now Alex has 37 cards. How many did Albie give him?

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


RESOURCE SHEET The relationship between addition and subtraction Addition is about the whole in terms of its parts; we add the parts together to find the whole.

8 + 12 = 20 part part whole

+

=

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

part

whole

Rearranging the parts doesn’t change the whole. Once you know the answer to one sum, you know the answer to its reverse.

Teac he r

12 + 8 = 20 8 + 12 = 20

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CONTENT DESCRIPTION: © Australian Explore the Curriculum, connection Assessment betweenand addition Reporting andAuthority subtraction 2012

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

=

Subtraction is about a part missing from a whole.

Take away part. =

20 – 8 = 12 whole part part

© R. I . C.Publ i cat i ons •f orr evi ew pur pos esonl y• Take whole

part

Rearranging the parts doesn’t change the whole, but you must start the sum from the whole.

20 – 12 = 8 20 – 8 = 12

away part. = part

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

whole You can see that these addition and subtraction number sentences use the same numbers (8, 12 and 20).

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This is because addition and subtraction are connected: if two numbers add up to a third number, then either number subtracted from the third number equals the missing number. If you see this sum: 20 – 12 =

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you could find the missing part by doing the sum ‘backwards’:

+ 12 = 20.

You can use addition (counting on) to find out the answer. 20 – 12 =

?

is the same as 12 +

12

13

14

? 15

= 20, so count on from 12 to 20:

16

17

18

19

20

=8

In this way … if

3 + 7 = 10,

then

7 + 3 = 10,

10 – 3 = 7

and

10 – 7 = 3

if

4+2=

6,

then

2+4=

6,

6–4= 2

and

6–2= 4

if 50 + 60 = 110,

then

60 + 50 = 110,

110 – 60 = 50

and

110 – 60 = 50 .

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

NAME:

DATE:

1. Work out the missing number in each number sentence. (a) 10 +

= 22

(b) 20 +

= 25

(c) 30 +

= 39

(d) 14 +

= 29

(e) 12 +

= 22

(f) 25 –

=5

r o e t s Bo r e p (k) 23 – = 15 o (l) 23 – 8 = (j) 22 – 12 = u Ssentences for the following sets ofk 2. Write four number numbers. = 30

4, 8, 12

(a)

(h) 29 –

4 + 8 = 12

= 14

8 + 4 = 12

9, 3, 6

(i) 22 –

12 – 8 = 4

= 10

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(g) 39 –

© Australian Curriculum, Assessment and Reporting Authority 2012

Assessment 1

12 – 4 = 8

© R. I . C.Publ i cat i ons (c) 20, 15,• 5f orr evi ew pur posesonl y• (b) 10, 7, 3

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(a) Aiden had made 11 party bags but needed 23. How many more did he need to make? (b) Noa needed $30 to buy a new game. She had saved $19. How much more money did she need to save? (c) Tia’s class had 35 students. Connor’s class had 22. How many more students were in Tia’s class? 56

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3. Add on to solve the number stories. Show your working out, then shade the bubble.

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$11 $49 $36

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CONTENT DESCRIPTION: Explore the connection between addition and subtraction

(d) 23, 7, 16


Checklist

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

Explore the connection between addition and subtraction (ACMNA029)

Solves word problems involving addition and subtraction

Develops fluency in partitioning numbers

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

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Teac he r

STUDENT NAME

Uses counting on to solve number problems with missing elements

© Australian Curriculum, Assessment and Reporting Authority 2012

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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www.ricpublications.com.au

57


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

Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION

Commutativity

What does this mean

• The ability to change the order of equation without changing the end result. When two numbers are added, the sum is the same regardless of the order of the addends; for example: 4+2=2+4

• Students should become fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10. The focus here is on solving addition and subtraction mentally.

• A line with points that have numerical value Equation

• A sentence stating that two expressions equate to the same number; for example: 9 + 11 = 20, or 9+7=8+8

• Students need to be able to model and represent simple additive and subtractive situations using materials such as 10 frames, 20 frames and empty number lines.

Teaching points

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Number line

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• Students should be given opportunities to break apart numbers (partition) using initially a ten frame to show the combinations of 10 and then two ten frames to show the combinations of 20.

• Students should be given the opportunity to solve and record the results of equations using a variety of written tools and methods; e.g. a number line. • Students should be given the opportunity to learn the concept of doubling through the use of two ten frames. This knowledge should be used when solving facts such as 7 + 5. The addition problem 7 + 5 could be thought of as 10 + 3 (using the combination of 10 solution) or 6 + 6 (using partitioning or doubling).

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Mental strategy • To break any whole number into whole number parts

• A strategy used to resolve a problem performed in one’s head, using knowledge and understanding

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Written strategy

• A problem-solving process in written form. When the individual steps are recorded they assist in the identification of errors

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• Students should also be given the opportunity to solve ‘near double’ number problems, using doubling as the strategy; e.g. 9 + 8 could be thought of as 10 + 7 (using the combination of 10 solution) or 9 + 9 – 1 or 8 + 8 + 1 (using partitioning and doubling).

What to look for

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Partition

• Students who have trouble counting by ones to 20 or skip counting by twos or threes. Students who have difficulty partitioning any numbers up to 20. Students who need to have materials to answer basic addition and subtraction for combinations to 10.

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• Students who do not understand the commutativity of addition. • Students who do not have a conceptual understanding of subtraction; for example, believe that 4 – 6 = 2.

Student vocabulary number line add subtract

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

double 10 frame

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

HANDS-ON ACTIVITIES Activities and games to practise 10 facts • Call out a number, for example ‘7’. Students call back the number that would be required to add to 10, in this example ‘3’. Continue with different combinations of numbers. Ask the students to then subtract that number from 10, making clear the connection between addition and subtraction. Teachers could also draw or hold up ten frames showing different numbers, with which students need to say or clap how much is needed to make 10. • Using playing cards (number cards only, with ace equalling 1), students play in pairs. Each student holds half the pack in his/her hands face down. At the same time, both students turn over one card each and place them face up between them. If the pair of cards equals 10, the players try to be the first to say ‘snap’.

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Activities and games to practise ‘doubles’

• Roll a dice. Students work out and record what the double of that number is.

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• Working in pairs with two ten frames and some counters, one student places counters on one ten frame. The other student must place counters in the same place on his/her ten frame and add up the doubles as quickly as possible. Both students record the equation.

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• Give the students pictures of things in the environment that include doubles; for example: an egg carton (6 + 6 sections), two hands (5 + 5 fingers), two weeks on a calendar (7 + 7), a spider (4 + 4 legs), a truck (10 + 10 wheels), a symmetrical building (8 + 8 windows). Students can identify the doubles, then count and record them.

• Make pairs of equal length in stacks or columns of Unifix™ or interlocking cubes. Students count one tower, find its pair, then calculate the double (work out how many there are altogether).

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

• Practise using the ‘almost double’ strategy with frames and counters. Give students sums such as 5 + 6 (use the ‘gloves’ on pages 63–66) and counters. Ask them to place the counters on the ten frames and discuss how 5 + 6 is the same as 5 + 5 + 1 or 10 + 1.

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• Play the ‘Double trouble game 1’ (page 67). Copy the spinner onto thick card, cut it out and use an arrow and a split pin. (Attach the arrow to the spinner using the split pin, placing a bead between the arrow and the spinner to allow the arrow to spin freely.) Give four students one number card each. They spin the spinner and place a counter on the sum of the double spun. The first student to have covered five counters in a row (going across) or column (going down) is the winner. Once students have become more fluent with doubles, they can play the second game (page 68) where they use doubles to solve subtraction problems.

Commutativity and number fact cards (pages 63–66)

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• Cut pairs of gloves into two individual sums. Hand out the sums to the students. They then try to find the classmate who has the same sum reversed, but can only do so by asking other students if they have one of the three numbers their sum has (both addends and the answer).

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• Copy and cut the individual gloves. On pieces of card that are the same size and shape, write one answer to each sum. Give half the class the questions and the other half the answers, placing the cards face down on their tables. On your word, the students turn over their cards then try to find the student with the matching answer or question.

• Give individual students a number of cut-out gloves. They glue them on a chart according to the sum of the two numbers.

• Use the number lines on page 16 of this book to solve simple addition and subtraction problems, or use an online number line at <http://www.ictgames.com/numberlineJumpMaker/index.html>.

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

HANDS-ON ACTIVITIES (CONT.) Activities and games to practise adding 10: • The website <http://www.ictgames.com/submarinenopad2.html> has an interactive game for two players. Players must add 10 to numbers correctly in order to ‘fire’ at their opponent. • Give each student two dice. They use the two numbers rolled to create a two-digit number; for example, a 5 and a 2 could be 25 or 52. The students then add 9 to that number using the ‘adding 10’ strategy (see page 62). • Play ‘Nearly ten’ (page 70). Each student has two ten frames and 20 counters. Copy the ‘9 + ‘ or ‘8 +’ sums onto card and cut each out. Place these sums face down. Students take a ‘9 +’ (or ‘8 +’) card and make the two addends, each on a separate ten frame with counters. They then rearrange the counters on the frames to make a ten and complete the second number sentence. Students then record both number sentences.

r o e t s Bo r e p ok u S 8+5

=

10 + 3

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• Play ‘Sink the submarine’ (page 69). Each student will need a playing board and access to enough ‘bomb blasts’ to cover the page. Copy and cut the question cards and ‘bomb blasts’ before the game. Students take one question card from a pile lying face down and solve it using doubles. They put a bomb blast on the number and return the question card to the bottom of the pile. The first student to get four bomb blasts in a row sinks their submarine and is the winner.

LINKS TO OTHER CURRICULUM AREAS

English

• Read Double the ducks by Stuart J Murphy. Discuss what doubling means and practise doubling items in your classroom, such as windows or doors.

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

Information and Communication Technology

• Practise facts to 10 at <http://primarygames.com/math/mathlines/index.htm> or partitioning to make 10 in order to add at <http://www.ictgames.com/spacejumps.html>

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Health and Physical Education

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• The website <http://www.coolmath-games.com/0-number-twins/index.html> has a game where a number is chosen (such as 10), then the students find pairs of numbers that add to that number.

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• Students can practise addition sums using the near doubles strategy at <http://www.ictgames.com/dinosaurDentist/index.html> or <http://www. ictgames.com/robindoubles.html>

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• Play an online bingo machine with various adding and subtracting questions, with printable student bingo cards, at <http://www.ictgames.com/numberFactsBingo/index.html>

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• Draw a grid on the ground such as the one opposite. The students have to jump across the grid starting from one number then jumping on the double of that number.

• Play ‘adding doubles hopscotch’. Draw a hopscotch grid as usual, with numbers up to 10. However, instead of hopping through it on one foot, students will hop twice on one foot and once on both feet, while saying, ‘1 + 1 is 2’, ‘2 + 2 is 4’ and so on, depending on what numbered box they are in.

The Arts • Sing ‘Inchworm’ (also known as ‘The inch worm’), originally performed by Danny Kaye in the film Hans Christian Andersen. The chorus is ‘Two and two are four; four and four are eight; eight and eight are sixteen; sixteen and sixteen are thirty-two’.

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

RESOURCE SHEET Strategies for addition and subtraction Commutativity When adding, we combine parts to make a whole. Rearranging the parts doesn’t change the whole. This is called commutativity. For example, 5 + 20 = 25 is the same as 20 + 5 = 25. Use commutativity to make it easier to count by starting with larger number first. 10 + 1 = ? is the same as 1 + 10 = ?, only easier to count on.

Doubles

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1+1=2

2+2=4

3+3=6

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A double is a number sentence where the same number is added to itself. Having a ready knowledge of doubles helps us work out other number sentences more easily. 4+4=8

Knowing doubles can also help solve subtraction problems. For example, because we know 4 + 4 = 8, we also know that 8 – 4 = 4.

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

Near doubles

Once you know doubles, you can use them and count up or down by 1 to find a near double. With the sum 5 + 7, you can move 1 from the 7 to the 5 to make 6 + 6.

+

(= 12)

If 4 + 4 = 8, then 5 + 4 is one more, which equals 9 (count up one).

5+4=?

7+8=?

