Number and Algebra (Australian Curriculum): Year 4 - Ages 9-10 by Teacher Superstore

RIC-6088 9.4/624

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) Published by R.I.C. Publications® 2012 Copyright© R.I.C. Publications® 2012 Revised edition 2013 ISBN 978-1-921750-72-4 RIC–6088 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.

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

© 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.

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

Name of Purchaser:

Date of Purchase:

ew i ev Pr

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)

Teac he r

Signature of Purchaser:

m . u

w ww

. te

Supplier:

o c . che e r o t r s super

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

View all pages online PO Box 332 Greenwood Western Australia 6924

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

AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: NUMBER AND ALGEBRA (YEAR 4) Foreword Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the number and algebra content strands of the national maths curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and assessment activities, along with links to other curriculum areas.

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

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

• F&D – 2

Count by quarters, halves and thirds, including mixed numerals Locate and represent these fractions on a number line (ACMNA078)

– Teacher information ...................... 90 – Hands-on activities ........................ 91 – Links to other curriculum areas ...... 92

Investigate and use the properties of odd and even numbers (ACMNA071)

– Teacher information ........................ 2 – Hands-on activities .......................... 3 – Links to other curriculum areas ........ 4

– Resource sheets ............... 5–7 – Assessments .................. 8–10 – Checklist ............................. 11

• F&D – 3

Recognise that the place value system can be extended to tenths and hundredths Make connections between fractions and decimal notation (ACMNA079)

– Teacher information .................... 104 – Hands-on activities ...................... 105 – Links to other curriculum areas .... 106

• N&PV – 2

Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

– Teacher information ...................... 12 – Hands-on activities ........................ 13 – Links to other curriculum areas ...... 14

– Resource sheets ........... 15–19 – Assessments ................ 20–22 – Checklist ............................. 23

– Resource sheets ........... 93–98 – Assessment ............... 99–102 – Checklist ........................... 103

ew i ev Pr

Teac he r

Number and Place Value .................................................... 2–77 • N&PV – 1

– Resource sheets ....... 107–118 – Assessments ............ 119–122 – Checklist ........................... 123

Answers ........................................................................ 124–125

• N&PV – 3

Money and Financial Mathematics ............................... 126–141 • M&FM – 1

Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

– Teacher information ...................... 24 – Hands-on activities ........................ 25 – Links to other curriculum areas ...... 26

– Teacher information .................... 126 – Hands-on activities ...................... 127 – Links to other curriculum areas ... 128

– Resource sheets ........... 27–31 – Assessments ................ 32–34 – Checklist ............................. 35

Answers ................................................................................ 141

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

w ww

– Teacher information ...................... 36 – Hands-on activities ........................ 37 – Links to other curriculum areas ...... 38

. te

– Resource sheets ........... 39–41 – Assessments ....................... 42 – Checklist ............................. 43

m . u

• N&PV – 4

• N&PV – 5

Patterns and Algebra .................................................. 142–184 • P&A – 1 Explore and describe number patterns resulting from performing multiplication (ACMNA081)

– Teacher information .................... 142 – Hands-on activities ............. 143–144 – Links to other curriculum areas .... 144

– Resource sheets ....... 145–150 – Assessment ............. 151–152 – Checklist ........................... 153

o c . che e r o t r s super

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

– Teacher information ...................... 44 – Hands-on activities ........................ 45 – Links to other curriculum areas ...... 46

• N&PV – 6

– Resource sheets ....... 129–137 – Assessment ............. 138–139 – Checklist ........................... 140

– Resource sheets ........... 47–54 – Assessment ................. 55–56 – Checklist ............................. 57

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder (ACMNA076)

– Teacher information ...................... 58 – Hands-on activities ........................ 59 – Links to other curriculum areas ...... 60

– Resource sheets ........... 61–71 – Assessment ................. 72–74 – Checklist ............................. 75

• P&A – 2

Solve word problems using number sentences involving multiplication or division where there is no remainder (ACMNA082)

– Teacher information .................... 154 – Hands-on activities ...................... 155 – Links to other curriculum areas ... 156

• P&A – 3 Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)

– Teacher information .................... 168 – Hands-on activities ...................... 169 – Links to other curriculum areas .... 170

Answers ............................................................................ 76–77 Fractions and Decimals .................................................. 78–125 • F&D – 1

– Resource sheets ....... 171–179 – Assessment ............. 180–181 – Checklist ........................... 182

Answers ........................................................................ 183–184 New Wave Number and Algebra (Year 4) student workbook answers ........................................................185–197

Investigate equivalent fractions used in contexts (ACMNA077)

– Teacher information ...................... 78 – Hands-on activities ........................ 79 – Links to other curriculum areas ...... 80

– Resource sheets ....... 157–164 – Assessment ............. 165–166 – Checklist ........................... 167

– Resource sheets ........... 81–85 – Assessments ................ 86–88 – Checklist ............................. 89

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

iii

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

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

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).

Teac he r

(NOTE: The Foundation level includes only Number and Place Value, and Patterns and Algebra.)

ew i ev Pr

The length of each content description section varies.

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

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

What this means provides a general explanation of the content description.

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

description.

w ww

m . u

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

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

. te

o c . che e r o t r s super Sub-strand: Number and Place Value—N&PV – 1

HANDS-ON ACTIVITIES

Even number patterns

Colour the even numbers on the 1–150 number grid on page 5 and discuss the patterns these numbers make.

Odd and even boxes

Revise student understanding of odd and even numbers by playing this game. On 15 cardboard cartons, draw on each an odd or even number between 100 and 1000. Then place them randomly outside, some distance apart. Students walk around the outside of the boxes until the teacher calls out ‘even’. The students have to run to a box with an even number and stand next to it (or to an odd-numbered box when ‘odd’ is called). The last student to locate an appropriately numbered box leaves the game.

Roll and tally

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.

Students work in pairs. One rolls a dice 20 times and the other keeps a tally of the odd and even numbers that are rolled on a chart (with columns for even and odd numbers). Then two dice are thrown together and one student calculates the sum of the numbers shown. The other student determines if the sum is odd or even and keeps a tally on a new chart. At the conclusion of the game, the class can then share their scores and each group can try to explain why there were more even than odd numbers thrown with the two dice.

Odd or even? This is a game for two players. One player is ‘odd’ and the other is ‘even’. They both decide on a number between one and five and show that number with their fingers held behind their backs. On a given signal, they reveal their finger numbers and if the sum of these numbers is even the ‘even’ player scores a point. Reversely, his/her opponent scores if it’s odd. The first player to reach five points wins. The game can also be played to find the difference between the two numbers or a multiple of them.

Take the pack Small groups of students can play this game. A pack of cards is placed face down with the top two cards face up, side by side and overlapping slightly. If the sum of the two cards is even, they are removed and replaced with two new cards. If the sum is odd, a third card is placed on top and added to the second card. If this sum is odd, continue adding cards until the sum is even. The game continues until there are no cards left. The students can then play the game to identify odd sums and discuss why it takes so long to ‘take the pack’.

How can I make an even number? Groups of four or five students are given a pack of playing cards which are placed facedown on the table. Each takes a turn to turn over the top two cards and identify which operation could be used to make an even number using these two numbers. If the others agree that he or she has identified an operation correctly, the player keeps those two cards. If not, the cards are replaced in the pack. The winner is the student with the most cards. Once the students are familiar with the game, a more challenging task is to identify an operation to produce an odd number.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) R.I.C. Publications® www.ricpublications.com.au

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

Sub-strand: Number and Place Valueâ&#x20AC;&#x201D;N&PV â&#x20AC;&#x201C; 1

LINKS TO OTHER CURRICULUM AREAS English t 3FBE Even Steven and Odd Todd CZ KathrZO $ISJTUBMEJ BOE )FOSZ .PSFIPVTF QVCMJTIFE CZ 4DIPMBTUJD BOE BTL UIF TUVEFOUT UP XPSL JO QBJST UP XSJUF BOE JMMVTUSBUF B TJNJMBS TUPSZ PS QPFN UP IFMQ ZPVOHFS TUVEFOUT VOEFSTUBOE UIF DPODFQUT PG PEE BOE FWFO OVNCFST. t 4UVEFOUT DBO QSFQBSF BO JOGPSNBUJPO UBCMF UP TVNNBSJTF BOE FYQMBJO BT TJNQMZ BT QPTTJCMF XIBU IBQQFOT XIFO FWFO BOE PEE OVNCFST Bre BEEFE TVCUSBDUFE NVMUJQMJFE BOE EJWJEFE.

Science t *OWFTUJHBUF UIF OVNCFS PG MFHT EJĂ˛ FSFOU BOJNBMT IBWF BOE TIPX UIF Ăś OEJOHT BT B DMBTT DIBSU $IBMMFOHF TUVEFOUT UP Ăś OE B TQFDJFT XJUI BO PEE OVNCFS PG MFHT BOE EJTDVTT QPTTJCMF SFBTPOT GPS UIJT 5IF DPODFQU PG NBJOUBJOJOH CBMBODF XIFO NPWJOH DPVME UIFO CF EFNPOTUSBUFE CZ BTLJOH QBJST PG TUVEFOUT UP SVO B UISFF MFHHFE SBDF BOE UIFO EJTDVTT XIZ UIJT JT EJĂł DVMU BOE UP BMTP USZ UP FYQMBJO XIZ B UISFF MFHHFE EPH DBO SVO CVU WFSZ GFX PUIFS GPVS MFHHFE BOJNBMT XIP UIFO MPTF B MFH XPVME CF BCMF UP EP UIJT. t &ODPVSBHF TUVEFOUT UP JOWFTUJHBUF UIF PDDVSSFODFT PG PEE BOE FWFO BNPVOUT JO UIF GFBUVSFT PG EJĂ˛ FSFOU BOJNBMT UP DPNQMFUF B DMBTT T-DIBSU VOEFS UIF IFBEJOHT PG AWhatâ&#x20AC;&#x2122;T PEE BOE XIBtâ&#x20AC;&#x2122;T FWFO JO OBUVSF 5IFZ DPVME FYQBOE UIF BDUJWJUZ UP JODMVEF QMBOUT.

Health and Physical Education t 4UVEFOUT DPNQJMF B MJTU PG CPEZ QBSUT PG XIJDI UIFZ IBWF BO FWFO BNPVOU PG 4UVEFOUT DBO UIFO EJTDVTT QPTTJCMF SFBTPOT GPS UIJT BOE UIF EJĂł DVMUJFT IVNBOT DPVME FYQFSJFODF JG UIFZ IBE PEE BNPVOUT PG UIFN

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

History and Geography t 4UVEFOUT DPNQMFUF B UJNF MJOF TIPXJOH NBKPS FWFOUT JO UIFJS MJWFT BOE XIBU UIFZ XFSF EPJOH XIFO UIFJS BHF XBT BO PEE OVNCFS 5IFZ DBO UIFO DIPPTF B EFDBEF GSPN UIF QBTU UP SFTFBSDI BOE MJTU JNQPSUBOU FWFOUT GPS FBDI PG UIF FWFO ZFBST.

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

t $SFBUF BOE ESBX PS DPOTUSVDU B DSFBUVSF XJUI PEE OVNCFST PG GFBUVSFT PS CPEZ QBSUT TVDI BT FZFT MFHT UBJMT BOE FBST %JTQMBZ VOEFS UIF IFBEJOH A4PNF WFSZ PEE DSFBUVSFTâ&#x20AC;&#x2122;. t 4NBMM HSPVQT PG TUVEFOU XPSL UPHFUIFS UP DSFBUF B CPBSE HBNF CBTFE PO ATOBLFT BOE MBEEFSTâ&#x20AC;&#x2122; VTJOH QBQFS XJUI MBSHF OVNCFSFE TRVBSFT *O UIF HBNF QMBZFST UISPX UXP EJDF BOE DBO POMZ NPWF GPSXBSE GPVS TQBDFT JG UIFZ DBO TUBUF BO PQFSBUJPO UP QSPEVDF BO FWFO OVNCFS VTJOH UIF UXP OVNCFST UISPXO 5IFSF DBO CF BT JO ATOBLFT BOE MBEEFSTâ&#x20AC;&#x2122;, QFOBMUJFT JNQPTFE PO QMBZFST XIP MBOE PO DFSUBJO FWFO OVNCFST TOBLFT PO UIF CPBSE BOE QPTJUJWF PVUDPNFT GPS QMBZFST MBOEJOH PO DFSUBJO PUIFS FWFO OVNCFST MBEEFST

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.

t 4UVEFOUT MFBSO UP DPVOU JO UXP PUIFS MBOHVBHFT BOE IBWF POF TUVEFOU DPVOU UIF PEE OVNCFST JO POF MBOHVBHF XIJMF BOPUIFS DPVOUT UIF FWFO OVNCFST JO UIF PUIFS MBOHVBHF.

ew i ev Pr

Teac he r

Languages

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. PublicationsÂŽ www.ricpublications.com.au

Assessment pages are included. ÂŠ R. I . C Pactivities ub l i c i ons These. support included ina the t corresponding workbook. Many of the questions the u assessment pages ine a so â&#x20AC;˘f orr evi e wonp r p oares nl yâ&#x20AC;˘ format similar to that of the NAPLAN tests to Checklist

Sub-strand: Number and Place Valueâ&#x20AC;&#x201D;N&PV â&#x20AC;&#x201C; 1

familiarise students with the instructions and design of these tests.

. te

Investigate and use the properties of odd and even numbers when divided

STUDENT NAME

Investigate and use the properties of odd and even numbers when multiplied

Investigate and use the properties of odd and even numbers when subtracted

w ww

Investigate and use the properties of odd and even numbers when added

ÂŠ Australian Curriculum, Assessment and Reporting Authority 2012

m . u

Investigate and use the properties of odd and even numbers (ACMNA071)

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 â&#x20AC;&#x201C; 1

Page 8â&#x20AC;&#x201D;Assessment 1 1. 1,3,5,7 and 9 2. 0, 2, 4, 6, and 8 3. (a) 12 (d) 88 or 90 4. (a) 101 (d) 201 5. 402 and 260 6. 811 and 521

(b) 30 (e) 98 (b) 153 (e) 99

Page 10â&#x20AC;&#x201D;Assessment 3 She would have an even number to frame. Yes, she would have one bead left. He had an odd number left. There was an odd number of teams. No, they hadnâ&#x20AC;&#x2122;t lost a sock.

N&PV â&#x20AC;&#x201C; 2

Page 20â&#x20AC;&#x201D;Assessment 1

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

1. (a) (b) (c) (d) 2. (a) 3. (a) 4. (a)

t t t t

Tens

t t t

Ones

t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t 22 876 t t tt t t t t t t t t t t t t t t t t t t t t t t t 76 091 t t t t t

1. (a) The odd numbers are: 27, 345, 367 (b) The even numbers are: 450, 34 562, 97 532 2. There would be 4 odd numbers and 6 even numbers. 3. (a) even (b) even (c) even (d) odd (e) even (f ) odd (g) odd (h) even 4. (a) 13 032 (b) 72 867 (c) 2117 (d) 4539 (e) 114 (f ) 7368

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) R.I.C. PublicationsÂŽ www.ricpublications.com.au

Tens of Thousands Hundreds thousands

19 603 t

Page 9â&#x20AC;&#x201D;Assessment 2

1. 2. 3. 4. 5.

Number

54 231 t t t t t

fifteen thousand, seven hundred and eighty-nine forty-six thousand, three hundred sixty-seven thousand and sixteen fifty-four thousand and nine 49 605 (b) 15 029 (c) 60 016 (d) 30 008 91 111 (b) 78 976 (c) 41 977 39 888 (b) 25 675 (c) 35 066

3. (a) 54 273 4. (a) 15 578

(b) 71 928 (b) 95 055

N&PV â&#x20AC;&#x201C; 3 Page 32â&#x20AC;&#x201D;Assessment 1 1. 2. 3. 4. 5. 6. 7. 8.

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

700 (b) 60 (b) 400 tens 7925 (b) 40 000 (b) 200 (b) 90 (b) 400 Ă&#x2014; 100

30 000 (c) 4000 4000 (c) 40 000 (b) 2000 tens (c) 700 hundreds 24 059 (c) 99 007 (d) 38 063 80 (c) 60 4000 (c) 80 500 (c) 670 (b) 980 Ă&#x2014; 100 (c) 30 Ă&#x2014; 3000

Page 33â&#x20AC;&#x201D;Assessment 2 1. (a) 100 (b) 100 (c) 1000 (d) 100 (e) 80 000 (f ) 100 2. Possible answer (a) 40 + 90 + 60 + 50 + 10 = 40 + 60 + 90 + 10 + 50 = 100 + 100 + 50 = 250 (b) 32 + 49 + 28 = 32 + 28 + 49 = 60 + 49 = 109 3. (a) 69 763 (b) 75 716 (c) 132 867 (d) 12 011 (e) 50 101 4. (a) 781 (b) 5141 (c) 6282 5. (a) 43 544 (b) 32 472 (c) 42 441 (d) 14 381 (e) 70 096 Page 34â&#x20AC;&#x201D;Assessment 3

1. (a) 496 (b) 60 (c) 1920 (d) 3688 (e) 1009 km (f ) $6.50 (g) 5003 kj (h) 165 000 bees 37 964, 37 965, 37 966 (b) 54 319, 54 320, 54 321 15 998, 15 999, 16 000 (d) 98 800, 98 801, 98 802 N&PV â&#x20AC;&#x201C; 4 87653 and 35678 (b) 97 331 and 13 379 Page 42â&#x20AC;&#x201D;Assessment 1 96 542 and 24 569 1. (a) 129, 132, 135, 138, 141, 144, 147, 150 10 675, 30 760, 30 765, 34 987, 45 067 (b) 444, 448, 452, 456, 460, 464, 468, 472 25 009, 25 099, 25 100, 25 670, 25 909 (c) 120, 126, 132, 138, 144, 150, 156, 162 < (b) > (c) > (d) < (d) 84, 91, 98, 105, 112, 119, 126, 133 (b) (c) 2. (a) 732, 728, 724, 720, 716, 712, 708, 704, 700, 696 (b) 549, 540, 531, 522, 513, 504, 495, 486 (c) 644, 637, 630, 623, 616, 609, 602, 595 56 021 31 243 12 433 (d) 912, 904, 896, 888, 880, 872, 864, 856 6. (a) 56 702 (b) 32 463 (c) 45 301 3. (a) Add to 3, 6, or 9 (b) Are even numbers (c) Add to 9 Page 22â&#x20AC;&#x201D;Assessment 3 4. (a) 576 (b) 423 (c) 459 (d) 248 1. (a) 24 173 (b) 40 527 (c) 53 064 (d) 5519 5. (a) 2160, 2163, 2166, 2169, 2172, 2175, 2178

Page 21â&#x20AC;&#x201D;Assessment 2 1. (a) (c) 2. (a) (c) 3. (a) (b) 4. (a) 5. (a)

(b) 621, 612, 603, 594, 585, 576, 567

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. PublicationsÂŽ

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4) R.I.C. PublicationsÂŽ www.ricpublications.com.au

www.ricpublications.com.au

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

Investigate and use the properties of odd and even numbers (ACMNA071)

RELATED TERMS

TEACHER INFORMATION

Even number

What this means

• A whole number is even if it is divisible by 2. Examples of even numbers are: 0, 2, 4, 6.

• Students try adding, subtracting, multiplying and dividing odd and even numbers in an effort to look for patterns.

Odd number

Begin with simple patterns, such as:

r o e t s Bo r e p ok u S • odd + odd

• even + even

• odd + even (and even + odd)

ew i ev Pr

Teac he r

• An odd number is an integer that is not divisible by 2. Examples of odd numbers are: 1, 3, 5.

Teaching points

Number

Extend by asking ‘What happens if?’—type questions; for example:

• A real number is rational if it can be expressed as a quotient of integers. It is irrational otherwise; e.g. 0, 1, 27.

• odd – odd

Properties

• The distinguishing features of a number type can be referred to as properties.

• odd × odd • even ÷ even • even ÷ odd • even × even

Ask students to explain how these patterns can be used to check a calculation.

w ww

. te

• Students who make simple calculation errors and, hence, miss spotting the various patterns. • Students who do not understand or know their basic number facts will have trouble using facts to make the required pattern.

m . u

and expressions. In the primary years, operations include addition, subtraction, multiplication and division.

See also New wave Number and Algebra (Year 4) student workbook (pages 2–7)

o c . che e r o t r s super

Student vocabulary odd number even number patterns remainder digit

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Even number patterns Colour the even numbers on the 1–150 number grid on page 5 and discuss the patterns these numbers make.

Odd and even boxes Revise student understanding of odd and even numbers by playing this game. On 15 cardboard cartons, draw on each an odd or even number between 100 and 1000. Then place them randomly outside, some distance apart. Students walk around the outside of the boxes until the teacher calls out ‘even’. The students have to run to a box with an even number and stand next to it (or to an odd-numbered box when ‘odd’ is called). The last student to locate an appropriately numbered box leaves the game.

Roll and tally

Teac he r

Odd or even?

This is a game for two players. One player is ‘odd’ and the other is ‘even’. They both decide on a number between one and five and show that number with their fingers held behind their backs. On a given signal, they reveal their finger numbers and if the sum of these numbers is even the ‘even’ player scores a point. Reversely, his/her opponent scores if it’s odd. The first player to reach five points wins. The game can also be played to find the difference between the two numbers or a multiple of them.

ew i ev Pr

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

Take the pack

. te

m . u

w ww

Small groups of students can play this game. A pack of cards is placed face down with the top two cards face up, side by side and overlapping slightly. If the sum of the two cards is even, they are removed and replaced with two new cards. If the sum is odd, a third card is placed on top and added to the second card. If this sum is odd, continue adding cards until the sum is even. The game continues until there are no cards left. The students can then play the game to identify odd sums and discuss why it takes so long to ‘take the pack’.

How can I make an even number?

o c . che e r o t r s super

Groups of four or five students are given a pack of playing cards which are placed facedown on the table. Each takes a turn to turn over the top two cards and identify which operation could be used to make an even number using these two numbers. If the others agree that he or she has identified an operation correctly, the player keeps those two cards. If not, the cards are replaced in the pack. The winner is the student with the most cards. Once the students are familiar with the game, a more challenging task is to identify an operation to produce an odd number.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS English • Read Even Steven and Odd Todd, by Kathryn Christaldi and Henry Morehouse (published by Scholastic), and ask the students to work in pairs to write and illustrate a similar story or poem to help younger students understand the concepts of odd and even numbers. • Students can prepare an information table to summarise and explain as simply as possible what happens when even and odd numbers are added, subtracted, multiplied and divided.

Science

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

• Investigate the number of legs different animals have and show the findings as a class chart. Challenge students to find a species with an odd number of legs and discuss possible reasons for this. The concept of maintaining balance when moving could then be demonstrated by asking pairs of students to run a three-legged race and then discuss why this is difficult and to also try to explain why a three-legged dog can run but very few other four-legged animals who then lose a leg would be able to do this.

Teac he r

ew i ev Pr

• Encourage students to investigate the occurrences of odd and even amounts in the features of different animals to complete a class T-chart under the headings of ‘What’s odd and what’s even in nature?’ They could expand the activity to include plants.

Health and Physical Education

• Students compile a list of body parts of which they have an even amount of. Students can then discuss possible reasons for this and the difficulties humans could experience if they had odd amounts of them.

History and Geography

• Students complete a time line showing major events in their lives and what they were doing when their age was an odd number. They can then choose a decade from the past to research and list important events for each of the even years.

The Arts

• Create and draw (or construct) a creature with odd numbers of features or body parts (such as eyes, legs, tails and ears). Display under the heading ‘Some very odd creatures’.

. te

m . u

Languages

w ww

• Small groups of student work together to create a board game based on ‘snakes and ladders’, using paper with large numbered squares. In the game, players throw two dice and can only move forward four spaces if they can state an operation to produce an even number using the two numbers thrown. There can be, as in ‘snakes and ladders’, penalties imposed on players who land on certain even numbers (snakes) on the board and positive outcomes for players landing on certain other even numbers (ladders).

o c . che e r o t r s super

• Students learn to count in two other languages and have one student count the odd numbers in one language while another counts the even numbers in the other language.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Number grid 1–150

63R. 64 65 66 67 68 69 © I . C.P ubl i cat i ons •72f or73 r evi ew p ur p ose son l y• 74 75 76 77 78 79

m . u

100

109

110

111

. te o 102 103 104 105 106 107 . 108 c che e r o ru st117 118 r pe 112 113 114s 115 116

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

w ww

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

r o e t s 25 26 B27 28 r e o p ok u S33 34 35 36 37 38

ew i ev Pr

Teac he r

101

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

+ even = even

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

even = odd

odd = odd

odd = even

–

even = odd

–

even

–

odd = m odd . Example: 4 – 1 = 3 u

Example: 3 – 2 = 1

odd

Example: 3 – 1 = 2

odd

o c . che e r o t r s super

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

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

Example: 2 + 1 = 3

even

Example: 1 + 2 = 3

odd

Example: 1 + 3 = 4

odd = even

– even = even

Example: 4 – 2 = 2

even

. te

odd

Example: 2 + 2 = 4

even

Subtraction Division

even

× even = even

even = even

odd = even

Example: 2 × 3 = 6

even

Example: 3 × 2 = 6

odd

Example: 3 × 1 = 3

odd = odd

even = even

÷ odd = odd

even

There can be a remainder. Examples: 6÷3=2 18 ÷ 4 = 4 r 2

odd = even

There will always be a remainder. Example: 15 ÷ 2 = 7 r 1

odd ÷ even = odd/even

Example: 9 ÷ 3 = 3

odd

even

Teac heExamples: 4÷2=2 Example: 4 × 2 = 8 r 10 ÷ 2 = 5

Multiplication

5=2

E-E=E

6 + 7 = 13 8-6=2

5 + 6 = 11

5+3=8

0-E=0

7-2=5

0x0=0 3 x 6 = 18

3x3=9

6 + 6 = 12

E+E=E

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

ew i ev Pr

w ww

Addition

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

RESOURCE SHEET

Odd and even numbers – Rules chart

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

RESOURCE SHEET Odd and even numbers

• Even numbers are numbers which divide by 2 without leaving a remainder. For example, 2, 4, 6, 8 … are even numbers. • Odd numbers are numbers which when divided by 2 leave a remainder. For example, 1, 3, 5, 7, 9 … are odd numbers.

r o e t s Bo r e p o u k • All numbers are either odd or even. S

ew i ev Pr

Teac he r

• Zero is an even number.

• You must look at the last digit of a number to work out if it is odd or even. – Odd numbers end with 1, 3, 5, 7 or 9. – Even numbers end with 0, 2, 4, 6 or 8. For example, 7 575 132 is an even number and 8 462 483 is an odd number. • You can find out if the answer to an operation (when you add, subtract, multiply or divide) should be an odd or an even number without having to complete it. You just need to know the odd and even number rules. For example: 5123 + 43 777 = an even number (odd + odd = even) 8493 × 2987 = an odd number (odd × odd = odd)

m . u

• If you know the rules about odd and even numbers, it is easier to check if your answer is likely to be correct. For example, if you know that odd – even = odd, then you know that the answer to 345 – 278 couldn’t be 68.

w ww

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

. teand even number rules can be useful when you’re o • Knowing odd trying to select c . the correct answers in multiple choice questions. ch e r er o st suitp r e • If you forget a rule, you can work out yourself using small numbers. For example: For odd × even, think 1 × 2 = 2 (even). For odd ÷ odd, think 9 ÷ 3 = 3 (odd).

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

ODD 425

EVEN 366

366 6

268

R.I.C. Publications®

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

1. What are the five digits that odd numbers must end with?

2. Which digits are written at the end of even numbers?

r o e t s Bo r e p o u k between 8 and 14 without a zero. S

3. Write any even number:

ew i ev Pr

Teac he r

(a)

(b) between 28 and 35 with a zero. (c) less than 45 and greater than 40. (d) less than 92 and greater than 87. (e)

w ww

(b) between 154 and 150 and greater than 151. (c) (d)

. teand greater than 258. less than 260 o c . che e r o greater than 199 and less than 202. t r s super

(e) with three digits and greater than 97. 5. Circle the even numbers greater than 213. 313

402

170

215

260

877

521

6. Circle the odd numbers less than 819. 811 8

909

624

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

(a) with three digits and less than 103.

m . u

4. Write any odd number:

Assessment 2

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

NAME:

DATE:

1. (a) Circle the odd numbers. 27

128

345

367

402

1476

5310

8644

(b) Circle the even numbers. 433

450

9767

34 562

60 441

59 111

r o e t s Bo r e p ok u S22 × 14 = 46 × 18 = 19 × 32 =

97 532

13 × 15 = 66 × 33 =

53 × 87 =

16 × 16 =

There are

odd-numbered and

35 × 15 =

ew i ev Pr

Teac he r

2. Use what you know about multiplying odd and even numbers to work out how many odd- and even-numbered answers there are below.

17 × 21 =

34 × 33 =

even-numbered answers.

(d) odd – even =

(e) even × even =

(f)

(g) even ÷ even =

odd × odd =

m . u

w ww

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

3. Write odd or even to make each problem correct.

(h) even ÷ odd =

. te

o c . e 13 032 13 051 36 × 362 = ?c her r o t s72 867 su r 72p 864e 65 879 + 6988 = ?

4. Use what you know about odd and even numbers to work out which answer is correct? Shade the bubble. (a) (b)

2116

2117

(d) 51 × 89 = ?

4539

4536

(e) 456 ÷ 4 = ?

117

114

7368

7365

(f)

6895 + 473 = ?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 3

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

NAME:

DATE:

Use the rules about adding, subtracting, multiplying and dividing odd and even numbers to work out the answers to these problems. You do NOT need to do the calculations. Shade the bubbles to show your answers.

r o e t s Bo r e p ok u an S even number of double picture frames.

1. A student at a school gave 13 pictures to an art teacher. The art teacher put all the pictures into double picture frames.

ew i ev Pr

Teac he r

She had:

an odd number of double picture frames.

2. Shahn is making necklaces with beads. She has 278 red beads and 181 green beads. If she makes two necklaces with the same number of beads in each, will there be one bead left over?

nob © R. I . C.Pu l i cat i ons •f orr evi ew pur posesonl y• 3. A bricklayer had 2500 bricks and he only used 2391 of them to build yes

w ww

an even number left. an odd number left.

. te

4. There were 165 boys playing in a cricket competition. There were 11 boys in each team. Was there an odd or an even number of teams playing in the competition? odd

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

5. The launderer had two baskets of socks to wash. He was worried because he thought a sock had fallen out of one of the baskets. He counted the socks and there were 143 socks in one basket and 177 in the other. Had he lost a sock? yes

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate and use the properties of odd and even numbers

He had:

m . u

a wall. Did he have an even or odd number of bricks left over?

Checklist

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

Investigate and use the properties of odd and even numbers when divided

Investigate and use the properties of odd and even numbers when multiplied

Investigate and use the properties of odd and even numbers when subtracted

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

ew i ev Pr

Teac he r

STUDENT NAME

Investigate and use the properties of odd and even numbers when added

Investigate and use the properties of odd and even numbers (ACMNA071)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

RELATED TERMS

TEACHER INFORMATION

Numbers as words

What this means

• A number is expressed as words in a particular way. How and when to use the word ‘and’ can present difficulties for some students.

• Students need to read, write and say numbers to at least five digits (tens of thousands).

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

Numerical representation

Teac he r

Numeral

• A representation of a number, whether it be a digit, or a group of letters (words) or digits.

• Numbers of five digits or more are written in groups of three with a space separating each group. • A hundreds–tens–ones pattern is used in each group of three digits. • This pattern is repeated in the thousands—hundreds of thousands, tens of thousands, thousands—then hundreds, tens, ones.

What to look for

ew i ev Pr

• A number can be represented mathematically in many different ways using digits.

Teaching points

• Students who read numbers rather than say them according to place value. That is, they say (for example) ‘two, five, seven, nine, one’ instead of ‘twenty-five thousand, seven hundred and ninetyone’. (Note: There are some numbers—for example, postcodes and phone numbers—which are read in this way.)

w ww

. te

Student vocabulary represent ordinal numbers digit

m . u

See also New wave Number and Algebra (Year 4) student workbook (pages 8–13)

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

numeral order greater than (>) less than (<) equal

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES How big can it be? Students work in pairs. They will need five dice and a five-digit number chart (see page 15). One student throws the five dice, then the other writes the biggest number possible on five rectangles using the digits rolled. They take turns to throw and record their numbers, then read the numbers they have written aloud. They order them from the biggest to the smallest and write these ordinal numbers in the final box of the chart. Groups can compare their biggest numbers to find which pair has thrown the longest number. The class’ numbers can then be ranked in order.

Card numbers

Calculator numbers

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

Two students each make a five-digit number on their calculators in which the number is made of five different digits. Each reads his or her digit to the partner. The pair has to decide which number is greater and write this down; e.g. 24 572 > 21 976. The student with the smaller number then selects one digit of his/her opponent’s number to change to 1 so this number is now smaller.

