RIC-6084 4.4/620

Australian Curriculum Mathematics resource book: Number and Algebra (Foundation) Published by R.I.C. Publications® 2012 Copyright© R.I.C. Publications® 2012 ISBN 978-1-92175-068-7 RIC–6084 Titles available in this series:

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. 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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© 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.

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

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: NUMBER AND ALGEBRA (FOUNDATION) Foreword Australian Curriculum Mathematics resource book: Number and Algebra (Foundation) 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 Australian mathematics 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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• • • • • • •

© R. I . C.Publ i cat i ons Contents •Format f oofr r e v i e w p ur po sesonl y• this book ................ iv – v • N&PV – 4 • N&PV – 1 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 – 5

– Teacher information .......................... 58 – Hands-on activities ..................... 59–60 – Links to other curriculum areas .......... 61 – Resource sheets .......................... 62–71 – Assessment ................................ 72–73 – Checklist ............................................ 74 Answers ........................................... 75

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Teacher information .......................... 20 Hands-on activities ............................ 21 Links to other curriculum areas .......... 22 Resource sheets .......................... 23–32 Assessment ................................ 33–34 Checklist ............................................ 35

• N&PV – 3 – – – – – –

Teacher information .......................... 46 Hands-on activities ............................ 47 Links to other curriculum areas .......... 48 Resource sheets .......................... 49–54 Assessment ................................ 55–56 Checklist ............................................ 57

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Number and Place Value .......... 6–75

Patterns and Algebra ............ 76–88 • P&A – 1

Teacher information .......................... 36 Hands-on activities ............................ 37 Links to other curriculum areas .......... 38 Resource sheets .......................... 39–42 Assessment ................................ 43–44 Checklist ............................................ 45

Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

– Teacher information .......................... 76 – Hands-on activities ..................... 77–78 – Links to other curriculum areas .......... 79 – Resource sheets .......................... 80–84 – Assessment ................................ 85–86 – Checklist ............................................ 87 Answers ........................................... 88

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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. It includes 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.

© R. I . C.Publ i cat i ons Teaching points provides a list of • f o r r e v i e w p u r p o s e s o nl y• the main teaching points relating Student vocabulary includes words which

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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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to the content description.

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

What to look for suggests 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 (Foundation)

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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 to 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.

These. support included ina the t © R. I . C Pactivities ub l i c i ons corresponding workbook. Many of the questions on the assessment pages are in a •f orr evi e w pur posesonl y• format similar to that of the NAPLAN tests to Assessment pages are included.

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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

Sub-strand: Number and Place Value

N&PV – 1

Page 17 Assessment 1 1. 2. 3. 4. 5.

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

4 13 9 7 8

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

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(c) 9 (c) 8 (c) 4

(d) 11 (d) 21 (d) 14

1. (a) 4 (b) 6 (c) 3 Bowl (b) should be shaded. 2. (a) 4 (b) 4 (c) 2 Bowl (c) should be shaded. 3. (a) The mouse should be shaded. (b) The hen should be shaded.

(c) 5

Page 18 Assessment 2

1. (a) 5, 6, 7, 8, 9 (c) 16, 17, 18, 19, 20 2. 8, 7, 6, (5), 4, 3, 2, 1 3. (a) 4, 3, 2, 1, 0 (c) 11, 10, 9, 8, 7 4. (a) ten (b) seven (e) three (f ) two (i) nine (j) eight

Page 56 Assessment 2

(b) 11, 12, 13, 14, 15 (d) 1, 2, 3, 4, 5 (b) 13, 12, 11, 10, 9 (d) 19, 18, 17, 16, 15 (c) one (d) five (g) four (h) zero

N&PV – 2 Page 33 Assessment 1

N&PV – 5 Page 72 Assessment 1 1. (a) 5 2. (a) 4

(b) 3 (b) 5

(c) 7 (c) 3

Page 73 Assessment 2 1. (a) 4 and 5 makes 9 (c) 6 and 1 makes 7 2. (a) 3 more spots (c) 4 more spots 3. (a) 3 fish each (b) 2 fish each

(b) 2 and 3 makes 5 (d) 4 and 2 makes 6 (b) 2 more spots

1. (Going from left to right, downwards) 5 frogs, 6 balls, 3 kangaroos, 1 horse, 0, 10 cupcakes, 12 bananas, 4 shirts Page 34 Assessment 2

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

1. Eleven eggs should be drawn; 7 apples should be drawn; 5 eyes should be drawn. 2. Four balls should be coloured; 9 shells should be coloured; 8 fish should be coloured. N&PV – 3 Page 43 Assessment 1 (a) 5 (d) 3

(b) 6 (e) 7

(c) 4 (f ) 6

Page 44 Assessment 2 1. (a) 6 (b) 3 (c) 5 (d) 2 (e) 4 2. (a) 8 apples (right side) (b) 6 flowers (right side) (c) 4 frogs (left side) (d) 6 presents (left side) N&PV – 4 Page 55 Assessment 1 1. (a) Car B (b) Car A (c) 4th 2. (a) 3rd child (b) 1st child

(d) Car C (c) 4th child

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

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What this means

Counting To name or list the units of a group or collection one by one in order to determine a total; to recite numerals in order Counting on

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Counting a collection or reciting numbers from a certain starting point Pattern

An arrangement of things (numbers, shapes, etc.) in which all the things are related by a specific rule

Teaching points

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Students become confident in using the language of counting, and understand that other cultures have other counting words. This does not mean they simply recite the number names in order. They can recite the number sequence forwards and backwards, from any starting number up to 20. A student who is fluent in using the counting sequence can provide the missing number in a sequence of numbers by using his/her knowledge of the 1 to 9 and decade patterns in the number sequence.

• Students need to know the number sequence in the correct order to 20. • Practise adding emphasis at different points during recitation of the counting sequence (e.g. every second number, every third) to move students away from reliance on reciting numbers as one long sentence in a sing-song fashion. • Students need to practise counting forwards and backwards from different starting points, initially by providing the next number in a spoken sequence. • Students then continue to provide more of the sequence themselves with limited teacher modeling; e.g. ‘What number comes after 18?’

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• Students who need to count from one, either aloud or under their breath, in order to find the number before or number after a given number. • Students who experience confusion with the terms ‘before’ and ‘after’.

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Student vocabulary

Understanding Fluency Problem solving Reasoning

count forwards backwards

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

HANDS-ON ACTIVITIES Clothes line (page 12) • Obtain small wooden pegs and a doll’s clothes line (or attach thin string or rope across two fixed items in the classroom). Enlarge, cut out and laminate the clothing items on page 12 and put them into a small basket. The students peg a certain number of the clothing items in the correct numerical sequence onto the clothes line, going forwards or backwards from different starting points. Teachers could also put a ‘middle’ number up, and have the students place the correct sequential numbers on both sides of that number.

Counting rhymes

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• Use rhymes (such as those on pages 9 and 10) to practise reciting number sequences forwards and backwards.

Lolly Land (page 14)

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• Practise counting aloud using this board game, starting at any point and moving forwards or backwards. Use a foursided dice and counters to practise moving along the board. Encourage students to say the name of the number they land on.

Read my mind

• The teacher or a student chooses a number between 0 and 10 without telling the other students. Allow one student at a time to try to ‘read your mind’ (guess which number you chose). If the answer is correct, the student wins. If not, another student tries to guess. Keep track of the incorrect answers given by recording them on a board. Increase or decrease the numbers according to ability level. Give clues such as ‘It’s before/after five.’

Number sticks

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• Write numerals on large craft sticks (tongue depressors); the students can write the numerals if able. Jumble the sticks and let the students put them back in order.

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• Talk about the page numbers in a book and how they can help us to find the information we want. Also discuss other examples of where numbers are sequenced in order, such as on houses, to be used as a tool/guide. Discuss numbers written on the uniforms of a sports team or the numbers of a bus route and why they might not be in order.