=

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CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

If you know 9 + 9 = 18, then you should also know that 18 – 9 = 8.

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If 8 + 8 = 16, then 7 + 8 = 15 (count down one).

You can do the same for subtraction.

With the sum 13 – 6 = ?, we know 6 + 6 = 12 and 12 – 6 = 6.

The number 13 is one more than 12, so the answer is one more than 6 (7).

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RESOURCE SHEET Strategies for addition and subtraction (continued) Adding ten When adding 10, the ones digit stays the same but the tens digit increases by one.

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When you are adding a number that is close to 10 (such as 9), sometimes it can be easier to add 10 then take away (subtract) 1. First add 10: 47 – 1 = 46

37 + 10 = 47 so

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Use a hundreds board to practise.

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37 + 9 = 46 .

Do the same for 8, except add 2 instead of 1.

Building to 10

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52 – 10 = 42

Then subtract 1:

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When subtracting 10, the same rule applies; the ones digit stays the same, while the tens digit decreases by one.

37 + 9 = ?

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10 + 7 = 17

21 – 10 = 11

2

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When adding, you can move some numbers over to make (or build) a 10 in the sum to make it easier to add (usually from the larger number). For example, with the sum 8 + 4, build to 10 by moving 2 from the 4 to make 10 + 2. 8+4

10 + 2

8 Move 2 to make 10:

Then take away 4 again.

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You can also use 10 to help when subtracting. 14 – 8

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Take away 4 to make 10.

14 – 4 – 4 = 6

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

5 + 10 = 15

1

© Australian Curriculum, Assessment and Reporting Authority 2012

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


RESOURCE SHEET Commutativity and addition number facts to 20

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RESOURCE SHEET Commutativity and addition number facts to 20

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

10 + 3

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

CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

0 + 10

© Australian Curriculum, Assessment and Reporting Authority 2012

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


Commutativity and addition number facts to 20

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

6 + 11

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Commutativity and addition number facts to 20

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

14 + 6 7 + 13

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© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

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


Double trouble game 1 (addition using doubles)

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

2+2

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RESOURCE SHEET Double trouble game 2 (subtraction using doubles)

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Put a counter over that number on your number board. Try to be the first to fill a row or column with counters. R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

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


‘Sink the submarine’ game. Enlarge and make one copy per student. Playing board

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

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Player 2

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Nearly ten (See page 60—use with counters.)

9 + 1 = 10 +

=

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9 + 2 = 10 +

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9 + 9 = 10 +

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9 + 3 = 10 +

o c . che e r o t r s8 + 6 = 10 + e 8 + 5 =s 10u +p = r

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8 + 9 = 10 +

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RESOURCE SHEET

CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

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


NAME:

DATE:

1. Decide whether each equation is true or false. Shade the bubble. (a) 5 + 15 = 15 + 5 (c) 6 + 7 = 6 + 6 + 1

True

False

True

False

(b) 9 + 3 = 10 + 2 (d) 4 + 5 = 5 – 4

True

False

True

False

r o e t s B r (a) 9 + 5 = 10 + e (b) 8 + 2 = 10 + o (c) 7 + 3 = 10 + p ok u (e) 8 + 9 = 10 + (f) 8 + 5 = (d) 8 + 7 =S 10 +

2. Finish the number problems.

(g) 9 +

= 10 + 2

(h)

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Assessment 1

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

+ 3 = 10 + 2 (i) 9 + 4 =

+ 10 + 10

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CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

3. Show the number problems on the number line and write the answer.

. t+ 2 = o 5 + 5e c . che e r o t r s super 20 – 11 = 0

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4. Double each number below and write the answer; e.g. the double of 9 is 18. (a) 3

(b) 6

(c) 10

(d) 7

(e) 4

(f) 5

(g) 1

(h) 8

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NAME:

DATE:

1. Write four number problems sums to describe each block picture;

e.g.

7 + 3 = 10

10 – 7 + 3

10 – 3 = 7

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questions.

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=9

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(b) 9 + 8 =

(c) 9 + 9 – 1 =

(e) 7 + 5 =

(f)

(h) 20 – 5 – 5 =

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+ 21 = 30 = 20

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

CONTENT DESCRIPTION: Solve simple addition and subtraction problems using a range of efficient mental and written strategies

Assessment 2


Checklist

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

Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Uses 10-frames, 20-frames and number lines to add and subtract

Uses 10 facts to solve simple addition and subtraction problems

Uses adding 10 and ‘nearly 10’ to solve simple problems

Builds to 10 to help solve simple addition and subtraction problems

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Uses ‘doubles’ to solve simple addition and subtraction problems

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

Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What does it mean

Multiplication • An operation calculated by finding the product of two numbers, the multiplier and the multiplicand (repeated addition) Array

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• An arrangement of objects into rows and columns Repeated addition

• A way of conceiving of multiplication as repeated addition of the multiplier by a given number

• Students should represent array problems by modelling with available materials, then explaining reasoning and recording the result • Students should be able to visualise a group of objects as a unit and use this to calculate the number of objects in several identical groups

Teaching points

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• Students need to be exposed to situations which show multiplication as repeated addition, groups and arrays

• Students should learn to recognise a range of problem types to which multiplication applies

• Introduce multiplication as ‘repeated addition’ by using a range of materials (including money) and diagrams

• Students need to be given situations which show multiplication as groups and arrays • Give students the opportunity to use multiplication when exploring a number with counters or other materials.

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• Check for students who continually use repeated addition when solving multiplication-type problems.

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

HANDS-ON ACTIVITIES Grouping • Explain to the students how grouping can make counting easier. Using concrete materials, ask them to make (for example) four groups of five, and record it as 4 x 5. They skip count to find how many there are altogether. • Give each student an empty egg carton and a collection of small manipulatives, such as coins, beads, buttons, paperclips, raw pasta, shells or small pompoms. State a multiplication problem (such as ‘6 times 2’, or ‘make 4 groups of 5’) which the students display using different sections of the egg carton. They can skip count to find the answer and record it. • Use connecting blocks, which students can group together in different ways.

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• Roll two dice. Ask the students to make groups of counters using the two numbers rolled. For example, if a 6 and 2 are rolled, students make six groups of two or two groups of six. The students calculate how many there are, using skip counting, and record using the multiplication symbol.

Making arrays

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• Students can colour in arrays on empty grids (page 77) or graph paper. With a problem such as 3 x 4, students would colour three rows with four squares in each row. They can turn the page sideways to see how the problem can also be presented as 4 x 3.

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• Once students understand grouping, they can move on to arrays to understand 5 × 4 not as five separate groups, but as a collection made up of five rows of four objects. Give students a collection of counters or other small manipulatives. Tell them you have (for example) 12 dots arranged in an array. Ask them to think what the array might look like. The students create possible arrays, such as one row of 12, six rows of two, two rows of six, four rows of three or three rows of four. Use other numbers. Encourage the students to describe their arrays using words such as three sets of four, three lots of four or three groups of four.

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• Make the connection between repeated addition and multiplication using calculators. Ask the students to add 5 + 5 + 5 + 5 + 5 and record the answer. Then they can use multiplication (5 x 5) and compare the results.

Concentration/Memory games (Arrays)

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• Play memory games with arrays (page 79). Copy the page onto card and cut out each array card. Place the cards facedown in a grid. Students try to find matching arrays to make a pair. For example, the 5 x 4 array and 4 x 5 array would be a pair. To keep the pair, the student needs to say how many dots are in the array altogether (e.g. for 5 x 4, there are 20 dots). • Play a different version by also using the cards on page 78. Copy the page onto card, then cut and laminate each picture and multiplication problem. Place all the cards facedown in a grid pattern. Students try to find matching pairs of array pictures and sums.

Dice activities

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• Students use two dice, pencils and an empty grid (page 77). They take turns to roll the two dice. Using the two numbers rolled, they colour in a matching array on grid paper. They try to be the first to colour in the grid paper. • Give small groups of students six six-sided dice. One student (or the teacher) tells another to create a multiplication problem using numbers 1 to 6, such as 4 x 5. That student must then arrange four lots of dice, each with the number 5 showing.

Lions vs tigers game • Students play in pairs with one game board (page 80), two dice, plastic counters and either the 27 lion or 27 tiger ‘counters’ (copy and cut out page 81). They roll the two dice and make an array of plastic counters using the two numbers rolled to find the product. They then place their lion or tiger counter on that number on the playing board if it is available. They continue until all the numbers are covered. The player with the most animal counters on the board is the winner.

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

LINKS TO OTHER CURRICULUM AREAS English • Read books involving simple multiplication such as: 2 x 2 = boo!: A set of spooky multiplication stories by Loreen Leedy; Under the sun and over the moon’ by Kevin Crossley-Holland; Too many kangaroo things to do! by Stuart J. Murphy; Ten times better by Richard Michelson; Grandpa’s quilt by Betsy Franco-Feeney (Author); How many ants? by Larry D. Brimner; Amanda bean’s amazing dream by Cindy Neuschwander; and The King’s commissioners by Aileen Friedman.

Information and Communication Technology • At <https://www-k6.thinkcentral.com/content/hsp/math/hspmath/ca/common/mega_math_9780153663963_/ megamathcd1/cm/launch.html?strActivityName=g13_1_2_W&strAssignID=1> students can make arrays, then count them.

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• Play games such as counting items in arrays at <http://www.harcourtschool.com/activity/space_arrays/>, <http://www. multiplication.com/flashgames/Bakery.htm> or <http://www.learnalberta.ca/content/me3us/flash/lessonLauncher. html?lesson=lessons/08/m3_08_00_x.swf>

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• Write numbers up to 10 and the operation symbols for addition, subtraction, multiplication and division on large sheets of paper and give one sheet to each student. Call out a number and have students form small groups that equal that number. For example, if you call out ‘six’, a student holding a 2 and a student holding a 3 tag a student holding a multiplication sign; or students holding a 5 and 1 tag a student holding an addition sign. • When playing games, talk about different ways the students can be grouped. For example, with 30 students ask: ‘We need to make five equal-sized groups. How many students will be in each group?’

The Arts

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• Find out what different numbers of musicians in a group are called (duet, trio, quartet, quintet, sextet, septet, octet, nonet and dectet). Investigate why two-member rock and pop bands are uncommon, or make a list of bands with four members to count by fours.

• Students can draw, paint or make a collage of monsters or aliens which match certain number sentences. For example, if the number sentence is 3 x 4, they could draw three monsters each with (for example) four horns.

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• Find arrays or groups of objects in nature, such as six legs on insects, or the three leaves of a clover plant. Make charts with these images to practise skip counting. (See below.)

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RESOURCE SHEET Blank grid for colouring, shading or cutting out arrays

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RESOURCE SHEET Concentration/memory game (arrays and sums)

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3x4

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4 x 10

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CONTENT DESCRIPTION: Recognise and represent multiplication as repeated addition, groups and arrays

4x5

3x5

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RESOURCE SHEET Matching arrays memory or snap game

Array match

Array match

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Array match

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Array match

Array match

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Array match

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RESOURCE SHEET Lions vs tigers game board

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CONTENT DESCRIPTION: Recognise and represent multiplication as repeated addition, groups and arrays

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


RESOURCE SHEET Lions vs tigers game counters

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RESOURCE SHEET Multiplication problems (Give individuals or pairs of students a problem to solve by drawing pictures or arrays on a separate sheet of paper, or with counters.)

1. James’ family orders 4 pizzas to eat every Friday. Each pizza is cut into 4 slices. How many pizza slices do they get? 2. Jemma planted 3 rows of sunflower seeds. She put 6 seeds in each row. How many seeds did she plant?

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3. Tran had a block of chocolate. The block had 5 rows and each row had 6 pieces. How many pieces of chocolate were there?

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4. One move ticket costs $10. How much would it cost for 6 people to go to the movies? 5. Peter gave his mum some flowers. There were 6 flowers. Each had 6 petals. How many petals were there altogether?

6. Jack had some hens. Each day, they laid 6 eggs. How many eggs did Jack collect each week (7 days)? 7. In Luke’s street there were 5 houses. Four people lived in each house. How many people lived in the street?