What’s the number?

ew i ev Pr

Teac he r

This game is played with a deck of playing cards with the 10s, jacks, queens and kings removed. The two players draw a card each to determine who starts. That player then shuffles the cards, deals the pack, then turns over his/her top card. Players sit side by side with their card grid placed in front of them. (See page 16, which should be printed on A3 paper.) They take turns at flipping over their cards in each pack and placing them on their grid, trying to make a large five-digit number. The player with the larger five-digit number is the winner and can take the cards from the middle if he/she can read the bigger number correctly. If not, the other player wins and takes the cards. The player with the most cards after four rounds wins the game.

m . u

Student One selects a number with five digits, writes it on a sheet of paper and hides it. Student Two has 10 counters and has to work out what the number is by asking no more than 10 questions. Before they start, Student One tells the range for the hidden number in tens of thousands; e.g. ‘The number is between 21 000 and 22 000’. Student Two can then ask questions; e.g. ‘Is it 21 500?’ and hands over one counter. Student One can only reply ‘yes’, ‘more’ or ‘less’. Student Two continues to ask questions until the hundreds place value has been identified. Student Two then asks questions to identify the tens and, finally, the ones values. If Student Two identifies the number, he/she scores a point. If not, the number is revealed after 10 questions. Student Two then writes a number for Student One to identify. The first student to score five points wins the game.

w ww

Number charts

Students can use the two number charts provided on page 19 in a variety of ways. Working with a partner, one student can draw an amount (from 0 to 9) of symbols (such as balls, stars or tally marks) in each column of the first chart for the partner to count and represent numerically in the column on the right. Numbers to be expanded on the second chart can be generated by throwing a dice or by a spinner.

Abacus

. te

o c . che e r o t r s super

The abacuses on page 18 can be used to represent numbers generated in a number of different ways by the students (e.g. dice, spinners) or provided by the teacher.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS English • Watch the film or read the book Around the world in eighty days and calculate how many hours and minutes there are in 80 days. Students can then try to estimate how many kilometres were travelled each day, hour and minute (on average) by the characters.

Science • Research the layers of the atmosphere; i.e. the Troposphere, Stratosphere, Mesosphere and Thermosphere and their distances from the Earth’s surface. Record this information in metres in a table. This information can be used to calculate the depth of each layer. The types of clouds formed in each layer could be a topic for further research.

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

Health and Physical Education

Teac he r

• Research food labels on different cereal packets to find how many kilojoules are in one kilogram of the cereal. Students could then find the amount of kilojules in one serve and calculate how many kilojoules could be consumed in one week.

ew i ev Pr

• Measure the heights of class members in millimetres and use a calculator to determine the total height of the boys and of the girls to find out which group is taller. Discuss the results and compare to those of adults; e.g. men are usually taller than women.

History and Geography

• Each student works with a partner to plan a flight around the world to visit places of interest. Once they have decided on their itinerary, they can plot it on a blank map of the world and research the distance of travel between each stop. Each group can then calculate the total distance they would fly. These distances can be compared with others in the class and the longest and shortest trips identified.

w ww

The Arts

m . u

• Students research the arrival of Aboriginal Australians about 50 000 years ago and write a report.

• Inflate balloons approximately relative to the size of the planets, cover them with papier-mâché and paint them. When dry, these different-sized shapes can be suspended from the ceiling with string, arranged by size in the correct order and set the appropriate distances apart. (See science activity above.)

. te

o c . che e r o t r s super

• Students each construct a simple model of a car odometer. Each needs five strips of white paper approximately 25 cm by 2 cm in size, and a sheet of coloured card about 20 cm by 6 cm in size. Along the length of each white strip, numbers from zero to nine are written vertically and evenly spaced. They then cut two 2 cm-long slits about 1 cm apart, five times horizontally along the length of the coloured card so that the five white strips can be threaded through the pairs of slits. (See diagram below for how to position slits.) Thread each strip, then glue together the ends of each to form a loop. Students then move the loops through the card to reveal a five-digit number. They can move any one strip at a time to create a new number, which they then need to read to determine how much larger or smaller this number is than the previous one. Students should then also state which place value changed to make the new number.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Five-digit number chart

• Throw three dice, add two zeros and write a number. • We’ve made the greatest/smallest numbers possible and we’ve put our numbers in order, starting with the greatest/smallest.

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

number.

ew i ev Pr

Teac he r

threw the

. te

m . u

w ww

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Card grid

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

ew i ev Pr

Teac he r

This grid will be the correct size for playing cards when enlarged and printed on A3-sized paper.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

w ww

. te

m . u

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Number lines

. te

Add/subtract 1

m . u

w ww

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

o c . che e r o t r s super

Add/subtract 10

Add/subtract 100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Add/subtract 1000

R.I.C. Publications®

Add/subtract 10 000

www.ricpublications.com.au

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

RESOURCE SHEET Blank abacuses

1. Write the number represented on each abacus.

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

(c)

(e)

(d)

ew i ev Pr

Teac he r

(a)

. te

o c . che e r o t r s super (b)

(c)

(d)

(e)

(f) Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

w ww

(a)

m . u

2. Draw the number on the abacus.

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

RESOURCE SHEET Number charts

Write the numbers represented by the symbols on the chart. Tens of thousands

Hundreds

Tens

Ones

Number

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

ew i ev Pr

Teac he r

Thousands

Number

Tens of thousands

. te

Thousands

Hundreds

m . u

Represent the numbers on the chart.

w ww

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

Ones

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

1. Write these numbers as words. (a) 15 789

(b) 46 300

(d) 54 009

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

2. Shade the bubble to show your answer.

ew i ev Pr

Teac he r

(a) The numeral for forty-nine thousand, six hundred and five is

(b)

49 605

49 6005

60 0016

60 160

w ww

30 008

60 016

(d) The numeral for thirty thousand and eight is: 13 008

. te

3008

o c .67 768 ch91e111 19 998 r e o 78 976 t r super 17 890 78s 076

3. Shade the bubble to show the largest number. (a)

67 766

(b)

43 290

(c)

41 677

m . u

41 687

41 977

14 677

4. Shade the bubble to show the smallest number.

(a)

40 000

40 090

39 888

40 900

(b)

25 675

52 678

50 989

50 909

(c)

35 666

35 066

35 660

35 960

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

Assessment 2

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

NAME:

DATE:

1. Write the number that comes before and after each number. (a)

37 965

(b)

54 320

(c)

15 999

(d)

98 801

2. Make the smallest and largest numbers you can using these digits. Digits

Largest number

Smallest number

r o e t s Bo r 3, 3, 7, 9,p 1 e ok u 4, S 9, 5, 2, 6

(a) 5, 7, 3, 8, 6 (b)

3. Start with the smallest and write the numbers in order.

ew i ev Pr

Teac he r

(c)

(a)

45 067

34 987

30 765

30 760

10 675

(b)

25 670

25 099

25 909

25 009

25 100

45 980

(b) 66 666

60 606

89 890

(d) 37 008

37 800

5. Show each number on an abacus. (a)

. te

56 021

(b)

m . u

(a) 45 890

w ww

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

(c)

o c . che e r o t r s super 31 243

12 433

6. What number is shown on each abacus? (a)

(b)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

(c)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 3

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

NAME:

DATE:

1. Write the numbers represented by the stars on the chart. Tens of thousands

Thousands

Hundreds

Tens

Ones

Number

Teac he r

Tens of thousands

Number

Thousands

Hundreds

Tens

54 231 19 603 22 876

ew i ev Pr

r o e t s Bo r e p ok u S 2. Represent the numbers on the chart by drawing dots.

Ones

76 091

w ww

m . u

(a) 50 000 + 4000 + 200 + 70 + 3 = (b) 70 000 + 1000 + 900 + 20 + 8 =

. teshown on these number lines? 4. What numbers are o c . c e her r (a) o t s s r u e p Shade the bubble. 15 678 15 578 15 688 (c) 10 000 + 4000 + 300 + 80 + 1 =

(b)

15 000

15 500

95 000

95 500

Shade the bubble. (c)

20 000

Shade the bubble. 22

95 555

95 545

95 055

20 500

20 005

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

21 000

20 500

20 050

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

CONTENT DESCRIPTION: Recognise, represent and order numbers to at least tens of thousands

3. Write the number for these expanded numbers.

Checklist

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

Orders numbers to tens of thousands and can use < and > signs

Can represent numbers to tens of thousands using expanded notation

Represents numbers to tens of thousands numerically

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

ew i ev Pr

Teac he r

STUDENT NAME

Can recognise and read numbers numerically and in words to tens of thousands

Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

RELATED TERMS

TEACHER INFORMATION

Rearranging

What this means

• Changing the order of numbers; numbers are rearranged to assist in calculations; for example: 7 + 8 + 3 = 7 + 3 + 8 = 10 + 8.

• Partitioning according to place value means that a number is split according to places; for example: 259 is split into 200 + 50 + 9. Splitting a number this way can help when performing a calculation.

Partitioning

Teaching points

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

• With standard partitioning, a number is split into parts according to the value of the places; e.g. 347 = 300 + 40 + 7.

What to look for

Teac he r

• In a number like 444, the four in the hundreds place is ten times greater than the four in the tens place. The four in the hundreds place is 10 × 10 greater than the four in the ones place.

• With non-standard partitioning, a number is split into parts that do not accord to place value; for example, taking some from one number to give to another: 9 + 8 = 10 + 7 = 17, so 59 + 38 = 60 + 37 = 97.

ew i ev Pr

• With partitioning, a number is divided into parts.

• Some students think in terms of addition rather than multiplication when comparing place values.

See also New wave Number and Algebra (Year 4) student workbook (pages 14–19)

w ww

• Numbers are reorganised in multiples of ten; e.g. from tens to ones, hundreds to tens and vice versa. Regrouping is also known as ‘trading’. For example, in the subtraction 426 – 123, the 426 can be regrouped as 300 + 120 + 6. In the addition 245 + 393, 4 tens + 9 tens = 13 tens, which can be regrouped as 1 hundred + 3 tens.

. te

Place value

• The position of a digit in a number determines its value. For example, the place value of 7 in 4765 is hundreds. The value of the 7 is 700 (digit × place value). Student vocabulary place value partitioning regrouping

m . u

Regrouping

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

rearranging calculate

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Seven what? Use one of the number expanders (see page 27) and write a four- or five-digit number with a seven in it. Students fold up their expander and ask another student what the seven in their number means; for example: 7 (7 ones), 70 (7 tens), 700 (7 hundreds), 7000 (7 thousands) or 70 000 (7 ten thousands). They then open their expander to reveal the answer. The two students can then work out together how many tens they would need to divide or multiply by to make both their numbers equal.

How did you do it?

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

Teac he r

ew i ev Pr

Demonstrate how rearranging numbers can make it easier to calculate an answer mentally; for example: 6 + 8 + 4 + 7 + 2 . By rearranging this as 6 + 4 + 8 + 2 + 7, the answer 27 (2 × 10 + 7) is easy. Set a problem with similar numbers, such as: ‘A basketball player shot only four points in the first quarter, 12 in the second, 16 in the third and 18 in the fourth. How many points did he score?’ Students then explain to another how they solved the problem and compare how each did it. After some practice, they could try writing similar problems for others to solve which can then be discussed.

How many tens?

Students can work with a partner. They start with a two-digit number and one asks the question, ‘How many tens?’ For example, with the number 29, the answer would be two tens. That student then adds one digit to the left of the number and repeats the question. They can continue to take turns of adding a digit to the left and repeating the question until there are six digits; for example: 429 (42 tens), 7429 (742 tens), 57 429 (5742 tens) 857 429 (85 742 tens).

Later, ‘How many hundreds?’ could be played in the same way.

Note: This important concept is challenging for some students, who may confuse it with expanded notation; e.g. 429 = 4 hundreds + 2 tens + 9 ones. It may take them some time and practice to understand. They should start with two and three digits and very gradually build up to working with five-digit numbers.

Hoop numbers

. te

m . u

w ww

Divide the class into teams of six, each with a team leader. Each team has five hoops, each representing a different place value: ones, tens, hundreds, thousands, ten thousands. Use the place value card resource sheets on pages 29 and 30 to create two sets of cards (one set for each group: 36 cards each). Each team leader randomly assigns each team member a different place value card. Each leader’s task is to place the team members in the correct place value hoops according to the cards. Each leader then writes down the number his or her team represents. Once the teacher has checked that a leader is correct, that team scores a point. Then a new leader is chosen, the cards are shuffled and randomly given to team members, and the task starts again. The first team with five points wins.

o c . che e r o t r s super

A more difficult alternative to this game is for the team members to choose a hoop to stand in and the leader writes down the number the team represents. This number is checked by the teacher and the game continues as above.

What’s the connection?

Remove the kings, queens, jacks and jokers from a pack of cards and deal pairs of students four cards and four similarsized cards with zero written on them. They need to write a number sentence using ‘=’ and which uses all four playing cards and connects them in some way. If the pair can’t make an operation with only the playing cards, then they can also use the ‘zero’ cards to help. If, after five minutes, they can create an operation with only the playing cards, they score five points. If they have had to also use any zero cards, they score one point. For example: if the pair were dealt the cards 9, 5, 7, 3, the possible number sentences could be: 9 – 7 = 5 – 3 (5 points), 9 – 5 = 7 – 3 (5 points), 90 – 70 = 50 – 30 (one point) or 9 + 3 – 5 = 7 (5 points). After five minutes, points scored are calculated, and five new cards are dealt.

The ‘Tell me how many’ game This game can be played by two students. One writes a four- or five-digit number in the ones column (see page 31) and asks the other three questions. These could be: ‘How many tens are in my number?’ ‘How many hundreds are in my number?’ ‘How many thousands are in my number ?’ or ‘How many ten thousands are in my number?’ The answers must be written correctly in the appropriate columns of the chart to score three points. The other student then writes a number in the ones column of the next row and repeats the process. The first student to score 15 points wins the game. Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education • Collect nutritional information panels from different brands of a particular food (e.g. chocolate or muesli bars) to investigate sugar or saturated fat content. Students can compare products (using subtraction) to decide which are healthier and then explain why.

Perth

History and Geography

33 kms

• Students compile a ‘similarities and differences chart’ comparing learning maths today to what it was like for their grandparents. They can discuss what happens in their own lessons, what they do, what their teachers do, where they work, what equipment they use etc. They then interview their grandparents or other older people to gather relevant information and make comparisons. See below for a follow-up English activity.

Armadale

33 + 132 + 67 + 37 + 104 =

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

English

• Debate the topic, ‘Learning how to do mental calculations is a waste of time.’

132 kms

Williams 67 kms

Beaufort River 37 kms

Kojonup

ew i ev Pr

• Students use maps of their state and choose two places. They write down the distances of three to five sectors between these two places. Ten destinations and the lengths of the sectors between them are compiled into lists, and a copy made for each child. The students compete to add the lengths of the sectors mentally within a set time, perhaps five minutes.

Teac he r

Perth - Mt Barker

104 kms

Mt Barker

• Discuss ideas with the class, then design and make a chart to advise others on ‘How to solve maths problems’. This could take the form of ‘Do’ and ‘Don’t’ instructions or a procedural text with simple steps to be followed when trying to solve a maths problem. For example: 1. Read the question carefully 2. Ask ‘What do I know?’ 3. Ask ‘What do I want to know?’ 4. Draw a diagram. 5. Estimate the answer.

w ww

The Arts

m . u

• As a follow-up activity to the history activity above, students write a persuasive text supporting the belief that either maths was taught better in the ‘olden days’ or that it is taught better today.

• Give small groups of students a shoebox and a number between 20 and 50. Their task is to decorate the box and put their particular number on it in a variety of interesting and decorative ways. Additional ways of representing this number can be to write it on separate cards and place them in the box. Groups can compete by looking in their boxes for cards with the nominated characteristic, such as the neatest card, the one with the most digits or the most colourful card.

. te

Design and Technology

o c . che e r o t r s super

• This simple interactive activity revises place value and demonstrates the additive aspect of expanded notation to four digits: <http://www.curriculumsupport.education.nsw.gov.au/countmein/children_arrow_card.html>.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

ten thousands

hundreds

. te

thousands

o c . che e r o t r s super

thousands

m . u

thousands

hundreds

Teac heones tens r

hundreds

tens

ones

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

ew i ev Pr

w ww

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ones

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

RESOURCE SHEET

Number expander templates

www.ricpublications.com.au

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

RESOURCE SHEET Mental calculations in addition and subtraction Rearranging Numbers can be added mentally if put in a different order to make groups of tens. Example 1: 4 + 7 + 8 + 3 + 6;

4 + 6 + 7 + 3 + 8 = 10 +10 + 8 = 28

Example 2: 37 + 56 + 43;

37 + 43 + 56 = 80 + 56 = 136

Bridging decades

r o e t s Bo r e p ok u S 8 + 2 + 5 = 10 + 5 = 15

Example 2: 79 + 45;

79 + 21 + 24 = 100 + 24 = 124

Splitting numbers

Numbers can split into tens and ones to be added or subtracted mentally. Example 1: 43 + 25;

40 + 20 + 3 + 5 = 68

Example 2: 234 + 124;

200 + 100 + 30 + 20 + 4 + 4 = 358

Example 3: 234 – 124;

200 – 100 + 30 – 20 + 4 – 4 = 100 + 10 + 0 = 110

Jumping

Start with one number, then break up another number and add the tens then the ones.

ew i ev Pr

Teac he r

Example 1: 8 + 7;

Example 1: 34 + 25;

34 + 20 + 5 = 54 + 5 = 59

Example 2: 456 + 23;

456 + 20 + 3 = 476 + 3 = 479

Example 3: 34 – 25;

34 – 20 – 5 = 14 – 5 = 9

Example 4: 456 – 23;

456 – 20 – 3 = 436 – 3 = 433

m . u

Jumping is also useful in subtraction.

w ww

Counting on or back from the front This is similar to jumping but the tens are added or subtracted by counting on.

. te

Example 1: 55 + 43;

Example 2: 524 + 37;

+10

o c . che e r o t r s super +10

+10

524, 534, 544, 554 + 7 = 561 -10

Example 3: 55 – 43;

+10 +10

55, 65, 75, 85, 95 + 3 = 98

-10

55, 45, 35, 25, 15 – 3 = 12

Number lines can also be useful when counting on to add or subtract; e.g. 55 + 43 = 98

100

105

Compensation In compensation, numbers are added to make mental addition easier. This is then reversed at the end. Example 1: 54 + 39;

54 + 40 – 1 = 93 (1 is added to 39.)

Example 2: 352 + 24;

350 + 24 + 2 = 376 (2 is subtracted from 352.)

In compensation, in subtraction the same number is added or subtracted to make subtraction easier.

Example 3: 54 – 39;

55 – 40 = 15 (1 is added to both.)

Example 4: 352 – 24;

350 – 22 = 328 (2 is subtracted from both.)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

It can be easier to add numbers if part of one of them is used to make the other number up to tens or hundreds.

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

RESOURCE SHEET Hoop game cards

Ones

ew i ev Pr

Tens

Teac he r

r o e t s Bo r e p ok u OnesS Ones

. te

Tens

m . u

w ww

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

Ones

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Tens

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Hoop game cards

Hundreds

Thousands

ew i ev Pr

Teac he r

r o e t s Bo r e p ok u HundredsS Hundreds Hundreds

w ww

. te

Tens of thousands

Tens of thousands 30

m . u

o c . cheTens of Tens of e r othousands r st super thousands Tens of thousands

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Tens of thousands R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

Hundreds

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

RESOURCE SHEET

m . u

Hundreds

TeacTens he r

. te

o c . che e r o t r s super

Ten thousands

Thousands

ew i ev Pr

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

w ww

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

Ones

The ‘Tell me how many’ game

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

1. Shade the bubble to show the value of the underlined digit. (a)

88 743

100

700

(b)

34 564

3000

300

30 000

(c)

24 561

400

1000

4000

2. Write the value of the underlined digit. 34 567

4 r o e t s Bo r e p ok u S (b) 54 876

(c)

9 766

3. Shade the bubble to show which amount is equal. (b)

20 000 equals

(c)

70 000 equals

Teac he r

4000 equals

400 ones

40 tens

400 tens

2 thousands

200 tens

2000 tens

70 tens

7 hundreds

4. Write the numbers. (a)

7000 + 900 + 20 + 5 =

(b)

20 000 + 4000 + 50 + 9 =

(c)

90 000 + 9000 + 7 =

(d)

ew i ev Pr

(a)

700 hundreds

5. Write the missing number. (a) 40 000 + 3000 +

+ 9 = 43 089

. tein: 6. How many tens are (c)

20 000 + 5000 +

(a)

2000?

(b)

40 000?

(c)

800?

m . u

w ww

(b)

+ 5000 + 600 + 90 + 3 = 45 693

+ 7 = 25 067

o c . che e (a) 9000? r o t r s sup(b)er 50 000? 7. How many hundreds are in:

(c)

67 000?

8. Circle the correct answer.

(a)

40 000 =

400 × 1000,

400 × 100,

400 × 10,

400 × 10 000

(b)

98 000 =

980 × 100,

980 × 10,

980 × 1000,

980 × 980

(c)

90 000 =

30 × 30,

30 × 40,

30 × 3000,

30 × 30 000

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

(a)

Assessment 2

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

NAME:

DATE:

1. Write the missing numbers. = 60 000

(a) 600 × (c) 90 ×

= 90 000

= 3000

(d)

× 50 = 5000

(f)

× 270 = 27 000

r o e t s Bo r e p ok u (b) 32 + 49 + 28 = 40 + 90 S + 60 + 50 +10 =

2. Change the order of these numbers to make it easier to make tens, add them in your head and write the answer.

ew i ev Pr

Teac he r

(a)

3. Complete these problems. (a) 45 927

(b) 54 094

+ 23 836

+ 21 622

+ 45 213

(d) 4122 + 7322 + 567 =

m . u

(e) 45 221 + 4562 + 305 + 13 =

w ww

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

(e) 200 × 400 =

(b) 30 ×

4. Show how you solved these problems.

. t327 = 5468 –e o c . e 8754 – 2472c =h r er o t s super

(a) 534 + 247 = (b) (c)

5. Complete these problems. (a) 45 927

(b) 54 094

– 2383

– 21 622

– 45 213

(d) 35 742 – 21 361 = Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

(e)

76 387 – 6291 =

R.I.C. Publications®

www.ricpublications.com.au

Assessment 3

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

NAME:

DATE:

Try to solve these word problems in your head first then write them down. Show how you calculated all your answers.

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

(c) Two boys put their marbles in a bag. If one boy had 722 marbles and the other had 1198, how many marbles were in the bag?

(d) At the carnival, Blue faction scored 1543 points, Green 1057 and Red 1088. How many points were scored?

(f) My auntie bought my brother and me a book each. Mine cost $21.92 and my brother’s cost $15.42. How much less did my book cost?

m . u

w ww

(e) Sydney to New York is 15 990 kilometres. How much further is it to London if it is 16 999 kilometres from Sydney?

. te

o c . che e r o t r s had 42 000 bees in one r up (g) A giant panda ate 18 200 kJ in s (h) e A beekeeper spring, 22 977 kJ in summer and autumn, and 23 203 kJ in winter. How much more did it eat in winter than in spring?

hive, 65 000 in another and 58 000 in a third. How many bees did he have in these hives?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

(b) Over the last four games, the team scored 16, 21, 14 and 9 goals. How many goals were scored in total?

ew i ev Pr

Teac he r

(a) 449 members attended a dance club function and 47 didn’t. How many members does the dance club have?

Checklist

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

Solves problems choosing appropriate rearranging, partitioning or regrouping

Regroups appropriately in calculations involving subtraction

Regroups appropriately in calculations involving addition

Understands that place value is built on the multiplication of tens

Uses place value to partition five digit numbers

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

ew i ev Pr

Teac he r

STUDENT NAME

Understands place value and the value of the digits in five digit numbers

Apply place value to partitioning, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

RELATED TERMS

TEACHER INFORMATION

Multiples

What this means

• A multiple of a number is the product of that number and an integer; e.g. 0, 3, 6 and 9 are multiples of 3.

• The multiples of three include 0, 3, 6, 9, 12, 15. For any number, there is an infinite amount of multiples.

Integer

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

Number sequence

• A series of connected numbers that follow a regular pattern and can be extended indefinitely; e.g. 4, 8, 12, 16, 20, 24.

Teaching points

• Students learn to skip count, but often don’t consider the patterns that exist. • Multiples should be linked to patterns.

What to look for

ew i ev Pr

Teac he r

• Integers are whole numbers. For example, 0, 1, 2 and 3 are integers.

• Various patterns may be discovered when examining various multiples. For example, when adding the digits of a number that is a multiple of three, it will always sum either 3, 6 or 9.

• Some students can only count in multiples from 0. They experience difficulty when counting from a different starting point; e.g. from 6 to 12 to 18 and so on. Some students have difficulty remembering skip counting and with the basic facts of multiples, particularly 6, 7, 8 and 9.

w ww

. te

Student vocabulary multiplication grid diagonal patterns

m . u

See also New wave Number and Algebra (Year 4) student workbook (pages 20–25)

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

sequence

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Counting by threes Students work in pairs and write multiples of three on the odd number counting pattern grid (see page 39). They look for patterns and write down any they have noticed. They then share this information with the class. Discuss why knowing multiple patterns can be useful and ask if any student groups used a known pattern to help them complete their grid. They can then describe the pattern and how they used it. If the students have failed to describe the pattern that the digits of all the multiples of three sum to 3, 6 or 9, help them to discover and test it. (Note: Some numbers, including 39 and 48, may not seem to follow this pattern as they add to 12, but if taken one more step they do, because 3 + 9 = 12 and 4 + 8 = 12, then 1 + 2 = 3.)

Counting by nines

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

Repeat the above activity by writing multiples of nine.

The students should realise that the digits of all the multiples add to 9. (Again, some numbers will need to be taken further step.)

Finger multiplication

ew i ev Pr

Teac he r

As an example, 99 (9 + 9 =18 and 1 + 8 = 9) and 198 (1 + 9 = 10 and 10 + 8 = 18, then 1 + 8 = 9).

Demonstrate how students can multiply by nine by using their fingers on both hands. Then have them work with a partner to test that it works. If you have trouble remembering the nine times table, then you might want to try turning your fingers into a calculator. With your palms facing down, imagine your fingers are numbered.

2 3

If you want to do 3 x 9, bend your third finger.

Count the number of fingers to the left of the bent finger. These fingers represent the number of tens. The fingers to the right of the bent finger represent the ones.

w ww

m . u

Thus you get the answer that 3 x 9 = 27.

Conduct a competition with a page of 20 multiples of nine for two students to complete. One student does the calculation using his/her fingers while the other writes the answers. The first pair to finish is the winner.

. te

Counting by twos, fours and eights

o c . che e r o t r s super

Use the 1–120 grid on page 41 to count first by twos, then fours and finally eights. They then mark these multiples on the grid, using a different coloured mark for each. For example, multiples of two could be a blue cross while for eight it’s a red dot. Discuss the patterns they see and why there are three dots or crosses in all the multiples of eight. (This activity will assist students to develop an understanding of common multiples and can be repeated using threes and nines.)

Finding multiples

A simple, but quite challenging, interactive activity requiring students to recognise multiples of self-selected numbers in a limited time span is available at <http://www.mathplayground.com/multiples.html>.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education • Students stand in two lines facing each other and about two metres apart. Number students in both lines from zero, making sure students with the same number stand opposite each other. Give one of the students numbered zero a ball and explain that he or she has to throw the ball to the next number on the opposite line, counting by twos. The ball should go from side to side in a pattern that misses out the odd-numbered students. The game can be repeated, but with counting by threes. In this pattern, the ball will zigzag across the lines but the pattern will not be repeated as often and fewer students will have a turn to throw and catch. • This activity can changed by:

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

– numbering students from different starting points (e.g. counting by fours from 3)

English

ew i ev Pr

Teac he r

– giving both lines only even numbers (if working with multiples of even numbers).

• After discussing the characteristics of rhyme and how much fun it can be to recognise and read it (especially aloud), the students can choose a string of multiples to write in amusing or nonsensical rhyming couplets; for example: – ‘Two, four, six, eight; don’t forget to shut the gate’ – ‘Twenty-one, twenty-four, twenty-seven, thirty; if you walk in mud your feet will get dirty’. • Once familiar with this task, students could: – write couplets linked to a theme and compiled them to make a class rhyme/s

– compile couplets written with multiples of the same numbers randomly or in counting order.

The Arts

• Use soft card to make colourful and attractive placemats, each showing a different pattern of multiples on a large 1–120 chart. An appropriately sized 1–120 chart could be drawn or photocopied and glued into the centre of each mat. The multiples of the number could be differentiated from other numbers on the chart in some way; for example: the digits of those multiples could be omitted and replaced with a decorative design.

m . u

w ww

• Multiples of the chosen number could be randomly placed around the chart as a border and decorated. The placemats could then be laminated and displayed in groups of similar patterns. • Some students may choose to show more than one multiple and to work out how to show the common multiples on their mats.

. te

Design and Technology

o c . che e r o t r s super

• Students work in groups to design and make a board game in which players throw a dice to move coloured counters around the numbered squares on the board. Each player throws the dice to determine which multiples they will be looking for. They then take turns to throw the dice and move that many spaces forward. Landing on a multiple of the original number thrown permits that player to move forward again to the next multiple. The first player to land on the greatest multiple on the board of his/her original thrown number, wins the game. • When students are familiar with this game, discuss if it an advantage or disadvantage to throw a lower number initially and to have to work with that smaller multiple.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Counting pattern grids starting at zero

Counting by

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

ew i ev Pr

Teac he r

. te

Counting pattern grids starting at one

m . u

w ww

CONTENT DESCRIPTION: Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

o c . che e r o t r s super Counting by

The pattern(s) I can see are:

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Number lines for number sequences

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

CONTENT DESCRIPTION: Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

s Couting by

Couting by

s Couting by

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

s Couting by

o c . che e r o t r s super

Couting by

w ww

. te

m . u

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

RESOURCE SHEET Number grid 1–120

63R. 64 65 66 67 68 69 © I . C.P ubl i cat i ons •72f or73 r evi ew p ur p ose son l y• 74 75 76 77 78 79

w ww

CONTENT DESCRIPTION: Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

101 111

100

109

110

119

120

. te o 102 103 104 105 106 107 . 108 c che e r o r st117 118 su r pe 112 113 114 115 116

I have shown multiples of

and

m . u

r o e t s 25 26 B27 28 r e o p ok u S33 34 35 36 37 38

ew i ev Pr

Teac he r

on the grid.

The pattern(s) I can see are:

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

1. Complete the skip counting patterns. (a) By 3s from 129:

(b) By 4s from 444:

(d) By 7s from 84:

r o e t s Bo r e p, , , , ok, 732, 728, 724, u S, , 513, , , 486 549, 540,

2. Fill in the missing numbers in the counting patterns.

(d)

, ,

, 888, 880,

, 602, 595 ,

3. Shade the bubble to show your answer. (a) Multiples of 3:

add tob 9. l add © R. I . C. Pu i cat i on sto 3, 6 or 9. Multiples of 8:r •f o r evi ew pur posesonl y• are odd numbers.

(b)

can be odd numbers.

are even numbers.

add to 4, 8 or 12.

add to 9.

add to 3, 6 or 9.

w ww

are odd numbers.

4. Shade the bubble to show which number is a multiple. (a) 4 (b) 3

. te

m . u

o c . c e her459 r 635 512 o t s 569 super 248 877 321 789 275

576

981

225

650

376

326

423

5. Skip count from: (a) 2160 to 2178 by 3s.

(b) 621 to 567 by 9s.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

(b)

ew i ev Pr

Teac he r

(a)

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

ew i ev Pr

w ww

. te

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

Understands that number sequences can be extended indefinitely in both directions

Recognises common multiples in the patterns of number sequences of 2, 3, 4, 6, 7, 8 and 9 on grids

Identifies patterns of multiples of 2, 3, 4, 6, 7, 8 and 9 from zero on number grids and uses patterns to assist in counting on

Can count on in multiples of 3, 4, 6, 7, 8 and 9 from numbers greater than zero

STUDENT NAME

o c . che e r o t r s super

m . u

Teac he r

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

Checklist

Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9 (ACMNA074)

www.ricpublications.com.au

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

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

RELATED TERMS

TEACHER INFORMATION

Multiplication terms

What this means

• A ‘multiplicand’ and a ‘multiplier’ are multiplied to make a ‘product’. For example, in 7 × 3 = 21, 7 is the multiplicand, 3 is the multiplier and 21 is the product. The multiplicand and the multiplier are also ‘factors’ of 21.

• Students will need to know the multiplication tables to 10 × 10 and link them to their related division facts.

Teac he r

Commutative law

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

• Some students may know one fact (e.g. 7 × 3) but not the related fact (3 × 7). The use of an array will help students understand the commutative property of multiplication.

ew i ev Pr

• A method of combining two numbers is commutative if the result of the combination does not depend on the order in which they are given. Addition and multiplication are commutative for all numbers, but subtraction and division are not; for example: 7 + 3 = 3 + 7 and 7 × 3 = 3 × 7.

• Links to division should be made as students develop fluency with basic multiplication facts (tables); for example, 7 × 3 = 21 can be linked to 21 ÷ 3 =7 and 21 ÷ 7 = 21.

• An array is an ordered collection of objects or numbers. Rectangular arrays with the same number of objects in each column (and likewise in each row) are used to model multiplication. Fluency

w ww

• Fluency refers to the immediate recall of basic number facts, including multiplication tables.