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• Recite numbers in sequence from different starting points. Emphasise the ‘important’ numbers of that sequence; e.g. emphasising 10, 20 with a slight pause after 20 if exploring tens. Ask questions such as ‘What part of the first ten numbers sound the same as the twenties?’. • As the students count to ten, coordinate body actions (such as clapping, clicking or stamping) with each number as it is counted. When ten is reached, continue counting on but repeat the patterns from one again (so students can begin to understand the patterns in the way numbers are recited verbally).

What’s next?

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• Hold up a number card, or say a number. The students tell you which number comes before (or after) that number.

Number hunt

• Hide number cards (see pages 25 and 27) around the classroom. The students hunt for the cards, and as a student finds one, he or she tells you which number was found. When all have been found, the class places them in order.

Number grids • Give each student a number grid (page 15). Starting from different numbers each time, the class counts out aloud, putting a finger on each numeral as it’s recited. They could use a counter or other object to move along the grid. Ask questions such as ‘What is the number before 19?’.

Line up • With the students standing in a line, students say in turn the next number in the counting sequence. Start at different numbers.

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

LINKS TO OTHER CURRICULUM AREAS English • Sing songs or rhymes such as ‘Alice the camel’, ‘Five currant buns in a baker’s shop’, ‘Five fat sausages sizzling in a pan’, ‘Five little speckled frogs’ and ‘Ten little Indians’ or ‘This old man’. (See pages 9 and 10.) • Read books about counting in order, such as Counting on Calico by Phyllis Tildes, Ten cats have hats by Jean Marzollo, Ten little ladybirds by Melanie Gerth, Ten in the bed by Penny Dale, Nine ducks nine by Sarah Hayes. • Obtain and read books about counting that include concepts or languages from other cultures, such as: An Australian 1, 2, 3 of Animals by Bronwyn Bancroft, Moja means one by Muriel Feelings (counting in Swahili), Anno’s counting book by Mitsumasa Anno, Counting on your fingers African style by Claudia Zaslavsky, The Token Gift by Hugh William McKibbon, My numbers = Mis numeros by Rebecca Emberley, Count on Pablo by Barbara deRubertis, Emeka’s gift: an African counting story by Ifeoma Onyefulu, Knots on a counting rope by Bill Martin and John Archembault. • Read Bananas for lunch at <http://www.storyplace.org/preschool/activities/lunch.asp> (a counting story about a monkey).

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Information and Communication Technology

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• Play games such as arranging snails with numbers on their backs into the right order at <http://www.topmarks.co.uk/ Flash.aspx?f=countandorder>; or practise saying numbers in order at <http://www.bbc.co.uk/cbeebies/tikkabilla/ games/#/lb/tikkabilla/tambasabacus>. Numbers can be dragged in place on a number track at <http://www.crickweb. co.uk/ks2numeracy-properties-and-ordering.html#ntrack>, while <http://www.kenttrustweb.org.uk/kentict/content/ games/numberSquare/> has an interactive number chart.

Health and Physical Education

• Place rows of five or so hoops on the ground. Students take a number card from a pile, or are told a number. They say the number, then jump into the first hoop and say the number that follows that on their card, saying the number each time they jump into a hoop. Use numbers according to ability. Students can be asked to count forwards or backwards. • Place a number of hoops on the ground in a long waving line. Mark each hoop with a numeral in order. As the students leap from hoop to hoop, they say the number they land on. • Ask individual students to complete actions such as skipping with a rope, bouncing a ball, star jumps or hopping, while the rest of the class counts each action in unison. • Spread number cards out on the floor and play music. The students move around and when the music stops, they stand on a number. The teacher calls out a number, such as ‘the number before 19’ or ‘the number after 4’. The student standing on that number is ‘the winner’. Make sure each student has a turn with stopping on a number and says the number that comes before or after it. • Put students into groups of five. Give each team a small container with counters with the numbers 1–10 written on them in it. At the other end of the court, place an empty number line. Students choose a counter randomly from the container, run and place it in the right place on the line, then run back to tag the next person in line.

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• Learn to count out loud in order in another language.

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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RESOURCE SHEET Counting rhymes One, two, three, four, five One, two, three, four, five Once I caught a fish alive. Six, seven, eight, nine, ten Then I Iet it go again. Why did you let it go? Because it bit my finger so. Which finger did it bite? This little finger on my right.

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

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Five little ladybirds, climbing up a door; One flew away and then there were four. Four little ladybirds sitting in a tree; One flew away and then there were three. Three little ladybirds landed on a shoe; One flew away and then there were two. Two little ladybirds looking for some fun; One flew away and then there was one. One little ladybird sitting in the sun; She flew away and then there were none!

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Five currant buns in the baker’s shop, Round and fat with a cherry on the top. Along came (student’s name) with a dollar one day, Bought a currant bun and took it away. Four currant buns in the baker’s shop, Round and fat with a cherry on the top. Along came (student’s name) with a dollar one day, Bought a currant bun and took it away. (Repeat verse three times, working down to one.)

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Five currant buns in a baker’s shop

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CONTENT DESCRIPTION: Establish understanding of the language of counting by naming numbers from different starting points

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Five little ladybirds

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Five fat sausages sizzling in a pan Five fat sausages sizzling in a pan, sizzle, sizzle, sizzle, ‘til one went BANG! Four fat sausages sizzling in a pan … (Continue until none are left.)

Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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Counting rhymes Five little speckled frogs

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One little child

One little child, standing on his/her own, Two little children, now they’re not alone. Three little children, happy as can be, Four little children, playing under a tree. Five little children, they are all good friends, Wave goodbye because that’s the end!

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Five little speckled frogs, sat on a great big log Eating some most delicious bugs: Yum, yum! One jumped into the pool, where it was nice and cool. Then there were four speckled frogs: Glub, glub! (repeat verse three times, working down to one.) One little speckled frog, sat on a great big log Eating some most delicious bugs: Yum, yum! She jumped into the pool, where it was nice and cool. Now there are no more speckled frogs: Glub, glub!

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Here is the beehive

Here is the beehive, but where are the bees? (Hold up a fist.) Hidden away where nobody sees. (cover fist with other hand.) Watch the bees come out of the hive: 1, 2, 3, 4, 5! (extend fingers from fist hand one by one.)

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One potato, two potatoes One potato, two potatoes, three potatoes, four, Five potatoes, six potatoes, seven potatoes, more! One potato, two potatoes, three potatoes, four, Five potatoes, six potatoes, seven potatoes, more!

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© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point

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

RESOURCE SHEET Frog jump cards (Copy and laminate, then students use a counter to jump the frog.)

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Clothes line

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

© Australian Curriculum, Assessment and Reporting Authority 2012

RESOURCE SHEET

CONTENT DESCRIPTION: Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point

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

Numbers in a row Copy and cut number cards (page 25). Give students four numbers, which they match to the numbers in the row.

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Lolly Land – Board game or counting aloud practice

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RESOURCE SHEET

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RESOURCE SHEET Number grid 0–30

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Putting numbers in order (cut each strip and allow students to re-order the numbers)

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

Date:

Teachers: Ask the students these questions and record their answers in the spaces provided. 1. Say the number that is missing. (a) 1, 2, 3,

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

(d) 15

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(b) 16, 17, 18,

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(b) 0 and 2

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Name:

Date:

Teachers: Ask the students the questions and record their answers. 1. Count forwards from the number given. Count on five numbers more.

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

Assessment 2

Checklist

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

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001) © Australian Curriculum, Assessment and Reporting Authority 2012

Count backwards from a given number (from 20)

Name whole numbers to 20

Name the number before or after a given number

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STUDENT NAME

Count forwards from 0 to 20, from any starting point

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

Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) © Australian Curriculum, Assessment and Reporting Authority 2012

RELATED TERMS

TEACHER INFORMATION What this means

Counting To name or list the units of a group or collection one by one in order to determine a total; to recite numerals in order

Students learn to count, and connect the different ‘languages’ of mathematics (number symbols, spoken number words and collections of things). They can do more than simply count a collection. They can add to or subtract from a collection by counting on without needing to recount the collection each time.

Counting on

Teaching points

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Quantity

The measurable, countable, or comparable property or aspect of a thing Cardinality

The last count in a set

• Students need to practise counting forwards while adding objects to a collection, recognising that adding one more in the collection results in the next number in the counting sequence, without needing to confirm by counting from one. • Similarly, students need to practise counting backwards while removing objects from a collection.