© R. I . C.Publ i cat i ons f o r evi ewforp r po sesThey on l y 9. Alexa and• Ben putr out some chairs theu school assembly. set out• 4 rows of 6 seats. How many people could sit down?

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10. If there are 9 rows on the bus and each row seats 4 people, how many people can sit on the bus? 11. The local swimming club had 7 members competing in a swimming competition. If each member swam in 3 races, how many races did the club have swimmers in?

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o c . chmoney e 13. The Year 2 class were raising by cleaning the tyres onr cars in the school e o t carpark. If each car had 4 wheelsr and there were 8 cars, how many tyres did they s s r u e p clean?

12. Owen was making cupcakes. The cupcake tin he was using had 5 rows. Each row had 3 cupcake holders. How many cupcakes could he make with the cake tin?

14. One spider has 8 legs. How many legs do 5 spiders have? 15. Each student in Year 2 was asked to bring in $2 for an excursion. If there were 20 students and they all gave their money to the teacher, how much money did the teacher collect? 16. Mark invited 3 friends over. Each friend brought 3 console games. How many games did Mark’s friends bring altogether? 82

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CONTENT DESCRIPTION: Recognise and represent multiplication as repeated addition, groups and arrays

8. There were 10 bikes in the bike rack at school. If each bike had 2 wheels, how many wheels were there?


DATE:

1. Draw a picture or array of each problem. Write the problem with numbers, then the answer. (a) A carpark has three rows of parking spaces, each with 10 spaces. How many cars can use the carpark?

(b) Ice-creams are $3 each. How much money would you need to buy five ice- creams?

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(d) One taxi can take four passengers. How many passengers can five taxis take?

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(e) Leah made four bracelets. Each bracelet had 10 beads. How many beads did she use?

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NAME:

(c) Finley filled each section of a muffin tray with muffin mix. The tray had four rows of four muffin pans. How many muffins did he make?

CONTENT DESCRIPTION: Recognise and represent multiplication as repeated addition, groups and arrays

Assessment 1

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

(f) Ben wanted to give each boy in his class three chocolates for Easter. There were 10 boys. How many chocolates did Ben need to buy?

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NAME:

DATE:

1. Shade the bubble.

(ii)

(iii)

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(a) Which array below shows 3 groups of 5? (i)

(ii)

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(b) Which array below shows 4 groups of 3?

(i)

2. What do the arrays below show? (a)

4 x 3 16 x 4 4 x 4

(b)

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4 x 3 16 x 1 4 x 4

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4 x 6 16 x 1 4 x 4

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3x2

(b) 10 + 10 + 10 + 10

4x5

(c) 2 + 2 + 2

5x4

(d) 4 + 4 + 4 + 4 + 4

6x3

(e) 3 + 3 + 3 + 3 + 3 + 3 •

4 x 10

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

© Australian Curriculum, Assessment and Reporting Authority 2012

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

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CONTENT DESCRIPTION: Recognise and represent multiplication as repeated addition, groups and arrays

Assessment 2


Checklist

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

Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)

Uses skip counting to solve multiplication stories

Calculates the number of objects in equal groups

Represents array problems with manipulatives and drawings

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STUDENT NAME

Understands a group of objects can be seen as a unit

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

Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS Division

What does this mean

• An operation where one number (the dividend) is divided by another number (the divisor) to get a third number (the quotient).

• Students should be able to divide the class or a collection of objects into equal-sized groups.

Sharing (in division)

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• Students should be able to identify the difference between dividing a set of objects into three equal groups (known as sharing) and dividing the same set of objects into groups of three (known as grouping).

Grouping (in division)

Teaching points

• Dividing an object or set of items into groups of a certain number or size.

• The language of division (grouping and sharing) is important and students should be involved in activities where mathematical manipulatives (such as counters) are use to represent division situations.

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• Students should be able to solve simple problems using both these types of division.

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• Dividing an object or set of items into equal groups.

• Link sharing to using sharing grids and then link this to number sentences that describe the mathematics of sharing; e.g. ‘Three boys had 15 lollies to share. How many lollies will each boy get?’

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

Student vocabulary set divide groups of

• Students who think three divided by six (3 ÷ 6) is the same as six divided by three (6 ÷ 3). Students need to practise their understanding of division as being where a number or item is separated into equal parts or amounts, then link this understanding to how division can be represented with symbols and number sentences.

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

HANDS-ON ACTIVITIES Division activities using counters and other manipulatives • Give the students counters when solving number problems such as ‘Twenty-four soldiers were getting ready to march in a parade. How many different ways could they arrange themselves into equal rows?’, or ‘If you had 16 marbles, how many friends could you share them with so that you all had the same amount?’ The students show as many different solutions as possible, using counters, pictures, numbers and/or words. • Give students a collection of counters. Show an opaque bag or container (or envelope) and tell the students that you have a certain number (e.g. 12) of counters. Then ask ‘If I divided them into (for example) three equal groups, how many counters would be in each group?’ Students work out the problem with counters.

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• Using a given number of counters or other manipulatives, students make equal groups. For example, ask the students to take 20 counters and make five equal groups. Then ask the students to count how many there are in each group by using skip counting. Ask students to write a number sentence and use a calculator to check their work. • Give the students a certain amount of straws divisible by three and ask them how many triangles they can make with them. Then give students an amount of straws divisible by four and ask them to do the same activity with squares.

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counters equally into the carton, how many • Give students empty egg cartons and ask questions such as ‘If I put would be in each section?’ or ‘If I wanted to fill section/s with counters, how many counters would be in each section?’ Students find answers to these questions using the materials provided and record them as division problems.

Divisions in the class

Count the number of tables or desks in the classroom. Students work out the different arrangements of equal groups that could be made from the desks. Challenge students to create a better functioning classroom layout using the groupings they make. Do the same with other items, such as basketballs (‘If we have six basketballs, how many students will need to share one ball?’), books etc.

Lego™ blocks

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Provide students with different sizes of Lego™ blocks. Give each student a long block (e.g. eight bumps long) and ask them to build an equal-sized row on top using a kind of smaller block, such as with two or four bumps. Ask: ‘How many groups of two fit evenly along the eight? What about four?’ Ask the students to record their findings using the ÷ sign: 8 ÷ 4 = 2, 8 ÷ 2 = 4. Let the students experiment with the different combinations they can make. Similarly ask them to use a small collection of Lego™ people and share that collection. For example, if there are four cars to use and eight people, how many people can go into each car?

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• Give students 12 Unifix™ cubes joined as a tower. Ask them to break it (divide) up into three equal-sized towers. After counting how many cubes are in each small tower, they record their results as a division equation. Rejoin the tower and divide it in other ways, such as into four, six, two or 12 towers. Discuss the connection among these equations. • Students can make block towers behind a screen or barrier. They give a partner on the other side of the barrier a brief description of the towers, then ask questions such as ‘I built three towers using 27 blocks. How many blocks are in each tower?’ The partner draws or creates towers to find the answers.

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

HANDS-ON ACTIVITIES (CONT.) Division word problems (pages 93-94) Cut out and give individuals or pairs of students a problem to solve using counters or other small manipulatives. (Students will need 40 counters.) They could also use playdough to solve some of the questions.

Sharing grids (pages 90-92) Cut out the different sharing grids. Give students counters, wrapped lollies or other items. Different numbers can be written in the space provided, depending on students’ ability. Using the grids, ask the students to share the number of items among the number of people. Students record their answers using appropriate symbols.

r o e t s Bo r e p ok u S LINKS TO OTHER CURRICULUM AREAS

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• Students can write their own division stories, using topics or items of interest to them.

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• Read Bean thirteen by Matthew McElligott, One Hungry cat by Joanne Rocklin, Everybody wins! by Sheila Bruce, The doorbell rang by Pat Hutchins and Divide and ride by Stuart Murphy.

• Find examples of other uses of the word ‘divide’ in literature. For example, dividing words into syllables, or in sentences in newspapers, such as ‘Community divided over council decision’. Discuss what this means and how it can be different from the mathematical definition.

Information and Communication Technology

• At <http://www.ngfl-cymru.org.uk/vtc/grouping_and_sharing/eng/Introduction/StarterActivity.htm> there is an interactive activity that shows how to divide using both sharing and grouping. The website <http://www.ictgames.com/ airlineGrouping/airlineGrouping.html> has an interactive activity where students practise repeated subtraction to divide.

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• Find out where the Great Dividing Range is in Australia. Research when it was first seen by European settlers and who gave it its current name.

The Arts

• The students can dramatise division stories they have written. Provide simple props such as a table, chairs and plastic plates and food for a cafe setting, or students can make their own props (such as menus). • Allow students to solve number stories using division with craft materials, such as ribbons or beads. For example, provide the students with string to make a necklace and ask them to draw or write a design for a necklace using 30 beads placed in equal-sized patterns based on colour. The students work out how many beads of the different colours they will need as part of their plan.

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Explanation of division

Division

÷ When we divide something, we break it into smaller, equal parts. We know how much of something there is, and how many parts (or portions) it needs to be made into. We want to find out how many or much will be in each part.

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among four friends. How many chocolates did each friend get?

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We can solve this problem by sharing the chocolates out, one by one. Then we count how many each person got. The number sentence for this problem is 12 ÷ 4 = 3. This is also called sharing. We also use division when we know how much we have and how much or many will be in each part (or portion). We want to find out how many parts there will be.

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RESOURCE SHEET

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CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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

Abbie had a bag of 12 lollipops. She wanted to give her friends three lollipops each. How many friends could she give lollipops to?

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We can solve this problem by taking away groups of three from the collection of 12. Then we count how many groups we made. The number sentence for this problem is 12 ÷ 3 = 4. This is also called grouping or repeated subtraction.

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Sharing grids (Teacher writes a number in the space provided.)

equally between 2 people.

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equally among 3 people.

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Share

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RESOURCE SHEET

CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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


equally among 7 people

equally among 6 people

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Share

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Share

equally among 5 people

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Sharing grids (Teacher writes a number in the space provided.)

Share

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RESOURCE SHEET

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CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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91


Sharing grids (Teacher writes a number in the space provided.)

equally between 8 people.

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Share

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET

CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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


Division word problems – Sharing

Cut out and give individuals or pairs of students a problem to solve with counters (students will need 40 counters). 1. Three friends had lunch in a cafe. All up, their food cost $18. How much did each person have to pay?

3. Ethan won a packet of 40 stickers and decided to share them among his 8 friends. How many did each friend get?

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r o e t s Bo r e 2. Mrs Jones had ap bunch of 30 flowers. ok u She divided them equally into 2 vases. S How many did she put in each vase?

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4. 4 children were sharing a block of chocolate that had 24 pieces. How many pieces of chocolate did each child get?

5. Three children got $12 for helping out in the garden. How much money would they each get when they shared the money out?

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CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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

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6. Hannah made 10 cupcakes. She had 30 chocolate drops to decorate them with. How many chocolate drops could she put on each cupcake?

7. Tia bought a pack of 12 seedlings. She had 4 pots to put them in. How many seedlings could she put in each pot? 8. Mrs Thomas brought home a packet of 15 biscuits for her 3 children to share. How many biscuits did each child get? Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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Division word problems – Grouping

Cut out and give individuals or pairs of students a problem to solve with counters (students will need 36 counters).

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9. Tim was making 4-wheeled cars with his Lego™ blocks. He had 16 wheels. How many cars could he make? 10. Sophie found 25 cm of ribbon. She wanted to cut it into pieces 5 cm long. How many 5-cm pieces could she cut? 11. The sports teacher wanted to make teams of 6. There were 30 students in the class. How many teams of 6 could be made? 12. Liam was making party bags. He had 40 lollies to put in. He wanted to put 4 lollies in each bag. How many bags could he make? 13. Faith spent $16 on cakes. Each cake cost $2. How many cakes did she buy?

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14. A group of friends shared the cost of lunch. The lunch cost $35 and each person paid $7. How many people shared the food? 15. Harry was packing 36 muffins into boxes. Each box could take 6 muffins. How many boxes could he fill? 16. There were 24 students in the class. The teacher wanted 6 students to sit at each table. How many tables did the teacher need to put in the classroom?

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

24?