. te

Student vocabulary multiplication division array multiplication grid

• Some students fail to make the link between a fact and its related fact; for example, that 7 × 3 = 3 × 7. • Some students fail to make the link between multiplication and division.

m . u

Array

See also New wave Number and Algebra (Year 4) student workbook (pages 26–31)

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Which tables do I still need to learn? Each student will need a copy of a basic facts table (see page 48) and a coloured pencil. Explain that you will be working as a class to colour in all the easy basic facts that are already known. Check that they understand that multiplying any number by zero gives a zero product and multiplying a number by one gives that number as a product. If they understand this, they can colour in the first two columns and the first two rows. Then talk about multiplying by 10 and five and how these columns and rows can be coloured too. Check that the students know their two, three and four times tables and then colour their corresponding columns and rows. Explain that they have been able to colour in so many squares because number order doesn’t make a difference when multiplying. (For example, if they know 8 × 4 they also know 4 × 8.) Then, if they know the squares of five, six, seven, eight and nine, they can colour them too. This should leave only 12 basic facts for most students to learn. Set them the task of learning the three facts 6×; when learnt, discuss why they are now able to colour them and three more squares, leaving only six to learn.

Flash card fun

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

ew i ev Pr

Teac he r

Students can use the flash cards they’ve made (see page 49) in a number of different ways. They should start with flash cards of just one times table until it is known, before practising another. The two sets of cards can then be mixed together, with other sets of cards added as learning progresses. Flash card activities include:

• Beat the clock Students work in pairs. One shows cards and the other answers. If the student answers correctly, that card in placed in a pile; if not, it is replaced at the back of the pack. The aim of the activity is to correctly answer as many tables as possible in a set time (such as one minute) or to use a timer to work out who completes one set of cards faster. • Snap Three students can play. One student flips a card and judges which of the other two students gives the correct answer first. The first student to give the correct answer and place a hand on the card, takes that card. Once a set is played out, the student with the most cards is the winner and flips the cards.

Playing card snap

m . u

Students can play this game in groups of three, four or five, using a pack of cards with the jokers and face cards removed. (Aces are worth one.) One student flips over two cards and the others need to multiply them and call out the answer. The first student to do this correctly takes those cards. Any student who calls out an incorrect answer misses a turn. The winner is the first student to hold all the cards. The winner can then be the dealer for the next game. It is recommended that students play this game regularly to improve their fluency with basic multiplication facts.

w ww

Clock multiplication

A clock face can be used for the class to practise recall of multiplication facts. The times table to be practised (e.g. 7) is placed in the middle of the clock face to remind the students that this is the number they multiply by. The teacher or a student then points to a numeral on the clock face (e.g. 6) and the students need to call out the answer (42). This can be a quick whole-class exercise or specific groups or rows of students, or individual students, can be required to respond correctly within a short time. This simple activity provides opportunities for the teacher to focus on harder-to-remember multiplication facts.

. te

Table bingo

o c . che e r o t r s super

Sets of bingo cards to be copied and cut out are on pages 50 to 54. One set is for the 2, 3, 4, 5 and 10 times tables, another for facts to 100 and another is blank. Students need one card and nine counters. The first student to cover all squares as multiplication facts are called out, wins.

Interactive games See the following websites: • <www.maths-games.org/times-tables-games.html> • <www.arcademicskillbuilders.com/games/meteor/meteor.html>

Worksheets • A useful resource is Maths basic facts: Multiplication, division and beyond by Paul Swan (R.I.C. Publications).

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education • Students repeat three different aerobic moves as they chant their tables while jogging on the spot. They could, for example, touch their head as they say ‘two’, stretch their arms above their head as they say ‘fives’, then stretch their arms out to both sides as the say ‘ten’. • Students could be divided into groups to plan their own set of aerobic moves and then compete with other groups to determine which group has, for example, the most interesting or energetic set of movements.

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

Teac he r

ew i ev Pr

• Students stand in two lines of 12, facing each other with the teacher in the middle at one end with a large ball. Multiples of the table being tested are given to students in order along each line, starting from opposite ends. For example, if 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 are given to students, the number 48 students will be opposite the number 4 students. The teacher then calls out a table (e.g. 8 × 4) as he or she rolls the ball down between the lines. The two students with the correct product have to run and try to grab the ball. The first to catch the ball wins a point for his or her team. If a student with a wrong product grabs the ball, that team loses a point and if there are more than 24 students in the class, that student leaves the game and can be replaced by one of the extra students.

English

• Have the students write some persuasive text on maths related topics; e.g. ‘Learning tables is a waste of time’ or ‘Everybody needs to learn his or her times tables’. The students’ ideas could then be collated on some form of graphic organiser, such as a ‘Plus, Minus, Interesting (PMI)’ chart. • This subject could then be the topic for two-minute student talks supporting one particular view. Alternatively, an informal debate could be held on the topic.

The Arts

• Students design and make a colourful, imaginative poster to promote and encourage other students to spend more time and to make more of an effort to learn their tables. A poster could have a negative focus (for example, a humorous or embarrassing situation that arose because someone didn’t know his/her tables) or on a more positive one (perhaps showing employment opportunities or situations in which knowing ones tables is an advantage).

. te

History and Geography

m . u

w ww

• Students make a set of flash cards that can be used for instant recall of multiplication facts. They should write the multiplication fact (e.g. 7 × 3) on one side and the answer (21) on the back. The cards could be colour coded for each table and used for self-practice or to ‘test’ another student. (The card templates on page 49 can be photocopied onto light card.)

o c . che e r o t r s super

• Students interview older people for information; for example, about the importance of learning tables when they were at school, how tables were taught in the past, what they did to try and remember them, how their tables were tested by their teachers, any incentives or punishments they received, how they felt about multiplication tables and if it was useful for them to know their tables after they left school. This information can be recorded in note form and used to write a simple report about the interview to be shared with the class. • The information gathered could be shared in a small group and used to complete a similarities-and-differences chart, comparing the past and the present.

Design and Technology • Students work in groups to design a game or activity to help other students learn their tables. This could be a board or card game or an activity using digital technology.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Learning multiplication facts

Remember: • Multiplication is just fast adding; e.g. 4 × 7 = 7 + 7 + 7 + 7. If you don’t know a certain number fact, you can count on to work it out. • Order doesn’t make a diﬀerence in multiplication; e.g. 7 × 4 = 4 × 7. If you know your four times table, you can understand the matching seven times table.

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

ew i ev Pr

Teac he r

• Multiplication and division are linked. If you know a multiplication fact, you can work out its matching division fact. For example, 28 ÷ 7 = 4 because 7 × 4 = 28. • Multiples of the same number can be added. If you don’t know 8 × 9, you can add 5 × 9 and 3 × 9 (45 + 27 = 72), or you can add 4 × 9 and 4 × 9 (36 + 36 = 72). • Multiples can be calculated from square numbers. For 8 × 9, calculate (8 × 8) + 8 = 72.

Tricks you can use:

m . u

• Multiplying be 3s – The digits all add to 3, 6 or 9; for example: 13 × 3 = 39, and 3 + 9 = 12 then 1 + 2 = 3.

• Multiplying by 4 – Doubling a number then doubling it again is the same as multiplying by four.

w ww

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

• Multiplying by 2s – All multiples are even numbers and end in 0, 2, 4, 6 or 8.

. te

• Dividing by 4s – If just the last two digits of a number are a multiple of 4, you know the whole number can be divided equally by 4. For example, 23 552 can be divided by 4 because 52 ÷ 4 = 13. (This trick works because 100 can be divided by four, so even for very big numbers it’s only the last two digits you need to test.)

o c . che e r o t r s super

• Multiplying by 5s – All multiples of ﬁve end with 5 or 0 and alternate as odd and even numbers. • Dividing by 6 – If a number is even and can be divided by 3, it is divisible by 6. For example, 45 684 can be divided by 6 because it’s an even number and is divisible by 3. • Multiplying by 9 – The digits in any number that has been multiplied by 9 will add up to 9. For example, 7 × 9 = 63 and 43 × 9 = 387 (3 + 8 + 7 = 18 and 1 + 8 = 9). Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Basic facts

10 12 14 16 18 20

12 18 24 30 36 42 48 54 60

14 21 28 35 42 49 56 63 70

16 24 32 40 48 56 64 72 80

18 27 36 45 54 63 72 81 90

12 18 24 30 36 42 48 54 60

14 21 28 35 42 49 56 63 70

16 24 32 40 48 56 64 72 80

18 27 36 45 54 63 72 81 90

10 20 30 40 50 60 70 80 90 100

Teac he r

ew i ev Pr

o 12t 15 r 18e 21B 24 27 30 s r e oo40 0 4 p 8 12 16 20 24 28 32 36 u k S 0 5 10 15 20 25 30 35 40 45 50

w ww

m . u

10 0

0 2 4 6 8 10 12 14 16 18 20 . te o 3 0 3 6 9 12 15 18 21 24 27 . 30 c c8 e e r 4 0 4 h 12r 16 20 24 28 t 32 36 40 o s super 5 0 5 10 15 20 25 30 35 40 45 50 2

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

10 R 20. 30 40P 50 60l 70a 80 90n 100 © I . C. ub i c t i o s •f orr evi ew pur posesonl y• Basic facts

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Flash cards

. te

m . u

w ww

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Bingo cards (2, 3, 4, 5 and 10 times tables)

27 100 14

16 100 28

r o e t s Bo r e 30up 60 16 32 8 ok5 S

32 9

m . u

ew i ev Pr

o 32 c . che e r o t r s s r u e p 30 4 6 100 15 3

w ww

Teac he r

. t18 14 e

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

16 12 24 9

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

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

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

RESOURCE SHEET Bingo cards (2, 3, 4, 5 and 10 times tables)

100 12

R. I . C .Pu bl i c21 at i on s 15 32©25 50 27 24

•f orr evi ew pur posesonl y•

w ww

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

o 25 c . 8

m . u

ew i ev Pr

Teac he r

r o e t s Bo r e p 5 9 18 o8k 35 u 90 S

. te 16

che e r o t r s s r u e p 6 2 4 8 2

28 100 16

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Bingo cards (Mainly 6, 7, 8 and 9 times tables)

r o e t s Bo r e 30up 14 48 32 27ok 48 S

64 24

ew i ev Pr

Teac he r

w ww

m . u

o 15 c . che e r o t r s s r u e p 100 40 10 54 36 50

. t20 64 e

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

42 54 21 28

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

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

100 54

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

RESOURCE SHEET Bingo cards (Mainly 6, 7, 8 and 9 times tables)

r o e t s Bo r e p 90 35 24 o 48 u 72 80 k S

56 100 21

R. I . C .Pu bl i c72 at i on s 90 42©72 81 18 72

o 45 c . 90

m . u

•f orr evi ew pur posesonl y•

w ww

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

Teac he r

ew i ev Pr

. te 28

che e r o t r s s r u e p 35 18 32 72 72

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Bingo cards (Blank)

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

w ww

. te

m . u

Assessment 1

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

NAME:

DATE:

1. Shade the bubble to show which problem is correct. 9×8=8×9 72 ÷ 8 = 8 ÷ 72

(a)

3×2=2×3 6÷3= 3÷6

(b)

12 ÷ 3 = 3 ÷ 12 3×4=4×3

(c)

2. Shade one bubble. Order makes a diﬀerence in: division. multiplication.

both.

3. Write the missing numbers.

(a) 7 × 5 =

35 =

×5

35 ÷

÷5=7

ew i ev Pr

Teac he r

(b) 7 × 8 =

56 = 7 ×

=6×9

÷7=8

54 ÷ 6 =

56 ÷ 8 =

9 = 54 ÷

4 = 36

9 = 81

(b) 2

10 = 20

30 = 10

4 = 24

5 = 45

m . u

(a) 9

w ww

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

4. Write the missing operation signs.

. 14 = 2 7 49 te7 = 4 o c . 42 6 =c 7 5 5 = 25 40 e her r o t s s r u e p 21 = 7 3 56 = 8 7 18 = 6

7=7 10 = 4 3

20 = 5

45 = 5

15 = 5

7 = 63

8 = 72

6 = 60

5 = 35

3 = 21

25 = 5

5. Shade the bubble to show which problem is correct. 6×4=7×3 4×3=2×6 (a) 9×7=8×8 21 ÷ 7 = 12 ÷ 3 (b) Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

18 ÷ 6 = 24 ÷ 6 2×9=6×3 www.ricpublications.com.au

Assessment 2

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

NAME:

DATE:

1. Complete these facts.

2. Complete these facts.

3. Complete these facts.

(a) 7 × 3 =

(a) 8 ÷ 2 =

(a) 8 × 4 =

(b) 5 × 8 =

(b) 24 ÷ 6 =

(b) 8 ÷ 1 =

r o e t s Bo(c) 24 ÷ 3 = r e p ok u S (d) 15 ÷ 3 = (d) 5 × 5 = (c) 3 ÷ 3 =

(e) 3 × 6 =

(e) 18 ÷ 2 =

(e) 5 × 9 =

(f)

8×6=

72 ÷ 9 =

(i)

8×7=

(i)

28 ÷ 7 =

(i)

9×6=

(j)

w ww

(j)

16 ÷ 8 =

(j)

64 ÷ 8=

5×4=

(k) 9 × 8 =

. te

m . u

(h)

(g) ÷P 7u = b (g)n 20 © R. I . C42. l i cat i o s÷ 4 = •f orr ev(h) i ew pur poses onl y• 10 × 0 = 20 ÷ 10 = (h) 9 × 7 =

(g) 2 × 9 =

o c . che e r o (l) r 32 ÷ 4 = t s (l) 3 × 8 = super (k) 12 ÷ 4 =

(k) 56 ÷ 7 =

(m) 10 × 7 =

(m) 63 ÷ 9 =

(m) 0 × 6 =

(n) 3 × 5 =

(n) 54 ÷ 6 =

(n) 48 ÷ 6 =

(o) 7 × 7 =

(o) 12 ÷ 6 =

(o) 10 × 8 =

(l)

81 ÷ 9 =

8×8=

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recall multiplication facts up to 10 × 10 and related division facts

(d) 9 × 9 =

ew i ev Pr

Teac he r

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

ew i ev Pr

w ww

. te

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

Understands the inverse relationship between multiplication and division and can use multiplication facts to solve division facts

Understands that division is not commutative

Understands that multiplication is commutative and uses this knowledge to solve multiplication problems

Fluency is demonstrated by immediate recall of multiplication facts to 10 × 10

STUDENT NAME

o c . che e r o t r s super

m . u

Teac he r

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

Checklist

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

www.ricpublications.com.au

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

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder (ACMNA076)

RELATED TERMS

TEACHER INFORMATION

Mental calculation

What this means

• A calculation performed in the head which uses knowledge and understanding of number facts and place value.

• The students are able to perform efficient mental, written and calculator-assisted calculations.

Written strategy

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

Teac he r

Digital technology

• An electronic device such as a calculator programmed to calculate answers to number problems after relevant information has been keyed in.

• Develop calculations from known multiplication facts (tables). For example: 5 × 8 = 40 and 10 × 8 = 80; therefore, 15 × 8 = 120 (80 + 40). • Division facts should be related to their associated multiplication facts, so that there will be no need for remainders; for example: 48 ÷ 6.

ew i ev Pr

• A calculation process recorded in written form. When the individual steps are recorded they assist in the identification of errors and their correction.

Teaching points

• Extend to slightly harder facts; for example: 96 ÷ 6 can be split easily into parts, 60 ÷ 6 and 36 ÷ 6.

What to look for

• Students who lack fluency with the basic multiplication and division facts will struggle with harder mental and written calculations.

• Students who experience trouble partitioning numbers. • Students who experience difficulty with place value.

steps identified.

See also New wave Number and Algebra (Year 4) student workbook (pages 32–37)

w ww

• The mathematical operation in which a number is grouped or divided into equal parts. For example, in 63 ÷ 9 = 7, 63 is the ‘dividend’, 9 is the ‘divisor’ and 7 is the ‘quotient’

. te

Student vocabulary mental strategy written strategy partitioning multiple product factor algorithm calculator key enter clear display constant

m . u

Division

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Using a calculator Students need opportunities to become familiar with the functions of a simple calculator and with terms such as display, key, enter, clear and constant. They need to know how to clear the display before starting and to use the numbers and operations keys as well as the ‘clear entry’ key to change an accidental entry. Students can explore the constant function of the calculator to improve their understanding of multiplication as repeated addition and division as repeated subtraction. Regular competitions to add lists of numbers and to subtract, multiply and divide examples using larger numbers can improve students’ confidence, speed and accuracy when working with a calculator. They can take part in both individual and small-group competitions. Working on the same tasks in a group enables students to check that they all have the same answer and if not, to repeat the task to ensure accuracy. By competing in this way, they should learn that errors are the result of incorrect data entry and they should gain experience in clearing incorrect entries using the ‘clear entry’ key on their calculators.

How did you do it?

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

Teac he r

ew i ev Pr

Students work with a partner to complete three or four number sentences involving multiplication and division which can be solved mentally using commutative properties; for example: 8 × 7 × 5 = ?, 99 × 68 = ?, 336 ÷ 3 = ?, 26 × 8 = ?

Each student needs to work out the number sentences mentally in the quickest and easiest way he or she knows. Students then compare their answers and explain to each other the particular method they used. They can work together to choose and write down the most interesting and cleverest way one or more of their answers was worked out. This method can then be shared and explained to another pair with some attempt made to decide which was the simplest, most efficient or most interesting method used by a member of the group. This activity is particularly effective when a number of word problems are given to the students to solve.

Why?

Give small groups of students examples of partitioning, reordering, rearranging, compensating or splitting up factors to multiply or divide. For example:

• 5 × 35 = 5 × 30 plus 5 × 5 = 150 + 25 = 175

• 16 × 7 = (8 + 8) × 7 = 8 × 7 + 8 × 7 = 56 + 56 = 100 + 12 = 112

w ww

• 69 × 4 = 70 × 4 – (1 × 4) = 280 – 4 = 276 • 12 × 16 = 12 × 4 × 4 = 12 × 4 × 2 × 2 = 48 × 2 × 2 = 96 × 2 = 180 + 12 = 192

. te

• 108 ÷ 9 = (90 ÷ 9) + (18 ÷ 9) = 10 + 2 = 12

m . u

• 2 × 6 × 5 × 7 = 2 × 5 × 6 × 7 = 10 × 6 × 7 = 10 × 42 = 420

o c . che e r o t r s super

• 336 ÷ 8 = 336 ÷ 2 ÷ 2 ÷ 2 = 168 ÷ 2 ÷ 2 = 84 ÷ 2 = 42 • 627 ÷ 3 = (600 ÷ 3) + (27 ÷ 3) = 200 + 9 = 29

Students need to work out why it was easier to work out the example mentally in the way it was done and then write a similar problem in the same way.

What’s the problem?

Give students working in pairs a multiplication or division example (e.g. 24 × 7 or 124 ÷ 4). Their task is to write three interesting word problems based on the multiplication or division. They then work in a group of six to solve their word problems and choose the most interesting one to present to the class.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS English • Write some persuasive text on the subject of word problems in mathematics; for example: – ‘Solving maths word problems is a waste of time’ – ‘Students need to do more word problems’ – ‘Word problems are the best thing about maths’ – ‘Maths needs words as well as numbers’.

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

• Write a step-by-step procedure to help other students learn how to solve maths word problems. Students may benefit from working with a partner to complete this activity. • Give an oral presentation to explain one way of multiplying or dividing a three-digit number by a one-digit number mentally. Provide an example and demonstrate the steps involved.

Teac he r

The Arts

• Design a poster promoting the use of calculators in all classrooms.

ew i ev Pr

• Illustrate written word problems. These can be done on cards and used in the board game described below.

• Conduct a competition to draw a cartoon or a cartoon strip with the slogan, ‘Learning tables will help you in life’.

History and Geography

• Research to find six interesting facts about the history of calculators.

• Complete a class similarities and differences chart comparing what students know about calculators and abacuses. They can then carry out additional research to find further information to add to the chart.

Design and Technology

w ww

. te

m . u

• Create a board game to be played with a dice. Include rewards and penalties, such as ‘Miss a turn’, ‘Move back three spaces’, ‘Have another turn’ and ‘Double your score’. Each player throws the dice then picks up a card with a simple word problem on it. The other players can then check the answer using a calculator. If correct, the player moves the number of squares shown on the dice. If incorrect, that player moves back one space. Word problems generated during ‘What’s the problem?’ on page 59 and those illustrated (see above) can be used on these cards.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET What you should know about multiplication

Multiplication:

r o e t s Bo r e p o u k • tables can help you do division; S for example, 54 ÷ 9 = ?

ew i ev Pr

Teac he r

• tables are important and you need to learn them well so you are quick at remembering them

If you know the 6 or 9 times tables (9 × 6 = 54 and 6 × 9 = 54), you will be able to work it out

• of numbers by tens, hundreds and thousands is easy … you just add zero(s); for example: 34 × 10 = 340, 34 × 100 = 3400, 34 × 1000 = 34 000

• is repeated addition; for example: 7 × 2 = 2 + 2 + 2 + 2 + 2 + 2 + 2. The constant function on a calculator uses repeated addition.

m . u

• number order doesn’t make any diﬀerence; for example: 7×2=2×7

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

• is the opposite of division; for example: 15 ÷ 3 = 5, so 5 × 3 = 15 and 3 × 5 = 15

• number order can be changed to make multiplying easier; for example: 5 × 7 × 2 = 5 × 2 × 7 = 10 × 7 = 70

. te

o c . c e r • can be easier if youh halve or double numbers; for example: e o t r s r 18 × 7 = (9 × 7) + (9 × 7) = 63s +u 63 =p 126, or e • can be easier if you partition (break up) numbers; for example: 14 × 7 = (10 × 7) + (4 × 7) = 70 + 28 = 98

124 × 5 = 124 × 10 ÷ 2 = 1240 ÷ 2 = 620

• can be easier if you split a number into factors; for example: 15 × 8 = 15 × 2 × 4 = 30 × 4 = 120 • can be easier if you change one number and compensate (make up) for it; for example: 19 × 4 = (20 × 4) – (1 × 4) = 80 – 4 = 76, or 31 × 6 = (30 × 6) + (1 × 6) = 180 + 6 = 186. Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET What you should know about division

Division:

r o e t s Bo r e 9 × 8 = 72 and 8u ×p 9 = 72—you will be able to work o out 72 ÷ 8 = ? k S • of numbers by tens, hundreds and thousands is easy, you just subtract zero(s); for example: 96 000 ÷ 10 = 9600

96 000 ÷ 100 = 960

ew i ev Pr

Teac he r

• is easy if you know your multiplication tables. For example, if you know these two number facts from the 8 and 9 times tables—

96 000 ÷ 1000 = 96

• is repeated subtraction; for example: 18 ÷ 3 = 18 – 3 – 3 – 3 – 3 – 3 – 3 The constant function on a calculator uses repeated subtraction.

and

m . u

w ww

These include:

• can be easier if you partition (break up) numbers; for example: 112 ÷ 4 = (100 ÷ 4) + (12 ÷ 4) = 25 + 3 = 28

. te o • can be easier if you halve or double numbers; for example: c . 64 ÷ 4 = (32 ÷ 4) + (32 c ÷ 4) = 8 + 8 = 16, or e h× 2r r o 130 ÷ 5 = (130 ÷ 10) × 2 = 13e =s 26 t s uper • can be easier if you split a number into factors; for example: 78 ÷ 6 = 78 ÷ 2 ÷ 3 = 39 ÷ 3 = 13

• can be easier if you change one number and compensate (make up) for it; for example: 124 ÷ 4 = (120 ÷ 4) +(4 ÷ 4) = 30 + 1 = 31, or 58 ÷ 2 = (60 ÷ 2) – (2 ÷ 2) = 30 – 1 = 29.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

• is the opposite of multiplication; for example: 7 × 2 = 14, so 14 ÷ 2 = 7 and 14 ÷ 7 = 2

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

RESOURCE SHEET Written calculation for multiplication When students are multiplying larger numbers, they may require an effective and efficient way in which to record their calculations. Neat and well organised setting out assists with accuracy and enables students to check for errors and to make any necessary corrections.

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

Blank templates are provided on pages 64–67.

Example 1

7 × 156

7 × (100 + 50 + 6)

7 × 100

7 × 50

700

350 1092

7×6

ew i ev Pr

Teac he r

Problem: 7 × 156

Example 2

Example 3

Problem: 7 × 156

7 × 100

7 × 50

7×6 1

. te

Example 4

Tens Ones

o c . che e r o t r s super Example 5

Problem: 46 × 32 ×

m . u

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

The algorithms below are written examples of partitioning into ones, tens and hundreds to multiply two- and three-digit numbers by one-digit numbers, and two-digit numbers by two-digit numbers. Each requires students to show how the numbers are partitioned and multiplied. Clearly defined columns are provided for ones, tens, hundreds and thousands, and rows for partitioning and calculations.

Problem: 26 × 37

Tens

Ones

Sum

1200

1200 180 (30 × 40) (30 × 6) 80 (2 × 40)

12 (2 × 6)

180 80 + 12

Sum

20 × 30 = 6 × 30 = 30 600 180

600

20 × 7 = 140

140

6×7= 42

180

+ 42 962

1472

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Blank templates for multiplication (page 1) Example 1

Problem:

= + r o e t s B r= e + o p ok u = S

Problem:

ew i ev Pr

Teac he r

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

w ww

Problem:

. te

m . u

1- × 3-digit numbers

+ o c . che = e r o r st super =

Problem: =

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

1- × 2-digit numbers

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

RESOURCE SHEET Blank templates for multiplication (page 2) Example 2 1- × 2-digit numbers Problem:

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

ew i ev Pr

Teac he r

Problem:

. te

Problem:

m . u

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

Problem:

o c . che e r o t r s super

Problem:

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Blank templates for multiplication (page 3)

Example 3

Problem:

ew i ev Pr

Teac he r

r o e t s B r e Th H T O Th H T o O oTh p u k S Problem:

w ww

Problem:

. te

Problem:

m . u

Problem:

o c . che e r o t r s super ×

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

1- × 2-digit numbers

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

RESOURCE SHEET Blank templates for multiplication (page 4)

Example 4

Problem:

Tens Ones

Tens

Sum

Example 5 2- × 2-digit numbers

Problem:

. te

Problem:

m . u

Ones

ew i ev Pr

Teac he r

Problem: r o e t s BoTens rSum e Tens Ones p ok × u S

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

2- × 2-digit numbers

o × c . che e r o r st super ×

Sum

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

Sum

www.ricpublications.com.au

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

RESOURCE SHEET A multiplication trick Indian Vedic mathematics offers a fun way of multiplying and it can be used to quickly work out basic facts beyond 5 × 5.

Subtract each number from 10 and record the difference beneath each number. This is the ‘lower pair’.

Step 2

Subtract either of the diagonal pairs to get the tens digit of the answer.

Step 3

Multiply the lower pair to get the ones digit.

Examples:

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

4×9=

Step 2

10 – 4 = 6

4×9

10 – 9 = 1

4–1=3

Step 4

6×1=6

Step 2

Step 4

Step 2

10 – 7 = 3

8–3=5

This gives the tens digit 5.

or 7 – 2 = 5

Step 3

2×3=6

8 × 7 = 56

This gives the ones digit 6.

. te

6×7=

o c . che e r o t r s super

10 – 5 = 5

5×7

10 – 7 = 3

5–3=2 or 7 – 5 = 2

Step 3

4 × 9 = 36

8×7

If Step 3 produces a two-digit answer, the tens digit is added to the tens digit already determined.

5×7=

Step 1

This gives the tens digit 3.

This gives the ones digit 6.

w ww

Examples:

10 – 8 = 2

or 9 – 6 = 3

Step 3

Step 1

5 × 3 = 15

2+1=3

m . u

Step 1

8×7=

ew i ev Pr

Teac he r

Step 1

Step 2

This gives the tens digit 2.

This gives the ones digit 5, with a 10 to add to the tens digit found in Step 2. This gives the final tens digit 3.

10 – 6 = 4

6×7

10 – 7 = 3

6–3=3

or 7 – 4 = 3

5 × 7 = 35

Step 3

Step 4

4 × 3 = 12

3+1=4

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

This gives the tens digit 3.

This gives the ones digit 2, with a 10 to add to the tens digit found in Step 2.

6 × 7 = 42

This gives the final tens digit 4.

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

There are three easy steps to follow, plus a fourth when carrying 10 is required.

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

RESOURCE SHEET Written calculation for division To save an unknown division fact, known multiplication facts of the divisor can be used. For example; 96 ÷ 8 =

You may know that:

divisor

quotient

r o e t s Bo r e p ok u S 10 x 8 = 80

Subtract the product of the known fact from the dividend:

ew i ev Pr

Teac he r

product

96 – 80 = 16 new dividend

You may know that:

2 x 8 = 16

(Subtraction continues until the new dividend is zero or less than the divisor.)

This may be represented in tables: 96 ÷ 8

Tens 9

96 ÷ 8

. te Ones 6

–8

–1

m . u

The unknown fact has been broken down into known facts:

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

dividend

Multiplication facts

o c . che e r o t r s super 10 x 8

2x8

Subtraction 96 – 80 = 16

(10 x 8)

12 eights

16 –16 = 0

96 ÷ 8 = 12

(2 x 8)

0 or using the division bar:

⁄8 = 80 + 16⁄8 = 80⁄8 + 16⁄8

= 10 + 2 = 12

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET Blank templates for division (page 1)

Ones

Tens

Ones

Tens

Ones

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

Problem:

Hundreds

Problem:

Ones

Problem: Hundreds

Tens

ew i ev Pr

Teac he r

Tens

Problem:

Ones

w ww

Problem:

Hundreds

Tens

. te Ones

m . u

o c . che e r o t r s super Problem:

Hundreds

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Tens

Ones

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

Problem:

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

RESOURCE SHEET Blank templates for division (page 2) Problem:

Problem: Multiplication facts

Subtraction

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

Multiplication facts

Subtraction

ew i ev Pr

Teac he r

Subtraction

Problem:

Multiplication facts

Subtraction

Problem:

. te

Problem:

Multiplication facts

Subtraction

m . u

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

Multiplication facts

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

Subtraction

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

Teac he r

357 × 5 =

2. Complete the division problems, showing your working out. (a) Problem: 8 176

(b)

Hundreds

Tens

Ones

– –

ew i ev Pr

r o e t s Bo r e p ok u So S So 234 × 3 = Problem: 203 ÷ 7 Multiplication facts

Subtraction

10 × 7 70 203 – 70 = © R . I . C . P u b l i c a t i o ns 8 0 (10 x 8) •f orr evi ew pur posesonl y•

w ww

sevens

. te

So 176 ÷ 8 =

m . u

– So 203 ÷ 7 =

o c . c e r 3. Write word problems for h these number sentences. Useo a calculator to find the e t r s s r upe answers.

(a)

67 × 9 =

(b)

240 ÷ 5 =

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

1. Complete the multiplication problems, showing your working out. (a) (b) Problem: 234 × 3 Problem: 357 × 5

Assessment 2

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

NAME:

DATE: Show the method you used to calculate these problems. Use a calculator to check your answers.

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

ew i ev Pr

Teac he r

Calculator check: Correct/Incorrect

2. 46 × 34 =

. te

m . u

Calculator check: Correct/Incorrect

3. 316 × 3 =

w ww

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

1. 127 × 6 =

o c . che e r o t r s super

= 52 × 65

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Calculator check: Correct/Incorrect

R.I.C. Publications®

www.ricpublications.com.au

Assessment 3

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

NAME:

DATE: Show the method you used to calculate these problems. Use a calculator to check your answers.

2. 7 441 =

ew i ev Pr

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

Calculator check: Correct/Incorrect

= 654 ÷ 3

w ww

. te

4. 6 828 =

Calculator check: Correct/Incorrect

m . u

o c . che e r o t r s super

Calculator check: Correct/Incorrect

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder

Calculator check: Correct/Incorrect

Teac he r

1. 752 ÷ 4 =

Checklist

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

Uses a calculator to multiply and divide and to check answers

Is able to record strategies used when multiplying and dividing

Uses efficient mental strategies to multiply and divide

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

ew i ev Pr

Teac he r

STUDENT NAME

Demonstrates understanding of a range of mental and written strategies for multiplying and dividing

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder (ACMNA076)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Answers

Sub-strand: Number and Place Value

N&PV – 1 Page 8 Assessment 1 1. 1, 3, 5, 7 and 9 2. 0, 2, 4, 6, and 8 3. (a) 12 (d) 88 or 90 4. (a) 101 (d) 201 5. 402 and 260 6. 811 and 521

(b) 30 (e) 98 (b) 153 (e) 99

3. (a) 54 273 4. (a) 15 578

(b) 71 928 (b) 95 055

•

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

Teac he r

Page 32 Assessment 1 1. 2. 3. 4. 5. 6. 7. 8.

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

700 (b) 60 (b) 400 tens 7925 (b) 40 000 (b) 200 (b) 90 (b) 400 × 100

Page 33 Assessment 2

30 000 (c) 4000 4000 (c) 40 000 (b) 2000 tens (c) 700 hundreds 24 059 (c) 99 007 (d) 38 063 80 (c) 60 4000 (c) 80 500 (c) 670 (b) 980 × 100 (c) 30 × 3000

ew i ev Pr

She would have an even number to frame. Yes, she would have one bead left. He had an odd number left. There was an odd number of teams. No, they hadn’t lost a sock.