What to look for

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Counting a collection or reciting numbers from a certain starting point

• Students who insist on counting items from left to right, and believe counting items in a different order is ‘wrong’. • Students who lose track of which items have been counted, especially when not counting items in a line from left to right, and recount some items. • Students who recount the collection when asked for the result of the count (‘So, how many are there?’). • Students who need to recount the collection each time an item is added or taken away.

Each item to be counted in a collection is given a number name as it is counted

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1 to 1 correspondence

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

Student vocabulary

Understanding Fluency Problem solving Reasoning

count how many number

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

HANDS-ON ACTIVITIES Drop and count • Put out a row of (initially) three to five cups or empty containers. Give the students a number of small items, such as marbles, counters, coins, nuts, buttons, shells or matchsticks. The students place them, one at a time, into the containers, counting the items as they are dropped. • Label the containers with numerals from 1 to 5, with one numeral for each container. Students drop the correct number of small blocks into each container as indicated by the number on the outside. As the students become proficient with the range of one to five, extend the activity to the numerals from one to ten.

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• Give each student two craft sticks and a collection of matchsticks. They take a number card (see pages 25–26), read the number, then put that quantity of matchsticks between two craft sticks to make a ladder.

5

• From a deck, give each student a large playing card with a number on it (take out the picture cards). The students use small counters to match the number of items on the card. • Deal the cards among four students. They can play games such as ‘go fish’ and ‘snap’, to match the numbers.

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Collections

• Give each student a small collection of counters or any other small items of interest and some paper or plastic plates. Call out a number. The students count out that number of items and put them one by one onto the plate. Students could make items from playdough. • Give students collections of objects and ask them how they can find out how many items they have. Demonstrate and practise different ways to count the items, such as putting them in a line to ensure each is counted only once. Move the objects into a different arrangement and ask ‘How many?’. Repeat with the same number of items in different arrangements so the students recognise that although the objects have moved the number is still the same.

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Number strips (page 28)

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• Give students strips of different numbers of items in a row. Students count the items then choose the right numeral card (page 25) to show how many items are in the set.

• Glue a few numeral cards (page 25) onto a sheet of paper. Leave space underneath each number for students to collect objects from the classroom to match the numeral. Or ask the children to count items in the classroom—books on a shelf, pencils in a cup, chairs at a desk etc. Each time you count, discuss how the last word in the list of words spoken tells us how many there are.

Egg cartons

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• Ask the students to put one object into each section of the egg carton, counting as they go, to develop 1 to 1 correspondence. Ask them to put (for example) four items into the egg carton in different spaces and discuss how the arrangement doesn’t affect how many items there are. • Number the bottom sections of a half-dozen egg carton from 1 to 6. Students read the numbers then fill each section with the correct number of items.

Birthday cakes • Supply cupcake papers, playdough, candles and birthday cards (with numbers on them). The students pick up a birthday card, read the number on it, then put that number of candles onto a cupcake they have made from dough.

Using pegs • Enlarge, cut and laminate the numbered clothing items (page 12). Give the students one of the clothing items and some small wooden pegs (available from craft shops). The students peg that number of small pegs onto the item of clothing. Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

HANDS-ON ACTIVITIES (CONTINUED) Correct collections • Place a collection of small (culturally appropriate) objects in front of a small group of students. The students take a numbered playing card from a pile then collects that number of objects. Then the student sitting next to him/her checks the collection to see if the first student is correct.

Quantity, name and numeral puzzles • Copy the quantity, name and numeral cards from page 27 onto thick card and cut each into a distinct puzzle piece, dividing the name, numeral and quantities. Students reconnect the correct numerals, names and quantities.

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

ENGLISH

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• Go to <http://library.loganutah.org/books/children/counting.cfm> for an extensive list of children’s counting and number picture books. Include books from other cultures such as How many donkeys?: An Arabic counting tale by Margaret Read MacDonald • Make class counting books; take photos of one teacher, two classroom helpers, three students with black hair, four tall students etc. • Students make a number book. Each page is dedicated to a number, one to ten. On page one, the child draws or glues one picture showing one of his or her favourite things. On page two, the student draws or glues two pictures, and so on.

Information and Communication Technology

• Play games such as post the letter at <http://www.ictgames.com/postletter.html> (students listen to a number then put the letter into the letter box with that numeral) or matching number names to numerals at <http://www.primaryonline. co.uk/sitetour/pol/blastoff1.html> or < http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/850/ calcbalancev3.swf>

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• Play games such as ‘Mother‚ may I?’ where the students are instructed to take a number of steps or jumps forwards or backwards. Or ask the students to make groups of different sizes. e.g say ‘Make a group of three’ and students make groups of three. • Play beanbag games where the students drop or throw a certain number of beanbags into baskets, or count how many landed in a hoop. • Play skittles (ten pin bowling). Students count how many pins/skittles they knocked down. • At snack time, give each student a napkin on which a grid with six or eight spaces has been folded or drawn. The students can count out a certain number of crackers or pieces of fruit, placing one piece in each space on their napkin. • Take students outside on a ‘Five Hunt’ walk. Pairs must look for five of the same object; for example, five leaves or five windows. Students record by drawing the objects.

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• If possible, ask a person of Chinese descent to demonstrate counting to 10 on one hand. • Sing ‘Sing a song of sixpence’. Discuss the line ‘Four and twenty blackbirds baked in a pie.’ Discuss what number this might be (twenty-four) and how we say that number differently today from how it was said at the time the rhyme was created.

Technology and Design • Design and make a necklace using; for example‚ six red beads and six blue beads.

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Quantity and numeral cards for ‘snap’, ‘concentration’ or ‘go fish’.

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

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Enlarge and display or give to students‚ who put counters over the dots and count, then say‚ the numeral and trace the number.

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CONTENT DESCRIPTION: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond

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

RESOURCE SHEET Number cards 1–30

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RESOURCE SHEET Number name cards (1–30)

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RESOURCE SHEET Quantity, name and numeral cards

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Number strips (Students place a numeral card [see page 25] at the end of each strip.)

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

RESOURCE SHEET Students take a numeral or number name card and place that number of items on the picture. (Enlarge and laminate each section separately, if desired.)

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caterpillars on the

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7 9 1 4 2 8 0 3 6

BINGO!

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Bingo cards (0–10)

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RESOURCE SHEET

Bingo cards (11–20)

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RESOURCE SHEET Counting stories from other cultures

Yarra’s secret Yarra was from the Wurundjeri people. One night the elders had a meeting. Yarra knew she shouldn’t watch. But she hid behind a bush and peeked through the branches. They were planning a corroboree. She wondered when it would happen. How many people would come? The elders touched different body parts to show how many.

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r o e t s Bo r e pdifferent numbers. Yarra knewothe Different body parts meant little finger u ktwo. The meant one. The nextS finger along was a little larger, it meant muscle on the upper arm meant ten.

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

© R. I . C.Publ i cat i ons •f o rr ev i ew ur posesonl y• ‘How many cattle have you got now,p Charlie’s pebbles

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showed him how many cattle he had. Each time he got another cow or bull, he would put in another pebble in the bag. If he lost one, or sold one, he’d take a pebble out. If Charlie wanted to make sure all his cattle were there, all he had to do was take out his pebbles and, as the cattle walked one-by-one through the gate, drop one pebble back into the bag. And that’s how Charlie knew how many cattle he had. 32

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Soon Yarra knew when the event would happen and how many people would be coming. Excited, she crept away, eager to tell her brothers her secret.