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© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

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


2

8

6

r o e t s Bo r e p ok u S 2 children How much money

(b) 14 Easter eggs

7 children

How many eggs will each child get? 3 2 4

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will each child get? $5 $1 $4

2. Divide each group by breaking it into equal groups.

2 pencils for How many people © R. I . C.P u b l i c a t i o n s each person get pencils? ofo 2)s •f orr evi ew (groups pur p esonl y 10 6 •8

(a) 16 pencils

(b) 18 eggs

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6 eggs in 1 carton (groups of 6)

How many cartons can be filled? 1 3 5

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© Australian Curriculum, Assessment and Reporting Authority 2012

NAME: DATE: 1. Divide each group by sharing it evenly between or among the number of people or things shown. Shade the bubble. (a) 12 balls 2 ball bags How many balls in each bag?

(c) $10

CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

Assessment 1

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

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(c) 15 tickets

3 tickets for 1 ride (groups of 3)

How many rides? 4

5

3. 6 cupcakes need to be decorated evenly with the decorations listed below. How many of the decorations will each cake get? 2

(a) 12 sugared flowers 1 2 (b) 18 Smarties™

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(c) 6 Maltesers™ (d) 24 liquorice bits R.I.C. Publications®

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NAME:

DATE:

1. Shade the bubble. (a) Mark has 9 balloons to share among his 3 friends. How many balloons will each friend get? 3

5

7

3

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7

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20 ÷ 4 =

(c) How many $3 muffins can Harry buy with $12? 3

4

5

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9÷3 = (b) How many groups of 4 different kinds of chocolates are there in this box of 20?

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

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(d) A flock of 16 birds shared 4 nests. How many birds could fit evenly into each nest?

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16 ÷ 4 =

20

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4

15 ÷ 3 =

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

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(e) Three children had to share one pack of 15 biscuits. How many did each child get? 5

DOLLAR

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12 ÷ 3 =

(f) Fiona put 24 books out evenly on 3 shelves. How many books did she put on each shelf? 24 ÷ 3 = 96

10

12

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

CONTENT DESCRIPTION: Recognise and represent division as grouping into equal sets and solve simple problems using these representations

Assessment 2


Checklist

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

Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Solves simple division stories or word problems

Divides a collection of objects into equal-sized groups of a certain number

Divides a collection of objects into a certain number of equal-sized groups

(÷)

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STUDENT NAME

Identifies the symbol for division

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Answers

Sub-strand: Number and Place Value

3. (a)

N&PV – 1

(b)

(c)

Page 17 Assessment 1 H

1. (a)

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10 11 12

13 14 15 16

17 18 19 20

(b)

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10 11 12

13 14 15 16

17 18 19 20

3

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9

10 11 12

13 14 15 16

17 18 19 20

(b) 25 (f ) 120 (b) 30c

(c) 92 (g) 11 (c) 70c

Page 18 Assessment 2

327 (b) 535 (c) 706 1000 (e) 152 (f ) 1111 239, 324, 456, 701 (b) 199, 210, 232, 408 465, 781, 990, 1001 (d) 112, 149, 200, 211 330 (b) 152 (c) 1006 420 (e) 257 (f ) 319

424 527

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(c) 1001 (f ) 250 (b) 611, 532, 501, 499 (d) 663, 636, 396, 366 982 (c) 753 853 (f ) 741

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Page 43 Assessment 1 1. (a) 548 2. (a) 391 3. (a) 3

(b) 301 (b) 215 (b) 4

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N&PV – 4

1. (a) (e) (i) 2. (a) (b) (c) (d) 3. (a) (b) (c)

12 (b) 5 (c) 9 (d) 15 10 (f ) 20 (g) 9 (h) 15 12 (j) 10 (k) 8 (l) 15 3 + 6 = 9, 6 + 3 = 9, 9 – 3 = 6, 9 – 6 = 3 7 + 3 = 10, 3 + 7 = 10, 10 – 7 = 3, 10 – 3 = 7 15 + 5 = 20, 5 + 15 = 20, 20 – 5 =15, 20 – 15 = 5 7 + 16 = 23, 16 + 7 = 23, 23 – 16 = 7, 32 – 7 = 16 Teacher check working out, answer 12 Teacher check working out, answer $11 Teacher check working out, answer 13

N&PV – 5 Page 71 Assessment 1 1. (a) true 2. (a) 4 (e) 7 (i) 3

(b) true (b) 0 (f ) 3

(c) true (c) 0 (g) 3

(d) false (d) 5 (h) 9

3. (a)

0

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=7

(b)

0

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9 10 11 12 13 14 15 16 17 18 19 20

= 19

(c)

0

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9 10 11 12 13 14 15 16 17 18 19 20

=6

(d)

0

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9 10 11 12 13 14 15 16 17 18 19 20

= 15

(e)

0

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9 10 11 12 13 14 15 16 17 18 19 20

= 12

(f ) 0 1 4. (a) 6 (f ) 10

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(c) 730 (c) 703 (c) 12

(d) 179 (d) 876 (d) 9

2

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(b) 12 (g) 2

7

8

9 10 11 12 13 14 15 16 17 18 19 20

(c) 20 (h) 16

(d) 14 (i) 4

=9

(e) 8

Page 72 Assessment 2

Page 44 Assessment 2 1. (a) 3 tens (c) 6 tens and 2 ones

(b) 8 tens and 1 one

2. (a) 352 is

3

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+

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(b) 598 is

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(c) 622 is

6

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(d) 230 is

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(e) 471 is

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230 (b) 171 (e) 921, 738, 137, 128 669, 485, 473, 202 410 (b) 962 (e)

N&PV – 3

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(d) 8 (c) 60, 65, 70 (f ) 63, 65, 67

Page 32 Assessment 2 1. (a) (d) 2. (a) (c) 3. (a) (d)

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Page 56 Assessment 1

Page 31 Assessment 1 1. (a) (d) 2. (a) (c) 3. (a) (d)

H

(e)

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1. (a) 40 (b) 12 (c) 20 2. (a) 9, 7, 5 (b) 22, 26, 30 (d) 93, 103, 113 (e) 80, 70, 60 3. Teacher check.

N&PV – 2

(d) 30

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(d)

1. (a) (b) (c) 2. (a) (f ) 3. (a) (f )

6 + 4 =10, 4 + 6 =10, 10 – 6 = 4, 10 – 4 = 6 1 + 9 = 10, 9 + 1 = 10, 10 – 1 = 9, 10 – 9 = 1 2 + 8 = 10, 8 + 2 = 10, 10 – 2 = 8, 10 – 8 = 2 21 (b) 61 (c) 24 (d) 31 (e) 45 58 (g) 19 (h) 24 (i) 34 (j) 9 9 (b) 17 (c) 17 (d) 17 (e) 12 9 (g) 10 (h) 10 (i) 13

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Answers

Sub-strand: Number and Place Value

N&PV – 6 Page 82 Resource Sheet – Multiplication problems 1. 4. 7. 10. 13. 16.

4 x 4 = 16 10 x 6 = 60 5 x 4 = 20 9 x 4 = 36 4 x 8 = 32 3x3=9

2. 5. 8. 11. 14.

Page 83 Assessment 1

3. 6. 9. 12. 15.

5 x 6 = 30 6 x 7 = 42 4 x 6 = 24 5 x 3 = 15 20 x 2 = 40

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Teacher check drawing, 3 x 10 = 30 Teacher check drawing $3 x 5 = $15 Teacher check drawing 4 x 4 = 16 Teacher check drawing, 4 x 5 = 20 Teacher check drawing, 4 x 10 = 40 Teacher check drawing, 3 x 10 = 30

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1. (a) (b) (c) (d) (e) (f )

3 x 6 = 18 6 x 6 = 36 10 x 2 = 20 7 x 3 = 21 8 x 5 = 40

Page 84 Assessment 2 1. 2. 3. 4.

(a) (iii) (b) (i) (a) 4 x 4 (b) 4 x 3 Teacher check the arrays (a) 5 + 5 + 5 + 5 • (b) 10 + 10 + 10 + 10 • (c) 2 + 2 + 2 • (d) 4 + 4 + 4 + 4 + 4 • (e) 3 + 3 + 3 + 3 + 3 + 3 •

N&PV – 7

(c) 4 x 6 • • • • •

3x2 4x5 5x4 6x3 4 x 10

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Page 93 Resource Sheet – Division word problems – Sharing 2. 30 ÷ 2 = 15 5. 12 ÷ 3 = 4 8. 15 ÷ 3 = 5

3. 40 ÷ 8 = 5 6. 30 ÷ 10 = 3

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1. 18 ÷ 3 = 6 4. 24 ÷ 4 = 6 7. 12 ÷4 = 3

Page 94 Resource Sheet – Division word problems – Grouping 9. 16 ÷ 4 = 4 12. 40 ÷ 4 = 10 15. 36 ÷ 6 = 6

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Page 95 Assessment 1 1. (a) 6 2. (a) 8 3. (a) 2

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10. 25 ÷ 5 = 5 13. 16 ÷ 2 = 8 16. 24 ÷ 6 = 4

(b) 2 (b) 3 (b) 1

11. 30 ÷ 6 = 5 14. 35 ÷ 7 = 5

(c) 5 (c) 5 (c) 3

(d) 4

(c) 4

(d) 4

Page 96 Assessment 2 1. (a) 3 (e) 5

(b) 5 (f ) 8

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

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What does it mean

Fraction • A fraction is part of a whole (an object or set of objects) that has been divided into equal parts Numerator

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Denominator

• The number underneath the line that shows how many equal parts the whole (item or collection) is divided into Partitioning

• Students need to see and demonstrate that a 2-D shape such as a square can be folded into two equal pieces called halves, four equal pieces called fourths (or quarters), or eight equal pieces called eighths. • Students need to make the link that a half is the same as two-fourths/quarters or four-eighths. Students should understand that this is the same as doubling or division by two; however, the problem with this doubling idea makes the result smaller rather than bigger as is the case with whole numbers.

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• The top number in a fraction, representing how many parts of the whole there are

• Students should be able to show different ways to demonstrate fractions of halves, quarters and eighths by folding a variety of 2-D shapes.

• Students should be able to link the idea to the symbols of ½, 2⁄4, 4⁄8.

• Students should also be able to partition collections such as counters into halves, fourths/quarters and eighths; e.g. ½ of 8 counters is 4 because you have to divide the whole (8) into two equal groups; i.e. the same as dividing by 2, a fourth/quarter of 8 is two because the whole 8 needs to be divided into four equal parts so on.

Teaching points

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• Dividing or separating a whole into parts, pieces or sections

• Students demonstrate one-half using a variety of 2-D shapes that can be easily folded and then drawn. Link the fraction to the symbol ½ and be able to demonstrate the amount/number by folding and drawing.

• Do the same with fourths/quarters and eighths and link the fraction size to the symbols ¼ and 1⁄8.

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Student vocabulary whole half/halves

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• Show how one-half is equal to two-fourths/quarters through paper folding and link this to eighths. Students should be able to demonstrate this and draw the result. • Students should be able to recognise the fraction ½, ¼, 1⁄8 in drawings.

• Introduce the idea of ½, ¼ and 1⁄8 using a collection involving multiples of 2, such as 8 or 16 (both can be partitioned into eight equal groups). Show with counters and drawings.

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

• Students have trouble with this concept because the idea of skip counting is reversed; rather than the quantities getting bigger, they get smaller even though the same numbers (2, 4, 8) are used. • Students have troubling folding into fourths/quarters so they need to be given plenty of opportunities to fold into halves and then onto fourths. They need to show how to fold fourths without help from the teacher and, therefore, they need to be able to demonstrate fourths without being told to fold into halves. • Students have trouble transferring the ½, ¼, 1⁄8 the part–whole relationship to the concept of partitioning a collection in equal groups. They fail to realise that the whole has changed and now is not a 2-D square but a group of 8 counters.

quarter/quarters eighth/eighths collection fair sharing

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Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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

HANDS-ON ACTIVITIES Fractions in everyday life Discuss and show examples of the instances in everyday life when fractions are used. For example, the students will have heard of items being advertised as being half price; would use fractions when they look at a clock and see it’s ‘half past’ or ‘a quarter to’; when they have half a glass of juice left; or use ¼ cup of sugar in a recipe. Students might notice how the game Trivial Pursuit™ has a player token with six small wedges that form a whole ‘pie’; that they can buy a halfdozen eggs; or see that ½ of the eggs in a pack were cracked. They might have a whole cupcake; or be able to buy half of a large cake at a cake shop. They might have their sandwiches cut into quarters; play netball on a court divided into thirds; or play king ball/four square in a court divided into four; order a half-serve of chips; or notice that a lunch box is divided into parts.