1. (a) 100 (b) 100 (c) 1000 (d) 100 (e) 80 000 (f ) 100 2. Possible answer (a) 40 + 90 + 60 + 50 + 10 = 40 + 60 + 90 + 10 + 50 = 100 + 100 + 50 = 250 (b) 32 + 49 + 28 = 32 + 28 + 49 = 60 + 49 = 109 3. (a) 69 763 (b) 75 716 (c) 132 867 (d) 12 011 (e) 50 101 4. (a) 781 (b) 5141 (c) 6282 5. (a) 43 544 (b) 32 472 (c) 42 441 (d) 14 381 (e) 70 096

w ww

Page 21 Assessment 2

. te

Page 34 Assessment 3 1. (a) 496 (d) 3688 (g) 5003 kj

m . u

Page 20 Assessment 1

1. (a) (c) 2. (a) (c) 3. (a) (b) 4. (a) 5. (a)

•••••• •••••• ••• ••• ••••• ••••• •••••• •• ••• •• • ••••• • •••••• •••

76 091 •• •• • • •

Page 10 Assessment 3

1. (a) (b) (c) (d) 2. (a) 3. (a) 4. (a)

19 603 •

•••

Ones

••••

22 876 • •

••

Tens

54 231 • • • • •

N&PV – 2

Tens of Thousands Hundreds thousands

N&PV – 3

Page 9 Assessment 2

1. 2. 3. 4. 5.

Number

o c . che e r o t r s super

37 964, 37 965, 37 966 (b) 54 319, 54 320, 54 321 15 998, 15 999, 16 000 (d) 98 800, 98 801, 98 802 N&PV – 4 87653 and 35678 (b) 97 331 and 13 379 Page 42 Assessment 1 96 542 and 24 569 1. (a) 129, 132, 135, 138, 141, 144, 147, 150 10 675, 30 760, 30 765, 34 987, 45 067 (b) 444, 448, 452, 456, 460, 464, 468, 472 25 009, 25 099, 25 100, 25 670, 25 909 (c) 120, 126, 132, 138, 144, 150, 156, 162 < (b) > (c) > (d) < (d) 84, 91, 98, 105, 112, 119, 126, 133 (b) (c) 2. (a) 732, 728, 724, 720, 716, 712, 708, 704, 700, 696 (b) 549, 540, 531, 522, 513, 504, 495, 486 (c) 644, 637, 630, 623, 616, 609, 602, 595 56 021 31 243 12 433 (d) 912, 904, 896, 888, 880, 872, 864, 856 6. (a) 56 702 (b) 32 463 (c) 45 301 3. (a) Add to 3, 6, or 9 (b) Are even numbers (c) Add to 9 Page 22—Assessment 3 4. (a) 576 (b) 423 (c) 459 (d) 248 1. (a) 24 173 (b) 40 527 (c) 53 064 (d) 5519 5. (a) 2160, 2163, 2166, 2169, 2172, 2175, 2178 (b) 621, 612, 603, 594, 585, 576, 567

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

Sub-strand: Number and Place Value

N&PV – 5

(a)

Problem: 234 × 3 Th

Page 55 Assessment 1 1. (a) 9 × 8 = 8 × 9 2. division 35

3. (a) 7 × 5 = 5×7=

35 = 7 × 7

35 =

×5

35 ÷ 35

÷5=7 5

× ×

÷ ÷

4 = 36

30 × 3

4×3

× 7 = 56

6×

= 54

=8×7

54 = 9 ×

So 234 × 3 =

(b)

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

56 = 7 × 56

÷7=8

(b) 2

9 = 81

= 56 ÷ 7

14 = 2

6=7

3 7

5 = 25

5 ×

7 5

= 54 ÷ 6 6

54 ÷

10 = 20 (c) 6

30 = 10

7=4

Problem: 357 × 5 Th

9 = 54 ÷

7 = 56 ÷

=6×9

54 ÷ 6 =

56 ÷ 8 = 8

× ×

49 40

4 = 24 5 = 45

÷ ÷

8 9

So 357 × 5 =

1785

2. Teacher check: setting out may vary. (a) Problem: 8 176

7=7

Hundreds

Tens

Ones

10 = 4

21 = 7 20 = 5 7 = 63 5 = 35

× × ÷ ÷

56 = 8

45 = 5

8 = 72

3 = 21

5. (a) 4 × 3 = 2 × 6

× × ÷ ÷

18 = 6

15 = 5

6 = 60

25 = 5

× × ÷ ×

–

3 3

–

(b) 2 × 9 = 6 × 3

w ww (b) (f ) (j) (n) (b) (f ) (j) (n) (b) (f ) (j) (n)

40 48 20 15 4 8 2 9 8 9 8 8

. te

36 18 72 49 1 6 3 2 8 5 8 80

(d) 81 (h) 0 (l) 64

So 176 ÷ 8 =

(b)

(10 x 8)

Page 56 Assessment 2 1. (a) 21 (e) 18 (i) 56 (m) 70 2. (a) 4 (e) 9 (i) 4 (m) 7 3. (a) 32 (e) 45 (i) 54 (m) 0

702

Problem: 203 ÷ 7 Multiplication facts

(10 x 8) (2 x 8)

m . u

4. (a) 9

= 35 ÷ 7

ew i ev Pr

Teac he r

7 = 35 ÷

200 × 3

(b) 3 × 2 = 2 × 3 (c) 3 × 4 = 4 × 3

(b) 7 × 8 =

Subtraction

o c . che e r o t r s super

N&PV – 6 Page 72 Assessment 1 1. Teacher check: setting out may vary.

(d) 5 (h) 2 (l) 8

(d) 25 (h) 63 (l) 24

133

10 × 7

133 – 70 = 63

5×7

63 – 35 = 28

4×7

28 – 28 = 0

sevens

203 – 70 =

So 203 ÷ 7 =

3. (a) 603. Teacher to check word problem (b) 48. Teacher to check word problem Page 73 Assessment 2 1. 762

2. 1564

3. 948

4. 3380

3. 218

4. 138

Page 74 Assessment 3 1. 188

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

2. 63

R.I.C. Publications®

www.ricpublications.com.au

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

Investigate equivalent fractions used in contexts (ACMNA077)

RELATED TERMS

TEACHER INFORMATION

Fractions

What this means

• A fraction is part of a whole; e.g. the fraction 3⁄7 represents three parts out of 7. The denominator is the bottom number and the numerator is the top number.

• Students develop a good understanding of the relationship between families of fractions; e.g.

Equivalent fractions

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

Teac he r

– thirds and sixths.

Teaching points

• Students need to link materials, words and symbols to represent the family of fractions.

ew i ev Pr

• Fractions that can be reduced to the same basic fraction; that is fractions that have the same value: 1 ⁄2 = 2⁄4 = 3⁄6

– halves, fourths and eighths

• A variety of models will be required to model equivalent fractions; for example: – folding 2-D shapes including circles

Family of fractions

– showing subset ideas using counters

• Fractions with common multiples as denominators; for example: halves, fourths and eighths.

– using Cuisenaire™ rods to construct number walls for the fractions: 1⁄2, 1⁄4, 1⁄6 and 1⁄8 – using number lines to show the fraction quantities.

© R. I . C.Publ i cat i ons • A visual representation useful for showing equivalent fractions and •fractions. f orr evi eWhat wtop ur posesonl y• the relative size of unit look for Rectangles, divided into different fractions, are placed together to form layers similar to the bricks of a ‘wall’.

w ww

Unit fraction

• A simple fraction which has a numerator of one. Whole

. te

• The ‘whole’ can be all of an object, the total amount of a quantity, or all of a collection.

Student vocabulary fraction fraction family represent equivalent

• Students make statements such as, ‘One-half is the same as four-eighths’ and they use symbols to record this: 1⁄2 = 4⁄8.

• Students may think of fractions as whole numbers and, therefore, think 1⁄8 is bigger than 1⁄4. • Students often see the pattern that is created but this does not mean they understand equivalent fractions.

m . u

Fraction wall

See also New wave Number and Algebra (Year 4) student workbook (pages 38–43)

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

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES What’s a half? Give pairs of students larger and smaller paper plates to cut in half. Check they understand the concept that there has to be two halves and they are both the same size. (To reinforce the idea that all of a plate must be used and that they can’t just cut a bit off the larger piece and discard it, ask them how their two pieces could be halves if one is bigger than the other.) Compare the sizes of half the bigger and smaller plates and ask them to explain why half of one plate isn’t the same size as the other. Students fold and cut one of their halves into two or four equal-sized pieces to make quarters or eighths and use them to identify the equivalent fractions of: 1⁄2, 2⁄4 and 4⁄8 by placing them over the other half.

Paper folding

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

For example:

Pour it out

ew i ev Pr

Teac he r

Each student folds a rectangular strip of paper into halves, quarters and eighths. Their task is to colour half of the strip. Some students may simply colour 4 of the eighths or 2 of the quarter next to each other, but others may realise there are other ways of showing one half. Provide opportunities for students to share and explain their innovative ideas.

⁄8 = 1⁄2

⁄4 = 1⁄2

Give small groups of students the task of finding one-third of the water in a plastic bottle by using three same-sized plastic glasses. Discuss criteria for completing this task successfully, such as each glass must have the exactly the same quantity of water in it, there can’t be any water left over and all of the water must be available to be shared—so none can be spilt. Repeat the task of finding one-third of the water using six plastic glasses to show that one-third is equal to two-sixths.

m . u

Share them out

w ww

Groups of five students are given 60 counters to share equally (i.e. 12 each) and given the task of discovering how many people could have an equal share of each set of 12 counters; i.e. dividing them into different fractions. Each group should have five different sets of counters, with each set clearly separated into twelfths, sixths, quarters, thirds or halves. (These sets can be used to check students understand the concept: ‘The greater the number of shares the smaller each share’.)

. te

o c . che e r o t r s super

Identify the set already divided into halves and set the task of showing one-half of each of the other four sets without moving the counters; i.e. the quarters (2), sixths (3) and twelfths (6)—but not the thirds. Discuss and write these equivalent fractions. Students then investigate which sets can be used to show thirds; i.e. sixths (2) and twelfths (4). Discuss and write the equivalent fractions.

Fraction dominoes and the fraction concentration cards

The fraction dominoes on pages 82 and 83 and the fraction concentration cards on page 84 provide practice in matching equivalent fractions.

Number lines Use page 85 to show equivalent fractions along a number line. For example, how 1⁄2 is equal to 4⁄8 or 2⁄3 is equal to 8⁄12.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education

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

English

• You may find the following books useful: – Piece = Part = Portion: Fractions = Decimals = Percents, by Scott Gifford is an appealing book, including interesting examples of fractions taken from everyday life which are presented in full-colour photographs, supported by straightforward text.

ew i ev Pr

Teac he r

• Is it more, less or equal to half? Give each small group of students eight beanbags and a skipping rope. When one of the fractions listed below is called out, the groups have to show that fraction by grouping their beanbags appropriately on the ground and by placing their skipping rope around the fraction called; for example: 1 2 ⁄8, ⁄8, 3⁄8, 4⁄8, 5⁄8, 6⁄8, 7⁄8, 8⁄8, 1⁄4, 2⁄4, 3⁄4, 4⁄4, 1⁄2, 2⁄2. When the groups have completed this task successfully, they all sit down. The teacher then calls out the word, ‘more’, ‘less’ or ‘equal’ and the students have to work out if the fractions they’ve made are more than, less than or equal to a half. If the group decides that the teacher’s statement matches, they all jump up waving their arms and cheering and their leader takes the skipping rope and skips to a finishing line. The first person there wins a point for his/her team. If the statement doesn’t match, any team to jump up and send a skipper to the finishing line loses a point.

– Funny and fabulous fraction stories, by Dan Greenberg includes 30 reproducible maths tales and follow-up problems that reinforce essential fraction skills.

• Work with a partner to prepare a set of instructions or rules for playing ‘fraction dominoes’ or ‘concentration’. (See pages 82–84.) Set out the procedure in numbered steps, using command verbs. Add some appropriate illustrations.

The Arts

w ww

Information and Design Technology

m . u

• Students can make their own set of 24 fraction dominoes by cutting out the dominoes on pages 82 and 83. These dominoes will be more durable and easier to play with if printed on card rather than paper. Students can then individualised their set of cards by adding a distinctive illustration or design on the back of each.

• This interactive game allows students to practise identifying and matching equivalent fractions in either a relaxed or a timed mode at five different levels of difficulty: <http://www.sheppardsoftware.com/mathgames/fractions/equivalent_ fractions_shoot.htm>.

. te

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Equivalent fractions Halves

⁄2

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

or one half is shaded

⁄6

or one half is shaded

⁄8

or one half is shaded

ew i ev Pr

⁄4

Teac he r

or one half is shaded

⁄10

⁄12

⁄2 = 2⁄4 = 3⁄6 = 4⁄8 = 5⁄10 = 6⁄12

w ww

m . u

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

Thirds

. te

o c . che e r o t r s super ⁄3

or one third is shaded

⁄6

or one third is shaded

⁄9

or one third is shaded

⁄12

or one third is shaded

⁄3 = 2⁄6 = 3⁄9 = 4⁄12

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Fraction dominoes (page 1)

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

w ww

. te

m . u

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Fraction dominoes (page 2)

. te

m . u

w ww

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

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

RESOURCE SHEET

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

ew i ev Pr

Teac he r

Fraction concentration game

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

w ww

. te

m . u

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

RESOURCE SHEET

twelfths

ninths

sixths

thirds

twelfths

eighths

sixths

quarters

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

ew i ev Pr

Teac he r

halves

Number lines for equivalent fractions

m . u

. te

o c . che e r o t r s super Thirds, sixths, ninths and twelfths

Halves, quarters, sixths, eighths and twelfths

w ww

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

1. Circle the picture which has one-third shaded. (a)

(b)

(c)

(a)

r o e t s Bo r e p ok u S ⁄2 =

⁄4

(b)

ew i ev Pr

Teac he r

2. Shade each picture to represent one-half and finish writing the fraction you shaded.

⁄2 =

⁄12

(c)

⁄2 =

⁄8

(d)

⁄2 =

⁄10

3. Shade the bubble to show which picture represents the fraction.

(b)

w ww

⁄5

. te

o c . cish e 4. Circle the picture which equivalent r er o t to this shaded fraction. s super (c)

(a)

⁄3

(b)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

m . u

⁄4

(a)

Assessment 2

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

NAME:

DATE:

1. Draw a line to connect each picture to another which shows the same fraction.

(b)

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

(c)

(d)

(e)

(f)

ew i ev Pr

Teac he r

(a)

w ww

m . u

2. Show and write the fraction that is equivalent to 2⁄3 on each number line.

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

. te

o c . che e r o t r s super

(a)

(b)

(c)

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

⁄3

www.ricpublications.com.au

Assessment 3

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

NAME:

DATE:

1. Shade the picture to show the fraction and finish writing its equivalent fraction. ⁄

(a)

(b)

⁄8 =

⁄4

r o e t s Bo r e p ok u ⁄ S⁄ (f) ⁄ = (e) ⁄ =

⁄10

⁄6 =

⁄8 =

⁄2

(c)

(d)

⁄10 =

ew i ev Pr

Teac he r

© R. I . C.Publ i cat i ons 2. Shade a bubble to show if each answer is more, less or the same. • f o r r e v i e w p u r p o s e s o n l y • (a) Anni ate ⁄ of her box of chocolates. If Tom ate ⁄ of another box of the 3

same chocolates, did he eat: the same?

w ww

(b) Jack and Kai shared the same bag of marbles. Kai lost 1⁄4 of them and Jack lost 2⁄8. Did Jack lose:

. te

o c ⁄ of it and Jess Jody and Jess shared a bottle of fruit juice. If Jody drank . c e her r drank ⁄ , did Jess drink: o t s the same? s uper more? less? more?

(c)

less?

the same? 1

(d) If Shane’s share of a pie was 2⁄5 and Alan’s was 2⁄6, Shane’s piece of pie was: more?

less?

the same?

(e) If 4⁄5 of the rain last year fell in winter and 8⁄10 of this year’s fell in winter, the winter rain this year was: more? 88

less?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

the same? R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Investigate equivalent fractions used in contexts

less?

m . u

more?

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

ew i ev Pr

w ww

. te

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Solves problems involving fractions in contexts

Represents equivalent fractions on number lines

Orders fractions and understands that the greater the number of shares the smaller the shares

Represents equivalent fractions in different ways

Differentiates between equivalent and non equivalent fractions

Partitions collections, quantities and objects into equal parts in different ways

STUDENT NAME

o c . che e r o t r s super

m . u

Teac he r

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

Checklist

Investigate equivalent fractions used in contexts (ACMNA077)

Sub-strand: Fractions and Decimals—F&D – 2

Count by quarters, halves and thirds, including mixed numerals Locate and represent these fractions on a number line (ACMNA078)

RELATED TERMS

TEACHER INFORMATION

Mixed numeral

What this means

• A number which includes a whole number part and a fractional part

• Students need to understand what quarters, halves and thirds are. They need to see, for example, that three thirds make a whole and to be able to show this with modelling with paper (e.g. folding and drawings) and to make sub-sets of a set (i.e. 1⁄2 of 12 is 6).

Improper fractions

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

Proper fractions

• A fraction with a value of less than one whole, in which the numerator is less than the denominator.

• This knowledge is extended to the idea of mixed numerals. For example, the idea of five-fourths could be shown with diagrams and folding and these numbers should be placed on a number line. • Students should be able to convert mixed numbers to improper fractions and vice versa.

Teaching points

ew i ev Pr

Teac he r

• A fraction in which the numerator is greater than the denominator. An improper fraction has a value which is greater than one whole.

• Use different shapes to show the fractions 1⁄2, 1⁄3 and 1⁄4.

• Extend this to show what, for example, 3⁄2 looks like, modelled with folding, diagrams and on a number line. • Have students look at comparative examples and consider what is larger, smaller etc.; for example, what is larger: 1⁄2 of a sheet of paper or 1⁄2 of 12 eggs? Show with diagrams, folding or counters.

• Number lines should be set up to show, for example, numbers between 0 and 3, and students should be asked to show mixed numbers such as 23⁄4. • Convert mixed number to improper fractions and vice versa.

w ww

. te

Student vocabulary number line proper fraction improper fraction

m . u

What to look for • Students who can’t cannot fold or draw equal-sized fraction quantities.

• Students who do not understand the part–whole notion and when asked to show 2⁄4 show 2⁄2 instead.

o c . che e r o t r s super

• Students who, when using a number line, think 1⁄4 is bigger than 1⁄2. See also New wave Number and Algebra (Year 4) student workbook (pages 44–49)

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

mixed number whole

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Fractions and Decimals—F&D – 2

HANDS-ON ACTIVITIES Making a four metre-long measuring tape Give each student a strip of paper one metre long. They need to fold their strip into quarters and mark each quarter with a short line. In groups of four, the students use adhesive tape to join their four strips. Establish that their tape is now four metres long and each metre is divided into quarters. They write 0 and 4 on the ends of the tape and are set the task of writing numbers and mixed numbers between zero and four on each fold and on each join on their tape. Give each group a different given length between 11⁄4 and 33⁄4 metres and set them the task of using their tape to find something that measures approximately that length.

How big is a half?

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

Teac he r

Students work in groups of three. Each group has two different lengths of rope and two clothes pegs. Their task is to find half of each rope and to mark it with a peg. They measure and record the lengths of their halves, then explain how their halves are different and why.

ew i ev Pr

Estimating mixed numbers

Students work in pairs. Each student has a page of number lines marked from 0 to 10 (see pages 95–97). They take turns to draw a line from zero along one number line that ends with two whole numbers. (Alternatively, a place along the number line could be indicated by a small arrow.) The mixed number indicated is then recorded on a separate page to be kept hidden from the partner. The partner has to estimate what the mixed number indicated on the number line is and then write the digits at the appropriate place on the line. Pairs then discuss if the intended number or the revealed estimated number is more accurate and why. If they can’t agree which is more accurate, another pair of students or the teacher is asked to adjudicate.

Mixed number models

Give small groups of students a mixed number (such as 22⁄3) and ask them to make a model of this mixed fraction by selecting suitable materials, then colouring, shading, folding or cutting them. Materials provided for this purpose could include small paper plates and paper squares, rectangles and triangles. They will also need a number of small cards and a marker to write with. They will need to use the cards to describe and label their model and for showing addition and equal signs and the improper fraction. This process would be best modelled with the whole class first.

w ww 22⁄3

31⁄4

. te =

Example 1:

o c . che e r o t r s super 3

⁄3

m . u

The students’ models can be discussed and evaluated for accuracy and clarity by the class, then displayed.

⁄4

⁄3

⁄4

+ Example 2:

⁄3

⁄4

⁄3

⁄4

Then have students use page 94 to see graphical representations of groups of objects in which the objects can be split into parts.

Ordering fractions Use sets of matching fraction cards displaying mixed numerals and improper fractions with the same denominator, and place them in order. Matching cards (those of equal value) can be placed on top of each other.

Matching fractions One page 98 are blank fraction cards which students can fill in themselves. Have the students create match pairs, which can then be cut out for matching games. Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Sub-strand: Fractions and Decimals—F&D – 2

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education • Draw a number line on the ground from zero to six, and mark each whole into halves. Students take turns to jump along the line, counting, ‘0, 1⁄2, 1, 11⁄2, 2, 21⁄2, 3 …’ as they make each jump. Add quarters to the number line and repeat the process. Students could also start from six and jump backwards along the line, counting as they go. Instead of jumping, students could repeat the activity by hopping or bunny hopping along the line. Students could repeat the activity with a line marked from 0 to 4 and divided into thirds and, later, ninths.

History and Geography

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

• Create a time line for the twentieth century, with each decade marked along it to the present. Mark the quarter and half centuries (1925, 1950, 1975, 2000) and research to find some events which could be written along the time line.

English

ew i ev Pr

Teac he r

Other time lines could be compiled to record historic events or a child’s personal family history, using time periods divided into halves or other fractions.

• Students work in pairs to compile and write a set of instructions; that is, a procedural text with steps to follow to change mixed numbers into improper fractions or vice versa. Include examples. • As a more interesting alternative to compiling their own definition of an improper fraction and a mixed number, students can write a ‘What am I?’ text for each, giving a number of clues to identify the required answer as an improper fraction or as a mixed number. • Discuss possible reasons with the class to explain why we don’t often use improper fractions in our everyday discussions. Compile a list of reasons why mixed numbers are easier to understand, giving some examples.

The Arts

• Small groups of students make sets of cards to be used in matching games (such as concentration, fish and snap). The non-numbered sides of the cards can be left blank or can all be decorated in exactly the same way. (Students could choose to design something suitable and photocopy and colour it to ensure accurate repetition). The other side should feature either an improper fraction or its matching mixed numerals.

w ww

Information and Design Technology

m . u

Students will need to first compile a list of the pairs they want to include in their pack of cards to determine how many cards they will need and to insure they have a good range of matching fractions to play with.

• This activity provides practice in identifying mixed numbers from diagrams. There are other related activities also available on this site: <http://au.ixl.com/math/year-4/what-mixed-number-is-shown>.

. te

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET Understanding improper fractions and mixed numbers

Example 1

m . u

Example 2

Teac he r

ew i ev Pr

w ww

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

r o e t s r e Diagram BooImproper fraction Mixed number p u A fraction A whole number k with a bigger top and a proper Sfraction

mixed number to an improper fraction : . te o c Write the wholes as fractions then add them. . che e r o t r s super

To change a

To change an

improper fraction

to a

mixed number :

Divide the top by the bottom.

* We often change improper fractions to mixed numbers because:

They’re easier to understand and to say. Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

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

ew i ev Pr

Teac he r

Mixed numbers using pictures and diagrams

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

Number lines for mixed numbers (halves)

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

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

ew i ev Pr

Teac he r

Number lines for mixed numbers (quarters)

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

Number lines for mixed numbers (thirds)

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

Sub-strand: Fractions and Decimals—F&D – 2

RESOURCE SHEET

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

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

ew i ev Pr

Teac he r

Fraction cards for matching and ordering

Assessment 1

Sub-strand: Fractions and Decimals—F&D – 2

NAME:

DATE:

1. Write the mixed number for each picture.

(a)

(b)

(c)

r o e t s Bo r e p• o u •k S (d)

2. Join the matching pairs of mixed numbers.

Teac he r

•

ew i ev Pr

32⁄5 •

• 35⁄6

• 22⁄3

•

3. Draw a picture to show each mixed number.

. te

(a) 31⁄3

m . u

15⁄8 •

w ww

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

31⁄2 •

• 21⁄4

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

(b) 13⁄4

(d) 22⁄5

R.I.C. Publications®

www.ricpublications.com.au

Assessment 2

Sub-strand: Fractions and Decimals—F&D – 2

NAME:

DATE:

1. Write the mixed number shown on each number line.

(b)

(c)

r o e t s Bo r e p ok u S 1

(a) 22⁄3 (b) 11⁄2 (c) 53⁄4

1 2 © R. I . C.P ubl i cat i o ns •f o rr e vi ew pu r po4seso nl y • 0 1 2 3 5 6 0

w ww 1

⁄3

. te

11⁄3

m . u

3. (a) Count by thirds on the number line.

(b)

ew i ev Pr

2. Draw an arrow to show the mixed number on a number line.

o c . Count by halves on number line. cthe e her r o t s super 0

100

⁄4

12⁄4

13⁄4

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

22⁄4

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

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

Teac he r

(a)

Assessment 3

Sub-strand: Fractions and Decimals—F&D – 2

NAME:

DATE:

1. Use the diagrams to help you to write the mixed numbers as improper fractions. (a) 22⁄5 =

⁄5

(b) 51⁄3 =

⁄3

(a)

⁄4 =

(b)

⁄5 =

(c)

⁄3 =

3. Count the halves to find how many apples there are.

ew i ev Pr

Teac he r

2. Change these improper fractions to mixed numbers.

(d)

⁄2 =

4. Count the thirds to find the number of pizzas.

. te

apples.

m . u

There are

w ww

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

(d) 41⁄2 =

r o e t s Bo r e p ok u S⁄ ⁄4

o c . che e r o t r s There are super

pizzas.

5. Count the quarters to find the number of oranges.

There are Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

oranges.

www.ricpublications.com.au

101

Assessment 4

Sub-strand: Fractions and Decimals—F&D – 2

NAME:

DATE: Shade the bubbles to show your answers. half of an 80-metre rope.

1. (a) Half of a 50-metre rope is shorter than

longer than

the same as

(b) My friend, Zac, had a bag with 200 marbles in it and his brother had 100 marbles in his bag. Both of them said I could have one-quarter of each of marbles from Zac. their marbles. I will get

was

mine.

less than

more than

the same as

(b) One-third of the students in my class have brown eyes, one-fifth have students green eyes and the rest have blue eyes. There are in my class with green eyes than brown ones.

3. Which fraction is the biggest?

⁄4

(b)

w ww

. te

⁄5

⁄4

m . u

⁄5

(a)

⁄4

4. Which is the smallest fraction?

o c che ⁄ (b) ⁄ ⁄ . e r o t r s s r u e p 5. Find a fraction which is equal to the one in the box and draw a circle around it. (a)

⁄8

102

2 3

⁄2

⁄8

1 5

(a) 21⁄2

31⁄2

(b)

⁄3

42⁄3

(c)

⁄4

13⁄4

21⁄4

(d)

⁄5

51⁄5

14⁄5

⁄3

⁄2

41⁄2

22⁄3

⁄4

⁄5

21⁄5

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

⁄2

⁄3

⁄4

41⁄4 ⁄5

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

CONTENT DESCRIPTION: Count by quarters, halves and thirds, including mixed numerals – Locate and represent these fractions on a number line

Teac he r

2. (a)

ew i ev Pr

r o e t s Bo r e fewer the same p more o u k S Mum gave me ⁄ of the apple pie she made and Dad ate ⁄ of it. His share

Checklist

Sub-strand: Fractions and Decimals—F&D – 2

Understands the smaller a denominator the larger the unit fraction

Orders fractions with the same denominator

Understands that the size of a fraction is determined by the size of the whole

Converts mixed numbers to improper fractions and vice versa

Locates and represents mixed numbers on a number line

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

ew i ev Pr

Teac he r

STUDENT NAME

Counts by halves quarters and thirds using diagrams, folding and number lines

Count by quarters, halves and thirds, including mixed numerals Locate and represent these fractions on a number line (ACMNA078)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

103

Sub-strand: Fractions and Decimals—F&D – 3

Recognise that the place value system can be extended to tenths and hundredths Make connections between fractions and decimal notation (ACMNA079)

RELATED TERMS

TEACHER INFORMATION

Place value system

What this means

• A system in which the value represented by a digit of a number depends on its place (position) relative to other digits in that number

• Students extend their understanding of the place value system to tenths and hundredths using division by 10 and 100.

Fraction

• Use knowledge of fractions to establish equivalences between fraction and decimal notation; for example: 1 ⁄2 is 0.5, 3⁄4 is 0.75.

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

• Students should be able to compare various representations of numbers and determine their relative value; for example, if 1⁄2 or 0.33 is bigger.

Mixed number

• A number which includes a whole number part and a fractional part Decimal number

• Every number in the base ten system. The value of any digit is ten times greater than that to its right, and smaller than that to its left

Teaching points

ew i ev Pr

Teac he r

• A part of a whole; for example, the fraction 7⁄10 represents 7 parts out of 10. The denominator is the bottom number and the numerator is the top number

• Students need to be given a range of materials to show 1⁄10 and be able to locate tenths along a number line from 0 to 2, so the knowledge of mixed numerals is extended to the concept of tenths. • Students should be able to count by tenths using fractions and decimal equivalences.

• Use the tens-ones-tenths place value grid to play place value games in tenths, then extend to hundredths.

• Show equivalences such as 1⁄2, 0.5 and 5⁄10 and state if 5 ⁄10 or 5⁄100 is bigger.

Decimal point

What to look for

w ww

Decimal place

• The value of the place/position to which a decimal extends; for example: 4.5 (one decimal place), 4.56 (two decimal places) Decimal fraction

. te

• Students who still think in terms of whole numbers and therefore believe that 1⁄100 is bigger than 1⁄10. • Students who think 0.45 is not between 0.4 and 0.5 because 0.45 has three digits.

o c . che e r o t r s super

• A fraction with a denominator of any power of ten. Any fraction can be expressed as a decimal fraction. Decimal

• Students who have trouble understanding 1⁄2, 1⁄3 and 1 ⁄4 will have trouble extending to 1⁄10 and 1⁄100.

m . u

• A full stop which separates a whole number from a decimal

See also New wave Number and Algebra (Year 4) student workbook (pages 50–54)

• A decimal fraction divided by its denominator Decimal equivalences • Decimals which have the same value as other fractions Proficiency strand(s): Student vocabulary decimal, decimal point, decimal place, fraction, mixed number, decimal fraction, equivalent

104

Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Fractions and Decimals—F&D – 3

HANDS-ON ACTIVITIES Linking fractions (tenths and hundredths) to decimals The blank sheets for colouring decimal fractions can be used to help students understand the relationship between either tenths and decimals (see page 108) or hundredths and decimals (see page 109). If the sum of the fractions coloured is less than one, they could also work our the fraction and decimal left uncoloured.

Decimal number cards The decimal number cards on pages 111 ( 0.1 to 0.9) and 112 (0.01 to 0.09 ) can be used for a number of different activities to help students understand some important decimal concepts. These include:

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

• ordering decimals – Students select four cards and place them in order from smallest to biggest (or vice versa). Identify any which are 10 times bigger or smaller than another.

Teac he r

ew i ev Pr

• comparing decimals – Students play this game in pairs. The cards are placed facedown between them. Each student takes two cards, turns them over, then places the card displaying the greater amount one on top of the other. They check each other’s cards and if they have been ordered correctly, one point is awarded. The first player with 10 points wins the game. • concentration – The cards are placed facedown and turned over to locate pairs in which one is either 10 times smaller or 10 times bigger than the other.

Number lines

The blank number lines for fractions (tenths) and decimals on page 114 can be used to order and place a number of tenths and decimals from either 0 to 1 and 0 to 2, or between two or three other whole numbers as selected by the teacher. The number lines with fractions, mixed numbers and decimals on page 113 show 0 to 1 and 1 to 2 in tenths, and 0 to 0.1 and 0.1 to 0.2 in hundredths. They could be cut out and glued together to make longer number lines. Students should be able to recognise that the third and fourth number lines on the sheet are expanded sections of the first number line and they should to be able to identify where they ‘fit’ in the first line.

Students can cut out the four sections of the 0-to-2 number strip marked in hundredths (see page 115) and glue them to make a longer strip. They should match the marks at the ends so the strips overlap. This longer strip can be used to locate decimals such as 0.85 and 1. 36 and to compare decimals.

m . u

Equivalent decimal fractions

w ww

The three decimal models on pages 116 to 118 can be used to demonstrate the relationship among whole numbers, tenths and hundredths. Students should be able to see that one is equivalent to ten-tenths and one hundred-hundredths. Give each student a specific number of tenths between one and nine and ask them to show this fraction in both tenths and hundredths by colouring it with the same colour on both the tenths and the hundredths sheets. They can then write this fraction in hundredths and as a decimal.