Date:

1. How many? Shade the bubble.

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

Assessment 2

Checklist

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

Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) © Australian Curriculum, Assessment and Reporting Authority 2012

Understands the last number counted is ‘how many’ (cardinal number)

Matches number names to numerals 0–20

Matches numerals to quantities 0–20

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Accurately and consistently counts small collections with one-to-one correspondence

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

Subitise small collections of objects (ACMNA003) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS

What this means

Placing objects in order according to an attribute (such as size or numerical value)

Subitising is the ability to recognise small collections without counting. Generally this ability includes quantities of up to six, or higher quantities in standard (e.g. dice) arrangements or patterns which encourage students to see smaller collections and combine them mentally to find the total. For example, students can calculate a total of seven from two dice showing a 2 and a 5 just by a glance rather than counting 1, 2, 3, 4, 5, 6, 7. The students can subitise by holding the 5 in their head and then counting on 2. This fast processing helps students hold the two quantities together in memory and to compare them simultaneously. Students can use this ability to put collections in order of size and make judgments about which collection is bigger/ smaller.

Estimation

Teaching points

An approximate calculation of the number (or value, quantity) of things in a collection

• Students need many opportunities to recognise and match dot patterns in different arrangements. This means they (for example) see the number five in different arrangements before going onto the number six. • Link dot patterns to number magnitude by responding to dot patterns by counting out objects, counting movements (e.g. jumping) or moving along a track (e.g. number line). • Encourage students to see the parts within the whole of larger dot collections. For example, in a picture that has six scattered dots on it, have students recognise different arrangements, such as a group of 4 and a group of 2, or a group of 3 and group of 3. • Show students regular arrangements of items or dots, before covering some and reasoning about how many are covered.

Subitising Recognising the number of objects in a collection without consciously counting (seeing at a glance)

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What to look for

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• Students who are unable to subitise one, two or three dots, and respond incorrectly to prompting or need to count every time. • Students who are unable to see that you should start with the bigger number; for example, when they see 2 dots and 4 dots on a page (or two dice), they subitise the 2 and count on the 4 rather than subitising the 4 and counting on 2 (commutivity). This could be a predictor of more serious difficulties with mathematics.

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

Student vocabulary order guess

Understanding Fluency Problem solving Reasoning

dot patterns more, most less, least

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

HANDS-ON ACTIVITIES Spotty bugs (page 39) • To use the spotty bug game, each student will need a spotty bugs grid (with six bugs) and 21 counters (or copy the page, cut out and laminate each bug separately, and give each student six differently numbered bugs). Each student rolls a dice with dots (not numbers). They then say the number rolled without counting. If they can say the number immediately (without counting), they put that number of spots on the corresponding bug. • Teachers could also give students a cut-out set of bugs and ask them to put them in order (from fewest spots to the most spots) without counting. • Another game involves putting a selection of cut-out (and laminated) bug cards in front of a small group of students sitting in a circle. Give each student a flyswat. The teacher or a student calls out a number and the students try to be the first to swat the bug with the corresponding number or dots. • A small group of students sit in a circle, each with six separate spotty bugs in front of him/her. Roll a large dice with dots to six. The students ‘snap’ as quickly as possible the spotty bug that matches the spots on the rolled dice.

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• Cut and laminate the dot and finger number cards. Lay the 12 cards out in front of a small group or pair of students. They take turns to turn over two cards at a time and try to find a matching pair. If they find a matching pair, they take and keep those two cards. The student with the most pairs at the end is the winner. Students could also make their own pairs of cards with groupings of one to six dots on them, and play matching games such as snap, fish or concentration. Teachers could substitute the domino/dice-style dot array cards for regular or irregular dot cards (see pages 41–42). These cards can be given to the students to arrange in order from 0 to 9 and back again. Or make multiple copies and divide between a pair of students. They turn one card over in front of them and they must try to snap the card with the most dots.

Paper plate flash cards • Use a circle stamp or dot stickers to create number (dot) patterns on paper plates, from one to six. Hold these plates up briefly (about two seconds) and ask the students to say how many there are as quickly as they can, without counting. As an individual activity, students can place counters over the dots on each plate.

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• Give each student a small collection of counters or other small objects such as shells, beans, coins, pebbles or buttons. Ask them to show some different ways of making arrangements with those items on a paper plate or sheet of paper. Ask the students to pick up or slide away small numbers of items without actually counting; e.g. ‘Pick up two shells’.

• Hold up two to ten fingers, alternating between showing all the fingers on one hand and some extra fingers on the second hand. The students say how many fingers are held up together. Ask the students to show, for example, six fingers in one way, then again in a different way.

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• Put out counters (or other small items) on a table in a familiar dice pattern without the students seeing. Cover the items with an opaque cloth or box lid. Uncover the pattern for a short time, then cover again. Ask the students to tell you how many items there are, or they can recreate that pattern with their own collection of counters.

Dominoes

• Giving the students sets of dominoes to play with will increase their exposure to (and ability to subitise) amounts of items up to six.

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

LINKS TO OTHER CURRICULUM AREAS English Read One is a snail, ten is a crab by April Pulley Sayre and Randy Cecil. Discuss how we can picture in our mind how different numbers can look (such as ‘ten’ being the arms of a crab) and count using group of objects.

Information and Communication Technology • Students can create arrays by copying and pasting images in groups of one to six. • Play games such as ‘Dot-spotter’ at <http://www.numbergym.co.uk/NGSdemos/BBstage1.html> or order ladybirds with spots at <http://www.topmarks.co.uk/Flash.aspx?f=countandorder>

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Health and Physical Education

• Hopscotch: Draw a hopscotch shape on a flat hard surface, with dot arrays instead of numbers. • Count up or down using fingers only to show numbers (without saying anything).

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History and Geography

Go into the environment and subitise easily identifiable objects such as bushes, hills or trees.

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The Arts

• Look at patterns of numbers of items on wrapping paper or fabric. • Use a stamp to create a pattern; e.g. two dots, three dots, two dots, three dots. • Dip fingertips into acrylic paint and dab different numbers of fingerprints onto the page. Find animals with that number of toes (e.g. a camel footprint has two toes, an emu has three, a dingo has four) and make ‘animal tracks’ across the page.

Science

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• Look at patterns of shapes on animals such as butterflies. • Make biscuits, placing choc-drops on them in different arrays before cooking. After cooking, see if the heat has changed the appearance of the dot arrays.

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RESOURCE SHEET Spotty bugs

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CONTENT DESCRIPTION: Subitise small collections of objects

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Concentration

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CONTENT DESCRIPTION: Subitise small collections of objects

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CONTENT DESCRIPTION: Subitise small collections of objects

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

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CONTENT DESCRIPTION: Subitise small collections of objects

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Checklist

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

Subitise small collections of objects (ACMNA003) © Australian Curriculum, Assessment and Reporting Authority 2012

Use subitising to order groups of objects

Use subitising to compare collections of numbers

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STUDENT NAME

Recognise the number of items in a small collection without counting

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

Compare, order and make correspondences between collections, initially to twenty, and explain reasoning (ACMNA289) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS

What this means

Collection A group of distinct objects

Comparison

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Looking at two or more things and considering their similarities and differences

Placing objects in order according to an attribute (such as size or numerical value)

Ordinal number

A number that tells the position of something in a list or in relation to other things or numbers

Teaching points

• Model and discuss the language of sequence, and how the language differs from, but is similar to, the counting numbers (e.g. ‘three’ vs ‘third’). • Give students opportunities to describe position (e.g. ‘What position is Sally in the line?’), and respond to questions (e.g. ‘Who is third?’) and directions (e.g. ‘Place the frog third on the log’) about position. • Use one-to-one matching to compare collections; e.g. matching eggs to eggcups, saucers to cups etc. • Construct and compare numbers in linear lengths (e.g. using interlocking cubes) and use the language of comparison related to numbers (longer, shorter, more, less). • Progress to comparing two collections of items and then sequencing three or more in order of size. Initially compare collections with identical items and then with different items, including where the larger set has smaller sized items.

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Ordering

• Students understand that numbers relate to quantity and not to other attributes (such as size). That is, they can say the collection of eight small bottle lids has more than the collection of seven large bottle lids. They understand that numbers can be used to describe the size of a collection, and also to order (first, second, third).

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Student vocabulary

• Students who have difficulty with sequencing (1st, 2nd, 3rd), including using terms such as ‘before’ and ‘after’, days of the week etc. • Students who attend to other features of collections rather than number (especially the size of items). • Students approaching the end of the foundation phase who are unable to compare abstract numbers (e.g. 6 and 4)‚ despite many experiences counting small collections, ordering lengths and sequencing subitisable collections.