Hands-on materials

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• Use playdough to make pizza, a chocolate bar or a cake and cut it into halves, quarters and eighths using plastic knives. Ask the students to roll 8 ‘sweets’, then to divide the collection in half. Repeat with other numbers, such as dividing a collection of four into fourths. Discuss how dividing a collection or object again and again into parts makes each part smaller. • Use interlocking cubes; for example, ask each student to create a tower of 10 connected cubes. Then ask them to divide the tower into two equal parts, or halves. • Fold paper in different ways to create different fractions; for example, fold a square of paper in half on the diagonal, then in half to create two rectangles. Discuss how although each half looks different, they are equal halves.

Dividing fairly

Discuss how fractions are equal parts of a whole. The parts you divide a whole into must be equal to be considered ‘fair’. Allow the students to use manipulatives to find solutions to scenarios, such as sharing a bar of chocolate with a friend who has divided the bar into unequal pieces.

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Paper planes and origami

Use the language of fractions to fold a sheet of paper into sections to create a paper plane or simple origami figures. Talk about folding the paper in half or folding the top corner down to the middle to make a quarter. Discuss the different ways to fold the paper to make a half.

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Spin and make a pizza (page 103)

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Copy and enlarge the game pieces (pizza slices and empty pizza trays) onto card and cut each out. Make one spinner using thick card and a split pin. Each student in a pair or group of three has an empty pizza tray. Students spin the spinner and collect that fraction of pizza, then put it on their tray. They try to be the first to fill their tray neatly (without going over 1 whole). Discuss the different ways a whole can be made.

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Cheddar chase game (pages 106–107)

Reproduce and enlarge the game and its playing pieces onto card. Cut and laminate the player pieces (mice), matching player cheese mats, cheese fractions and whole cheeses (make two sets of the cheese pieces). To play, students each choose a mouse and matching cheese mat. Place the cheese pieces (1⁄8, ¼, ½) in one pile, and the whole cheese in another. Students take turns to roll a dice and move their playing piece. The fraction they land on indicates the size of cheese they take to put onto their cheese mat. When a player has filled his or her mat (without overlapping), he/she puts the fractions back into the central pile and takes a whole cheese. The person who reaches the finish with the most whole cheese is the winner.

Fraction dominoes (page 105) Enlarge, cut and laminate the domino cards on page 105. Students take five cards each. One domino card is placed in the middle. The students try to match one of the fractions shown with a picture, word or set of symbols that shows the same fraction. Teachers could also cut the dominoes in half and place them facedown in a grid. Students turn two cards over at a time and try to find a matching fraction.

Fractions bingo (page 108) Copy and cut one bingo card for each student. Write ¼, ½ and 1⁄8 on separate pieces of paper (four of each, so there are 12). Draw these fractions one by one at random and call out. Students place a counter or cross out that fraction if they have it.

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

LINKS TO OTHER CURRICULUM AREAS English • Read Eating fractions by Bruce Mcmillan, Give me half by Stuart J Murphy, Picture pie by Ed Emberly, Apple fractions by Jerry Pallotta, and Gator pie by Louise Mathews. • Learn the meaning of phrases or sayings that use fraction terms, such as ‘half-hearted’, ‘my better half’, ‘it’s all good’, ‘six of one, half a dozen of the other’ or ‘a fraction of the price.’ • Divide narratives into parts. For example, identify four parts (a beginning, an event, a resolution and an ending) in a familiar story. • Sort words according to how many parts they can be broken into; for example, words with four parts such as opposition, motorcycle, kilometre and television.

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Information and Communication Technology

Health and Physical Education

• Introduce the students to the game of four square (sometimes called ‘king ball’). See <http://www.youtube.com/ watch?v=wL4cA7rNofc> Discuss what would happen to the game if the playing areas were not divided into equal-sized parts.

History and Geography

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• Play games at the websites <http://www.ngfl-cymru.org.uk/vtc/ngfl/ngfl-flash/fractions/fractions.html> or <http://primarygames.com/fractions/start.htm>

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• Find out about the significance of occasions when a flag is lowered to half mast (as a sign of mourning), such as on Anzac Day.

The Arts and Design

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• Look at the effect of dividing an artwork into different parts, such as some of Andy Warhol’s artworks or various triptych pictures. (See Frederick McCubbin’s ‘The pioneer’ at <http://www. australiantraveller.com/images/galleries/1679/011culture15.jpg>) • The students can design a fruit platter (for example, for a class party). What would be the best way to provide equal shares of different fruits for groups of two, four and eight children? How could the students ensure everyone gets an equal share?

Science

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• Make mixtures involving the combination of different amounts of materials; for example, make an orange juice mixture comprising one-quarter water compared to one that is one-quarter juice. Describe the differences in taste, smell and appearance. • Look at and draw a full moon and half moon.

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Spin and make a pizza (halves, quarters and eighths)

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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

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

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One-quarter, one-half and one-eighth explained

Two people are sharing this pizza. It is cut into two equal pieces. Each piece is called a half (½). Two halves make one whole.

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Half a packet of cheese

r o e t s B r e ocan be folded Half ap glass A piece of papero k ways. ofu into halves in different Swater

Four people are sharing this pizza. It is cut into four equal pieces. Each piece is called a fourth (¼). Four quarters make one whole. A quarter is less than a half.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• A fourth of the biscuits

A piece of paper can be folded into four fourths in different ways.

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A quarter of an hour

o c . c e hr r Eight people are sharing this e o t s super pizza. It is cut into eight equal pieces. Each piece is called an eighth (1⁄8). Eight eighths make one whole. An eighth is less than a quarter and less than a half.

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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

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


Fractions dominoes (match pictures, symbols and words)

1 4

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

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Cheddar chase – game pieces 1 8

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Each player takes a player mat and matching mouse. Roll a dice and move on the board (page 107). Take the fraction of cheese you land on. When the mat is full, put the pieces back and take a whole cheese. The winner is the player who has the most whole cheeses.

1 2

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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

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


Cheddar chase – game board

1 8

1 8

1 4

1 2

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1 4 1 1 2 8 8 1 1 1 1 2 8 4 2 1 1 © R. 1i I . C.Publ i cat ons 1 8 4 8 son 4 •f orr evi ew pur pose l y• 1 1 1 1 8 8 4 8 1 1 1 1 4 8 8 8 1 1 1 1 2 2 4 2 1 1 1 1 1 8 4 8 8 4 1 1 2 8 1 1 1 1 1 1 8 8 2 8 4 8

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

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Bingo (call out ½, ¼ or 1⁄8)

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RESOURCE SHEET

CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

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


RESOURCE SHEET Problem cards (give each student a card and manipulatives to solve the problems)

The Year 2 class visited a pet shop. The children enjoyed seeing the kittens and puppies the most. They counted 8 puppies and kittens. Of all the animals, 1⁄8 were kittens. The rest were puppies. How many puppies were there?

The class was having an end-of-year party. They made pizzas to share. Tom, Ava, Axel and Ruby shared one pizza fairly among themselves. Savindu and Ella shared another pizza fairly between themselves.

© R. I . C.Publ i cat i ons 1. What fraction ofv pizza didp Tom get? •f orr e i ew ur posesonl y• 2. What fraction of pizza did Ella get?

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3. Who got more pizza, Axel or Savindu?

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measuring. How many ½ cups of flour would they need to put in to make one whole cup?

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r o e t s Bo r Tonia and Frank weree cooking a cake. They p ok needed to put 1 u (whole) cup of flour into the Sonly find a ½ cup to do the bowl. They could

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Connor had 8 biscuits. He gave ½ of his biscuits to his friends. How many did Connor have left?

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o c . Ben and Lara hadc four solar panels on their e her r o roof. During a big storm, ½s of the panelss t r upe were blown off the roof. How many panels did they have left on the roof? David had a lunch box that was divided into 4 equal parts (fourths). He had a different food in each part. He had carrot sticks in one part, an apple in another, jam sandwiches in the third and celery in the last part. What fraction of his lunch box had fruit in it? Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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NAME:

DATE: Shade the bubble

1. Write the missing numbers to show: (b) one-half.

(a) one-fourth.

(c) one-eighth.

r o e t s B r e oo 2. Which fraction is shaded? p u k (a) (c) S (b) 2 2

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3. What fraction of pizza will each child get if it is shared fairly? (a)

1 2

4. (a)

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1

1 4

2 1

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2 1

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(b) How many eighths make a whole?

8

1

0

(c) How many halves make a whole?

1

2

5

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(d) Which symbol means ‘one whole’? 110

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

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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

Assessment 1


DATE:

1. Write what fraction of each collection is shaded. (c) (b) (a)

2. Shade the shapes to show the fraction. 1 1 (a) 4 (b) 8

r o e t s Bo r e p ok u Sdoes each coloured section of the flags show? 3. What fraction

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(b)

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(c)

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© R. I . C.Publ i cat i ons 4. The children have a part of a chocolate bar. •f orr evi ew pur posesonl y• Sophie –

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Joe –

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Jenna –

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(a) Shade how much of the bar they each have.

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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

Assessment 2

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

. te o 5. The farmer needs separate fields for his animals. . c cdivide e r (a) Draw lines toh the farmer’s lando fairly into separate fields for e t r s s r pe the different animals. u (b) Draw a circle around the person who has the most chocolate.

(b) Write the fraction of the land each animal gets

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Checklist

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

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Understands the greater the number of parts, the smaller the fraction (fraction numbers are different from counting numbers)

Reads and writes symbols for 1⁄8, ¼ and ½

Shades or draws pictures to represent ½, ¼ and 1⁄8 or objects and collections

Identifies ½, ¼ and 1⁄8 using concrete materials

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STUDENT NAME

Partitions (divides) collections to create fractions

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Answers

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

Page 110 Assessment 1 1. 2. 3. 4.

(a) (a) (a) (a)

¼ ½ ¼ 4

(b) (b) (b) (b)

½ 8⁄8 1⁄8 8

(c) (c) (c) (c)

1⁄8 ¼ ½ 2

(d) 1

Page 111 Assessment 2 (b) ¼ (b)

3. (a) 4⁄8 4. (a)

(b) ½

(c) 1⁄8

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1. (a) ½ 2. (a) (c)

5. Sheep’s field – any of the following:

Each sheep gets ½ of the field. Cows’ field – any of the following:

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Each cow gets ¼ of the field.

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

Count and order small collections of Australian coins and notes according to their value (ACMNA034) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What does this mean

Value • The estimated or assigned worth of something in terms of the amount of other things for which it can be exchanged Denomination

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• One grade in a series of designations of value Currency

• Any form of money used as a medium of exchange Money

• Denomination of currency (notes and coins) issued as a medium of exchange or payment

• Students need be able to recognise coins and amounts from pictures of money and to select a range of coins to make certain amounts of money; e.g. two five-cent coins have the same value as one 10-cent coin • Students need to be able to count collections of coins or notes to make up particular values, such as those shown on a range of price tags.

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• Students need to know what each coin looks like and its value. They need to be able to skip count by 5s, 10s, 20s, 50s and understand that there are 100 cents in a dollars .

• Students should be able to use their understanding of partitioning and apply the same strategy to money collections.

Teaching points

• Students need to be given the opportunity to count (skip count) amounts of money using plastic coins or real money. They need to be able to state how much they have at the end of the count. This count can be supported by the 1–120 board.

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

• They need to be able to exchange any given monetary amount with a variety of coin collections (partitioning); e.g. ‘Show $2.00 using a mixture of coins. How else could you make $2?’

• Students need to be shown how to keep a record of a collection of coins by drawing.

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• Play place value coin games using a coin place value grid and coin dice in which coin amounts can be substituted for notes whenever possible.