. te

o c . che e r o t r s super

This activity could also be used to demonstrate why a zero in the hundredths place is not needed when writing decimals to two decimal places; for example, 0.7 is equivalent to 0.70.

How many tenths, how many hundredths?

Explain that it is easy to write other fractions as decimals but they need to be changed to tenths or hundreds first. Demonstrate doing this with 1⁄2, 1⁄4 and 3⁄4 and set small groups the task of working out how to change fifths to decimals. A useful resources for developing understanding of tenths and hundredths is Middle school maths games by Richard Korbosky (R.I.C. Publications).

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

105

Sub-strand: Fractions and Decimals—F&D – 3

LINKS TO OTHER CURRICULUM AREAS Geography • Research to compile a chart showing five other countries that use the decimal system for their currency. Include the country, the continent it is located in, the units it uses and some interesting facts; for example: country – Australia, continent – Australia, currency – dollars and cents, interesting fact – decimal currency was introduced in 1966 to replace pounds, shillings and pence. • Students show the five countries they have chosen on a large world map and give a brief report to the class about the currency of the two most interesting countries they selected.

History

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

• Many countries have changed to using decimal currency in the last 50 years. Choose a country that changed its currency and write a report, including information about the old and new currencies, when and why they made the change, and any interesting facts about it.

Teac he r

English

ew i ev Pr

• Write a procedure in the form of a set of numbered steps to follow to change quarters or fifths to tenths or hundredths and to decimals.

• Prepare a chart to explain place value. Include hundreds, tens, ones, tenths and hundredths. Include information about face, place and total value. Make the chart clear, attractive and colourful. • Write word problems for other students to solve in which fraction need to be changed to decimals and vice versa, or decimals need to be compared and/or placed in order according to their relative size.

The Arts

• Use a 100-square grid printed on paper and four different coloured pencils to make a pattern or a picture with 0.5 of the squares in one colour, 0.02 in each of two other colours and 0.09 in another colour. Plan how you will do this work before you start and work out how many squares of each colour you’ll need.

• Place value games of different difficulties—requiring students to identify numbers which have specified amounts of hundreds, tens, ones, tenths and hundredths—can be found at: <http://www.mrnussbaum.com/placevaluepirates1.htm>.

w ww

m . u

• This game requires students to place decimals in order. It includes some decimals to three decimal places and is suitable for students with a good understanding of place value: <http://www.kidsmathgamesonline.com/numbers/ decimals.html>. • R.I.C. Publications® and Richard Korbosky have developed interactive Middle school maths games that develop understanding of tenths and hundredths.

. te

106

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET Face, place and total value in the decimal system

Whole numbers For the number 426: • the face value depends on what you see

r o e t s Bo r e – 6 has a face value ofp 6 ok u • the place valueS depends on where it is

ew i ev Pr

Teac he r

– 2 has a face value of 2,

– 4 has a place value of hundreds because it’s in the hundreds place – 2 has a place value of tens because it’s in the tens place

– 6 has a place value of ones because it’s in the ones place

• the total value depends on what you see AND where it is

– 4 has a total value of 400 because 4 (face value) × 100 (place value) = 400

– 2 has a total value of 20 because 2 (face value) × 10 (place value) = 20 – 6 has a total value of 6 because 6 (face value) × 1 (place value) = 6.

Decimal fractions

m . u

Decimal fractions are like whole numbers because they have the same face value, but they have diﬀerent place values. This means their total values are diﬀerent, too.

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

– 4 has a face value of 4,

Decimal fractions are written after a decimal point:

. te o This chart shows the face, place and total values for the number 24.63. c . che e r o r st super • the ﬁrst decimal place is tenths

• the second decimal place is hundredths.

Value

Tens

Ones

Decimal point

Tenths

Hundredths

Face value

Place value

tens

ones

tenths

hundredths

Total value

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

⁄10 or 0.6

⁄100 or 0.03

www.ricpublications.com.au

107

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET Blank sheet for colouring decimal fractions (tenths) Teacher to write a fraction in the first box for each colour. (The sum of these numbers must be less than 10.)

Tenths

Blue

out of 10

⁄10 = 0.

Yellow =

Red

ew i ev Pr

Teac he r

Green =

r o e t s Bo r e p ok out of 10 u S

⁄10 = 0.

out of 10

⁄10 = 0.

out of 10

Complete the equations and colour the grid to show the decimals. = = Green = = Yellow =

Red

108

w ww

Blue

out of 10

. te

⁄10 = 0.

out of 10 ⁄10 = 0.

m . u

Tenths

o c . che e r o t r s super

out of 10

⁄10 = 0.

out of 10

⁄10 = 0. Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Complete the equations and colour the grid to show the decimals.

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET Blank page for colouring decimal fractions (hundredths) Teacher to write a fraction in the first box for each colour. The sum of these numbers must be less than 100.

Hundredths Complete the equations and colour the grid to show the decimals. =

out of 100

⁄100 = 0.

Yellow = =

Red

ew i ev Pr

Teac he r

Green =

r o e t s Bo r e p ok out of 100 u S ⁄100 = 0. out of 100

⁄100 = 0.

out of 100

Hundredths

m . u

Complete the equations and colour the grid to show the decimals.

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Blue

Green = = Yellow =

Red

out of 100

⁄100 = 0. . t e

o c . out of 100 che e r o t r s super ⁄100 = 0. out of 100

⁄100 = 0.

out of 100

⁄100 = 0.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

109

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET Tenths and hundredths

Tenths

r o e t s B r e oand as a decimal: These two equal parts are tenths and can be written as a fractiono p u k = ⁄ = 0.2 S 10

ew i ev Pr

Teac he r

Hundredths

Each tenth can be divided again into ten equal parts.

w ww

A whole number can be made up of 10 tenths or 100 hundredths.

. te

m . u

Whole numbers

o c . c e 1= ⁄ h 1 =t ⁄ r er o s super Whole numbers and decimals 10

100

Numbers with whole numbers and decimals are mixed numbers.

⁄10 + 3⁄10 = 13⁄10 = 1.3

110

⁄100 + 3⁄100 = 1.03

100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

To divide a whole number into tenths, there needs to be ten equal parts.

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

0.3

0.2

0.1 Teac he r

ew i ev Pr

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

0.6

m . u

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

0.9

0.8

o c . che e r o t r s super

0.7

. te

0.5

0.4

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Decimal number cards – tenths

www.ricpublications.com.au

111

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

0.06

0.05

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

0.09

0.07 112

m . u

w ww

. te

0.08

0.04

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

0.03

0.02

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

ew i ev Pr

Teac he r

0.01

Decimal number cards – hundredths

0.1

⁄10

1.1

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

1.2

12⁄10

0.01

⁄100

0.02

0.1

⁄100

0.11

⁄100

0.12

Hundredths number line: 0.1 to 0.2

⁄100

0.3

⁄10

0.13

⁄100

⁄10

⁄100

0.14

0.04

1.4

14⁄10

0.4

m . u

0.03

⁄100

1.3

13⁄10

o c . che e r o t r s super

Hundredths number line: 0 to 0.1

11⁄10

⁄10

0.2

. te

Tenths number line: 1 to 2

Tenths number line: 0 to 1

0.15

⁄100

0.05

⁄100

1.5

15⁄10

0.16

⁄100

0.06

⁄100

1.6

16⁄10

0.6

0.17

⁄100

0.07

⁄100

1.7

17⁄10

0.7

⁄10

Teac he r

⁄10

18⁄10

0.8

19⁄10

0.9

⁄10

⁄100 0.18

0.08

⁄100

1.8

0.19

⁄100

0.09

⁄100

1.9

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

ew i ev Pr

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

0.2

⁄100

0.1

⁄100

110⁄10

⁄10

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

Fraction, mixed number and decimal number lines

www.ricpublications.com.au

113

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Tenths

Tenths 0–1

114

o c . che e r o t r s super

Tenths 0–2

w ww

. te

m . u

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

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

ew i ev Pr

Teac he r

Blank number lines for fractions and decimals

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET Number strip – 0 to 2 in hundredths

Add

glu

Add

glu

Add

glu

Add

glu

1.4

1.8

1.3

0.9

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

1.9

glu

ew i ev Pr

Teac 0.3 he 0.4 r

Add

0.8

glu

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

1.5

1.1

R.I.C. Publications®

1.6

m . u 1.7

1.2

0.7 0.6

o c . che e r o t r s super

0.1

. te

0.5

0.2

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Add

Cut out the four strips, line up the last mark on one strip with the first mark on the next and glue them together.

www.ricpublications.com.au

115

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

w ww

. te

116

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

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

ew i ev Pr

Teac he r

Decimal model – 1

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Decimal model – 2

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

117

Sub-strand: Fractions and Decimals—F&D – 3

RESOURCE SHEET

w ww

. te

118

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

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

ew i ev Pr

Teac he r

Decimal model – 3

Assessment 1

Sub-strand: Fractions and Decimals—F&D – 3

NAME:

DATE:

1. Complete the place value chart for these numbers. Hundreds

Tens

Ones

Tenths

(a) 6.3

(b) 7.89

Hundredths

. r o e t s Bo r e (d) 235.21 . p ok u S 2. Write the face, place and total values for the digits in bold. Number

Face value

Place value

(a) 24.56

(b) 16.98

ew i ev Pr

Teac he r

Total value

(e) 67.92

. te

(a) 4

⁄100

m . u

3. Shade the bubble to show what fraction or decimal is shaded.

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

Number

o c (b) . che e r o t ⁄ ⁄ r ⁄ ⁄ ⁄ s super 10

100

(c)

100

(d) 0.9

0.09

9.0

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

0.5 R.I.C. Publications®

0.2

0.02

www.ricpublications.com.au

119

Assessment 2

Sub-strand: Fractions and Decimals—F&D – 3

NAME:

DATE:

1. Shade these grids to match the fractions then write the decimals. 24

⁄100

(b)

⁄100

(c)

⁄10

(d) 2⁄10

Teac he r

(a) sixty-one hundredths

(b) one hundredth

(d) seven tenths

3. Shade these grids to match the decimals.

(b)l 1.25 © R. I . C.Pub i cat i ons •f orr evi ew pur posesonl y•

w ww

. te

(d) 0.04

m . u

(a) 0.85

ew i ev Pr

r o e t s Bo r e p ok u S 2. Write these fractions as decimals.

o c . che e r o t r s super

(e) 3.7

120

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

(a)

Assessment 3

Sub-strand: Fractions and Decimals—F&D – 3

NAME:

DATE:

(a) 0.1 =

(b) 0.76 =

(d) 0.44 =

(e) 1.34 =

(f) 2.6 =

r o e t s Bo r e p (b) ⁄ o (c)k ⁄ u S

2. Write these fractions as decimals. ⁄10

(d)

⁄100

(e)

113

100

⁄100

(f)

203

100

ew i ev Pr

Teac he r

(a)

⁄10

3. Write the decimals as shown and place them in order from smallest to largest.

. te

m . u

4. Write the decimals as shown and place them in order from smallest to largest.

w ww

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

1. Write these decimals as fractions.

o c . che e r o t r s super

5. Place the decimals in order from smallest to largest. (a) 0.14, 0.07, 0.9, 0.75

(b) 0.17, 0.01, 0.1, 0.11

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

121

Assessment 4

Sub-strand: Fractions and Decimals—F&D – 3

NAME:

DATE:

(a) 0.4 and 0.04

(b) 0.35 and 0.3

(d) 0.77 and 0.7

r o e t s Bo r e p o (b) 0.8 and 0.4 k 0.67 and 0.6 u S

2. Write the smaller number of each pair.

(d) 1.45 and 1.5

3. Shade 0.6 on one grid and 0.06 on the other, then label each.

ew i ev Pr

Teac he r

(a)

0.1

w ww

(a)

0.2

. te

0.3

0.4

0.5

0.6

0.7

0.8

m . u

4. What number is shown on each number line. 0.9

o c . che e r o t r s super 5. Use an arrow to show each number on the number line. (b)

2.5

(a) 0.6 0

0.5

1.5

(b) 1.71 (c) 0.99 0

122

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Recognise that the place value system can be extended to tenths and hundredths – Make connections between fractions and decimal notation

1. Write the larger number of each pair.

Checklist

Sub-strand: Fractions and Decimals—F&D – 3

Orders decimals

Compares the size of decimals

Represents decimals on a number line

Converts fractions in tenths, including mixed numbers, to decimals and vice versa Converts fractions in hundredths including mixed numbers to decimals and vice versa

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

ew i ev Pr

Teac he r

STUDENT NAME

Recognises tenths and hundredths in the place value system

Recognise that the place value system can be extended to tenths and hundredths Make connections between fractions and decimal notation (ACMNA079)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

123

Answers

Sub-strand: Fractions and Decimals

F&D – 1

F&D – 2

Page 86 Assessment 1

Page 99 Assessment 1

1. (a) 2. The shading of each diagram may vary but must match these equivalent fractions

(a)

⁄2 = 2⁄4

(b)

1. (a) 31⁄4

(b) 24⁄5

(d) 41⁄2 or 42⁄4

2. 31⁄2

⁄2 = 6⁄12 35⁄6

⁄2 = 4⁄8

⁄2 = 5⁄10

3 2 ⁄5

(b)

2 2 ⁄3

15⁄8

21⁄4 3. Answers will vary, teacher check.

Page 87 Assessment 2

1. (a) and (c) should be joined, (b) and (e) should be joined and (d) and (f ) should be joined. 2. (a) (b) (c)

0 0 0

⁄6

⁄9

Page 100 Assessment 2 1. (a) 11⁄2

⁄12

2. (a)

(b)

(c)

3. (a)

Page 88 Assessment 3

(b) ⁄8 = ⁄2 4

(b)

w ww

(c)

(d) 6⁄10 = 3⁄5

(e) 6⁄12 = 1⁄2 (f )

. te

⁄5 = 10⁄10

2. (a) less (d) more

(b) the same (e) the same

1. 2. 3. 4. 5.

⁄3

⁄4

2 4 2 4

⁄ ⁄

⁄4

11⁄3

⁄2

⁄3

Page 101 Assessment 3

12⁄3

21⁄3

11⁄2

11⁄4

12⁄4

13⁄4

22⁄3

21⁄2

21⁄4

22⁄4

23⁄4

(b) 16⁄3 (c) 7⁄4 (d) 9⁄2 (a) 12⁄5 (a) 13⁄4 (b) 22⁄5 (c) 22⁄3 (d) 71⁄2 1 1 1 1 ⁄2, 1, 1 ⁄2, 2, 2 ⁄2 There are 2 ⁄2 apples. 1 2 1 2 ⁄3, ⁄3, 1, 1 ⁄3, 1 ⁄3, 2 There are 2 pizzas. 1 2 3 ⁄4, ⁄4, ⁄4, 1, 11⁄4, 12⁄4, 13⁄4, 2, 21⁄4, 22⁄4, 23⁄4, 3, 31⁄4, 32⁄4, 23⁄4 There are 33⁄4 oranges

o c . che e r o t r s super (c) the same

Page 102 Assessment 4 1. 2. 3. 4. 5.

124

(b) 23⁄5

1. (a) 2⁄6 = 1⁄3

ew i ev Pr

Teac he r

3. (a)

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

m . u

(c)

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

shorter than less than 5 ⁄5 (b) 3⁄4 1 ⁄8 (b) 3⁄10 5 ⁄2 (b) 10⁄3

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

(b) more (b) fewer

(d) 21⁄5

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

Answers

Sub-strand: Fractions and Decimals

Page 122 Assessment 4

F&D – 3 Page 119 Assessment 1 1.

Number

Hundreds Tens Ones

Tenths Hundredths

(a) 6.3

(b) 7.89

(d) 235.21 2.

Face value

Place value

(a) 24.56

tenths

(b) 16.98

tens

hundredths

(d) 437.21

ones

(e) 67.92

hundredths

3. (a) 4⁄10

3. 4. (a) 0.29

(b) 0.35 (b) 0.4

0.6

0.06 (b) 2.85

0.5

(b)

1.5

(c)

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

(b) 7⁄100

⁄10 or 0.5

0.24

(b)

⁄100 or 0.08 7

⁄100 or 0.02 (d) 0.02

Page 120 Assessment 2

1. (a)

(d) 0.77 (d) 1.45

5. (a)

Total value

ew i ev Pr

Teac he r

Number

1. (a) 0.4 2. (a) 0.6

0.13

0.07 (b) 0.01

(d) (c) 0.15

0.02 (d) 0.7

m . u

3. (a)

w ww

(b)

. te

(c)

(d)

(e)

o c . che e r o t r s super

Page 121 Assessment 3 1. (a) (e) 2. (a) (e) 3. (a) 4. (a) 5. (a)

⁄10 (b) 76⁄100 34 1 ⁄100 (f ) 26⁄10 0.6 (b) 0.56 2.03 (f ) 0.4 0.1 (b) 0.3 0.12 (b) 0.22 0.07, 0.14, 0.75, 0.9 1

(d)

(d) 0.07

⁄100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

125

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

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

RELATED TERMS

TEACHER INFORMATION

Money

What this means

• A form or denomination of notes and coins used as currency

• Students are given a chance to recognise that not all countries use dollars and cents; e.g. India uses rupees. Research other countries’ currencies; e.g. New Zealand (dollars), Japan (yen) and many European countries (euro).

Currency

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

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

• The act of giving cash as payment for something Transaction

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

Teaching points

ew i ev Pr

Teac he r

Tendering cash

• Students carry out realistic calculations in Australian dollars and cents, and estimate change from purchases to the nearest five cents or 10 cents.

• Students should be given the opportunity to manipulate larger amounts of money using play money and pictures of money.

• Students should be given everyday problems involving rounding to the nearest five or 10 cents.

• Students solve meaningful two-step problems which involve purchasing items, taking away from a starting amount and buying multiples of the one item in the process of purchasing.

w ww

– A price ending in 6c or 7c is rounded down to the nearest 5c.

. te

– A price ending in 8c or 9c is rounded up to the nearest 10c.

• Students should be given a range of problems involving money and the use of addition, subtraction, multiplication and division to solve the problems.

What to look for

m . u

• The price of an item in a shop needs to be rounded to the nearest 5c at the time of purchase as there are no 1c or 2c coins to make up the amount. (Cash purchases only.)

• Students who do not understand the role of the decimal point in currency and think of it as merely a separation and ignore it; e.g. $5.50 is just $5 or $550. This leads to problems when students add quantities. These students are treating decimals as whole numbers.

o c . che e r o t r s super

Student vocabulary money cash cents dollars coins notes

See also New wave Number and Algebra (Year 4) student workbook (pages 55–60)

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

currency change rounding value transaction

126

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Money for hands-on activities Templates of Australian notes and coins have been provided on pages 129 to 131. They can be photocopied onto card and laminated for durability. Commercially bought plastic coins and paper money can be used.

Shop rounding rules and shopping dockets

Wel com e to

Shops such as supermarkets and department stores often sell items at prices that cannot be made with cash; e.g. a litre of milk might cost $1.99 or a pedestal fan might be priced at $24.47. (There are no 1c or 2c coins to make up 47c or 99c). It is only on credit card, EFTPOS or cheque payments that these exact amounts can be made. The reference chart on page 132 gives a summary of rounding rules for shops. Provide supermarket or department store catalogues for students to view these prices.

TAX INVOICE 3:45 PM Assis ted By: Amel ia

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

Counting on to give change If the school has a canteen/tuckshop, provide copies of the price of items on the menu. Students can use these in a practical activity to work out change and count on to give the change required. Play money can be used. Give students a set amount, such as $15, $10 or $7.50. They choose an item from the menu and work out the change from that amount by counting on—not subtracting the price of the item from the set amount. For example, if a chicken and salad wrap costs $3.75 and $10 is the set amount, count on 5c from $3.75 to $3.80, then 20c to reach $4 (or count on 25c from $3.75 directly to $4), then count on $6 to reach $10; i.e. $6.25 change. Increase difficulty by choosing two or three items which have to be added first before working out change.

TRAN : 2133 48 On Lane : 002 $ Price

Item Purch ased

SR FLOU R 1Kg SPRIN GWTR 12 400m L* *PRO MO! Item Usua lly: $10. 57 AVOC ADO 2 @ $1.5 0 EACH LARG E CHIC KEN BBQ each PAPE R TOWE L WHIT E TwinP ack POTA TOES LOOS E Kg 1.100 Kg @ $2.9 9 Kg FRES H MILK 1L 2 @ $1.9 9 EACH

3.23 8.99 3.00 9.99 3.43 3.29

ew i ev Pr

On a shopping docket, all items purchased are added together before the final total is rounded. The cost of multiple items that are the same will appear as a subtotal on the docket next to the items. Collect a variety of shopping dockets for students to identify how the price is calculated and rounded for cash payments.

Teac he r

Savemore Supermarket

3.98

No. of items in Sale Total Price Sub Total Roun ded Down By

7 $35. 91 $00. 01

Pric e to Pay Cas h Cha nge

$35 .90

$40 .00 $04 .10

The Tota l Price inclu des GST of $0.8 8 & indic ates Taxa ble Supp ly

You save d $1.5 8 on the USUA L PRIC ES

Tha nk you for you r cus tom !

. te

m . u

w ww

Three sets of game cards with a variety of money problems have been provided on pages 133 to 135. These can be photocopied onto card and laminated. Students can work individually or in pairs (with or without teacher guidance) to solve the problems. (An example of a think board has been provided on page 136 to assist students in representing and solving the problem.) One set of cards are placed facedown and a card picked up. It is placed on the number story section of the think board. Students read it, work out a picture/diagram to represent the problem, write a number sentence, solve the answer and explain how they did this. Calculators can be used or written and/or mental methods used. Play money can also be provided. The teacher should check students’ answers. Answers have been provided for each card on page 141. Note: the sets of cards can also be combined as one large set. The type of questions for each set are:

o c . che e r o t r s super

• Set 1: Money problems involving the four operations (+ – × ÷)

• Set 2: Money problems involving shop rounding at a time of a single purchase and working out the change from a given starting amount • Set 3: Money problems involving calculating the cost of multiple items before working out the change from a given starting amount. Rounding is not involved.

Currency conversion

Students can use a website such as <http:/www.currencyconverter.com.au/> to convert, for example, what $10 Australian dollars is equal to in other currencies (such as the Japanese yen, Singapore dollar, United States dollar, English pound sterling or euro). R.I.C. Publications’ Lower primary maths games (by Richard Korbosky) includes games useful for teaching the concept of money.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

127

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

LINKS TO OTHER CURRICULUM AREAS English • Money by Joe Cribb (DK Eyewitness Books) This nonfiction title contains a comprehensive collection of fascinating money facts—photographs and information about early coins and modern currencies around the world, how coins and notes are created, how to detect forged currency, why coins were once put in the mouths of dead people, and much more! • Money makes the world go round: Vol. 2 by Greg Smith There are three volumes in this fiction series dealing with three children who travel back in time from the year 3050 to present-day Australia to learn about money concepts. The second book in the series is suitable for this age group.

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

• Animals unique to Australia feature on our coins: platypus, echidna, kangaroo, emu and lyrebird. Write a report on a chosen animal using the structural features of a report: title; classification (general statement about the subject of the report); description (detailed and accurate account of physical features, location/habitat, behaviour, diet, reproduction and so on); and conclusion (comment giving the writer’s opinion about the subject of the report).

Teac he r

History

ew i ev Pr

• A brief history of Australian currency and the features on present-day Australian coins and notes can be found at the website: <http://www.australian-information-stories.com/australian-money.html>

• A virtual tour of the Reserve Bank of Australia‘s Museum of Australian Currency Notes is available at: <http://www.rba. gov.au/Museum/VirtualTour/hifi/01_foyer_home.html>

Communication and Information Technology

• The following web page is an interactive game involving Australian currency. Students identify the notes and coins needed to give the correct change for a set price: <http://www.funbrain.com/cgi-bin/cr.cgi?A1=s&A14=hard&country [aus].x=49&country[aus].y=25>

• Find images of currencies used in other countries; e.g. South Africa – rand, Japan – yen, China – renminbi. Students could also bring samples from home (left over from a holiday/parent’s business trip) so others can view. Strict supervision will be necessary. Compare the denominations of the notes and coins to Australian notes and coins.

w ww

• Research currencies from around the world, comparing them with Australian currency. Find out the name, code and symbol for each currency; if it is based on a decimal system like Australia’s; and the denominations of the notes and coins in circulation. A research worksheet has been provided on page 137. (The blank space at the bottom of the sheet is for students’ own choice.)

. te

Science

m . u

Economics

o c . che e r o t r s super

• Since 1988, Australian notes have been made from polymer, a type of plastic, instead of paper. Students can investigate the advantages of using this material rather than paper (e.g. the banknotes last four times as long and are harder to counterfeit).

128

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Coin templates

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

129

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

RESOURCE SHEET

w ww

. te

130

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

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

ew i ev Pr

Teac he r

Note templates – $5, $10, $20

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

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Note templates – $20, $50, $100

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

131

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

RESOURCE SHEET Shop rounding

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

81c = 80c

$75.42 = $75.40

r o e t s Bo r e Examples: p 83c = 85c $75.44 =o $75.45 u k S When purchased, an item with a price ending in 6c or 7c is rounded down to the nearest 5c.

Examples:

86c = 85c

$75.47 = $75.45

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

w ww

$77.84

. te

$19.93

m . u

How would these item’s prices be rounded when purchased?

o c . che $15.78 e r o t r s$169.99 super $88.62 $24.47

132

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

ew i ev Pr

Teac he r

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

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

RESOURCE SHEET

Card 2

Card 3

An excursion to the museum costs $14 per student. If six students have already paid their teacher, how much has been collected so far?

Jake found that a remote control car in one catalogue cost $78.80, while the same car was $89.50 in another catalogue. How much more expensive was the car in the second catalogue?

Matilda wants to buy a boogie board for $72. If she saves $8 each week, how many weeks until she has enough money to buy it?

Accommodation at a holiday chalet is $1150 a week. If two families share the chalet, how much will it cost each family?

Dad went shopping and spent $78. He came home with $56 left in his wallet. How much money was in his wallet before he went shopping?

A group of friends went to the movies during the holidays. Tickets cost $10 each. Altogether, the friends paid $110. How many friends went to the movies?

Card 7

Card 8

Card 9

Olivia’s goal is to save $200. So far, she has saved $126.50. How much more does she need to save to reach her goal?

Four people bought a lottery ticket and won $5000. How much will each receive if the prize is shared equally?

A grandmother bought each of her grandchildren a DVD as a gift. If each DVD cost $24.95 and the total was $124.75, would she have four or five grandchildren?

Noah gets $10 a week as pocket money if he does his jobs around the house. How much pocket money would he receive in a year?

Card 4

r o e t s Bo r e p ok u S Card 5 Card 6

ew i ev Pr

Teac he r

Card 1

A school held a Food Feast fundraiser. The ‘BBQ Delight’ stall made $125.50, the ‘Cute Cupcakes’ stall made $115 and the ‘Curry in a Hurry’ stall made $85. How much was raised?

. te

Card 10

m . u

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Set 1 game cards – Money problems involving +, –, × and ÷

o c . che e r o t r s Card 12 s Card 11 uper

A restaurant has a deal by which the cheapest meal is free if three or more meals are ordered at a table. If the meals at a table cost $25, $28.50 and $24, how much will the bill be?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

133

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

RESOURCE SHEET

Card 2

Card 3

Mum buys 1 kg mince worth $7.99 per kg and gives the butcher $10. How much change will he give her?

Dad wants to buy a cover for the barbecue that costs $27.98. How much change will he receive from a $50 note?

Bailey got $50 from his gran for his birthday. He bought a board game for $24.47. How much money does he have left?

Card 4

Card 5

Card 6

A sports bag is advertised at $35.66. What change will you get from $50?

DVDs were on special for $9.97 each. How much change will you receive from $20?

You have $20. You buy a T-shirt priced at $17.86. How much money will you have left?

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

ew i ev Pr

Teac he r

Card 1

Foodies Supermarket advertised marinated chicken wings at $8.96 per kg. If you bought 1 kg with a $20 note, how much change will you receive?

You save up to buy a digital camera advertised at $89.54. You give the shop assistant five $20 notes. How much change will you receive?

A hot cooked chicken costs $11.93 at the local deli. You give the shop assistant $15. What will be your change?

Sharky’s Fish Shop sells uncooked tiger prawns for $13.62 per kg. If you bought 1 kg and handed over $20, how much change would you get?

You have $35. A bike helmet costs $21.43. After buying it, how much money will you have left?

. te

Card 10

o c . che e r o t r sCard 12 uper Card 11 s

A new corner desk for your room will cost $177. 23. What will be the change from $200?

134

m . u

Card 8

w ww

Card 7

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Set 2 game cards – Money problems involving shop rounding and giving change for a single item from a given amount

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

RESOURCE SHEET

Card 2

Card 3

You have a $20 note. If you buy a chicken and salad wrap for $3.50, an orange for 70c and a flavoured milk drink for $1.80, how much change will you receive?

Breakfast cereal costs $5.35 a box. If you bought two boxes, how much change would you get from $20?

Ripe plums are on special for $3.90 per kg. You buy 4 kg and give the shop assistant a $50 note. How much change will you get?

Card 4

Card 5

Card 6

Movie tickets cost $11.50 each. If you buy one for yourself, two for your brothers, and one for your cousin, how much change will you get from $50?

Mum bought four loaves of bread, on special at $1.70 a loaf, to freeze for school lunches. How much change did she get from $20?

At the newsagents you buy a 2B pencil for 95c, a file for $1.45, a pack of highlighters for $4.35 and a metal ruler for $4.90. How much change will you get if you hand over $15?

Card 7

Card 8

Card 9

We bought six croissants for $1.60 each, a jar of fig jam for $4.80, a jar of honey for $4.45 and a tub of margarine for $5.35. How much change did we get from $30?

A sailing ship model costs $79.55 and a construction set costs $26.65. If the shop assistant is given six $20 notes, how much change will be received?

Five kilograms of sausages are needed for the sausage sizzle. If they cost $5.80 per kg, how much change will be needed from $50?

You have two $5 notes. You buy a salad tray for $4.70, a fruit yoghurt for $1.75 and a bottle of water for $1.35. How much change do you receive?

Beach towels are advertised for $19.75 each. Mum buys four and hands over two $50 notes. How much change will she get back?

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

ew i ev Pr

Teac he r

Card 1

. te

Card 10

m . u

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Set 3 game cards – Money problems involving calculating price of multiple items (no rounding) and working out change from a given amount

o c . che e r o t r s Card 12 s uper Card 11

Six avocados are required to make a guacamole dip. If they cost $1.60 each and a $10 note is given as payment, how much change is received?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

135

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

RESOURCE SHEET Think board template

Picture/Diagram

Teac he r

ew i ev Pr

r o e t s Bo r e p ok u S Number sentence How did you work out the answer?

w ww

. te

Picture/Diagram

m . u

Number story

o c . che e r o t r s sup er Number sentence How did you work out the answer?

136

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Number story

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

RESOURCE SHEET Currency research

Currency– Code–Symbol

Nation

Coins

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

ew i ev Pr

Teac he r

Banknotes

India

. te

New Zealand

m . u

Japan

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Australia

Units

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

137

Assessment 1

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

NAME:

DATE:

1. Round each of these prices to the nearest five cents. Write the new price on the line under the picture. (a)

(b) $22.99 kg

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

2. You have these notes. You buy a DVD for $25.48. How much change would you receive after rounding?

Shade one bubble. (b) $5

(d) $5.50

m . u

w ww

(a) $14.50

. te o c You buy a backpack for $47.82. . che e r o t r s super How much change

3. You have these notes and coins.

would you receive after rounding?

Shade one bubble.

138

(a) $1.20

(b) $13.00

(d) $2.25

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

ew i ev Pr

Teac he r

$39.94

Assessment 2

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

NAME:

DATE: Solve each of these money problems. Show how you worked out each problem in the space.

Teac he r

ew i ev Pr

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

2. Katia bought a board game for $25.75 and a book for $12.25. How much change will she receive from $50?

m . u

3. A school held a Healthy Food Day to raise money. The ‘Fresh Fruit Kebab’ stall made $44.45, the ‘Scrumptious Salads’ stall made $43.25 and the ‘Beaut Baked Potatoes’ stall made $42.15. How much was raised?

w ww

CONTENT DESCRIPTION: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

1. The local sports store had three-piece snorkel sets (flippers, goggles and snorkel) on special. Adult sets were $31.90 and kid sets were $23.65. How much more expensive was an adult set?

. te

o c . che e r o t r s su 4. Liam’s dad had four $50 notes. He bought a fishing rod and reel for $154.83. er p How much change will he receive?