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

eighth ninth tenth

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

HANDS-ON ACTIVITIES Who has more? (page 49) • Initially ensure you teach the concepts of more and less with items that are of a similar size. For example, set out collections of toy cars in front of different students and the ask students to tell you who has more cars. This way, students will understand that ‘more’ relates to the number, not the size, of the objects. Group students into differentsized groups and ask which group has more people. Students collect leaves during an outdoor walk and count the leaves, asking pairs of students who has more and who has less. Then students group their leaf collections by other criteria; e.g. into which colour or kind of leaf there is more, less or the same amount of. Ask students to make a group of items (such as counters) that is the same amount as their group of leaves.

Ages and stages

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• Divide a sheet of card into thirds. Write the three age groups that the students in your class could be. Each student places a piece of paper with his/her name on it into the correct section of the card, according to age. When a birthday occurs, the student can move his/her name into another age category. At the end of the school year, discuss which group has more or less students in it and give reasons for this.

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Comparing collections (pages 51, 52 and 53)

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• Give the students a group of objects, such as coins from different currencies, shells, or even jewellery. Pairs of students make a small collection with certain features, such as the items are all small, all red, all have zigzags etc. The students compare their collections, discussing the sizes and features of the collections, and try to guess which feature all the items other students’ collections have.

Ordinal number activities

• Discuss who was first into the classroom that morning, … second, third etc. As the first 10 students enter the room, give them a ‘place’ card (see page 53). Once they are all in, ask them to put themselves in order in a line from first to tenth. • Talk about recent sporting events and discuss which team came first, second etc. in the league table. • Divide a strip of paper into six sections. Give the students a selection of small manipulatives, such as toy animals. Use to practise understanding of ordinal numbers as directed; ‘Put the lion in the first section’, ‘Put a fish in the third section’.

Balloons

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• Open and sort a packet of balloons by colour. Use one-to-one correspondence to count the numbers of the different colours, then work out which colours there were more or fewer of.

More or less dice

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• Give each student two dice (with dots) and a sheet of paper divided into two lengthwise. Students roll the two dice. They collect counters for each number and compare the two collections to decide which is more. They write down the one that is greater in the first column and the number that is less in the next column, and write nothing if the numbers are the same.

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• Paint dried lima beans two different colours (so that the two sides are coloured differently). Place ten beans in a cup. Students shake the beans and tip them onto a mat. They group, then count each colour to see how many beans landed on the (e.g. red) side and how many landed on the other to find out which colour there is the most, least or same number of.

Card games

• In pairs or small groups, give each student 10 numeral cards (page 25) or numbered playing cards. Each student takes a card from his/her pile of cards (face down) then places it on the table face up. The students in each group decide which card is the greater value. The student whose card is worth most gets to keep all the cards played. If the cards are all the same, they tie and each student keeps his or her own card.

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

LINKS TO OTHER CURRICULUM AREAS English • Read The very hungry caterpillar by Eric Carle and discuss what the caterpillar ate on the first day, the second day etc. • Read the following books and discuss what happened to the first, second, third etc. characters: – The three little pigs – The enormous turnip – The three billy goats Gruff – 10 little rubber ducks by Eric Carle – Who sank the boat? by Pamela Allen – Eleven elephants going up! by Bethany Roberts and Patricia Hubbell. • Write simple recipes or procedures describing what to do first; second etc. • Read number rhymes describing ordinal position such as ‘This little piggy’

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Information and Communication Technology

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• Play games, such as deciding which hand has more (or fewer) bugs at <http://ictgames.com/mucky.html>; or a more advanced game where students have to choose a number that is higher or lower than a given number at <http:// ictgames.com/rabbit2.html>

Health and Physical Education

• Place hoops in a row parallel to the students, and supply different-coloured beanbags. Make a deck of cards with instructions to follow written on them, such as ‘Put the blue beanbag in the 1st hoop’. Students take an instruction card from the pile, read it aloud, then follow the instructions. • Discuss the kinds of foods you should eat more of (vegetables, fruit) and less of (sugar, fat). • Put students into groups of four, and in each number students from first to fourth. Give each group a hoop, which each student holds on to with one hand. All the groups of four move around slowly in a large circle. The teacher calls out an ordinal position, such as fourth, and all the fourthnumbered students must run around the large circle and get back to their hoop as fast as they can.

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• Talk about the British Royal family, and the names of monarchs‚ such as Queen Elizabeth the Second, King Henry the Fifth, and so on.

The Arts

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• Learn to sing ‘The twelve days of Christmas’. • After reading a book about monsters (such as The Gruffalo by Julia Donaldson or Where the wild things are by Maurice Sendak), students can design and paint their own monsters. Students can compare monsters and say which monster has the most eyes, has more horns, the fewest legs etc.

Civics and Citizenship • After learning about bus drivers, line up seats and set up a pretend bus. Students (passengers) get on the bus and the bus driver tells them where to sit: in the first seat, the second seat etc. The passengers tell the bus driver where they want to get off the bus; e.g. at the third stop.

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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Ordering collections Cut and laminate the pictures in each column to make a set of four. Students count the items shown in each picture then put the pictures in order.

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

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CONTENT DESCRIPTION: Compare, order and make correspondences between collections, initially to twenty, and explain reasoning

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

© Australian Curriculum, Assessment and Reporting Authority 2012

Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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CONTENT DESCRIPTION: Compare, order and make correspondences between collections, initially to twenty, and explain reasoning

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

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Jacob has 5 blocks. He has more than Tom.

Morgan has 6 blocks. She has more than Jacob.

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Tom has 3 blocks. He has less than all the other children. He has the least.

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Sophie has 6 blocks. She has the same number of blocks as Morgan.

More‚ the same‚ the most‚ less‚ the least

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Date:

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(a) Who has the most lollies?

1st child 2nd child 3rd child

(b) Who has the least lollies?

1st child 2nd child 4th child

(c) Who has the same number 1st child 3rd child 4th child of lollies as the 2nd child? Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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Name:

Date:

1. Which bowl has the most fish? Count, then shade the bubble.

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

Assessment 2

Checklist

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

Compare, order and make correspondences between collections, initially to twenty, and explain reasoning (ACMNA289) © Australian Curriculum, Assessment and Reporting Authority 2012

Uses comparative Groups objects language‚ such giving reasons to as more, less explain how they and same as‚ have ordered to describe or compared collections objects

Identifies a number as being more or less than another number

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Uses correct language to describe the order of objects to 20

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

Represent practical situations to model addition and sharing (ACMNA004) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS

What this means

A mathematical process, such as addition, in which one set of numbers is produced from another

• Students can solve number problems with physical objects by adding some and then taking some away. They may initially recount the resulting collection to find the amount‚ but should move to counting up as items are added and counting back as items are subtracted. At this age‚ students remain reliant on modelling problems with objects or pictures.

Addition

Teaching points

Operation

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Subtraction

The opposite operation to addition, where from a given collection a number of objects are taken away

Sharing

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A gathering of 2 or more people or items considered together because of a similar feature

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Student vocabulary

• Students who have trouble ‘counting out’ items in story problems‚ as opposed to counting objects arranged in a line. • Students who have difficulty with understanding and using mathematical language (such as ‘more’, ‘less’, ‘went away’).

m . u

Splitting a number, collection or object into equal parts

Group

• Use children’s literature as a basis for modelling stories with small numbers that involve adding or taking away. Use toys, pictures or objects (e.g. counters) for modelling. • Model and solve problems that involve grouping (combining two or more groups to find the total; or when given a group‚ to find how much more is required to reach a given total) and changes to small collections (find the total after a given number is added/ taken away; or find how many have been added/taken away given the starting number and the total). • Have students make up simple number stories and number problems for their peers to solve. • Practise adding one or taking one away from a small collection and noticing the result (the number after/before in the counting sequence).

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more add take away share group

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

less plus altogether

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

HANDS-ON ACTIVITIES How many more? • Display two or three counters or other small objects. Ask the students how many more they would need to make a number (such as 8 or 10). Do a similar activity but roll a dice with dots. Ask the students how many more dots they would need to make a certain number.