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coins

• Keep a lookout for students who seem to have trouble with some of the fundamental principles of counting. In particular, help those who are confused by different arrangements of a given collection of coins; e.g. that a 4-by-3 arrangement of 10-cent coins is of the same value as a 2-by-6 arrangement of 10-cent coins. In such cases, have the students count out the amount of coins in each collection so they realise that the last number reached in each count is what shows how many coins there are in each collection (as well as the monetary worth of the collection).

notes

• Watch for students who have trouble with skip counting.

Student vocabulary dollars cents

value gold silver cash money

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• The collections that students manipulate should be extended to include a variety of amounts from $2.00 to $5.00; e.g. ‘What coins could you use to show $3.75? Can you show it another way?’

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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

HANDS-ON ACTIVITIES Money dice Students work in groups of four or five with one dice and a collection of five-cent coins. Students take turns to roll a dice. With each roll they collect that number of five-cent coins. After four rolls they count how much money they have. If a student has 20 or more five-cent coins, ensure he/she says ‘one dollar’ when counting instead of ‘100 cents’. Repeat the game using 10-cent coins. Students could record the activity using repeated addition; for example: 5c + 5c + 5c + 5c + 5c + 5c = 30c. Use the ‘Give and take game’ (page 127) to practise counting coins of one denomination. Play a number of times, changing the denomination each time.

Make a dollar

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Once students are able to count multiples of one kind of coin, move on to counting different denominations. Give a small group of students a shared collection of different coins and a six-sided dice. Prepare a chart such as the one adjacent showing the action to take with each number rolled on the dice. The students take turns rolling the dice and try to be the first to get exactly a dollar (without going over).

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Number rolled

Concentration (pages 122–123)

Action

1

Take a 5c coin.

2

Take a 10c coin.

3

Take a 20c coin.

4

Take a 50c coin.

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Cut out the cards with the amount written and the amount shown in coins and dollars. 5 Miss a turn. The students take turns turning two cards over and trying to find the matching amount 6 Take any coin. (see pages 122–123). Use the cards with the images of coins on them to play ‘Who has more?’ Deal the cards between two players. Each player turns one card face up at the same time and the players determine who has more money. They player with the most keeps both cards.

Dragon’s gold game (page 119)

Enlarge the game onto A3 card and laminate for durability, if desired. Students will need a dice, a counter each and a large collection of 10c, 20c and 50c coins. The students take turns to roll the dice and move their counters. They collect a coin to the value of that shown on the space they land on. When a student has collected exactly one dollar, he or she swaps the silver coins for a $1 coin. The winner is the student who, at the end of the game, has collected the most $1 coins.

© R. I . C.Publ i cat i ons School canteen (page 124)r •f or evi ew pur posesonl y•

Copy the page and cut out each item. Students can make up the amount shown using plastic coins or real money. Students could also be given an amount of money and work out which items they could buy.

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Enlarge, cut and laminate the cards of toys and price tags. Students can take one card each and make the amount shown on the price tag with coins and notes. The students could also order a selection of the cards from least expensive to most expensive. Students could try to find which items they can buy with a given set of coins or particular Peta’s Pizza Parlour note. Small pizza

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How much do I have?

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Students work in pairs with a collection of coins and/or notes. One student makes an amount using the coins or notes and shows it to the other. The other student counts how much money there is and writes it down, using the dollar or cents sign as appropriate. The student reads the amount to the first student.

Pizza shop (page 126) Copy the page onto card, cut and laminate each coin/note, and laminate the top section (with the menu and prices) separately. If necessary, give the students a pile of coins and notes to count out the amounts. They put each money card next to the correct item on the menu according to its price.

$6.50

(three toppings) Large pizza (four toppings)

$10.00

Family deal: Two large pizzas, 1.25 L soft drink and one garlic bread

$25.50

Double deal: 2 large pizzas with 4 desserts and a 1.25 L drink

$28.00

3 small pizzas

$16.00

Garlic bread

$4.00

Salad

$6.00

Soft drink (1.25 L bottle)

$1.90

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

LINKS TO OTHER CURRICULUM AREAS English • Discuss sayings or phrases about money, such as ‘A penny for your thoughts’, or ‘I’m not made of money’. • Read My rows and piles of coins by Tololwa M Mollel and discuss the way the boy sorts and counts his coins. • Read Small change by Rob Lewis. Discuss how the value of coins, rather than the size, helps us decide what to do with them.

Information and Communication Technology • <http://www.rosettaprimary.tased.edu.au/mathsobjects/waysOfmaking.htm> has an interactive activity where students can practise making amounts with different coins.

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• Play a game at <http://www.practicalmoneyskills.com/games/moneymetropolis/>, where students can ‘earn money’ by doing jobs and save it to buy certain items.

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The Arts

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• Discuss the designs on coins and notes. Find out what the designs represent. Students can make their own designs, stating the reason for their choice of images and words. • Discuss the commemorative designs often found on 20c, 50c and $1 coins.

Science

• Find out what materials Australian coins are made from. Discuss how and why the composition of coins changes over time, as materials become more or less expensive. • Find out more about the animals that feature on Australian currency.

• Australia was the first country in the world to have a complete series of polymer notes. Find out more about this material and what makes it good for making notes.

© R. I . C.Publ i cat i ons History and Geography •f orr evi ew pur posesonl y• • Discuss special times of the year when money might be given as a gift, such as Chinese New Year or Christmas.

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• Find out more about the people that feature on Australian currency. What role did they play in Australia’s history?

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• Look at past issues of currency from Australia. Discuss the change from the imperial to the decimal system. Students can order coins of the same denomination from different years in chronological order.

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• Design and make a container for keeping money. The students will need to decide if the money can be taken out easily or not, depending on the needs; for example, if it is purely for saving, it might be better for it to not be as easy to open as one that is designed to have money both put in and taken out frequently.

Economics and Business

• Discuss the ways people earn money. The students can discuss goods and services. • Visit a mint and find out about making and collecting coins.

Civics and Citizenship • Run a class stall to raise money for a charity, appeal or other cause. The students can decide how the items being sold are to be priced, how the money will be stored and how they can best count the money they make.

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

RESOURCE SHEET Australian coins and notes

5c

10c

five cents

ten cents

$0.05

$0.10

20 cents twenty cents $0.20

$1 r o e t s B r e o one dollar o fifty cents p u k $1.00 $0.50 S

$2

50c

two dollars

$5

five dollars $5.00

© R. I . C.Publ i cat i ons $10 •f orr evi ew pur posesonl y • ten dollars

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$2.00

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$20

twenty dollars

$20.00 o c . che e r o $50 r st super fifty dollars $50.00 $100

one hundred dollars $100.00 Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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RESOURCE SHEET Counting coins DOLLAR DOLLAR

1. Put the coins that are the same together.

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

DOLLAR

2. Make groups.

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50c and 50c make $1. So together, these four coins make $1.

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These two coins make $1.

3. Count the coins (usually from the largest denomination to the smallest).

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$2

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$1

DOLLAR

+

$1

+

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

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RESOURCE SHEET Dragon’s gold game Roll a dice. Collect the coin shown on the space you land on. When you have collected a dollar’s worth of coins, swap them for a $1 coin from the dragon’s cave. The person with the most $1 coins at the finish wins.

Start

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

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RESOURCE SHEET

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Can you find other ways to make 50c?

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

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Equivalent amounts – 1

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


© Australian Curriculum, Assessment and Reporting Authority 2012

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

RESOURCE SHEET Equivalent amounts – 2

Can you find other ways to make $2?

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DOLLAR

DOLLAR

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DOLLAR

Can you find other ways to make $5?

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DOLLAR

DOLLAR

DOLLAR

DOLLAR

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RESOURCE SHEET Concentration cards – Amounts in numbers and coins (enlarge to A3)

70c

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55c

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DOLLAR

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

$1.00

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© Australian Curriculum, Assessment and Reporting Authority 2012

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


RESOURCE SHEET Concentration cards – Amounts in numbers and notes (enlarge to A3)

$10

$20

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p u S

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ok

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

r o e t s Bo r $25 e

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School canteen – Items with price tags ($0.50–$5.00)

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RESOURCE SHEET

CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

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


RESOURCE SHEET Toy shopping – Items with price tags ($5–$30)

$15

$20 $19

$30

r o e t s Bo r e p ok u S $25 $5.50

$24

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$29

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

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$25.40

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Pizza shop (Match the money to the correct price)

Peta’s Pizza Parlour Small pizza (three toppings)

$6.50

Large pizza (four toppings)

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Family deal: Two large pizzas, 1.25 L soft drink and one garlic bread Double deal: 2 large pizzas with 4 desserts and a 1.25 L drink

$28.00

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$10.00 r o e t s Bo r e p ok u S $25.50

$6.00

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Salad

Soft drink (1.25 L bottle)

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RESOURCE SHEET

CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

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


RESOURCE SHEET Give and take game

Finish

+2

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Start

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

–3

+2

The teacher chooses which single denomination will be used. Students roll the dice, then give or take the number of coins shown to or from a central collection. Students count and record how much money they have as they go along.

+2

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

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NAME:

DATE: Shade the bubble to show your answer

1. How much money is shown in each box? (a)

(b)

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2. Which two coins make the amount shown?

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(d) and (e)

(b) and (e)

(iii) $2.50

(a) and (c)

(c) and (d)

(b) and (c)

(iv) $0.70

(b) and (e)

(b) and (d)

(a) and (d)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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

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CONTENT DESCRIPTION: Count and order small collections of Australian coins and notes according to their value

Assessment 1


NAME:

DATE: Shade the bubble to show your answer

1. Which collection shows the most money? (a)

(b)

(c) DOLLAR

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2. How much do the coins in each wallet add up to? (b)

(c)

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3. Colour the coins or notes to make the amount shown.

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Assessment 2

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

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(d) $1.30

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Checklist

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

Count and order small collections of Australian coins and notes according to their value (ACMNA034)

Identifies equivalent values in collections of coins and notes

Counts small collections of notes and coins

Counts small collections of notes

Counts small collections of coins of different denominations

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STUDENT NAME

Counts small collections of coins of the same denominations

© Australian Curriculum, Assessment and Reporting Authority 2012

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Answers

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

Page 128 Assessment 1 1. (a) (d) 2. (i) (iii)

40c $4 (a) and (c) (b) and (c)

(b) 20c (e) $15

(c) $1 (f ) 50c (ii) (b) and (d) (iv) (b) and (e)

Page 129 Assessment 2

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1. (c) 2. (a) $1.50 (b) 50c (c) 60c 3. The following coins should be shaded or coloured. (a) two 10c coins (b) two 20c coins and one 10c coin (c) two $10 notes (d) all coins except the $2 coin

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

Describe patterns with numbers and identify missing elements (ACMNA035) © Australian Curriculum, Assessment and Reporting Authority 2012

Number • A number is a count or measure. A numeral is a symbol or name that stands for a number. Pattern

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What this means • Students should be able to show a repeating pattern (with shapes) and also a growing pattern. • Students should be able to describe whether a pattern starting at any number is an oddnumbered pattern or an even-numbered pattern. • Students should be able to describe an increasing or decreasing pattern, starting from any number, created by skip counting in twos, threes, fives and tens and represent the pattern on a 1–120 grid and on a number line. • Students should be able to describe what number is missing from the pattern in a 1–120 chart and on a number line. • Students should be able to investigate features of number patterns resulting from adding by twos, threes, fives or tens, and describe what is happening in a 1–120 chart to a number or a sequence of numbers in a number pattern. Students should be able to describe the pattern and state the missing elements in a range of patterns. • Students should be able to balance equations using either number balances or balance scales to assist in terms of equivalence or balance; e.g. Put three small bears on one side of the balance and put one small bear on the other side; how many small bears do you have to put in the balance to make it level? This is known as finding the missing element(s).

Element

• An element is a member of a set, a part of a geometric figure, or any one of the units which go to make up an array. Repeating pattern

Teaching points • Students should show what makes a even- or odd-numbered pattern with counters and show this in diagrammatic form on grid paper. • Students should be able to describe an increasing or decreasing pattern starting from any number created by skip counting in twos and represent the pattern on a 1–120 grid and on a number line. This should be extended so students are able to describe an increasing or decreasing pattern starting from any number created by skip counting in threes, fives and tens and representing the pattern on a 1–120 grid and on a number line.