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

139

Checklist

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

Solves money problems involving the four operations (+ – × ÷ )

Solves problems involving multiple purchases and giving change from a set amount

Works out the change required for single purchases involving rounding to the nearest five cents or 10 cents

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

ew i ev Pr

Teac he r

STUDENT NAME

Demonstrates how to round prices to the nearest five cents or 10 cents

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

w ww

. te

140

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

Sub-strand: Money and Financial Mathematics

Answers for Resource sheet: Currency research (page 137)

M&FM – 1 Answers for Resource sheet: Set 1 game cards (page 133) Card 1: Card 2: Card 3: Card 4: Card 5: Card 6: Card 7: Card 8: Card 9: Card 10: Card 11: Card 12:

$14 x 6 = $84 $89.50 – $78.80 = $10.70 $72 ÷ 8 = 9 weeks $1150 ÷ 2 = $575 $78 + $56 = $134 $110 ÷ 10 = 11 friends $125.50 + $115.00 + $85.00 = $325.50 $200 – $126.50 = $73.50 $5000 ÷ 4 = $1250 $28.50 + $25 = $53.50 5 grandchildren $24.95 x 5 = $124.75 52 × $10 = $520

Nation

Australia

India

Japan

Teac he r $2 $22 $25.55 $14.35 $10.05 $2.15 $11.05 $10.45 $3.05 $22.75 $6.40 $13.55

New Zealand

Page 138 Assessment 1 1. (a) $23 2. (c) $4.50 3. (a) $1.20

(b) $39.95

Page 139 Assessment 2

w ww

$14 $9.30 $34.40 $4 $13.20 $3.35 $5.80 $13.80 $21 40c $2.20 $21

. te

1. 2. 3. 4.

Teacher check the method students used to work out each problem. One example of a possible method is given for each. Students can use mental and or written methods or use a calculator but must demonstrate on the sheet how they worked out the answer. $8 ($31.90 – $23.65 = $31 – $23 and 90c – 65c = $8 + 25c = $8.25) $12 ($25.75 + $12.25 = $25 + $12 and 75c + 25c = $37 + $1 = $38. $50 – $38 = $12) $129.85 ($44.45 + $43.25 + $42.15 = $44 + $43 + $42 and 45c + 25c + 15c = $129 + 85c = $129.85 $45.15 (4x $50 = $200. $200 – $154.83 = $45.17. After rounding = $45.15)

m . u

Answers for Resource sheet: Set 3 game cards (page 135) Card 1: Card 2: Card 3: Card 4: Card 5: Card 6: Card 7: Card 8: Card 9: Card 10: Card 11: Card 12:

ew i ev Pr

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

Answers for Resource sheet: Set 2 game cards (page 134) Card 1: Card 2: Card 3: Card 4: Card 5: Card 6: Card 7: Card 8: Card 9: Card 10: Card 11: Card 12:

Currency–Code– Units Banknotes Coins Symbol Australian one hundred dollars $100, $50, $20, $2, $1, 50c, 20c, cents (c) equals AUD $10, $5 10c, 5c one dollar ($) A$ or $ 1000 rupees one hundred Indian rupee (Rs), 500 Rs, 5 Rs, 2 Rs, 1 Rs, paisa (p) 50 paisa (p), INR 100 Rs, 50 Rs, equals one 20 Rs, 10 Rs, 25 p, 10 p `or Rs rupee (Rs) 5 Rs one hundred sen equals one yen (sen not used in ¥10 000, Japanese yen ¥500, ¥100, ¥50, ¥5000, ¥2000, everyday JPY (¥) ¥10, ¥5, ¥1 ¥1000, currency exchanges as too small a unit) New Zealand one hundred dollar $100, $50, $2, $1, 50c, 20c, cents (c) equals $10, $5 10c NZD one dollar ($) NZ$ or $

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

141

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

Explore and describe number patterns resulting from performing multiplication (ACMNA081)

RELATED TERMS

TEACHER INFORMATION

Number pattern

What this means

• A sequence of numbers arranged according to a specific rule

• Students should be familiar with addition and subtraction patterns. They should be able to explore missing elements in repeating and growing patterns.

Element

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

Repeating number pattern

• Students should be able to recognise patterns in everyday life and describe them in some form; e.g. a table.

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

• A list of numbers that increase or decrease in size as a rule; e.g. 5, 10, 15, 20, 25, 30 …

ew i ev Pr

Teac he r

• When referring to a number pattern, an element is a member of the pattern

• Students should be able to explore and describe multiplication patterns and state whether the pattern is going up (+ or ×) or going down (– or ÷).

Teaching points

• Students should be able to skip count by 2s, 3s, 4s, 5s, 10s, 20s, 50s and so on and describe and write these patterns in some form; e.g. a table. • Students should explain what is happening with a function machine; e.g. 5 goes in and 35 comes out. What happened in the function machine? (See page 143 for description of function machines.)

• Students should be able to use number balances and see that 3 × 2 balances with 2 × 3. They need to be able write this in a number sentence, such as 3 × 2 = 2 × 3. • Students should recognise patterns in a table. Example:

w ww

• A list of numbers that increase or decrease in size with a non-constant but predictable difference; e.g. 1, 2, 4, 7, 11, 16, 22 … Skip counting

. te

• Counting forwards or backwards in multiples of a specific number

Student vocabulary number pattern

Position

Pattern

Ask: ‘What is happening in the pattern? State the rule in your own words’.

m . u

Non-routine growing pattern

Students need to be able to describe the rule by looking at the pattern (e.g. ‘Start at 5 and add 5 each time’) or look at the position of numbers and say ‘The position is multiplied by 5 each time’.

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

• Students learn to skip count, but often don’t consider the patterns that exist. • Some students can only count by multiples from 0 and experience difficulty when counting from a different starting point; e.g. 12. • Some students fail to make the links between one multiplication fact and its related fact; e.g. 3 × 7 = 7 × 3.

repeating pattern growing pattern

See also New wave Number and Algebra (Year 4) student workbook (pages 61–66)

element, missing element repeat, continue forwards, backwards skip counting add, subtract, multiply, divide

142

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

HANDS-ON ACTIVITIES Revising addition and subtraction patterns Give students practice in finding the missing element in repeating and growing addition and subtraction patterns. They need to be familiar with this before exploring number patterns resulting from performing multiplication. The cards on page 145 consist of a variety of addition and subtraction patterns. Students could work individually or in pairs, choosing a card from a pile that has been placed facedown. They copy the pattern on a sheet of paper, work it out, add the missing element and add three more numbers in the sequence. Answers have been provided on page 183. These patterns can be shown and described in a table. Refer to the teaching points on page 142 for further information. Blank pattern identification tables for up to seven places have been provided on page 148. Students can compare their answers with others who used the same cards as there can be more than one way of describing the pattern and stating the rule.

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

As an extension, students can make up their own number patterns with a missing element and give to other class members to solve.

Teac he r

Investigating skip counting patterns

ew i ev Pr

Use the completed or blank 1–120 charts on pages 146 and 147 (or the 1–150 grid on page 5) to show skip counting by 2s, 3s, 4s, 5s, 10s, 20s and so on. Multiple copies can be used or different skip counts colour-coded. (Divide a number square into sections for skip counts that use the same numbers and colour accordingly.) Commercially bought flip array boards are another resource that can be used. Students should also investigate skip counting backwards as well as forwards. These patterns can be shown and described in a table. Refer to the teaching points on page 142 for further information. Blank pattern identification tables for up to seven places have been provided on page 148.

Using a ‘function machine’

Function machines are an effective way to encourage algebraic thinking in students to ready them for the solving of higher level equations in later years. There are several ways to represent function machines (refer to pages 149 and 150 for examples), but all are based on the principle of investigating the relationship between the input and output values and to identify what function or rule has been used to generate the output. FUNCTION INPUT As an example: the number 5 ‘goes into’ the function machine and the number 35 ‘comes out’. The function machine could have multiplied the 5 by 7 to get 35, or added 30 to the 5 to get 35. (Other functions are also possible.)

w ww

m . u

Students can make up rules (functions) to apply to numbers that enter the input section of the function machine. Other students can apply the rules to work out the output number. Alternatively, the teacher or students create a rule and work out the input and output number. Only the input number or output number is given to the function machine. Individuals or pairs of students have to work out the rule/ function they want the machine to apply. As explained in the example above, there can be more than one rule. Rules need to be specific for an expected answer to be given. As this descriptor is concerned with multiplication, a rule could be ‘multiply by 7’. If ‘5’ is the input number and this rule applied, ‘35’ will be the output. Note: Refer to page 144 for a list of interactive function machine websites students can use.

. te

o c . che e r o t r s super

Suggestions for using pages 149 and 150: Students can colour the ‘robot’ function machines on page 149 before laminating so the page becomes a reusable resource when written on with a whiteboard marker. Page 150 can also be laminated for re-use.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

143

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

HANDS-ON ACTIVITIES (CONT.) Using number balances Number balances are a useful way of helping students identify and write the type of equations necessary in higher algebra in later years. Students will notice that 3 × 2 will balance with 2 × 3 on the number balance, or 8 × 1 will balance with 2 × 4. These can be written as the equations (number sentences) 3 × 2 = 2 × 3 and 8 × 1 = 2 × 4. As this description is concerned with multiplication, balances could be used to create and write various multiplication equations. These are commercially available in teacher demonstration form and individual student form.

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

Investigating number patterns in everyday life

Teac he r

The table shows that seven rows of chairs are needed.

Science

Row

Chairs

LINKS TO OTHER CURRICULUM AREAS

ew i ev Pr

Students can investigate patterns in everyday life (around the school, home and local community) and describe them in some form, such as in a table or number sequence. This can help them predict the pattern further along in the sequence. For example, students identify that 10 chairs fit in a row on one side of the assembly area and there is room for up to 15 rows of chairs. If 65 parents are expected at the assembly, how many rows of chairs would be needed?

• Leonardo Fibonacci is widely considered the greatest Western mathematician of the Middle Ages. In the 13th century, he discovered a number pattern (known as the Fibonacci sequence) that occurs in the way many things grow in nature. Examples are the way in which rabbits multiply, an ocean wave breaks and a tiger’s claws or a walrus’s tusks grow. Note: The sequence is 1, 1, 2, 3, 5, 8, 13 … Rule: The next number in the sequence is the sum of the previous two numbers.

– Growing patterns by Sarah Campbell

w ww

– Rabbits rabbits everywhere: A Fibonacci tale by Ann McCallum – Wild Fibonacci: Nature’s secret code revealed by Joy N Hulme

. te

– Blockhead: The life of Fibonacci by Joseph D’Agnese

m . u

• The following books are about Fibonacci and his number sequence:

o c . che e r o t r s super

Communication and Information Technology

• The following websites include interactive function machine activities:

– <http://teams.lacoe.edu/documentation/classrooms/amy/algebra/3-4/activities/functionmachine/functionmachine3_4. html> – <http://www.mathplayground.com/functionmachine.html>

– <http://pbskids.org/cyberchase/math-games/stop-creature/>

English • Patterns can be found in the area of language. A limerick is a five-line rhyming poem. Each line has a specific number of syllables—9, 9, 6, 6, 9—with the first, second and fifth lines rhyming and the third and fourth rhyming. Students can create limericks to read out and display. At the following website, students can create limericks by choosing from a selection of given phrases: <http://www.learner.org/teacherslab/math/patterns/limerick/limerick_acttxt.html> • The following website provides activities for students to explore the syntax and word order patterns in the way sentences are constructed: <http://www.learner.org/teacherslab/math/patterns/syntax/syntax_acttxt.html>

144

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

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

RESOURCE SHEET Identifying missing elements in patterns involving addition and subtraction, and extend the pattern Card 1

Card 2 , 14, 16,

0, 2, 4, 6, 8, 10, Card 3

0, 1, 3, 6, 10,

, 21, 28,

r o e t s Bo r e p ok u S Card 4

, 7, 3,

27, 23, 19, 15,

, 45, 55,

10, 15, 25, 30,

Card 7

Card 8

, 77, 73, 69,

93, 89, 85,

, 21, 22,

12, 13, 15, 16, 18,

Card 6

, 65, 60, 55,

85, 80, 75,

ew i ev Pr

Teac he r

Card 5

7, 10, 14, 19,

, 32, 40,

Card 10a © R. I . C.Pub l i c t i ons • or r e i e ur p e son l y• , 40, 39,v , w, p , 125, , 48, 46, 45, 43,f 25,o 45,s 65, 85,

Card 9

110, 210, 310, Card 13

Card 12 , 510, 610,

. te

0, 5, 3, 8, 6, 11, 9, Card 15 4, 6, 10, 16, 24,

o c . che e r o t r s super

, 12, 17,

35, 33, 37, 35, 39, 37,

, 39, 43,

, 143,

Card 16

, 46, 60,

122, 123, 125, 128, 132,

Card 18 , 170, 150,

Card 19 0, 4, 7, 9, 13, 16, 18,

, 36, 40,

16, 20, 24, 28, Card 14

Card 17 250, 230, 210,

m . u

Card 11

w ww

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

22, 25, 28, 31,

, 37, 40,

, 41,

Card 20 , 25, 27,

53, 50, 49, 46, 45,

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

145

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

RESOURCE SHEET 1–120 grid

. t e 93

101

102

111

112

146

w ww

m . u

103

99 o c . che e r o t r s 108 109 sup 104 105 106 107 er

110

113

114

120

115

116

117

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

118

119

100

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

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

Teac he r 32

ew i ev Pr

r o e t s Bo28 29 r 23 24 e25 26 27 p ok u S 34 35 36 37 38 39 33

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

RESOURCE SHEET

. te

m . u

w ww

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

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

ew i ev Pr

Teac he r

Blank 1–120 grid

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

147

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

RESOURCE SHEET Position Pattern What is happening in the pattern? Describe it in your own terms.

r o e t s Bo r e p this pattern? ok u Is there another way of describing S Pattern

What is happening in the pattern? Describe it in your own terms.

w ww

Is there another way of describing this pattern?

. te

m . u

o c . che e Pattern r o t r s sup r What is happening in the pattern? Describe it ine your own terms. Position

State the rule.

Is there another way of describing this pattern?

148

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

Position

ew i ev Pr

Teac he r

State the rule.

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

RESOURCE SHEET

FUNCTION

o c . che e r o t r s super

INPUT

. te

m OUTPUT . u

INPUT

w ww

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

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

ew i ev Pr

Teac he r

OUTPUT

‘Robot’ function machines

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

149

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

RESOURCE SHEET Function machines in table form

Out

Input

Function

Out

Input

Out

Input

Out

ew i ev Pr

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

Out

Input

Out

w ww

. te

150

Out

Input

Function

Out

m . u

Input

Out

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

Out

Input

Out

Input

Out

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

Function

Teac he r

Input

Assessment 1

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

NAME:

DATE:

1. Which number is missing in each pattern? Shade one bubble. (a) 41, 45, 49,

, 57, 61, 65 …

(b) 120, 115, 110,

105

115

Teac he r

, 110 …

, 175 …

102

106

187

186

ew i ev Pr

230, 219, 208, 197,

104

195

© R. I . C.Publ i cat i ons 3. Create your own input, function 2. Complete the input, function (rule) • f o r r e v i e w p u r p oand se sonl y• output for each machine. The or output for each of these.

(a)

(b)

115

Function

(c)

(d)

rule must involve multiplication.

Output 99

(a)

Input

. teSubtract 60 o c . che e Function r o Divide by 10 r 8 t s super

Input

Function

128 Output

(e)

(b)

m . u

Input

w ww

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

, 31, 39 …

(e) 62, 68, 76, 82, 90, 96,

(f)

r o e t 20 24 25 s B r e oo p u S81, 80, , 76, 73 … 77 83 k79 88, 85, 84,

(d)

, 100, 95 …

Output

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

151

Assessment 2

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

NAME:

DATE:

1. Look at the pattern and the position of the numbers in it in the identification table below. Then answer the questions about the pattern. Position

Pattern

Is there another way of describing this pattern?

w ww

Position Pattern

. te

m . u

positions in it in the table. Then answer the questions about your pattern.

What is happening in the pattern? Describe it in your own terms.

State the rule.

o c . che e r o t r s super

Is there another way of describing this pattern?

152

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Explore and describe number patterns resulting from performing multiplication

State the rule.

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

ew i ev Pr

Teac he r

What is happening in the pattern? Describe it in your own terms.

Checklist

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

Creates a skip counting pattern and uses a table to describe what is happening in it

Uses a table to describe what is happening in a number pattern

Identifies the input, rule and output in a function machine

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

ew i ev Pr

Teac he r

STUDENT NAME

Identifies missing elements in number patterns

Explore and describe number patterns resulting from performing multiplication (ACMNA081)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

153

Sub-strand: Patterns and Algebra—P&A – 2

Solve word problems using number sentences involving multiplication or division where there is no remainder (ACMNA082)

RELATED TERMS

TEACHER INFORMATION

Word problem

What this means

• A mathematical problem expressed in narrative form, which can be converted to an equation and solved mathematically

• Students should be able to solve word problems by stating number sentences involving multiplication.

Number sentence

• Students should be able to solve word problems by stating number sentences involving division.

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

Teac he r

Multiplication

• The addition of a number (the multiplicand) to itself a specified number of times as indicated by another number (the multiplier)

• Multiplication can be represented in many different forms. Students should be able to solve word problems by stating number sentences involving multiplication.

• Students need experience in modelling all the common types of multiplication problems. Modelling should include using physical tools, such as counters, MABs and number balances, as well as using mental calculation with pencil and paper.

• The mathematics number operation in which objects and numbers are grouped into equal parts Modelling

Teaching points

• The process of using various mathematical structures to represent real-world situations

w ww

Number balance

. te

• An activity which supports the exploration and investigation into number properties, particularly equivalence Semantic structure

• The ways in which an interpretation of a text points to a particular mathematical relationship; e.g. multiplication or division

• They need to learn to represent problems in number sentences and then solve the problem using mental, written or calculator computation. This links elementary algebra to multiplication. • Division can be represented in many different forms. Students should be able to solve word problems by stating number sentences involving division.

• Students need experience in modelling all the common types of division problems. Modelling should include using physical tools, such as with counters, MABs and number balances, as well as using mental calculation with pencil and paper. This links elementary algebra to division.

m . u

Division

• Students should be able to write a word problem using a division number sentence.

ew i ev Pr

• The representation of an equation expressed using numbers and operation symbols

• Students should be able to write a word problem using a multiplication number sentence.

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

• Students who, when solving a word problem, cannot recognise whether multiplication (repeated addition) or division (finding part of a whole) is best suited for finding an answer. Instead many may just guess which operation is best suited and cannot solve the problem. Others may be able to conceive of what operation to use, but have difficulty constructing a number problem that reflects the semantics of the problem. See also New wave Number and Algebra (Year 4) student workbook (pages 67–72)

Student vocabulary Word problem Number sentence Multiplication Division

154

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Patterns and Algebra—P&A – 2

HANDS-ON ACTIVITIES Can we share? Divide the class into groups of three, four, five or six students. Each group is given six number cards. (See page 157 for cards numbered from 20 to 49.) • Task One: The six number cards are sorted into two piles: those that could be shared equally among their particular group and those that couldn’t. Counters should be provided for this task, if required. • Task Two: Write a number sentence to show how one of the numbers could be shared equally among the group. For = 24. example, a group of six could write 24 ÷ 6 = ? or 6 × • Task Three: Write a word problem to match the number sentence.

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

The process could be repeated for another number card.

The word problems written by one group can be shared with another, with the most interesting problems shared with the class.

Teac he r

How do I work out the answer?

For example, with the number sentence 7 × the number sentence.

ew i ev Pr

Students work in groups of two with some or all of the ‘How do I work out the answer?’ number sentence cards from page 161. Their task is to work out if they would need to use a multiplication or a division algorithm to find the missing part of the number sentence. = 21, they would need to divide 21 by 7 to find the answer and complete

After working out and recording which operation they would need to use, they can complete the number sentence. Note: Although many students may choose to skip count or may be able to recall the appropriate multiplication fact, the idea of this activity is that they gain understanding of the inverse relationship between multiplication and division and that they will be more able to complete the similar but more challenging number sentences on page 162. They will find these more difficult to work out mentally.

After recording the operation, they can use a calculator to complete the number sentence.

Each of the word problems on page 163 can be matched with one of the number sentences on page 164.

m . u

Note: Many of the problems involve the same numbers, so in order to match them correctly, the students will need to look carefully beyond the actual numbers used in some of them.

w ww

Four players in two teams are given a set with both word problem and number sentence cards. One player in each team holds the word problem cards and the other holds the number sentence ones. On the teacher’s signal, each player places the top card from his or her set on the table. The aim is for each team is to be first to identify two matching cards within the two-minute time span. Any player who correctly identifies a matching pair keeps them. The team with the most pairs wins the game, but any player who incorrectly claims a match loses a point for his or her team.

. te

o c . che e r o t r s super

The number sentence cards could be used on a separate occasion to provide further practice in generating new word problems.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

155

Sub-strand: Patterns and Algebra—P&A – 2

LINKS TO OTHER CURRICULUM AREAS Health and Physical Education Hoop Game Equipment: 20 hoops, 4 beanbags, word problem cards (see page 164) and a box of marbles Place the hoops on the ground about 50 centimetres apart to form a circuit. Place each of the four beanbags randomly in four of the hoops. Place the box of marbles beside the last hoop in the circuit. Students should form a line beside the first hoop. The aim is to jump around the circuit from hoop to hoop, collecting a marble each time the circuit is completed. The player with the most marbles wins the game. Eight students are needed to stand in pairs beside the hoops with beanbags in them. Their task is to give a player landing in ‘their’ hoop a word problem card and to check he or she answers correctly. (Answers can be written in pencil on the backs of the cards.) Any student who gives an incorrect answer or is unable to answer has to go to the end of the line and start again. Rules:

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

• Any player who steps outside a hoop has to go to the end of the line.

• If a player drops a marble, it is forfeited and must be replaced in the marble box.

ew i ev Pr

Teac he r

• Players can’t jump into a hoop if someone is in it.

After a set time, perhaps 10 minutes, the card givers join the line. The students with the most marbles take their places and another game is played.

Note: The calculation required for solving a word problem can be relatively easy. The emphasis is on the semantics of the word problem in the first place and on deciding which process is needed.

History and Geography

Work in a small group to write word problems based on the expedition of an explorer studied in history. Consider problems concerning issues such as supplies and equipment, time, temperature and distance travelled, and write related mathematical word problems. A number sentence could then be written to show how each problem can be solved. Word problems could be exchanged with other groups and worked out.

English

. te

m . u

The Arts

w ww

Write some persuasive text taking either a positive or the negative position on the topic: Word problems make maths more interesting.

Illustrate one or more of the explorer mathematical word problems (see History and Geography above) by drawing appropriate diagrams or pictures.

o c . che e r o t r s super

These illustrations could be displayed with information about the explorer and his journey(s). The appropriate word problem and number sentence could be attached to the display.

156

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Number cards (20–40)

r o e t s Bo r e p ok u 25 S 26 27 28

ew i ev Pr

Teac he r

32 33 34 ©31 R. I . C.Pu bl i cat i o ns •f orr evi ew pur posesonl y• . te

m . u

w ww

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

o c . che e r o t r s 43 41 sup 42 er

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

48 R.I.C. Publications®

www.ricpublications.com.au

157

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Word problem cards for ‘Hoop game’

Card 2

Card 3

Tia, Sarah and Julia found a ring. It belonged to a rich lady who gave them a $300 reward. How much money did each girl get?

The football club’s new supporters’ scarfs cost $5.00. How much would need to paid if someone bought 20 of them?

Hal and his brother had $24. How many pairs of socks could they buy if the socks cost $6.00 a pair?

Card 5

Card 6

If a 100-gram bar of nut and fruit chocolate costs a man $2.50, how much would 400 grams of the chocolate cost him?

I measured one of the sides of my new square rug. If it was three metres long, what would be the length of the edge of my rug?

Juan paid $24 for a packet of pens. If there were six pens in the packet, how much did each pen cost him?

If one kilogram of very large bananas costs $3.00, how many kilograms of them could you buy for $15.00?

If my dad’s car uses 10 litres of fuel to travel 100 kilometres, how far could it travel on 40 litres of fuel?

Emily gets three times as much pocket money as I do. If I get $4.00 pocket money, how much does she get?

How many swimmers would there be in each relay team if there are 28 swimmers and seven teams?

Brad walked to school and back in 40 minutes. How long would it take me to do the same thing if I was twice as fast as Brad?

. te

Card 10 Kim bought seven CDs. How many times more CDs does her brother have if he bought 21 of them?

158

m . u

Card 8

w ww

Card 7

o c . che e r o t r sCard 12 Card 11 s uper

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

Card 4

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

ew i ev Pr

Teac he r

Card 1

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Background teaching notes Writing number sentences for mathematical word problem Students may experience difficulties with word problems for a number of reasons, which can include: • reading the words • the wording of the question • determining what information is relevant

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

• identifying the question

• insufficient past practice • lack of confidence.

Teac he r

However, working with word problems is an essential element of a student’s mathematics program. Any activity which links mathematics to real-life situations makes it more relevant and meaningful for students.

The writing of a number sentence can simplify and clarify a word problem for students and can assist them to identify the operation required to solve the problem. Some students may consider the writing of a number sentence to be an unnecessary step, but it is something they need to master. This is because it will help them to understand and solve more complex word problems in the future. Although there are often a number of different number sentences that can represent a particular word problem, it is advisable that (where possible) the number sentences students write match the wording and structure of the word problems they relate to. This will make some of the basic algebraic concepts students will need to understand and work with in the future easier to group.

For example:

Sarah ate 10 ice-creams from the box in the freezer and Emma only ate two of them. How many times more ice-creams did Sarah eat?

To find the answer mathematically, 10 needs to be divided by 2:

m . u

10 ÷ 2 =

w ww

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

ew i ev Pr

Students need to be able to represent a particular word problem mathematically. Doing this can often help them to sort the information provided in the question, so they can decide what is relevant and separate it from what isn’t. It also helps them to identify what the question being asked is, so they can focus on finding the answer.

However, this number sentence, while it’s mathematically correct, doesn’t match the structure of the word problem as well as that below:

. te

2×

= 10 (Two times how many equals 10?)

o c . che e r o t r s super

Practice with this type of word sentence (linking multiplication and division to algebra) will assist students to more readily understand and solve the pro-numeral ‘x’ in number sentences such as: 2x = 10

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

159

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Background teaching notes for multiplication and division Students need experience in solving word problems involving different approaches to multiplication and division, some of which are listed below (with examples). They should be encouraged to use modelling to solve problems by using a variety of materials (including counters, MABs, diagrams and drawings) as required and to write a number sentence. 1. Equal quantities added (×) I ride my bike to school everyday. If I ride 10 kilometres each day, how far do I ride in one week?’

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

2. Equal quantities shared (÷) (Number of portions known – Sharing) If I ride 50 kilometres when going to school five days a week, how far do I ride each day?

ew i ev Pr

4. Rates (×) If hair ribbon costs $3 per metre, how much will it cost for 12 metres? 5. Rates (÷) (Number of portions known – Sharing) If 12 metres of ribbon costs $36, how much will 1 metre cost?

6. Rates (÷) (Cost of portions known – Grouping) I spent $36 on ribbon that costs $3 per metre. How many metres did I buy?

7. Comparisons ratio (×) My dad weighs three times as much as my brother. If my brother weighs 30 kilograms, how much does Dad weigh?

8. Comparisons ratio (÷) (Ratio known) My dad weighs 90 kilograms. How much does my brother weigh if Dad is three times heavier than he is? 9. Comparisons ratio (÷) (Sizes/Weights known) My brother weighs 30 kilograms. How many times heavier is my dad if he weighs 90 kilograms?

m . u

w ww

10. Combinations (×) I have three different-sized drinking glasses. If I bought five different types of coloured drink, how many different types of drink could I organise for my friends? 11. Combinations (÷) I have a number of different-sized drinking glasses and five different types of coloured drink I can put in them. How many different-sized glasses are there if I can serve 15 different types of drink?

. te

o c . che e r o t r s super

12. Measures involving products (×) What is the distance around a square if one side measures 12 centimetres?

13. Measures involving products (÷) The distance around the edge of a square is 48 centimetres. How long is one side?

160

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

Teac he r

3. Equal quantities divided (÷) (Size of portions known – Grouping) How many trips did I make if I rode 50 kilometres going to school and each trip was 10 kilometres long?

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET How do I work out the answer? – 1

× 2 = 18

I need to

= 10

I need to

20 ÷

r o e t s BoI need to r e p ok u 5 ×S = 15 I need to I need to

÷ 15 = 2

I need to

÷. 7I I need ©= 56R . C.Publ i cat i o nsto •f orr evi ew pur posesonl y• ×6

63 ÷ 3 =

. te 2× 72 ÷

I need to

m . u

12 =

w ww

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

40 ÷ 10 =

ew i ev Pr

Teac he r

24 × 3 =

I need to

= 32

I need to

× 7 = 49

I need to

36 =

×4

I need to

96 ÷

= 48

I need to

o c . che e r o t r s I need to super ÷ 5 = 100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

161

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET How do I work out the answer? – 2

324 ×

= 1620

I need to

876 ÷

= 219

I need to

r o e t I need to s B r e oo p u k = 936 I need to S

488 ÷ 4 =

I need to

÷ 21 = 315

I need to

ew i ev Pr

Teac he r

78 ×

It need © R. I . C.Publ i ca i otons •f orr evi ew pur posesonl y• = 666 ÷ 10 ×5

w ww

564 ÷ 4 =

I need to

m . u

955 =

. te o c 45 × = 360 I need to . che e r o t r s s r u e p ÷ 24 = 9 I need to 243 ÷

= 81

I need to

× 98 = 882

I need to

492 =

× 12

366 ÷ 6 = 162

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

567 × 24 =

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Number sentences for word problem matching

24 × 2 =

30 ÷ 6 =

Teac he r

36 ÷ 4 =

. t12 = 60 ÷e

2×4=

m . u

88 ÷ 11 =

w ww

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

24 ÷

ew i ev Pr

r o e t s Bo r e 20 × 5 = 4×9= p ok u S

o c . che e r o t r s super 36 ÷ 9 =

12 × 5 =

48 ÷ 4 =

8 × 11 =

48 ÷ 6 =

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

163

Sub-strand: Patterns and Algebra—P&A – 2

RESOURCE SHEET Word problems for number sentences matching

There are 24 children in the pre-primary class. If they all took oﬀ their shoes and put them in a basket, how many shoes would be in it?

Juan loves reading. If he reads six books a week, how many weeks would he take to read 30 books?

r o e t s Bo r e p ok u S There were six relay teams competing in How many horses could a blacksmith the race. How many girls were in each team if 24 girls ran in the relay?

shoe if he only had 36 horseshoes in his shop?

If grapes cost $5 a kilogram, how much would you need to pay if you wanted four kilograms of grapes?

The average maximum temperature is six times higher in summer than in winter. If it’s 30 degrees in summer, what is the winter temperature?

. te

m . u

w ww

There are 11 players in a hockey team. My new laptop is four times lighter How many teams could you make if you than my old computer. If it weighs had 88 people? two kilograms, how much did my old computer weigh? Mum has to make muffins for the school fair. If her muffin tin makes 12 muffins, how many lots of muffins will she need to cook if she needs 60 muffins?

How many times faster is a car driving along a running track at 36 kph than a runner who is running around the track at nine kph?

pieces are in the block if Shahn and her 11 friends get ﬁve pieces each?

were in the race if they each drank four litres of water?

o c . che e r o t r s suThe Shahn has a block of chocolate for her cyclists drank 48 litres of water r e p friends and herself to share. How many during the race. How many of them

The corner of a box of eight egg cartons The fishermen on the boat caught 48 was squashed and one of the 12 eggs fish. If they each caught six fish, how in each carton was broken. How many many fishermen were on the boat? eggs were not broken? 164

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

My car uses nine litres of fuel to travel 100 kilometres. How much fuel would I need to travel four times that distance?

ew i ev Pr

Teac he r

If it takes Sam and Kai 20 minutes to walk to school each day, how many minutes would they spend walking to school in ﬁve days?

Assessment 1

Sub-strand: Patterns and Algebra—P&A – 2

NAME:

DATE:

1. Write a number sentence for each word problem, then solve your number sentence. (Draw a picture, or use counters, blocks or a calculator.)

There are

ew i ev Pr

Teac he r

(b) There are 32 students in the class and four teams. How many students would be in each team?

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

Riding speed is

in each team.

(d) A fisherman sold his fish for $24 a kilo. If he collected $72, how many kilos of fish did he sell?

. te

He bought

cartons.

He sold

kilos.

o c . che e r o t r s super

(e) Caleb has 12 blocks of chocolate. How many times as much does Ella have if she has 96 chocolates?

She has

m . u

w ww

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

(a) A bike travels four times faster than someone walking. What’s its speed if the walking speed is five kph?

(f) There were 144 people attending a wedding. How many tables would be needed if eight people could sit at each table?

times as many. tables would be needed.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

165

Assessment 2

Sub-strand: Patterns and Algebra—P&A – 2

NAME:

DATE:

1. Write a word problem for each number sentence. × 20 = 120

r o e t s Bo r e p ok u S = 12 cm

(d)

÷5=9

w ww (e) 15 ×

166

m . u

. te o = 45 (f) 72 ÷ 8 = c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Solve word problems using number sentences involving multiplication or division where there is no remainder

(b)

ew i ev Pr

Teac he r

(a) 25 × 8 =

Checklist

Sub-strand: Patterns and Algebra—P&A – 2

Writes a word problem using a division number sentence

States division number sentences to solve word problems

Writes a word problem using a multiplication number sentence

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

ew i ev Pr

Teac he r

STUDENT NAME

States multiplication number sentences to solve word problems

Solve word problems using number sentences involving multiplication or division where there is no remainder (ACMNA082)

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

167

Sub-strand: Patterns and Algebra—P&A – 3

Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)

RELATED TERMS

TEACHER INFORMATION

Equivalent • Having the same value but expressed in a different way; e.g. 32 + 16, 50 – 2 and 2 × 24 = 48

• Students should be given many opportunities to write number sentences to represent and answer questions, such as: ‘When a number is added to 23, the answer is the same as 57 minus 19. What is the number?’ The number sentence is: 57 – 19 = 23 + ? This can be shown with counters, craft sticks, MABs, a 120-chart or a calculator.