Number stories • Give the students multiple opportunities to create number stories (see the number stories picture resource on page 62). Allow them to choose items and situations that interest them. Use words such as ‘There were two and then five more arrived’, ‘If there were five in the basket and I put in five more‚ how many were there altogether?’, ‘If I had three but ate one‚ how many were left?’‚ ‘There were two birds in the tree but one went away, how many were still on the tree?’ Allow the students to create the stories with objects, then draw them as pictures before using symbols. (See page 63.)

Magic beans

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• Give each student 10 dried lima beans painted gold on one side and silver on the other. Toss them onto a table and then count how many of each colour there are. Record the results as an equation.

‘Take-away’ counter

• Put a number of counters on a table and count them. Ask the students to look away while you or a selected student removes some of the counters. Ask ‘How many counters did I take?’ Students count how many are left to work out how many were taken.

Number bonds with cubes

• Give the student a tower of 10 unifix™ cubes joined together. Ask them to break the tower into parts to find and record the different number combinations that make 10.

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Dice or dominoes

• Students roll two dice and add the dots rolled. Similarly‚ students can take a double-sided domino and add the two sides, trying to find the highest number of dots in the domino set. Students could also do this with playing cards, the quantity and numeral cards (page 23) or the quantity, name and numeral cards (page 27). The students could make their own dot cards and put them together to make different numbers.

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• Introduce a number line (0–10) as a series of numbers to jump along in a line on the floor. Ask one student to take two jumps. Then ask the others how many more jumps he or she would need to do to reach five.

Fact families (Page 62)

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• Give students a picture from page 62 and a set of counters (7–10), or copy and cut out the images that match the picture. Ask the students to make stories with the counters (or pictures) and then to show some different ways of making 7. For example, 6 penguins are on land and 1 is in water, then 5 on land and 2 in the water and so on‚ to make the number bonds.

Think board (page 63)

• The think board can be used to show a number problem in different ways. Students can display understanding of a story with real things (such as small plastic toys); for example: ‘There were three dinosaurs having a drink. Then two more came, so there were five’. They then draw a picture to show the story, followed by writing it as a problem with numbers and symbols (e.g. 3 + 2 = 5).

Five ball clowns (page 65) • Give students one clown picture each from page 65. Enlarge if desired and cut the dot cards, and place them in a pile face down. Students take turns to turn over two cards. If the dots on the two cards add up to five, they can put a counter on one of the clown’s juggling balls. If not they put the cards back into the pile.

Groups • Use the term ‘groups’ to describe a collection. Ask students to make groups of three students, four, five etc. Then ask them to make groups with manipulatives before allowing them to find groups of a certain number of pictures.

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

HANDS-ON ACTIVITIES (CONTINUED) Go fish • Make copies of number cards from 0 to 10 (such as those on page 23 with both numerals and pictures). Shuffle and deal the cards among students in groups of two to four. The students look through their cards and make pairs of cards that add up to 10. If they have a pair‚ they put them face up in front of them. If they don’t have a pair‚ they take turns to ask another student for a particular card to try to make 10. If that student has the card‚ she or he hands it over. The student with the most pairs at the end of the game is the winner.

Dominoes

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• Use the dominoes on page 66 to add and subtract in a variety of ways: – Pick up a domino. Place it so the bigger number (more dots) is on the left‚ then count on from that number to find out how many dots are on the domino. Similarly, do subtraction using the dominoes, taking the smaller number of dots away from the bigger number. – Place a number of dominoes in front of a small group of students. The dots on these dominoes should add up to two set numbers, such as 6 or 7. One students chooses one of the dominoes without telling the others which one they selected, saying only the number of dots on the domino. The other students take turns to guess which domino the student chose. – Give students a number line from 1 to 10. For each number on the line‚ they find a domino with dots that add up to that number. When playing this game, encourage the students to subitise and count on from the larger number, rather than counting all the dots each time. – The teacher or one student chooses and shows a domino to a small group of students. They must then find a domino from a collection in front of them that has one more dot. Repeat, but instead finding a domino with one less dot.

Sharing stories

• Give each student a small paper plate and demonstrate sharing a number of items‚ such as dried pasta or biscuits. Demonstrate giving one to each person before giving a second to each. Discuss what might happen when there are pieces ‘left over’. • Make multiple copies of page 64. Give the children two or more large pictures (such as the dogs, koalas or the train engines) and ask them to share the smaller items among the larger ones (such as sharing the puppies among three dogs, sharing the gumleaves among four koalas). • Allow the students to share manipulatives equally among clearly identified areas; for example, put plastic toy animals into the carriages of a train, dolls into the rooms of a doll’s house, plastic frogs onto cut-outs of lily pads.

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• Pairs of children are given two cards with a number of pictures or dots on them. The students add the dots together then collect matchsticks or craft sticks that equal the total and use that number of sticks to construct a pretend campfire.

Divided plates

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• Use divided plates for addition and subtraction stories, or to demonstrate sharing. For addition, put manipulatives in both small sections (5 + 3). Move all of them down to the larger bottom section to show the sum. For subtraction, begin with all of the manipulatives in the large section and then remove some to the smaller section to find out how many are left.

How many frogs jumped? (page 69)

• Working in pairs, the 10 frogs are placed onto one lily pad. One student closes his or her eyes while the other moves a number of frogs from one lily pad to the other, then covers the second pond with a sheet of thick paper. The other student works out how many frogs jumped over.

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

LINKS TO OTHER CURRICULUM AREAS English • Sing songs and rhymes that involve adding or taking away items, such as ‘Three jellyfish’, ‘Five grey elephants balancing’, ‘Ten in the bed’, ‘Five little ducks went out one day’. • Read books involving sharing/division and addition, such as: – The doorbell rang by Pat Hutchins – Two of everything by Lily Toy Hong – 12 ways to get to 11 by Eve Merriam – Each orange had 8 slices by Paul Giganti – The Lion’s share by Matthew McElligot.

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Information and Communication Technology

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• Use an interactive whiteboard to demonstrate moving pictures of items away from or into a collection, or to share items. Allow the students to move pictures across the board. • Play games such as adding the dots on ladybirds at <http://www.bbc.co.uk/schools/laac/numbers/ch1.shtml>, one or two more or less at < http://www.kenttrustweb.org.uk/kentict/content/games/giraffe_v5.html>, and adding spots on a ladybird at <http://www.kenttrustweb.org.uk/kentict/content/games/ladyBirdSpots/index.html>.

Health and Physical Education

• Draw a large shape such as a circle or target on the floor with chalk. Divide the shape into different sections‚ then draw a different number of dots in each section. Students take turns to throw two beanbags into the shape, then add the number of dots their bean bags landed on. • Play ten pin bowling. Each time a student knocks some pins down, he/she counts how many were knocked over and says it as a sentence: ‘There were ten pins and three were knocked over‚ so there are seven left’.

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• Try subtractive monoprinting where students ‘take away’ paint. Spread paint evenly on a flat surface such as a tabletop. Students use a finger or tool to remove paint to make a picture, then place a sheet of paper over the picture to take a print. • Experiment with combining (adding) different coloured poster paints.

Science

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• Use things found in the natural environment (such as sticks, shells, gumnuts or leaves) to make collections, and add or take away from those collections. For example, get students to form pairs and combine their collections, then two sets of pairs combine and add the collections and so on. Similarly‚ share a collection of such objects among groups of students. • Discuss how there is a limited supply of fresh water on Earth and the need to share it fairly.

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RESOURCE SHEET

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Number stories and fact families

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CONTENT DESCRIPTION: Represent practical situations to model addition and sharing

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RESOURCE SHEET Number ‘Think’ board

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Pictures for number stories

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RESOURCE SHEET Five ball clowns Put one counter on a clown’s ball for each two dot cards turned over that add up to five.

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Dominoes

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RESOURCE SHEET Strategies for adding and subtracting Combining two groups to find the total • Count all the items in both groups to find how many there are altogether.