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

• Students should be able to describe what number is missing from the pattern starting at any number in a 1–120 chart and on a number line, initially in twos, then threes, fives and tens. • Students should be able to describe a pattern and state the missing element in a range of patterns; e.g. 4, 6, 8, ?, 12, 14, 16, ?, 20. Any number pattern can be put into a table. These patterns can be illustrated in a table: Position 1 2 3 4 5 6 7

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• A repeating pattern occurs when a sequence is repeated and remains the same. Nothing is added to the pattern.

Growing pattern • A growing pattern changes each time it repeats, as one element is added to the sequence.

Student vocabulary number pattern repeating missing odd even

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• A pattern is the method by which things are arranged following a rule or set of rules.

TEACHER INFORMATION

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RELATED TERMS

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4 6 8

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Position Pattern

1 2 3 4 5 6 7 3 5 7 11

Position 1 2 3 4 5 6 7 Pattern 10 15 20 35 40 What to look for • Students who have trouble with early count principles, particularly how the arrangement of the objects does not affect how many there are in a group, and how the last number in a count tells how many is in the whole collection. (It does not describe the last object touched.) • Students who have trouble with skip counting and need a variety of different strategies to understand the concept. Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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

HANDS-ON ACTIVITIES Percussion patterns Demonstrate patterns of sounds by using percussion instruments and ask the children to predict the next sound in a pattern. Once they understand the repeating nature of a pattern, allow them to record it in different ways, such as with pictures, then numbers; for example: 1, 2, 1, 2, 1, 2, 1, 2 … Then ask students to do the same thing with a growing pattern, such as 1 click, 2 claps, 3 stamps ... with different students adding to the pattern.

Pattern hunt Allow the students to go on a pattern hunt. They can find different visual patterns and record them as number patterns; for example, a blue and white stripe on a uniform could be recorded as 1, 2, 1, 2, 1, 2.

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Building growing patterns

3

6

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Allow the students to make growing patterns of triangles using Unifix™ cubes (or other suitable materials). Students then write the number of cubes used to build each triangle. Discuss the patterns they can see in the numbers and the shapes made. See pages 135–137 for examples of different types of growing patterns the students can make.

12

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

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Write a number pattern on the board with one number that does not fit (e.g. 1, 3, 5, 7, 10). Tell the students there is a ‘stranger’ in the pattern and ask them to find it. Repeat the game with different number patterns, including some that do not include a ‘stranger’. Allow the students to create their own number patterns which include a ‘stranger’ (or not) for other students to solve.

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Hands-on materials

• The students write a number sequence and ‘post’ them in the classroom letterbox for their classmates to finish. • The students use pattern blocks to create repeating patterns of different shapes or different colours.

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• The students use number balances or balance scales to create balanced equations. (Refer to ‘What this means’ in the teacher information section of this content description and page 140 for a balance scales format.)

Calculator patterns

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Use calculators to add repeatedly. The constant key on your calculator will make an addition pattern that increases. Find the first three numbers in the pattern and record them on paper, then trade with a partner to find three or more numbers to add to the pattern.

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

LINKS TO OTHER CURRICULUM AREAS English • Read Two of everything, by Lily Toy Hong, a book which adapts a Chinese folktale and shows the pattern of doubling; Mr Noisy’s book of patterns by Rozanne Williams; and One grain of rice: A mathematical folktale by Demi. This is the story of Rani, a clever girl who outsmarts a selfish rajah and saves her village. As a reward for a good deed, she asks only for one grain of rice, doubled each day for 30 days. Eventually, this provides enough rice to feed the entire village for a long time. • Have the students create two or three different groups of words with features common to each group; for example, words beginning with a blend such as ‘bl’, or which end in ‘ing’. Use cards to create a pattern of words, such as a ‘bl’ word, ‘ing’ word, ‘bl’ word, ‘ing’ word etc.

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• Students should know what adjectives are and have plenty of practice using them to describe objects and people in oral and written activities. Patterns can be developed from, for example, objects described in different ways.

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• Have the students keep a pattern book as an ongoing activity. Include patterns of double attributes, repeating patterns and growing patterns. Have them leave selected open pages of the book in the maths centre for others to guess the pattern.

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Information and Communication Technology

• Visit <http://www.ixl.com/math/grade-2/repeating-patterns> to practise repeating patterns. The site includes activities such as ‘Which pattern follows the same sequence as the one given?’, ‘What comes next?’, ‘What’s missing?’ This site also has games for growing patterns and describing patterns using pronumerals (for more capable students). • Visit <http://teams.lacoe.edu/documentation/classrooms/linda/algebra/activities/pattern_grow/pattern_farm.html> to manipulate patterns and make them grow.

• Visit <http://www.nelson.com/mathfocus/grade3/teacher/surf/ch1_4.html> to find two ‘Spooky sequences’ games to play based on decreasing numbers of twos and tens.

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

• Visit <http://www.ezschool.com/Games/Pattern.html> to play ‘Pattern chomper’, where students find the number missing in a number pattern.

• Learn to dance the waltz, a dance which has a repeated numbers of steps in the pattern of 1, 2, 3, 1, 2, 3.

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• After the students have created a repeating or growing pattern, ask them to transfer it to grid paper and continue the pattern to fill up the cells until a pattern similar to a quilt is created. • Read The deep blue sea: A book of colours, by Audrey Wood (a cumulative text that introduces a new colour and object on each page). As each page is read, have the students draw and colour the objects to create their own ‘growing picture’.

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The Arts

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• Men and women have used patterns in art for as long as art itself has existed. A lot of cubist and impressionist paintings incorporate fun patterns. View some of these and select one to recreate.

• The students look at and ‘read’ the pattern(s) on necklaces, or create some of their own. • Ask the students to listen to a musical pattern—for example, clap, clap, snap, stamp— and repeat and identify it. Select students to repeat and extend the original pattern.

Science • Look for increasing and decreasing patterns in nature, such as those found on fern or palm leaves, spiders’ webs or the centre of a sunflower. Use found or scrap materials (such as bubble wrap) to try to recreate these.

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RESOURCE SHEET Examples of growing patterns for the students to make using materials – 1 Matchsticks or toothpicks

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

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CONTENT DESCRIPTION: Describe patterns with numbers and identify missing elements

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RESOURCE SHEET Examples of growing patterns for the students to make using materials – 2 Cubes and counters

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

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Patterns of odd numbers (top row)

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Patterns of even numbers (bottom row)

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Patterns of even numbers (bottom)

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CONTENT DESCRIPTION: Describe patterns with numbers and identify missing elements

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RESOURCE SHEET Examples of growing patterns for the students to make using materials – 3 Patterns blocks and other methods Hexagonal dragons

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

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CONTENT DESCRIPTION: Describe patterns with numbers and identify missing elements

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Caterpillar at two years

Caterpillar at three years

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RESOURCE SHEET Skip counting patterns on the number line 0

1

2 3

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8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Counting by 2s: • If you start counting from 0 (or another even number) by twos, the numbers are even numbers. 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 …

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• If you start counting from 1 (or another odd number) by twos, the numbers are all odd numbers. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41 …

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Counting by 3s:

© Australian Curriculum, Assessment and Reporting Authority 2012

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

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42 …

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• If you start counting from 0 by threes, the numbers are even then odd numbers. • If you start counting from 1 by threes, the numbers are odd then even numbers. 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40 … Counting by 5s:

© R. I . C.Publ i cat i ons • If you start counting with a diff erent number, number ends with same •f or r ev i eweverypsecond ur p ose s othe nl ydigit. •

• If you start counting from 0 by fives, then each number will end in either 5 or 0. 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 …

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• If you start counting from 0 by tens, then the final digit of each number will be 0. 0, 10, 20, 30, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110 …

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• If you start counting from any number, each number will end with the same digit as the number you started counting with.

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3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, 123, 133, 143 …

The first digits in two-digit and three-digit numbers are in counting order (e.g. 3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, 123, 133, 143.) Counting by 4s: • If you start with an even number, all of the numbers are even. 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 … • If you start counting by 4s with an odd number, then all the numbers are odd. 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57 …

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CONTENT DESCRIPTION: Describe patterns with numbers and identify missing elements

Counting by 10s:

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

RESOURCE SHEET Examples of number patterns Adding 1 1, 2, 3, 4, 5, 6 … (increasing)

Adding 2

1

2, 4, 6, 8, 10, 12, 14, 16; or 1, 3, 5, 7, 9, 11, 13, 15 … (increasing)

Adding 3

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81, 84, 87, 90, 93, 96 … (increasing)

Patterns in addition

Adding 5

Adding 10

10 9 8 7 6 5 4 3 2 1 0

+ 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

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5, 10, 15, 20, 25, 30, 35 … (increasing)

0, 10, 20, 30, 40, 50, 60 … (increasing)

The numbers in the first column decrease from top to bottom.

Subtracting 1

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

Subtracting 2

48, 46, 44, 42, 40, 38 … (decreasing)

© R. I . C.Publ i cat i ons orr evi ew pur posesonl y• Subtracting• 5 f 30, 27, 24, 21, 18, 15 … (decreasing)

The numbers in the middle column increase from top to bottom.

295, 290, 285, 280, 275 … (decreasing)

Patterns in subtraction

Subtracting 3

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900, 890, 880, 870, 860 … (decreasing)

Doubling

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The numbers in the last column decrease from top to bottom.

1, 2, 4, 8, 16, 32 … (increasing)

Halving

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… 64, 32, 16, 8, 4, 2; or 160, 80, 40, 20, 10, 5 (decreasing)

Repeated pattern 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4 …

10 10 10 10 10 10 10 10 10 10 10

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Subtracting 10 CONTENT DESCRIPTION: Describe patterns with numbers and identify missing elements

9

Number patterns on a number line (adding 3)

– 0 – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10

= = = = = = = = = = =

10 10 10 10 10 10 10 10 10 10 10

= 10 = 9 = 8 = 7 = 6 = 5 = 4 = 3 = 2 = 1 = 0

The numbers in the middle column increase from top to bottom.

2 + 4 = 6, 20 + 40 = 60, 200 + 400 = 600, 2000 + 4000 = 6000

10 – 7 = 3, 100 – 70 = 30, 1000 – 700 = 300, 10 000 – 7000 = 3000

Diagrams of increasing number patterns

1

(1 + 2) = 3

(1 + 2 + 3) = 6

(1 + 2 + 3 + 4) =10

Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

(1 + 2 + 3 + 4 + 5) =15

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(1 + 2 + 3 + 4 + 5 + 6) = 21

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RESOURCE SHEET Balance scales format View the examples in the first row and use the blank formats to show visually how to find a missing element. This approach can be useful for visual-spatial learners. The missing element may also include the function (–, +, x or ÷).

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NAME:

DATE:

1. Write the numbers missing from each pattern and what is happening in the pattern. ,

(a) 150, 160, 170, 180,

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(c) 120, 110, 100,

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Assessment 2

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(d) 33, 30, 27,


Checklist

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

Describe patterns with numbers and identify missing elements (ACMNA035)

Identifies missing elements in a pattern

Describes patterns with numbers

Identifies patterns with numbers

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STUDENT NAME

Identifies patterns with shapes

© Australian Curriculum, Assessment and Reporting Authority 2012

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Sub-strand: Patterns and Algebra—P&A – 2

Solve problems by using number sentences for addition or subtraction (ACMNA036) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION

Number

What this means

• A number is a count or measure. A numeral is a symbol or name that stands for a number.

• Students should be able to represent a word problem as a number sentence; for example: ‘Peter has 7 swap cards. His friend, John, gives him another 8. How many cards does he have now?’ The number sentence for this word problem relates to the concept of ‘part + part = whole’. For example: ‘A basket of apples contains 34 apples. Some are red and some are green. If there are 16 green apples, how red apples are there?’ The number sentence is: 16 green +? red = 34 apples. Students need to recognise that in this problem they have one part and the whole, and they need to find the other part that ‘matches’ to make the whole. It is important for students to be able to write a number sentence that matches the semantic structure of the word problem.

Number sentence

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Addition

• Addition is an operation which involves finding the total, or sum, by combining two or more numbers.