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

Number sentence • The representation of an equation expressed using numbers and operation symbols Note: Inequalities can also be expressed in number sentences; e.g. 15 > 7 + 7

Equation • A mathematical statement which asserts the equality of two expressions

Standard partitioning • Separating a number into place value parts (expanded notation); e.g. 245 = 200 + 40 + 5

• Students should be given a variety of question types in which they need to balance both sides of an equation. • Students should use non-standard partitioning to find unknown quantities in number sentences. For example; 740 – 197 could be considered as 540 + 200 – 197.

ew i ev Pr

Teac he r

What this means

Notice the 740 has been partitioned into 540 + 200. The reason for doing this is to make the subtraction easier: 540 + 3 = 543, so 740 – 197 = 543 This is less complicated than using a standard algorithm and it shows students other ways to think about a problem.

Non-standard partitioning • Separating a number into parts other than place value to facilitate mental calculation; e.g. 49 + 23 = 50 (49 + 1) + 22 (23 – 1)

• Students should be given the opportunity to learn concepts like these so they are able to employ a range of strategies to solve different addition and subtraction problems.

Addition • A mathematical operation which involves finding the sum or total value when two or more numbers are combined

• Give students the opportunity to learn strategies so they can develop number sentences based on the semantic structure of the question.

w ww

Subtraction • A mathematical operation which involves taking one number away from another to find the difference

. te

• Questions should be developed to give students the opportunity to balance both sides of its corresponding equation.

• These questions can be solved by using manipulative materials, such as MABs, play money, number balances or calculators. Students need to write number sentences before using the materials or technology.

o c . che e r o t r s super

Semantic structure • The ways in which interpretation of text points relate to a particular mathematical relationship; e.g. addition or subtraction. Unknown quantity • A variable whose values are solutions of an equation Student vocabulary

m . u

What to look for

• Students who, when solving an equation with a missing element (whether it be addition or subtraction), cannot conceive that both sides of an equation must reflect the same value. They have difficulty understanding the semantic structure of the equation and how the operations on either side of the equals sign must balance, and therefore are unable to conceive of what the missing value is. Instead, they guess which value is missing.

equivalent number sentence

See also New wave Number and Algebra (Year 4) student workbook (pages 73–78)

balance partitioning equation

168

Proficiency strand(s): Understanding Fluency

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

Problem solving Reasoning R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Patterns and Algebra—P&A – 3

HANDS-ON ACTIVITIES Solving equations on a number grid Students can work with a partner to solve equations similar to the types given below using the 1–120 grids on page 171. 5 + 12 =

+ 10

24 +

= 15 + 18

+ 56 = 42 + 37

35 + 27 = 19 +

Initially, they should be encouraged to follow the procedure below. Once they are familiar with it, they can develop one they prefer and which they find is easier and more efficient. 1. Write the number sentence below a grid. 2. Identify the equals sign and the side of the equation which has two numbers.

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

3. Find the bigger of these two numbers on the grid and put a dot in it. 4. Count on to add the smaller number and put a cross in that square. 5. Put a dot in the square with the single number in it.

6. Count on to find how many squares there are before the number with the cross.

ew i ev Pr

Teac he r

7. Complete the number sentence.

Note: Equations involving subtraction can also be solved in a similar way on a number grid. After identifying which side of the equation has the two known numbers, find the bigger number, subtract the smaller one and put a cross in that square. Find the square with the given number from the other side of the equation, put a dot in its square and count to work out the difference between that number and the one in the crossed square.

Solving equations on a number line

Number lines can be used in a similar manner to number grids to solve equations. A page with 0–100 number lines marked in tens and ones has been provided for this purpose. See page 173.

Think board

Think boards (see page 172) have connections to Gardner’s multiple intelligences in that they encourage students to think about problems in different ways. They can assist students to better understand and ‘see’ some mathematical (particularly algebraic) concepts.

m . u

Students should use a think board in the way they find most helpful. For example, once familiar with a concept, some may prefer to draw the number story or equation while others may find it better to use concrete materials. As such, it may not always be necessary nor useful for some students to complete each section of a think board.

w ww

Number balances

A balance scale can be very effective in helping students to conceptualise mathematical relationships and to solve elementary algebraic equations. Balance tasks require interpretation rather than mechanical response and so encourage understanding. (See page 144 for more information.)

. te

o c . che e r o t r s super

The equivalent number sentences and the word problem cards on pages 174 and 175 can be used in matching games or as a partner activity. With such games, after matching the cards students can work together to solve the equations. They should be encouraged to use non-standard partitioning to facilitate mental calculations. The ‘missing sign’ game and sign cards on pages 176 and 177 also provide pairs of students with opportunities to work with balance scales. These two sets of cards can be used in a game in which both sets are placed face down on the table. Students take turns to take the top card from each. If they can match both the missing signs with a sign card, they can keep that pair of cards. If not, both cards are replaced at the bottom of their sets. The student with seven card pairs wins the game. The missing sign cards can also be used by students to practise writing corresponding word problems.

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

169

Sub-strand: Patterns and Algebra—P&A – 3

LINKS TO OTHER CURRICULUM AREAS History • Research to find examples of inequality, where groups of people or individuals in the past were treated differently. Describe, compare and contrast some of the different ways in which they were treated and provide some possible reasons why this happened. What needed to happen so groups were treated equally? • Expand the research to the present day and find out what has changed or is changing and whether these inequalities still exist. What caused any changes and how did they happen? • Will these inequalities exist in the future? Suggest what is most likely to happen and explain why you believe this.

English

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

• Write a procedure to explain how to use a 1–120 number grid to solve equations involving subtraction; e.g. as 43 – 25 = 38 – Use the procedure on page 169 as a model Number the steps and use an example in your explanation.

Teac he r

ew i ev Pr

• Write a poem to explain what ‘equals’ means. It could be humorous or serious and be restricted to the mathematical concept of equality or expanded to include equality in different aspects of life. Encourage students to think about examples to explain their ideas and to include them where possible. The poems can be illustrated and displayed.

The Arts

• Draw a balance scale on a large sheet of paper or card with the heading ‘Keeping the balance’ and place it in the class wall. Make sure the scales look level and balanced. Glue two shapes in each balance pan (see page 178), along with a sign card (see page 177) giving the operation which is needed in order to make both sides equal. For example, on one side of the balance there could be two shapes with 87 and 49 with a minus sign. The other side could have two shapes with 94 and 56 with a minus sign card, or 21 and 17 joined with a plus sign card.

• The students’ task is to use the shapes and signs on pages 177 to 179 to make other equivalent number combinations that could replace one of those in the two pans. The combinations should first be checked by another student, coloured in one colour, then glued together on the chart. Encourage students to think of unusual combinations. Calculators could be used to generate bigger numbers and to check that other students’ combinations are correct. • This book may be of interest: Math-terpieces: The art of problem-solving, by Greg Tang and Greg Paprocki.

m . u

Communication and Information Technology

w ww

The following websites are games of different levels of difficulty in which students need to add numbers to both sides of a balance board. Such games help students to develop greater understanding of the concept of equivalence: • http://www.to14.com/game.php?id=4d486a337d0bf

. te

• http://www.agame.com/game/monkey-math-balance.html

o c . che e r o t r s super

• http://pbskids.org/cyberchase/math-games/poddle-weigh-in/

170

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET 1–120 grids for solving equivalent number sentences 1

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Teac he r

11 12 13 14 15 16 17 18 19 20

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

101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

Equation: 5

ew i ev Pr

101 102 103 104 105 106 107 108 109 110

Equation:

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

49 50

51 61

59 60 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

Equation: 1

. te 4

m . u

71 72 73 74 75 76 77 78 79 80

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

Equation:

o c . che e r o t r s super 6

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

Equation:

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

171

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET

MATERIALS

o c . che e r o t r s super

172

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

m . u

w ww

. te

THINK BOARD

NUMBER SYMBOLS

Teac he r

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

ew i ev Pr

WORD STUDY

PICTURE

Think board

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET

r o e t s Bo r e p ok u S 20

100

. te 20

m . u

ew i ev Pr

Teac he r

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

0–100 number lines for solving equivalent number sentences

o c . che e r o t r s super

100

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

173

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET Balance scale word problem cards

When a number is added to 41, the answer is the same as 59 minus 11. What is the number?

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

If 75 and 19 are added, the answer is the same as 43 added to what number?

w ww

. te

m . u

as 19 subtract 7?

added to 24?

o c . che e r o t r s super

The number you get when you subtract 49 from 87 is the same as what number added to 35?

When you add 12 and 47, the number you get is the same as 24 added to what number?

What number do you need to add to 15 to equal 34 subtracted from 91?

If you subtract 39 from 78, the number you get is equal to what number added to 16?

174

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

What number added to 56 is the same as 35 added to 61?

ew i ev Pr

Teac he r

When you add 67 and 21, the answer is equal to 45 and what number?

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET Balance scale cards

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

–

. te

–

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

–

m . u

–

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

ew i ev Pr

Teac he r

–

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

175

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET Find the missing signs cards

r o e t s Bo r e p ok u S 31

ew i ev Pr

Teac he r

w ww

. te =

o c . che e r o t r s super

= 176

m . u

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET Sign cards

+ Teac he r

– –

. te

– –

m . u

–

+ +

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

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

–

ew i ev Pr

+ +

– –

o c . che e r o t r s super

– +

–

– +

–

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

177

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET Blank number balance scales

w ww

. te =

o c . che e r o t r s super

= 178

m . u

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

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

ew i ev Pr

Teac he r

Sub-strand: Patterns and Algebra—P&A – 3

RESOURCE SHEET

Teac he r

ew i ev Pr

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

. te

m . u

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

‘Keeping the balance’ cards

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

179

Assessment 1

Sub-strand: Patterns and Algebra—P&A – 3

NAME:

DATE:

1. Are these pairs equal? Shade a bubble to give your answer. (a) 34 + 45 and 27 + 52 Yes

(b) 67 – 33 and 23 + 11

Yes

(d) 63 + 24 and 98 – 25

Yes

(f)e 56 – 29 and 29 – 56 r o t s Bo r e p ok No Yes No Yes u Sto make these balance. 2. Add the missing sign

(b)

–

w ww

. te

3. Shade the bubble to show which number sentence matches the word problem.

o c . c e r 94 – 47 = 23 + h 94 – 23 = 47 + er o t s super When a number is added to 38, the answer is the same as 72 minus 29.

(a) What number added to 47 equals 94 minus 23?

(b)

What is the number? 72 – 29 = 38 +

29 + 38 = 72 +

65 – 46 = 54 –

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

(c)

m . u

(a)

ew i ev Pr

Teac he r

(e) 15 + 44 and 44 + 15

Assessment 2

Sub-strand: Patterns and Algebra—P&A – 3

NAME:

DATE:

1. Write a number sentence for each word problem, then work out the answer. (a) If 22 is added to a number, it is the same as 38 and 42 added. What is the number? Number sentence: Answer:

r o e t s Bo r e Number sentence: p ok u Answer: S

2. What is the missing number on each balance scale?

–

= ©R . I . C.Publ i cat i ons = •f orr evi ew pur po esonl y• (d)s

–

m . u

(c)

(b)

w ww

CONTENT DESCRIPTION: Use equivalent number sentences involving addition and subtraction to find unknown quantities

(a)

ew i ev Pr

Teac he r

(b) What number added to 39 is the same as 99 minus 22?

. te

3. Show how you could work out these number sentences mentally by adding to or subtracting from a number to make it easier. The first has been done for you. (a)

o c 99 – 27 = 60 (b) 45 – 19 =. 10 + c+he e r o t r s s r u e p 100 – 28 = 60 + 72 = 60 + 12

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

(d) 41 + 29 = 30 +

R.I.C. Publications®

www.ricpublications.com.au

181

Checklist

Sub-strand: Patterns and Algebra—P&A – 3

Uses non-standard partitioning to solve addition and subtraction problems

Balances both sides of equations involving addition and subtraction to find unknown quantities

Writes equivalent number sentences to represent word problems and vice versa

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

ew i ev Pr

Teac he r

STUDENT NAME

Demonstrates understanding of mathematical equivalence

Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)

w ww

. te

182

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

Sub-strand: Patterns and Algebra

P&A – 1

Answers for Resource sheet: Identifying missing elements … (page 145)

Page 151 Assessment 1

Note: The missing element and the next three numbers that would occur in the pattern are in bold print. A summary of the pattern is given in the brackets. Card 1: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 (+ 2 …) Card 2: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 (+ 1 + 2 + 3 + 4 …) Card 3: 39, 35, 31, 27, 23, 19, 15, 11, 7, 3 (– 4 …) Card 4: 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27 (+ 1 + 2 + 1 + 2 …) Card 5: 85, 80, 75, 70, 65, 60, 55, 50, 45, 40 (– 5 …) Card 6: 10, 15, 25, 30, 40, 45, 55, 60, 70, 75 (+ 5 + 10 + 5 + 10 …) Card 7: 93, 89, 85, 81, 77, 73, 69, 65, 61, 57 (– 4 …) Card 8: 7, 10, 14, 19, 26, 32, 40, 49, 59, 70 (+ 3 + 4 + 5 + 6 …) Card 9: 48, 46, 45, 43, 42, 40, 39, 37, 36, 34 (– 2 – 1 – 2 – 1 …) Card 10: 25, 45, 65, 85, 105, 125, 145, 165, 185 (+ 20 …) Card 11: 110, 210, 310, 410, 510, 610, 710, 810, 910 (+ 100 …) Card 12: 16, 20, 24, 28, 32, 36, 40, 44, 48, 52 (+ 4 …) Card 13: 0, 5, 3, 8, 6, 11, 9, 14, 12, 17, 15, 20 (+ 5 – 2 + 5 – 2 …) Card 14: 35, 33, 37, 35, 39, 37, 41, 39, 43, 41, 45, 43 (– 2 + 4 – 2 + 4 …) Card 15: 4, 6, 10, 16, 24, 34, 46, 60, 76, 94, 114 (+ 2 + 4 + 6 + 8 …) Card 16: 122, 123, 125, 128, 132, 137, 143, 150, 158, 167 (+ 1 +2 +3 + 4 + 5 …) Card 17: 250, 230, 210, 190, 170, 150, 130, 110, 90 (– 20 …) Card 18: 22, 25, 28, 31, 34, 37, 40, 43, 46, 49 (+ 3 …) Card 19: 0, 4, 7, 9, 13, 16, 18, 22, 25, 27, 31, 34, 36 (+ 4 +3 + 2 + 4 + 3 + 2 …) Card 20: 53, 50, 49, 46, 45, 42, 41, 38, 37, 34 (– 3 – 1 – 3 – 1 …)

1. (a) 53 (b) 105 (c) 24 (d) 77 (e) 104 (f ) 186 2. Teachers will need to check the students’ answers for the function rules they create as there can be more than one correct answer. Two different answers for the rules in (a), (d) and (e) have been given as examples. (a) add 28; add double 14 (b) 55 (c) 80 (e) multiply by 32; add 124 (f ) multiply by 4; add 66 3. Teacher check Page 152 Assessment 2

Teac he r

1. Possible answers to each part: What is happening … (The numbers are increasing by 5.) Rule … (Start at 5. Add 5 each time.) 2. Teacher check

ew i ev Pr

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

w ww

. te

m . u

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

183

Answers

Sub-strand: Patterns and Algebra

P&A – 2

P&A – 3

Page 165 Assessment 1

Page 180 Assessment 1

1. (a) 4 × 5 = (b) 32 ÷ 4 = (c)

There are 8 in each team.

× 2.40 = 19.20 or 19.20 ÷ 2.40 = bought 7 cartons.

(d)

× 24 = 72 or 72 ÷ 24 =

(e)

× 12 = 96 or 96 ÷ 12 = many.

(f ) 144 ÷ 8 =

1. (a) yes (d) no 2. (a) –

Riding speed is 20 kph.

He sold 3 kilos.

1. Answers will vary. Teacher check

(d) –

(b) 72 – 29 = 38 +

1. Teacher check. Some number sentences may differ a little in order from those given below. (a) 38 + 42 =

+ 22

Answer 58

(b) 99 – 22 = 39 + Answer 38 2. (a) 43 (b) 10 (c) 43 3. Answers may vary. Teacher check. (b) 45 – 19 = 10 + 46 – 20 = 10 + 26 = 10 + 16 (c) 56 – 31 = 70 – 57 – 30 = 70 – 27 = 70 – 43

(d) 2

ew i ev Pr

Teac he r

3. (a) 94 – 23 = 47 +

r o e t s Bo r e p ok u S She has 8 times as

18 tables would be needed.

Page 166 Assessment 2

(b) yes (e) yes (b) –

184

m . u

w ww

. te

(d) 41 + 29 = 30 + 40 + 30 = 30 + 40

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

NEW WAVE NUMBER AND ALGEBRA (YEAR 4) STUDENT WORKBOOK ANSWERS N&PV – 1 Page 2

Australian postcodes – even or odd? Postcode

Odd/ even pattern

The sum of four digits

Odd or Even

Abbeyard

3737

OOOO

even

Abbotsford

3067

OEEO

even

Aberfeldie

3040

OEEO

odd

Aberfeldy

3825

OEEO

even

Acheron

3714

OOEE

odd

Aarons Pass

2850

EEOO

odd

Abbotsbury

2176

EOOE

even

Abbotsford

2046

EEEE

even

Abercrombie

2795

EOOO

odd

Abercrombie River

2795

EOOO

odd

Abbeywood

4613

EEOO

even

Abbotsford

4670

EEOE

odd

Abercorn

4627

EEEO

odd

Abergowrie

4850

EEOE

odd

Abingdon Downs

4871

EEOO

even

Abba River

6280

EEEE

Abbey

6280

EEEE

1. 2. 3. 4. 5. 6.

404, 518, 744 444, 108, 28 193, 607 881 1455, 507, 923, 577, 919, 121 411, 281, 117, 263, 95

Page 7

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

48 28 53 300 96 95

Prove the rule!

Teacher check

N&PV – 2 Page 8 1.

Football crowds

Team

58 410

Pumas

48 724

Doughnuts

46 735

even

Kookaburras

45 994

even

Falcons

37 710

6280

EEEE

even

Cardinals

Adamsvale

6375

EOOO

odd

Superstars

6435

EEOO

even

Angels

. te

Even phone numbers – or are they odd?

Teacher check Page 4

Four-digit soup

Teacher check Page 5

36 683

36 073

35 444

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

2. Answers will vary – teacher check Page 3

Attendance average

Cockatoos

Acton Park Agnew

1. 2. 3. 4. 5. 6. 7. 8.

Just keep circling

m . u

NSW suburb/town QLD suburb/town

Page 6

w ww

WA suburb/town

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

ew i ev Pr

Teac he r

Victorian suburb/town

9. 9098, 9100, 9102, 9104, 9106, 9108 10. (a) 188, 190, 192, 194, 196, 198 (b) 2002, 2004, 2006, 2008, 2010, 2012 (c) 662, 664, 666, 668, 670, 672 (d) 264, 266, 268, 270, 272, 274 (e) 820, 822, 824, 826, 828, 830 (f ) 412, 414, 416, 418, 420, 422

Write the 6! and write them in order!

14, 16, 18, 20, 22, 24 193, 195, 197, 199, 201, 203 40, 42, 44, 46, 48, 50 73, 75, 77, 79, 81, 83 314, 316, 318, 320, 322, 324 599, 601, 603, 605, 607, 609 1710, 1712, 1714, 1716, 1718, 1720 1207, 1209, 1211, 1213, 1215, 1217

33 827

Hawks

32 634

Surfers

31 609

Dinosaurs

23 732

Wombats

23 428

Cygnets

21 497

Pirates

20 771

Leopards

20 491

Gorillas

13 676

Lifeguards

12 775

2. Cockatoos 3. Cardinals 4. Lifeguards

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

185

Answers Page 9

New Wave Number and Algebra Student Workbook

Unlucky 13!

Page 13

Teacher check Page 10

Hundred less

New postcodes

Teacher check Page 11

What’s in a 7?

Number

7 is worth …

Wipe out 7

37 891

7000

30 891

11 709

700

11 009

71 469

70 000

1469

20 073

23 765

700

67 009

7000

73 550

70 000

17 080

7000

10 080

43 667

43 660

18 701

700

18 001

14 678

14 608

37 663

7000

30 663

57 012

7000

50 012

61 070

61 000

Page 12 Ten less

1889

1999

8999

9099

9199

9569

9669

9769

901

1001

1101

983

1083

1183

6002

6102

6202

8007

8107

8207

6499

6599

6699

320

45 690

19 809

19 909

20 009

20 003

11 903

12 003

12103

23 065

21 911

22 011

22 111

60 009

10 001

10 101

10 201

3550

88 901

89 001

89 101

6902

7002

7102

70 001

70 101

70 201

94 919

95 019

95 119

72 840

72 940

73 040

49 905

50 005

50 105

40 903

41 003

41 103

38 101

38 201

38 301

Wipe out 7 – It’s for real!

Ten less … ten more

Value of 7

7 wiped out

Ten more

55 789

700

55 089

1889

1899

78 029

70 000

8029

9089

9099

9109

37 661

7000

30 661

9659

9669

9679

19 070

19 000

991

1001

w ww

1011

70 012

70 000

1083

1093

56 807

56 800

33 744

700

33 044

98 765

700

98 065

40 379

40 309

19 919

22 753

700

22 053

6092 8097 6589

6102

8107

6599

. te

6112

8117

6609

m . u

1879

1073

186

1789

ew i ev Pr

7000

2. Teacher check

Hundred more

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

7 320 45 697

Teac he r

Now a hundred less and a hundred more

o c . che e r o t r s super

19 899

19 909

11 993

12 003

12 013

78 429

70 000

8429

22 001

22 011

22 021

27 029

7000

20 029

10 091

10 101

10 111

38 471

38 401

88 991

89 001

89 011

14 070

14 000

6992

7002

7012

70 012

70 000

70 091

70 101

70 111

84 708

700

84 008

95 009

95 019

95 029

87 644

7000

80 644

72 930

72 940

72 950

92 748

700

92 048

49 995

50 005

50 015

76 899

70 000

6899

40 993

41 003

41 013

27 088

7000

20 088

38 191

38 201

38 211

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

New Wave Number and Algebra Student Workbook

2. (a) (e) 3. (a) (d)

7 wiped out

43 874

43 804

71 990

70 000

1990

33 070

33 000

29 971

29 901

Page 18

67 880

7000

60 880

79 624

70 000

9624

57 660

7000

50 660

75 401

70 000

5401

1. 4. 7. 10.

44 709

700

44 009

76 901

70 000

6901

43 274

43 204

71 960

70 000

1960

87 090

7000

80 090

29 971

29 901

70 220

70 000

220

29 724

700

29 024

16 470

16 400

87 401

7000

80 401

44 007

44 000

94 701

700

94 001

Page 15

9642 1190 4356 30 654

(b) 1759 (c) 3837 (d) 4545 (f ) 4168 (g) 8414 (h) 3465 (b) 2761 (c) 49 610 (e) 64 958

Solve these word problems

3018 34 935 $322 $1044

2. 5. 8. 11.

$11.15 $7.80 $23.35 Yes

3. 6. 9. 12.

$3229 3790 3844 $433.85

r o e t s Bo r e p ok u S Page 19

Numbers and words

1. (a) Two thousand, nine hundred and eighty–three (b) Thirty-eight thousand, nine hundred and ninety– seven (c) Thirty-three thousand, nine hundred and nine (d) Twenty-seven thousand, one hundred and twelve (e) Fourteen thousand, eight hundred and thirty– seven 2. (a) 100 (b) 100 (c) 100 (d) 100 (e) 1000 (f ) 100 (g) 1000 (h) 100 (i) 10 (j) 100 (k) 90 000 (l) 400 (m) 16 000 (n) 20

N&PV – 4

Hop to it – there’s work to be done!

ew i ev Pr

Teac he r

Value of 7

Page 16

109 465 22 742 6054 96 311 18 017

810 23 45 24

. te

90 54 39 58

67 457 35 227 82 926 44 919 23 274 (d) (h) (d) (h)

71 120 37 92

Hop to it again – this time there are more!

1. (a) 87 456 (d) 185 726 (g) 7970 (j) 62 875 (m) 46 829 (p) 18 576 2. (a) 67 (e) 98 3. (a) 88 (e) 98 Page 17

(b) (e) (h) (k) (n)

(b) (f ) (b) (f )

(b) (e) (h) (k) (n)

90 56 53 40

155 457 6767 97 766 95 359 59 334 (d) (h) (d) (h)

79 980 17 96

It’s all about numbers – really it is!

1. (a) 40 000 (e) 10 000 (i) 1000 (m) 300

(b) (f ) (j) (n)

200 6000 900 3000

(a) (c) (e) (g) (i)

Who is the odd man out?

250, 248, 252 164, 162, 168 110, 108, 112 124, 120, 128 151, 144, 153

(b) (d) (f ) (h)

246, 243, 252 121, 119, 126 244, 240, 246 118, 117, 120

Page 21

Your time starts now

1. (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) 2. (a) (e)

92, 95, 98, 101, 104, 107 129, 135, 141, 147, 153, 159 309, 318, 327, 336, 345, 354 123, 127, 131, 135, 139, 143 217, 225, 233, 241, 249, 257 99, 106, 113, 120, 127, 134 158, 161, 164, 167, 170, 173 195, 201, 207, 213, 219, 225 179, 183, 187, 191, 195, 199 492, 501, 510, 519, 528, 537 152 (b) 230 (c) 165 217 (f ) 191 (g) 74

o c . che e r o t r s super

96 765 18 722 17 996 96 597 38 017

890 87 65 86

Page 20

m . u

(b) (f ) (b) (f )

w ww

1. (a) 95 456 (d) 45 124 (g) 11 970 (j) 92 275 (m) 32 835 (p) 20 574 2. (a) 47 (e) 12 3. (a) 22 (e) 18

80 4 20 000 30

(d) 2000 (h) 40 (l) 80 000

Page 22

(d) 204 (h) 61

Keep counting!

3s 18, 21, 24, 27, 30, 33, 36 51, 54, 57, 60, 63, 66, 69 68, 71, 74, 77, 80, 83, 86 4s 28, 32, 36, 40, 44, 48, 52 88, 92, 96, 100, 104, 108, 112 121, 125, 129, 133, 137, 141, 145

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

187

Answers

New Wave Number and Algebra Student Workbook

6s 30, 36, 42, 48, 54, 60, 66 51, 57, 63, 69, 75, 81, 87 107, 113, 119, 125, 131, 137, 143 7s 35, 42, 49, 56, 63, 70, 77 80, 87, 94, 101, 108, 115, 122 168, 175, 182, 189, 196, 203, 210 8s 40, 48, 56, 64, 72, 80, 88 93, 101, 109, 117, 125, 133, 141 235, 243, 251, 259, 267, 275, 283 9s 36, 45, 54, 63, 72, 81, 90 93, 102, 111, 120, 129, 138, 147 358, 367, 376, 385, 394, 403, 412 Number patterns

1.–2. See diagram below red

Teac he r

, pink

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

21 31 41 51

Page 26 1.

Number facts errors

10 12 14 13 18 20

11 15 17 21 23 27 30

10 12 16 20 24 28 33 36 40

100

12 15 21 26 31 35 42 45 50

14 18 25 30 35 42 49 54 60

15 21 29 35 43 49 55 63 70

17 24 32 40 48 56 65 72 80

18 26 35 44 53 58 62 71 81 90

w ww

Page 24

N&PV – 5

3. 36, 72, 84

Backwards counting!

3s 198, 195, 192, 189, 186, 183, 180 133, 130, 127, 124, 121, 118, 115 50, 47, 44, 41, 38, 35, 32 4s 150, 146, 142, 138, 134, 130, 126 97, 93, 89, 85, 81, 77, 73 280, 276, 272, 268, 264, 260, 256 6s 102, 96, 90, 84, 78, 72, 66 215, 209, 203, 197, 191, 185, 179 171, 165, 159, 153, 147, 141, 135 7s 126, 119, 112, 105, 98, 91, 84 186, 179, 172, 165, 158, 151, 144 87, 80, 73, 66, 59, 52, 45 8s 144, 136, 128, 120, 112, 104, 96 185, 177, 169, 161, 153, 145, 137 297, 289, 281, 273, 265, 257, 259 9s 72, 63, 54, 45, 36, 27, 18 139, 130, 121, 112, 103, 94, 85 304, 295, 286, 277, 268, 259, 250

. te

188

, blue

3s 25, 28, 31, 34, 37, 40, 43, 46 66, 69, 72, 75, 78, 81, 84, 87 108, 111, 114, 117, 120, 123, 126, 129 4s 132, 136, 140, 144, 148, 152, 156 385, 389, 393, 397, 401, 405, 409 1001, 997, 993, 989, 985, 981, 977 6s 204, 210, 216, 222, 228, 234, 240 375, 381, 387, 393, 399, 405, 411 107, 101, 95, 89, 83, 77, 71 7s 238, 245, 252, 259, 266, 273, 280 593, 600, 607, 614, 621, 628, 635 1033, 1026, 1019, 1012, 1005, 998, 991 8s 172, 180, 188, 196, 204, 212 1635, 1643, 1651, 1659, 1667, 1675, 1683 1887, 1879, 1871, 1863, 1855, 1847, 1839 9s 86, 95, 104, 113, 122, 131, 140 658, 667, 676, 685, 694, 703, 712 3113, 3104, 3095, 3086, 3077, 3068, 3059

ew i ev Pr

, orange

Keep counting – only 2 clues!

m . u

Page 23

Page 25

o c . che e r o t r s super

10 10 20 30 40 50 60 70 80 90 100

2. 9 × 1 = 9 2 × 2 = 4, 3 × 2 = 6, 4 × 2 = 8, 5 × 2 = 10, 6 × 2 = 12, 7 × 2 = 14, 8 × 2 = 16, 9 × 2 = 18 9 × 3 = 27 3 × 4 = 12 , 5 × 4 = 20, 6 × 4 = 24, 7 × 4 = 28, 9 × 4 = 36 5 × 5 = 25, 9 × 5 = 45 3 × 6 = 18, 5 × 6 = 30, 6 × 6 = 36, 7 × 6 = 42, 9 × 6 = 54 9 × 7 = 63 2 × 8 = 16, 3 × 8 = 24, 4 × 8 = 32, 5 × 8 = 40, 6 × 8 = 48, 7 × 8 = 56, 8 × 8 = 64, 9 × 8 = 72

Page 27

And the answer is …

1. How does a number speak? 2. Teacher check

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

New Wave Number and Algebra Student Workbook

Page 28

It’s game on!