Counting on • Count one set of items. Then add another set, counting on without having to recount the first (unchanged) set. For example, place five items into a cloth bag, counting as each is placed. Ask how many objects there are in the bag. Place‚ two more objects into the bag‚ counting each. Ask how many objects there are in the bag now, using counting on to find the answer.

Partitioning

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• Learn to separate (partition) a given number of objects into two groups. Practise by throwing a set number of beanbags at a target and talking about how many landed in the target and how many missed, or separating all the dominoes with the same number of dots to form a new group. • Other examples include: – exploring different combinations of how one lot of 10 (for example) toy monkeys and 10 toy elephants can be placed in a ‘zoo enclosure’ that can hold only 10 animals in total – making towers 10 blocks high using two different sets of coloured blocks.

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© Australian Curriculum, Assessment and Reporting Authority 2012

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

Adding doubles

• Students learn basic facts such as 5 and 5 makes 10. A student can use doubling as a strategy for adding; for example, given a sum of 6 and 5, he/she might say 5 and 5 is 10, and one more is 11.

Taking away

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• Subtract a number of items from a set and count how many are left.

Counting backwards

• Take a smaller number of items from a larger set and find how many are left by counting back from the larger number. For example, say there are five children at the table and two leave; how many are still at the table? (from 5, count back 2: 5 – 1 = 4‚ 4 – 1 = 3)

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• Find out how many items have been removed from a larger group of objects by counting forwards to the larger number. For example, if 10 biscuits were on a plate but now there are only 4‚ find out how many were taken by counting forward from 4 to 10.

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Counting forwards

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• Copy/Match visual and spatial patterns to solve problems—allowing students to learn by listening, observing and imitating.

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RESOURCE SHEET Division

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Share the lollies among the people.

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RESOURCE SHEET How many frogs jumped?

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RESOURCE SHEET Sharing

Ten people are sharing 2 spots.

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One person is on each chair. Six cupcakes are shared on 3 plates.

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Two people are sharing 2 chairs.

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Five people are at each spot. Six cupcakes are shared on 2 plates.

Two cupcakes are on each plate. Eight bees are sharing 4 leaves.

Three cupcakes are on each plate. Eight bees are sharing 2 leaves.

Two bees are on each leaf.

Four bees are on each leaf.

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3

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3

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makes

makes

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Combining groups

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

Name:

Date:

1. How many more do you need to make 10?

o e 2t 4r 3B 5 8 7 s r e o (b) (c)o (a) p u k are left? 2. Take away (cross Sout) the number shown. How many 5

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Assessment 1

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1. Count how many dots are on each side of the domino. Then add the two sides.

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(d)

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2. Draw more dots on the dogs to make the amount shown.

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(a)

makes 4

makes 10

3. Share six fish among the birds. How many does each bird get? (a)

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Checklist

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

Represent practical situations to model addition and sharing (ACMNA004) © Australian Curriculum, Assessment and Reporting Authority 2012

Subtracts small groups of numbers using concrete materials

Adds small groups of numbers by drawing or using pictures

Subtracts small groups of numbers by drawing or using pictures

Shares a collection equally

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STUDENT NAME

Adds small groups of numbers using concrete materials

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Answers

Sub-strand: Number and Place Value

N&PV – 1

Page 56 Assessment 2

Page 17 Assessment 1 1. 2. 3. 4. 5.

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

4 13 9 7 8

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

16 20 16 19 1

Page 18 Assessment 2

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(d) 11 (d) 21 (d) 14

(c) 5 N&PV – 5

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N&PV – 2

Page 72 Assessment 1 1. (a) 5 2. (a) 4

(b) 3 (b) 5

(c) 7 (c) 3

Page 73 Assessment 2

1. (a) 4 and 5 makes 9 (c) 6 and 1 makes 7 2. (a) 3 more spots (c) 4 more spots 3. (a) 3 fish each (b) 2 fish each

(b) 2 and 3 makes 5 (d) 4 and 2 makes 6 (b) 2 more spots

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1. (a) 5, 6, 7, 8, 9 (c) 16, 17, 18, 19, 20 2. 8, 7, 6, (5), 4, 3, 2, 1 3. (a) 4, 3, 2, 1, 0 (c) 11, 10, 9, 8, 7 4. (a) ten (b) seven (e) three (f ) two (i) nine (j) eight

(c) 9 (c) 8 (c) 4

1. (a) 4 (b) 6 (c) 3 Bowl (b) should be shaded. 2. (a) 4 (b) 4 (c) 2 Bowl (c) should be shaded. 3. (a) The mouse should be shaded. (b) The hen should be shaded.

Page 33 Assessment 1

1. (Going from left to right, downwards) 5 frogs, 6 balls, 3 kangaroos, 1 horse, 0, 10 cupcakes, 12 bananas, 4 shirts

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Page 34 Assessment 2

1. Eleven eggs should be drawn; 7 apples should be drawn; 5 eyes should be drawn. 2. Four balls should be coloured; 9 shells should be coloured; 8 fish should be coloured.

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(b) 6 (e) 7

(c) 4 (f ) 6

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1. (a) 6 (b) 3 (c) 5 (d) 2 (e) 4 2. (a) 8 apples (right side) (b) 6 flowers (right side) (c) 4 frogs (left side) (d) 6 presents (left side) N&PV – 4 Page 55 Assessment 1 1. (a) Car B (b) Car A (c) 4th 2. (a) 3rd child (b) 1st child

(d) Car C (c) 4th child

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

Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005) © Australian Curriculum, Assessment and Reporting Authority 2012

TEACHER INFORMATION

RELATED TERMS

What this means

Sort To separate or arrange items into groups according to a certain type or rule Classify

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A repeated arrangement of items (numbers, shapes, colours etc.) Similarity

An item’s aspect, trait or feature that resembles another’s

• Discuss the similarities and differences among objects. Seek out and discuss and/or record things with particular attributes; e.g. long things, round things, yellow things. • Have students follow a given rule for sorting objects. • Sort items into groups and have students determine the rule used for sorting. • Have students create their own rules for sorting. Sort common items (e.g. buttons, bottle caps or tops) in different ways. • Draw attention to patterns in nature (e.g. shells, leaves, butterfly markings, petals on flowers, spiderwebs). Copy them and have students create their own. • Have students (a) copy patterns, (b) provide the next element in a repeating pattern, and then (c) create their own patterns with movements, sounds and objects. • Describe patterns in abstract ways; e.g. labelling the first element ‘A’‚ the second ‘B’ and so on. Express the same pattern in different ways (e.g. an AAB pattern with stamps and claps, and then with red and blue blocks).

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An item’s aspect or feature that is dissimilar to or unlike another’s

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stripes, spots, curvy lines pattern

What to look for

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Teaching points

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To put objects into groups based on some property they have in common Pattern

Students are able to recognise, describe and continue patterns of many kinds. This could include talking about the vein patterns on a leaf or the spiral pattern on a snail’s shell. They can join in with and provide the next element in a pattern of movements (e.g. jump, jump, clap); sounds (e.g. high note, low note); or colours (e.g. three yellow blocks and one red block). They can notice similarities and differences among things and group them according to these characteristics (e.g. colour, size, function).

• Students who lack the vocabulary to describe objects. • Students who can copy a pattern but are unable to extend or create one.

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repeat same similar different copy

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

continue create make

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

HANDS-ON ACTIVITIES For sorting and classifying familiar objects Things to collect for classifying and patterning: • These can include: shells, buttons, coins (different currencies‚ if possible), feathers, leaves from different plants, strips or pieces of fabric with distinct patterns, wrapping paper with a repetitive pattern, cupcake papers, matchsticks and craft sticks, craft pom-poms, Unifix™ cubes, pattern blocks, rubber stamps, bear family counters, bottle tops, plastic jewellery and beads, coloured dry pasta‚ and small pebbles.

Guess my collection • Place a collection of objects, such as those listed above, in the centre of a small group of students sitting in a circle. One student makes a small collection (about 4 to 5 items) with one common feature, such as the items are all small, all red, all have zigzags etc. The others in the group must try to guess which characteristic all the items have in common.