• Students should be able to write a word problem to represent a number sentence; for example: ? people + 10 people = 35 people. This is the type of numerical problem that they should be able to write based on a word problem: ‘At the theatre there were some people already seated; another 10 people walked in. Now there are 35. How many people were in the theatre to start with?’

Teaching points

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• Subtraction is an operation which involves taking one number away from another to find the difference.

• Students should be given the opportunity to listen to/read books that explore partitioning of numbers to show what is meant by a number sentence. Students should say and write number sentences from the story. One is a snail and ten is a crab, by April Pulley Sayre, is one such book that could be used.

• Have students use a partitioning grid and written number sentences to replicate how the counters can be changed to show a number; for example, ‘12’ can be ‘6 and 6’, or ‘8 and 4’.

Problem

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• A problem is a question that needs a solution.

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• Students should be able to use both an actual balance (with counters) and a number balance to state number sentences when they are used, and be able to write those number sentences.

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• A number sentence is an equation or inequality expressed using numbers and common symbols.

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• Students should be given the opportunity to use the function machine (page 152) to describe and write number sentences; for example, ‘When five goes into the function machine and 12 comes out, what happened in the machine?’

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• Students should use a think board (pages 148–149)and show how a number sentence can be written from a story or vice versa.

What to look for

• Young students who can count on by ones but have trouble counting by twos (or other amounts). • Students who have trouble skip counting.

Student vocabulary number sentence problem addition

• Some students do not understand that you can say 3 + 5 = 5 + 3. Time needs to be spent modelling with counters, number balances and number lines to explain this. This notion of ‘commutativity’ is very important in developing in students an ability to think in a flexible way in the lead up to learning algebra.

Proficiency strand(s): Understanding

Fluency

Problem solving

Reasoning

subtraction

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Sub-strand: Patterns and Algebra—P&A – 2

HANDS-ON ACTIVITIES Balance scales and number balance scales

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Students should have experience with manipulating materials by using balance scales with counters or blocks, and with number balance scales to replicate a word problem in terms of numbers. The principle for using both types of balances is the same—the centre support of the scales can be thought of as representing an equals sign. (Students may find it helpful if a cardboard equals sign is stuck on the support.) Each side of the scales holds an expression and, once balanced, both sides have the same value and the equation is correct. Extend the activity by substituting numeral cards for the materials. This will also help reinforce the concept of partitioning since the students will be ‘splitting up’ the totals on each side of the scales into parts. Use the blank format on page 140 to record number sentences.

Think boards

Use the blank formats on pages 148 and 149 to assist the students to record individual number sentences in a variety of ways. This will connect the word problem to its numerical equivalent. This activity can be completed by small groups of students or individually.

English

INKS TO OTHER CURRICULUM AREAS © RL. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

• Read and discuss the story The grapes of math: Mind-stretching math riddles, by Greg Tang, to discover different strategies to complete simple computations. The doorbell rang, by Pat Hutchins, also provides simple subtraction problems to be solved.

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• Reinforce the understanding and use of numerical words, especially the written numbers from one to ten, then twenty to one hundred ... and beyond. Write them on cards and have students practise making up numbers with words—such as thirty-eight, forty-nine and sixty-two—and making the matching numbers in digits. • Have the students make up ‘word stories’ for number sentences provided by the teacher. Refer to ‘What this means’ for some examples.

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Information and Communication Technology

• Visit <http://mathwire.com/games/addsubgames.html> to download a copy of instructions and resources for three hands-on games to practise addition and subtraction facts. • Visit <http://www.sheppardsoftware.com/math.htm> to practise simple addition and subtraction fact games. • Visit <http://www.dadsworksheets.com/v1/Worksheets/Word%20Problems.html> to find many examples of word problems.

The Arts • Look at works of art by famous artists and learn about different ways to add in Math-terpieces: The art of problem-solving, by Greg Tang. Some of the artists include Monet, Van Gogh, Matisse, Dali, Pollock and Warhol. After a maths lesson involving the problems in the book, select one of the artists to study.

Drama • As an extension of the think board, ask the students to ‘act out’ number problems for other students to guess what they are doing. Ensure students carefully mime the number of ‘objects’ placed out, needed or taken away. Writing in the air could be used to show a total.

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RESOURCE SHEET Number sentence

Story problem think board

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Manipulatives or materials

Think board example – 1

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Picture or drawing

Story 148

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RESOURCE SHEET

WRITE IT IN NUMBERS

Think board example – 2

WRITE IT IN WORDS

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RESOURCE SHEET Place value chart for partitioning numbers by thousands, hundreds, tens and ones

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RESOURCE SHEET Tens and ones for partitioning numbers

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RESOURCE SHEET Examples of function machines

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Out

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RESOURCE SHEET Types of addition and subtraction problems Students should be exposed to a variety of addition and subtraction problems. Some of these include those where students have to: (a)

change one quantity by adding to or taking from it. For example, ‘Mum made 6 cakes for the cake stall at the fete and sold 5 of them. How many didn’t she sell?’

(b)

consider two quantities separately or combined. For example, ‘Mum made 6 chocolate cakes for the cake stall at the fete, and then decided to make 5 lemon cakes, too. How many cakes did she bake altogether?’

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Sub-strand: Patterns and Algebra—P&A – 2

compare or make two quantities equal. For example, ‘Mum made 6 chocolate cakes for the cake stall at the fete, and then decided to make 5 lemon cakes, too. If each chocolate cake was sold with a lemon cake, how many chocolate cakes were sold without a lemon cake?’

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‘Mum made 6 chocolate cakes for the cake stall at the fete, and then decided to make 5 lemon cakes, too. How many more chocolate cakes were there than lemon cakes?’

OR

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For example, in the word problem, ‘Sam had 6 cards and Tim gave him 9 more. How many does Sam have now?’ the students are required to find the unknown end result (or the whole).

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Other ways to express the same problem would be:

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Students should be exposed to a variety of problems where the unknown element is not always the same part of the equation.

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CONTENT DESCRIPTION: Solve problems by using number sentences for addition or subtraction

‘Mum made 6 chocolate cakes for the cake stall at the fete, and then decided to make some lemon cakes, too. If she made one less lemon cake than chocolate cakes, how many lemon cakes did she make?’

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‘Sam had 6 cards and wanted 15. How many more did he need to collect?’ (The change in number [or one part] is unknown.) ‘Sam had some cards and was given 9 more by Tim. He now has 15 cards. How many cards did he have to begin with?’ (The beginning quantity is unknown.)

NOTE: Examples of all types of addition and subtraction have been included on the assessments sheets on page 156 to 157.

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Sub-strand: Patterns and Algebra—P&A – 2

NAME:

DATE:

1. Write each word problem as a number sentence. Word problem

Number sentence and answer

(a) Kevin is collecting eggs from the henhouse. He has collected 66 already. He then finds 8 more. How many eggs does he have now?

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does Jane have?

(c) Sarah has lots of raisins and gets 3 more for her friend, Ashley. She now has 95 raisins. How many raisins did Sarah have to begin with?

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© Australian Curriculum, Assessment and Reporting Authority 2012

Assessment 1

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CONTENT DESCRIPTION: Solve problems by using number sentences for addition or subtraction

© R. I . C.Publ i cat i ons •word f or r evi e pur p osesonl y• 2. Write each problem asw a number sentence.


NAME:

DATE:

1. Solve the word problems using number sentences. Word problem

Number sentence

(a) Todd has 96 miniature figurines and 6 action figures. How many toys does he have?

96 + 6 = ?

Working and answer

cookies at the end, how many oat cookies did she bake? (c) Bruce measured out some rope, and then 95 cm more because he needed 130 cm. How many centimetres of rope did he measure first?

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Assessment 2

Sub-strand: Patterns and Algebra—P&A – 2

? + 95 = 130

Number sentence

(a) Max has 100 toy cars and 80 toy trucks. If each truck carries a car, how many cars will not have a truck?

100 – 80 = ?

(c) Raj scored 155 on one computer game and more points on another. The total for both games was 180. How many points did he score on the second game?

180 – 155 = ?

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CONTENT DESCRIPTION: Solve problems by using number sentences for addition or subtraction

© R. I . C.Publ i cat i ons 2. Solve word problems subtraction sentences. •the f o rr e vi ewusing pu r posenumber sonl y•

o c . ch (b) Rachael has 52 blue lollies and e r er o 38 red lollies. How many more 52 – 38 = ? t s s r u e p blue lollies does she have?

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NAME:

DATE: Write a word problem for each addition number sentence.

Number sentence

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1. 66 + 44 = ?

Word problem

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Assessment 3

2. 114 + ? = 120

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CONTENT DESCRIPTION: Solve problems by using number sentences for addition or subtraction

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NAME:

DATE: Write a word problem for each subtraction number sentence.

Number sentence

Word problem

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Assessment 4

Sub-strand: Patterns and Algebra—P&A – 2

2. 57 – ? = 9

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5. 42 – ? = 26

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Checklist

Sub-strand: Patterns and Algebra—P&A – 2

Solve problems by using number sentences for addition or subtraction (ACMNA036)

Writes word problems for number sentences

Solves word problems using number sentences for subtraction

Solves word problems using number sentences for addition

Interprets a word problem as a number sentence

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STUDENT NAME

Understands that word problems can be represented as number sentences

© Australian Curriculum, Assessment and Reporting Authority 2012

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Answers

Sub-strand: Patterns and Algebra

P&A – 1

P&A – 2

Page 143 Assessment 1

Page 156 Assessment 1

1. (a) even (b) odd 2. (a) odd (b) even 3. (a) Start at 67 and add 2 to each number. (b) Start at 254 and add 3 to each number. 4. Start at 31 and add 3 to each number. Page 144 Assessment 2

r o e t s Bo r e p ok u S Page 157 Assessment 2

1. (a) 96 + 6 = ?, 96 + 6 = ?, 100 + 2 = 102; Todd had 102 toys altogether. (b) 24 + ? = 60, 24 + ? = 60, 24 + 36 = 60; Mandy’s mum baked 36 oat cookies. (c) ? + 95 = 130, ? + 95 = 130, 35 + 95 = 130; Bruce measured out 35 cms first. 2. (a) 100 – 80 = ?, 100 – 80 = ?, 100 – 80 = 20; 20 cars will not have a truck. (b) 52 – 38 = ?, 52 – 38 = ?, 52 – 38 = 14; Rachael has 14 more blue lollies than red lollies. (c) 180 – 155 = ?, 180 – 155 = ?, 180 – 155 = 25; Raj scored 25 points on the second game.

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1. (a) 150, 160, 170, 180, 190, 200, 210; Start from 150 and add 10 to each number. (b) 85, 90, 95, 100, 105, 110, 115, 120; Start from 85 and add 5 to each number. (c) 120, 110, 100, 90, 80, 70, 60; Start from 120 and subtract 10 from each number. (d) 33, 30, 27, 24, 21, 18, 15, 12, 9; Start from 33 and subtract 3 from each number. 2. (a) 157 (b) 102

1. (a) 66 + 8 = ?, 66 + 8 = 74; There are now 74 eggs in total. (b) 53 + ? = 111, 53 + 61 = 111; Jane has 61 silver stickers. (c) ? + 3 = 95, 92 + 3 = 95; Sarah had 92 raisins to begin with. 2. (a) 94 – 26 = ?, 94 – 26 = 68; Josh, Tim’s dad, weighs 68 more kilograms than Tim. (b) 83 – ? = 76, 83 – 7 = 76; Tess borrowed 7 pencils. (c) ? – 57 = 65, 122 – 57 = 65; Elly had 122 cards in her original collection.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Pages 158 Assessment 3

1. 64 + 44 = 110 2. 114 + 6 = 120 3. 95 + 20 = 115 4. 370 + 50 = 420 5. 86 + 32 = 118 Teacher check word problems.

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Pages 159 Assessment 4 1. 98 – 14 = 84 2. 57 – 48 = 9 3. 145 – 30 = 115 4. 4. 210 – 50 = 160 5. 42 – 16 = 26 Teacher check word problems.

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Australian Curriculum Mathematics resource book: Number and Algebra (Year 2)

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Number and Algebra (Australian Curriculum): Year 2 - Ages 7-8