Copy mine

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• Give each student in a small group (sitting in a circle) a collection of items. One student takes one of his/her items and places it in the centre of the group. The others find an item in their collection that is similar in some way and place it in the centre too. Discuss how the secondary items are similar to and different from the initial object.

Matching games

• Play matching games such as concentration, go fish, bingo and dominoes to help students compare two items and find similarities between them.

My team

• Students work in pairs. One student makes a small collection of buttons (or other such items) using a ‘secret’ classification rule. The student keeps all the buttons hidden from the partner. He or she takes one of the selected items, places it so the other student can see it and says‚ ‘This is on my team’. He or she then puts an item that is not part of the collection out and says‚ ‘This is not on my team’. The other student tries to guess the classification rule by taking items from a central collection and asking ‘Is this on your team?’ until the rule is identified.

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• Children can sort as they clean up. (The teacher can label shelves or toy boxes with pictures of the items that belong there.) Bring in clean socks and ask the children to find pairs of socks and put them together.

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• Give the students a collection of coins or attribute blocks. Ask them to choose one item (coin or block) and describe it (in terms of its shape, colour and size). Then ask them to choose another item, choosing one that is different in some way from the first item. For example, if the first choice is a small gold coin, a large gold coin could be next. Then ask them to choose an item that is different in two ways, such as a different colour and shape.

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Different in different ways

DOLLAR

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

HANDS-ON ACTIVITIES For copying, continuing and creating patterns with objects and drawings Making rows • Give the students a collection of counters or Unifix™ cubes in two different colours. Ask them to put the counters in a row. Discuss the ways they lay them out and any patterns that are shown. Model a repeating pattern for the other students to copy. Discuss how many items there are in each set that repeats.

Copy and continue patterns (page 82) • Copy the pattern strips onto card and laminate if desired. Cut (and laminate) the individual pattern items. Give the students one pattern strip and ask them to read it. Then give them the items and ask them to put them onto (or above/ under) the pattern strip in the correct pattern. They then try to continue the pattern.

Making patterns

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• Ask the students to line up in different ways, such as boy–girl, light hair–dark hair, sit–stand, or with happy–sad faces. • Give the students strips or cardboard and some craft items to glue onto the card in a pattern. Limit the number of different kinds of items initially (so there are only two variables or attributes). For example, use red and blue craft sticks before moving onto more colours or different items such as craft sticks and pompoms. The students can make different patterns using the two different items and the different colours they come in. Encourage the students to read and describe their patterns.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Patterns around us (page 81) Pattern cards (page 83)

• Copy the page onto card and cut each strip into three (lengthways). Mix the strips up‚ then let the students find the three patterns that are the same from a collection. Once they have found the three matching pattern strips‚ they can make that same pattern using different materials, or as a movement or sound pattern.

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Movement patterns

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• Give each student one of the pictures. The students identify and read the patterns they see, then recreate them with materials such as matchsticks or counters. They can record the patterns with numbers or letters.

• Children create patterns of movement with their body using claps, taps, pats, stomps and jumps. For example, an AB pattern could be ‘clap, pat, clap, pat’ or ‘stomp‚ hop‚ stomp‚ hop’.

Sound patterns

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• Students make sound patterns with musical instruments. Give one group of students (for example) bells and give another group triangles. The students play in a pattern as directed by the teacher (such as bells, triangles, bells, triangles) for an AB pattern. You could also try making different sound patterns with animal noises, such as ‘Baaa, woof‚ woof’.

Patterns in numbers

• Play counting games where, for example, every second number is said loudly, or every third number is clapped. Colour number grids in a pattern, such as colouring all numbers ending with 2 red. Look at the classroom calendar and discuss the dates that the days fall on. Is there a pattern?

Is this pattern right? • Make a pattern with items‚ with one of the items included an obvious mistake from the rest. Ask the students to identify and ‘fix’ the problem for you.

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

LINKS TO OTHER CURRICULUM AREAS English • Read The button box by Margarette S Reid and discuss the different kinds of buttons and how the boy sorts them. • Read A dark, dark tale by Ruth Brown and discuss the pattern of repeated words. • Read The mouse and the apple by Stephen Butler and discuss the pattern of events. Try to guess what will happen next if the pattern continues.

Information and Communication Technology • Practise grouping objects in different ways at <http://www.abc. net.au/countusin/games/game9.htm> or sorting objects at <http://www.onlinemathlearning.com/sort-game.html>

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Health and Physical Education

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• Learn about the different food groups (dairy, meats, grains etc.) and sort a collection of foods into the groups.

History and Geography

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• Sort clothing from different cultures. • Look at designs (such as rangoli) with repeating patterns.

The Arts

• Look at patterns in carpets and rugs. Weave simple AB patterns using strips of fabric or paper in and out of slotted cardboard. • Make symmetrical patterns like those on a butterfly’s wings by putting blobs of acrylic paint on one side of a piece of paper, then folding it and spreading the paint. • With crayons or pencil‚ rub over different leaves to find their vein patterns. Use the patterns to classify the leaves according to what type of tree they came from. • Examine different patterns used in certain styles of painting, such as Aboriginal dot painting or X-ray style. • Make prints with vegetables in certain patterns; for example to make wrapping paper. • Make sound patterns with different instruments and record the patterns on paper. • Give students two copies of the same picture and have them to paint or decorate the pictures in different ways to make them look different.

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Science

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• Sort to recycle different materials. For example, if the class has a worm farm, sort the rubbish and scraps from lunchtime into two bins—one for scraps the worms can have‚ and the other for rubbish they can’t have. • Classify animals in different ways, such as according to whether they live on land or in water. • Observe patterns on insects and discuss how we use these patterns to help identify the insects.

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Design and Technology • Design and make a simple necklace.

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RESOURCE SHEET Same and different

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These things all show the number 2.

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CONTENT DESCRIPTION: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

These things all have one handle.

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These two monsters These two monsters These two monsters are the same. are similar. are different.

© Australian Curriculum, Assessment and Reporting Authority 2012

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

RESOURCE SHEET Patterns around us

Patterns on animals

Patterns in our homes

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Patterns on the street

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2007

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CONTENT DESCRIPTION: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

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

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RESOURCE SHEET

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

CONTENT DESCRIPTION: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

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Patterns (to copy and continue)

© Australian Curriculum, Assessment and Reporting Authority 2012

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

RESOURCE SHEET Pattern cards

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A

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RESOURCE SHEET Simple sorting rules

Size: Big things

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Shape: Round things

Weight: Light things

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Other features: Things with a hole in the middle

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Other features: Things with patterns

Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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Colour: Yellow things

© Australian Curriculum, Assessment and Reporting Authority 2012

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

Name:

Date:

Shade the bubble 1. What comes next? (a)

(b)

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Assessment 1

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© R. I . C.Publ i cat i ons 2. Which teddy is same asu the first teddy? •f orr ethe vi e wp r p os esonl y•

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(c)

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

Name:

Date:

Shade the bubble 1. Which group does each item best belong to? (a)

2. Continue the pattern on the snake.

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3. Colour the circles with two different colours to make a pattern.

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© Australian Curriculum, Assessment and Reporting Authority 2012

Assessment 2

Checklist

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

Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005) © Australian Curriculum, Assessment and Reporting Authority 2012

Continues patters

Creates patterns

Sorts objects

Explains how objects were sorted

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STUDENT NAME

Copies patterns

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Answers

Sub-strand: Patterns and Algebra

P&A – 1 Page 85 Assessment 1 1. (a) dog (b) flower (c) tennis ball 2. The 2nd (middle) teddy bear 3. The 4th (last) dinosaur Page 86 Assessment 2 1. (a) 3rd (last) group 2.

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(b) A‚ B‚ B

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3. Teacher check 4. (a) 1‚ 2‚ 1‚ 2

(b) 2nd (middle) group

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Australian Curriculum Mathematics resource book: Number and Algebra (Foundation)

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

Number and Algebra (Australian Curriculum): Foundation - Ages 5-6

Published on Dec 19, 2013

Australian Curriculum Mathematics resource books - 'Number and Algebra' (Foundation to Year 6) is a series of seven books specifically writt...

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