Player A

Page 32 Winner and margin

Player B

Tally

1. B

5 × 6 = 30

B by 2

9 × 4 = 36

4 × 10 = 40

B by 4

7 × 8 = 56

5 × 9 = 45

A by 11

3 × 4 = 12

2 × 7 = 14

B by 2

3 × 7 = 21

5 × 4 = 20

A by1

6 × 6 = 36

4 × 8 = 32

A by 4

7 × 7 = 49

8 × 6 = 48

A by 1

9 × 9 = 81

10 × 8 = 80

A by 1

+10

4 × 12 = 48

5 × 10 = 50

B by 2

6 × 12 = 72

7 × 11 = 77

B by 5

8 × 8 = 64

6 × 12 = 72

B by 8

9 × 6 = 54

7 × 8 = 56

B by 2

48 ÷ 4 = 12

54 ÷ 3 = 18

B by 6

+13

66 ÷ 11 = 6

36 ÷ 9 = 4

A by 2

+11

96 ÷ 8 = 12

22 ÷ 11 = 2

A by 10

55 ÷ 5 = 11

44 ÷ 2 = 22

B by 11

+12

28 ÷ 4 = 7

35 ÷ 5 = 7

equal

+12

30 ÷ 10 = 3

55 ÷ 5 = 11

B by 8

+20

42 ÷ 6 = 7

81 ÷ 9 = 9

B by 2

+22

33 ÷ 11 = 3

48 ÷ 12 = 4

B by 1

+23

15 ÷ 3 = 5

18 ÷ 2 = 9

B by 4

+27

$92.40

Ben earns $5.45 per hour and works for 9 hours each day

$98.10 $245.25 $490.50

Hugo earns $6.10 per hour and works for 6 hours each day

$73.20

$231

$183

$129.80 $324.50

Abbie earns $9.50 per hour and works for 5 hours each day

$95

$237.50

Page 33 1.

w ww 18 ÷ 3 =7

32 ÷ 4 =9

48÷ 8 =6

63 ÷ 7 =9

30 ÷ 3 =9

50 ÷ 5 =9

64 ÷ 8 =6

32 ÷ 8 =6

72 ÷ 9 =7

54 ÷ 9 =7

36 ÷ 9 =6

56 ÷ 7 =8

16 ÷ 8 =2

54 ÷ 9 =6

18 ÷ 9 =2

40 ÷ 4 =9

16 ÷ 2 =6

18 ÷ 9 =3

63 ÷ 9 = 11

40 ÷ 4 = 11

63 ÷ 9 =7

21 ÷ 7 =3

81 ÷ 9 =9

54 ÷ 9 =6

64 ÷ 8 =8

63 ÷ 7 =9

27 ÷ 9 =4

36 ÷ 4 =8

32 ÷ 4 =3

42 ÷ 6 =7

49 ÷ 7 =7

36 ÷ 9 =9

32 ÷ 8 =4

72 ÷ 8 =9

63 ÷ 7 =6

90 ÷ 9 = 10

24 ÷ 4 =7

54 ÷ 6 =9

30 ÷ 5 =6

36 ÷ 6 =6

35 ÷ 7 =5

24 ÷ 8 =3

80 ÷ 8 = 10

16 ÷ 4 =5

45 ÷ 9 =7

21 ÷ 7 =6

72 ÷ 9 =8

81 ÷ 9 =6

18 ÷ 9 =3

72 ÷ 9 =9

63 ÷ 9 =6

24 ÷ 4 =6

36 ÷ 9 =6

48 ÷ 6 =8

21 ÷ 7 =6

56 ÷ 8 =7

14 ÷ 2 =6

49 ÷ 7 =8

30 ÷ 3 =8

27 ÷ 3 =7

14 ÷ 7 =2

49 ÷ 7 =6

30 ÷ 6 =6

24 ÷ 3 =9

. te

$981

$366

$732

$649

$1298

$475

$950

5-day hire

7-day hire

Hiking gear for hire Gear

2-day hire

3-day hire

Waterproof jacket @ $3.55 per day

$7.10

$10.65

$17.75

$24.85

GPS tracker @ $8.60 per day

$17.20

$25.80

$43

$60.20

$9.90

$14.85

$24.75

$34.65

Tent @ $11.25 per day

$22.50

$33.75

$56.25

$78.75

Hiking boots @ $6.80 per day

$13.60

$20.40

$34

$47.60

m . u

Facts shape the world

36 ÷ 6 =7

$924

2. (a) Jake, Ben, Abbie, Suzie, Hugo (b) $566

Sleeping bag @ $4.95 per day

Divide and conquer!

20 days?

$462

24 ÷ 6 =5

Page 31

How much over … 5 days? 10 days?

Suzie earns $6.60 per hour and works for 7 hours each day

Jake earns $5.90 per hour and works for 11 hours each day

Teacher check Page 30

2 days?

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

The winner is B. Page 29

Rate and hours per day

ew i ev Pr

Teac he r

7 × 4 = 28

Everybody wants to work

2. (a) Waterproof jacket – yes, GPS tracker – yes (b) Waterproof jacket – $3.85, GPS tracker – $5.20 Page 34

Summer is here! – bring out the toys!

o c . che e r o t r s super 1.

Gear

2-hour hire

3-hour hire

45 ÷ 9 20 ÷ 10 =5 =3

Noodle lilo @ $4.55 per hour

$9.10

$13.65 $18.20 $26.70

42 ÷ 7 =6

36 ÷ 9 =4

8÷2 =6

Giant crocodile @ $3.60 per hour

$7.20

$10.80 $14.40 $28.80

28 ÷ 7 =4

32 ÷ 8 =5

45 ÷ 9 =6

35 ÷ 5 =6

56 ÷ 8 =7

40 ÷ 8 =6

27 ÷ 9 =3

24 ÷ 8 =4

20 ÷ 2 =7

63 ÷ 9 =8

28 ÷ 7 =6

64 ÷ 8 =6

34 ÷ 9 =5

18 ÷ 6 =3

48 ÷ 9 =6

16 ÷ 4 =5

28 ÷ 7 =6

40 ÷ 4 =8

10 ÷ 2 =6

45 ÷ 9 =5

32 ÷ 8 =5

28 ÷ 7 =6

28 ÷ 4 =7

63 ÷ 9 =9

42 ÷ 6 =6

18 ÷ 3 =6

27 ÷ 9 =4

45 ÷ 9 =6

81 ÷ 9 =8

Star boulevard

Giant inflatable seahorse @ $6.95 per hour

4-hour hire

All-day hire

$13.90 $20.85 $27.80 $34.75

Giant water pistols @ $2.85 per hour

$5.70

Noodle beanbags @ $5.80 per hour

$8.55

$11.40 $28.65

$11.60 $17.40 $23.20 $34.80

2.–3. Teacher check 4. $201.60 5. Teacher check

Teacher check

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

189

Answers

New Wave Number and Algebra Student Workbook

Car wash coffee

Job and pay rate Waiter/waitress @ $14.60 per hour

1.5 hours

2.5 hours

5.5 hours

$21.90

$36.50

$80.30

30 min

$7.30

$20.25

$33.75

$74.25

Dish washer @ $6.95 per hour

$3.48

$10.43

$17.38

$38.23

Car washer @ $12.90 per hour

$6.45

$19.35

$32.25

$70.95

28 ÷

Car vacuumer @ $15.80 per hour

$7.90

$23.70

$39.50

$86.90

Coffee barista @ $16.10 per hour

$8.05

$24.15

$40.25

$88.55

Cashier @ $12.70 per hour

$6.35

$19.05

$31.75

$69.85

Kitchen hand @ $11.60 per hour

$5.80

$17.40

$29

$63.80

$16.35

$27.25

$59.95

28 ÷

5 40 ÷

× 4 = 24

× 4 = 20

= 10

7×3=

× 5 = 20

16 ÷

18 ÷

4 6

× 10 = 20

16 ÷

10 × 7 =

= 10

× 10 = 100

× 8 = 88

36 ÷

× 10 = 0

× 9 = 90

× 9 = 45

× 10 = 90

32 ÷

× 9 = 63

× 9 = 81

54 ÷

99 ÷

× 9 = 36

9×7=

× 10 = 80

× 8 = 72

72 ÷

80 ÷

27 ÷

70 ÷

× 6 = 36

35 ÷

14 ÷

× 5 = 25

8×7=

21 ÷

63 ÷

× 10 = 70

×4=8

27 ÷

× 5 = 10

× 6 = 60

× 6 = 18

. te

54 ÷

8 42 ÷

× 5 = 40

× 4 = 32

6 5

15 ÷

× 5 = 35

35 ÷

8×3=

× 6 = 54

30 ÷

× 6 = 30

24 ÷

5×3=

× 9 = 81

24 ÷

16 ÷

× 6 = 24

× 5 = 15

12 ÷

7×7=

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

(b) $9.35

w ww

10 × 3 =

× 9 = 27

63 ÷

× 8 = 32

10 × 7 =

Teac he r

I know my 3s, 4s, 5s and 6s

4×3=

36 ÷

× 8 = 24

80 ÷

$5.45

ew i ev Pr

Page 36

72 ÷

$6.75

2. (a) $28.60

I know my 7s, 8s, 9s and 10s

8×7=

Table clearer @ $13.50 per hour

Drain clearer @ $10.90 per hour

190

Page 37

6×3=

F&D 1 Page 38

× 9 = 81

40 ÷

× 6 = 42

9×3=

21 ÷

×5=5

× 10 = 10

× 8 = 64

I just want my fair share

1. Name

Simplest fraction

$ of the prize they receive

⁄20

$15 000

⁄5

$20 000

⁄10

$30 000

⁄20

$5000

⁄10

$10 000

Fraction of ticket cost

$ spent on ticket

⁄20

$12

⁄20

$18

⁄20

o c . che e r o t r s super 18 ÷

× 6 = 48

9×7=

m . u

Page 35

Bill

Sandra

Jai

Kim

Ali

⁄20

Benny

⁄20

⁄10

$10 000

Guy

⁄20

$5000

Jack

⁄20

$5000

× 4 = 36

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

New Wave Number and Algebra Student Workbook

Name

Fraction of ticket cost

$ spent on ticket

⁄20

$3.75

Jai

⁄20

$3.75

Kim

⁄20

$3.75

Ali

⁄20

$3.75

Benny

⁄20

$3.75

Guy

⁄20

$37.50

Jack

$11.25

⁄20

$12 500

⁄20

$12 500

⁄2

$125 000

⁄20

$37 500

Teac he r ⁄2

⁄6

⁄2

⁄4

⁄5

⁄6

⁄8

⁄6

⁄5

⁄4

⁄10

⁄4

⁄3

⁄8

⁄4

⁄3

⁄6

⁄3

⁄6

⁄3

⁄2

⁄10

⁄6

7 3

Page 45

9 Prize-eating line

⁄3

⁄4

⁄6

⁄5

⁄6

⁄2

⁄3

⁄2

⁄8

1. 1

⁄4

⁄2 0

Andy

Bruce

⁄2

Callum

Dean

Eddie

Frankie

Gene

Hugo

⁄4

Ian

⁄4

Round 5 6

⁄2

⁄2 0

⁄4

⁄4 0

⁄3

⁄4

⁄6

⁄2 0

⁄4 0

⁄2

⁄4 0

⁄3

⁄4

⁄3

⁄2

⁄4 0

⁄2 0

⁄4 0

⁄2 0

⁄2

⁄4

⁄2 0

⁄2

⁄2 0

⁄2

⁄2 0

⁄4

Round 5 6 7

⁄2

⁄4

Andy

⁄6

Bruce

⁄2

⁄8

Callum

⁄4

⁄2

⁄4

⁄2

Dean

⁄2

⁄4

Eddie

⁄2

⁄4

Frankie

⁄8

Gene

Hugo

⁄4

Ian

⁄2

⁄4 0

⁄4

⁄4 or 31⁄4

⁄2

⁄2 0

⁄4 0

⁄2

⁄4 or 33⁄4

⁄4

Total game time

⁄2 0

⁄2

⁄4 0

⁄4

⁄2

⁄4

⁄8

⁄2 0

⁄4 0

⁄4

⁄4 0

⁄4

⁄2 0

⁄4

Who played the most footy?

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

⁄10

⁄4 or 31⁄4

⁄4

⁄4 or 21⁄4

⁄2 0

⁄4

⁄4 0

⁄4 or 3

⁄2 0

⁄4 or 23⁄4

⁄4 or 3

⁄4 or 31⁄4

⁄2

Total game time

⁄2

⁄4

33⁄4

⁄4

⁄2

⁄4

41⁄4

⁄4

31⁄4

⁄4 or 31⁄4

⁄2

⁄2 0

⁄4

⁄2

⁄4

⁄2

⁄4

⁄2

⁄4 0

⁄4

⁄2

⁄4

⁄2 0

⁄4

⁄2

⁄2 0

⁄2

⁄2 0

⁄2

⁄4

⁄2

⁄3

⁄4

⁄3

⁄4

⁄2

⁄4

⁄8

⁄4

⁄3

⁄6

⁄3

⁄6

⁄8

⁄6

⁄3

⁄6

⁄2

⁄3

⁄4

⁄6

⁄2

⁄6

⁄10

⁄4

⁄6

⁄4

⁄10

⁄4

⁄2

⁄6

⁄5

⁄6

⁄3

⁄6

⁄2

⁄6

⁄8

⁄3

⁄4

⁄8

Page 46

More than one way to name a fraction

w ww

1. 2⁄6 or 1⁄3 4. 4⁄12 or 1⁄3

2. 5.

⁄12 or ½ 3 ⁄9 or 1⁄3 6

. te

3. 6.

⁄8 or ¼ 4 ⁄10 or 2⁄5

⁄3, 8⁄12 or 2⁄3 1 6 ⁄3, ⁄12 or 1⁄2 1 8 ⁄3, ⁄12 or 2⁄3 1 10 ⁄6, ⁄12 or 5⁄6 1

⁄3, 8⁄12 or 2⁄3 ⁄3, 4⁄12 or 1⁄3 3 2 ⁄5, ⁄5

1 2

⁄2 0

⁄4

⁄2

⁄4

⁄4 0

You ate what? Week Week Week Week 1 2 3 4

⁄5

Albert

Bennie

Callum

Dana

Edwina

Freddie

Georgie

Harry

India

Jenni

Kyle

Luc

Minnie

Nara

⁄5

Pizza, pizza and the great quarter eat-off!

⁄5

Table 2 Table 4 Table 6 Table 8 Table 10

= 18⁄4, 41⁄2 pizzas = 10⁄4, 21⁄2 pizzas = 11⁄4, 23⁄4 pizzas = 16⁄4, 4 pizzas = 9⁄4, 21⁄4 pizzas

⁄5

Total

⁄5

o c . che e r o t r s super (b) 1⁄4, 3⁄4 2 ⁄4 or 1⁄2, 2⁄4 or 1⁄2 3 1 ⁄4, ⁄4 (d) 3⁄8, 5⁄8 5 3 ⁄8, ⁄8 4 ⁄8 or 1⁄2, 4⁄8 or 1⁄2 6 ⁄8 or 3⁄4, 2⁄8 or 1⁄4 2 ⁄5, 3⁄5

F&D 2

= 11⁄4, 23⁄4 pizzas = 10⁄4, 21⁄2 pizzas = 17⁄4, 41⁄4 pizzas = 12⁄4, 3 pizzas = 15⁄4, 33⁄4 pizzas

Two sides to each fraction

1. (a) 4⁄12 or 6 ⁄12 or 4 ⁄12 or (c) 2⁄12 or 5 ⁄12, 7⁄12 4 ⁄12 or 8 ⁄12 or (e) 4⁄5, 1⁄5

Table 1 Table 3 Table 5 Table 7 Table 9

1, 6

⁄3

Page 42

Page 44

3, 4

ew i ev Pr

⁄6

Page 43

⁄20

It’s an equivalence grid

$12 500

Use your new fraction wall

⁄20

Build your own word wall

⁄3

$12 500

⁄20

Sandra

⁄4

$12 500

Page 41

⁄20

$7.50

Teacher check

$25 000

⁄20

Page 40

⁄10

Teacher check

$ of the prize they receive

Bill

Page 39

Simplest fraction

m . u

⁄5 = 9 bars 3 pieces

⁄5 = 5 bars 1 piece

⁄5 = 5 bars 2 pieces ⁄5 = 3 bars 3 pieces

⁄5 = 4 bars 3 pieces ⁄5 = 6 bars 3 pieces ⁄5 = 4 bars 2 pieces

⁄5 = 5 bars 2 pieces ⁄5 = 4 bars 4 pieces

⁄5 = 4 bars 3 pieces ⁄5 = 5 bars 3 pieces ⁄5 = 5 bars 2 pieces

⁄5 = 5 bars

⁄5 = 7 bars 2 pieces

2. Albert, Nara, Freddie 3. Dana, Georgie, Luc 4. Minnie

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

191

Answers

New Wave Number and Algebra Student Workbook

Page 47

A new type of dominoes

⁄4

⁄3

13⁄4

⁄4 or 21⁄2

⁄6

⁄4

31⁄2

4 ⁄4 1

⁄2

⁄4

⁄4 or 5 ⁄2 1

⁄4

⁄8 or 11⁄2 13⁄4

2 ⁄4

⁄6

⁄4

⁄3

Country

Time — seconds

1st

Kenya

43.08

2nd

South Africa

43.12

3rd

Australia

43.16

4th

Germany

43.57

5th

USA

43.87

6th

Italy

44.07

7th

England

44.12

8th

Iceland

44.17

9th

China

45.07

10th

France

46.53

r o e t s Bo r e p ok u S ⁄3

⁄6

⁄4

12⁄4

⁄6 or 41⁄6

13⁄4

21⁄4

⁄4

⁄3

Page 51

⁄4 or 2 ⁄2

⁄6

21⁄3

⁄6

2 ⁄6 5

That’s egg stealing

(b) 80⁄115 1. (a) 35⁄115 2. (a) 22⁄88 or 11⁄44 or 1⁄4 (c) Teacher check 3. (a) 26⁄104 or 13⁄52 or ¼ (c) Teacher check 4. (a) 29⁄87 (b) 58⁄87

⁄3

3 ⁄6

Page 48

25⁄6

⁄8

⁄3

⁄6

⁄8

4 ⁄3

42⁄3

⁄6

⁄3

Position

The great radio dial

FM position

Station

State

Heart

TAS

SA FM

Nova

QLD

Frequency

107.3

ew i ev Pr

Teac he r

34⁄6

32⁄3

⁄3

21⁄3

⁄8

⁄4

22⁄3

⁄3

31⁄3

43⁄4

11⁄6

31⁄2

⁄6

107.1 106.9

B105

QLD

Triple M

VIC

105.3

2Day FM

NSW

4MBS

QLD

WA FM

4ZZZ

QLD

Fox

VIC

101.9

7HO

TAS

101.7

WS FM

NSW

101.7

Sea FM

TAS

100.9

WOW FM

100.5

Power FM

100.3

SBS

The Edge

NSW

Mix

Bay

VIC

Nova

Triple J

TAS

92.9

Fresh FM

92.7

Smooth

VIC

91.5

2RRR

NSW

88.5

105.1

104.1

103.7 102.3

F&D 3 Page 50 1.

192

⁄104 or 36⁄52 or 3⁄4

Mixed numbers ⁄4 = 21⁄4 11 ⁄2 = 51⁄2 2 5 ⁄3 = 17⁄3 19 ⁄3 = 61⁄3 9

w ww

32⁄5 = 17⁄5 10 ⁄3 = 31⁄3 3 3 ⁄4 = 15⁄4 17 ⁄4 = 41⁄4

. te

The real champions

Position

Country

⁄5 = 22⁄5 21 ⁄5 – 41⁄5 1 7 ⁄2 = 15⁄2 16 ⁄2 = 8 12

m . u

Page 49

(b)

102.1

96.9

96.1

94.5

93.9

o c . che e r o t r s super

Distance — metres

1st

Kenya

8.23 m

2nd

South Africa

8.12 m

3rd

Italy

8.07 m

4th

Australia

7.36 m

5th

England

7.15 m

6th

France

6.58 m

7th

China

5.37 m

8th

USA

4.67 m

9th

Germany

4.55 m

10th

Iceland

4.17 m

Page 52

93.7

1st, 2nd, 3rd – can you do it?

1.11, 1.1, 1.01 11.01, 11.0, 10.11 3.33, 3.3, 3.03 15.5, 15.1, 15.01 6.61, 6.16, 6.06 20.2, 20.11, 20.02 21.21, 21.11, 21.01

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

8.7, 8.17, 8.07 13.3, 13.11, 13.03 4.44, 4.41, 4.04 9.99, 9.1, 9.09 18.81, 18.8, 18.08 11.21, 11.11, 11.1 4.45, 4.44, 4.04

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

Answers

New Wave Number and Algebra Student Workbook

Page 53

Page 59

Welcome to Flagtopia

Teacher check Page 54

The totals

Rounded off to the nearest 5c

Change from $20

Change from $50

$8.82

$8.80

$11.20

$41.20

$11.97

$11.95

$8.05

$38.05

$18.03

$18.05

$1.95

$31.95

$9.09

$9.10

$10.90

$40.90

$14.44

$14.45

$5.55

$35.55

$17.11

$17.10

$2.90

$32.90

$4.66

$4.65

$15.35

$45.35

$19.11

$19.10

$0.90

$30.90

$13.54

$13.55

$6.45

$36.45

$16.08

$16.10

$3.90

$33.90

$4.87

$4.85

$15.15

$45.15

$10.19

$10.20

$9.80

$39.80

How much is shaded?

⁄100, 47% ⁄100, 33% 8 ⁄100, 8% 61 ⁄100, 61%

⁄100, 73% ⁄100, 90% 82 ⁄100, 82% 28 ⁄100, 28%

⁄100, 60% ⁄100, 15% 55 ⁄100, 55% 67 ⁄100, 67%

M&FM 1

Teac he r

1. (a) $2.05 (b) $50 using 4 notes = $20, $10, $10, $10 $50 using 5 notes = $10, $10, $10, $10, $10 $50 using 6 notes = $10, $10, $10, $10, $5, $5 $50 using 3 notes = $20, $20, $10 2. (a) $2.85 (b) $25 using 5 notes = $5, $5, $5, $5, $5 $25 using 7 notes and/or coins = $5, $5, $5, $5, $2, $2, $1 $25 using 6 notes and/or coins = $20, $1, $1, $1, $1, $1 $25 using 3 notes = $10, $10, $5

Page 56 (a)

Page 60 Item bought

Sausages, sausages and more sausages!

ew i ev Pr

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

Coins, notes and change

Supermarket round up – Bring your cash! Cost

To nearest 5c

Change from $10

Change from $20

Sausages ’R’ Us

Deal 1

Deal 4

Deal 7

8 kilos of sausages at a price of $32.

10 kilos of sausages at a price of $55.

7 kilos of sausages at a price of $35.

Price per kilo

$5.50

Deal 2

Deal 5

Deal 8

5 kilos of sausages at a price of $15.

12 kilos of sausages at a price of $30.

Price per kilo

$15

Change from $50

Biscuits

$4.99

$45

Carrots

$0.88

$0.90

$9.10

$19.10 $49.10

Milk

$2.35

$7.65

$17.65 $47.65

Crackers

$2.93

$2.95

$7.05

$17.05 $47.05

Pumpkin

$3.69

$3.70

$6.30

$16.30 $46.30

Fruit salad

$4.54

$4.55

$5.45

$15.45 $45.45

Toothpaste

$2.12

$2.10

$7.90

$17.90 $47.90

Jelly

$3.07

$3.05

$6.95

$16.95 $46.95

Ice-cream

$9.99

$10

Broccoli

$1.59

$1.60

$8.40

$18.40 $48.40

w ww

Sam’s Sausages

m . u

Page 55

Round off and change too!

3 kilos of sausages at a price of $18.

$2.50

Deal 3

Deal 6

Deal 9

6 kilos of sausages at a price of $24

10 kilos of sausages at a price of $35.

10 kilos of sausages at a price of $65.

Chops

$5.05

$4.95

$14.95 $44.95

Chocolate

$3.26

$3.25

$6.75

$16.75 $46.75

Price per kilo

Muesli

$2.99

$3.50

$6.50

Chips

$3.12

$3.10

$6.90

$16.90 $46.90

Sauce

$4.47

$4.45

$5.55

$15.55 $45.55

. te

o c . che e r o t r s super

(b) Top three deals are Deal 8, Deal 2 and Deal 6 Page 57

$10

$17

$40

$47

$100 a day – where can I go?

Teacher check Page 58

The great Cheesy Puff investigation

1. Deal 1 = 27c Deal 2 = 14c Deal 3 = 30c Deal 4 = 13c

2. Deal 4 Deal 2 Deal 1 Deal 3

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

193

Answers

New Wave Number and Algebra Student Workbook

Page 63

P&A 1

29 225

China

114 54

23 191

Great Britain

Russia

South Korea

Germany

The Bullants

The Vampires

—

The Shuttles

The Geese

r o e t s Bo r e p ok u S 19 140

The Lunar Landers

—

32 156

The Containers

The Wombats

The Bellbirds

Hungary

Australia

China Germany South Korea Hungary

—

The Cygnets

The Bullants

The Vampires

The Shuttles

The Geese

The Lunar Landers

—

The Containers

The Wombats The Bellbirds

Club

3. Russia 6. France

Total score

Drop goal

Penalty goal

Converted goal

Try

Italy

ew i ev Pr

The 2020 Olympics – I see all!

Silver medals

Bronze medals

Total medal points

Tajikistan

Morocco

Kuwait

Saudi Arabia

Hong Kong, China

Bahrain

w ww

Gold medals

. te 7

Page 64 1.

Aussie rules scoreboard Club

Goals

Behinds Total score

m . u

Page 62

Afghanistan

2. 5. 8. 10.

USA Great Britain Australia Italy

France

2. 1. 4. 7. 9.

Total score

138 58

Drop goal

104

Penalty goal

Gold medal points

Converted goal

Medal total

The Cygnets

Club

Total medal points

Bronze medals

Silver medal points

Silver medals

United States of America

Teac he r

Gold medals

Try

The real value of medals Bronze medal points

Page 61

Which rugby rules?

The Unicorns

The Helicopters

The Planets

The Beasts

The Fighters

110

The Screamers

126

The Machines

139

The Falcons

The Tornadoes

The Bellringers

117

o c . che e r o t r s super 12

Singapore

Qatar

Moldova

Greece

Portugal

Montenegro

Guatemala

Gabon

2. Teacher check

194

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

New Wave Number and Algebra Student Workbook

Club

Goals

The Unicorns

The Helicopters

The Planets

The Beasts

The Fighters

The Screamers

The Machines

The Falcons

The Tornadoes

The Bellringers

Page 65

(f ) 63, 65 – pattern is –10, –9, so number must be 63 (g) 150, 160 – pattern is +4, so number must be 159 (h) 234, 238 – pattern is –10, –9, –8, –7, –6, –5, –4, so number must be 237 (i) 361, 251 – pattern is –10, so number must be 351 (j) 67, 77 – pattern is +7, +6, so number must be 88

Behinds Total score

P&A 2 Page 67

Polo Paints

Fluoro Flash Paints

Waterless Colours

Albright Paints

$30 for 12 colours

$60 for 12 colours

$39.60 for 12 colours

$52.80 for 12 colours

1 colour is

$2.50

$5.00

$3.30

$4.40

Spilt Paints

Wet Paints

Magenta Moods

Cyan Colours

$37.20 for 12 colours

$33.60 for 12 colours

$74.40 for 12 colours

$44.40 for 12 colours

1 colour is

$3.10

$2.80

$6.20

$3.70

Perfect Paints

Slowdry Paints

Universal Colours

Animal Colours

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

In a league of their own Conversion

Penalty goal

Field goal

Total score

The Sirens

The Battering Rams

The Vipers

—

$46.80 for 12 colours

$73.20 for 12 colours

$45.60 for 12 colours

$35.40 for 12 colours

The Seagulls

1 colour is

Club

ew i ev Pr

Try

Teac he r

Paints for painting

$3.90

$6.10

$3.80

$2.95

The Lucky Legends

—

The Caribs

Wayout Paints

Dipping Paints

Rainbow Colours

Zebra Paints

The Whirlwinds

$36 for 12 colours

$50.40 for 12 colours

$42 for 12 colours

$32.40 for 12 colours

The Bombshells

1 colour is

$3.00

$4.20

$3.50

$2.70

Conversion

Penalty goal

Field goal

Total score

The Globals

. te 7

The Battering Rams

The Vipers

The Seagulls

2. Magenta Moods, Slowdry Paints, Fluoro Flash Paints Albright Paints 3. Polo Paints, Zebra Paints, Wet Paints, Animal Colours Page 68

m . u

w ww Club

The Sirens

Try

Your name in gold

o c . che e r o t r s super 1.

Number Total Cost of … of cost of letters vowels consonants name

—

Ryan Napolean

$375

$385

$760

Ashleigh Brennan

$375

$550

$925

Athlete’s name

The Globals

The Lucky Legends

—

Casey Eastham

$375

$385

$760

The Caribs

Jamie Dwyer

$300

$330

$630

The Whirlwinds

Anna Mears

$300

$275

$575

The Bombshells

—

Emily Seebohm

$375

$385

$760

Lauren Jackson

$375

$440

$815

$300

$275

$575

$525

$605

$1130

Page 66 1. (a) (b) (c) (d) (e)

Not these two—but why? 22, 25 – pattern is +3, +2, so number must be 24 66, 65 – pattern is +5, +10, so number must be 68 156, 155 – pattern is +10, so number must be 151 77, 67 – pattern is +4, +3, so number must be 68 22, 24 – pattern is double the previous number, so number must be 32

Joe Ingles Matthew Dellavedova

2. Teacher check

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

195

Answers Whose stable is the most stable?

(a)

Trainer Fred Shackles

Day 1 Day 2 Day 3 52 horseshoes 68 horseshoes 48 horseshoes

Ted Horsefield

Page 70

horses horses horses 40 horseshoes 76 horseshoes 20 horseshoes horses horses horses 68 horseshoes 16 horseshoes 76 horseshoes horses horses horses 60 horseshoes 36 horseshoes 44 horseshoes horses 36 horseshoes

horses 4 horseshoes

horses 64 horseshoes

Page 72

Now it’s your turn

Answers will vary – teacher check 4 × 24 = 96 15 × 3 = 45 16 × 4 = 64 64 ÷ 8 = 8 36 ÷ 6 = 6 7 × 8 = 56 36 ÷ 3 = 12

P&A 3 Page 72

54÷ 9 = 6 88 ÷ 8 = 11 6 × 20 = 120

Balance the scales

1. (a)

13+

= 29 – 4

(b)

79 –

(c)

58 –

= 16 + 16

(d)

66 +

(e)

34 +

= 99 – 47

(f )

(g)

66 +

= 27 +59

(h)

91 –

(i)

110 –

(j)

101 +

(k)

55 –

(l)

72 –

= 26 + 17

(n)

66 +

= 99 + 13

(p)

41 + 33 = 101 –

horses 8 horseshoes

(2 × 2) + (4 × 8) + (6 × 8) = 84 legs (4 × 2) + (2 × 8) + (3 × 8) + (5 × 8) = 88 legs (2 × 2) + (2 × 4) + (5 × 8) + (2 × 8) = 68 legs (3 × 2) + (6 × 8) + (2 × 8) = 70 legs (8 × 2) + (3 × 8) + (10 × 8) = 120 legs (5 × 2) + (4 × 6) + (2 × 8) + (12 × 8) = 146 legs (10 × 2) + (6 × 6) + (2 × 8) + (3 × 8) = 96 legs (3 × 2) + (4 × 6) + (6 × 8) = 78 legs (5 × 2) + (2 × 8) + (3 × 8) + (5 × 8) = 90 legs (2 × 4) + (3 × 2) + (6 × 6) + (3 × 8) = 74 legs (1 × 2) + (9 × 8) + (6 × 6) = 110 legs (11 × 2) + (8 × 8) + (6 × 6) + (3 × 4) = 134 legs

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

horses horses horses 72 horseshoes 28 horseshoes 80 horseshoes

Teac he r

Lionel Mare

horses

horses horses 64 horseshoes 80 horseshoes horses

Cup day word problems 12 × 4 = 48 legs 64 ÷ 4 = 16 waiters 12 × 5 = $60 tip 12 × 3 = 36 glasses $108 ÷ 12 = $9 per diner 12 × 6 = 72 meals 126 ÷ 2 = 63 waiters 72 × 9 = 648 meals per tent 3 × $22.50 = $67.50 each 108 ÷ 9 = 12 bottles 117 ÷ 9 = 13 hot dogs 12 × 6 = 72 pieces of cutlery

w ww

196

horses horses horses 56 horseshoes 40 horseshoes 72 horseshoes

Miles Footlock

1. (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) (k) (l)

It’s about legs!

ew i ev Pr

Karen Course

horses horses horses 56 horseshoes 12 horseshoes 52 horseshoes

Ian Equine

Jenny Stall

horses horses horses 32 horseshoes 36 horseshoes 48 horseshoes

Thomas Track

Peter Miles

(b)

Total Trainer horses ranking

horses horses horses 36 horseshoes 24 horseshoes 44 horseshoes

Frank Furlong

Ron Stayer

Page 71

. te

horses

20 16

(m) 81 – 17 (o)

= 57 + 33 = 4 + 35 = 45 + 19

89 + 7 = 55 +

41 25

o c . che e r o t r s super (q)

13 + 29 = 67 –

(s)

71 +

(u)

26 + 33 = 48 +

= 66 + 12

= 23 + 45

= 100 – 28

+ 22 = 11 + 39

= 33 + 48

= 77 +44

m . u

Page 69

New Wave Number and Algebra Student Workbook

(r)

51 – 18 = 7 +

(t)

50 +

= 120 – 58

2. Teacher check

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

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

Answers

New Wave Number and Algebra Student Workbook

Page 74

Page 77

I sense a number and it is …

When a number is added to 32, the answer is the same as 65 minus 14.

When a number is subtracted from 88, the answer is the same as 29 plus 14.

When a number is added to 49, the answer is the same as 99 minus 12.

The number is

Are all the pairs equal? I don’t think so!

= coloured green

≠ coloured red

16 + 39

≠

22 + 34

20 + 18

16 + 22

33 + 39

≠

22 + 48

When a number is subtracted from 78, the answer is the same as 36 plus 8.

When a number is added to 83, the answer is the same as 122 minus 9.

When a number is subtracted from 64, the answer is the same as 17 plus 7.

25 + 36

≠

44 + 19

9 + 44

≠

12 + 44

39 + 45

22 + 62

37 + 29

≠

18 + 64

The number is

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

When a number is subtracted from 63, the answer is the same as 11 plus 22.

When a number is added to 57, the answer is the same as 120 minus 25.

24 + 38

≠

32 + 56

21 + 41

≠

17 + 41

52 + 30

26 + 56

21 + 17

≠

9 + 34

34 + 18

25 + 27

16 + 41

≠

22 + 36

49 + 32

≠

43 + 29

28 + 69

≠

55 + 31

The number is

When a number is added to 54, the answer is the same as 85 minus 11.

When a number is subtracted from 77, the answer is the same as 32 plus 8.

Teac he r

When a number is subtracted from 97, the answer is the same as 41 plus 12. The number is

When a number is added to 21, the answer is the same as 52 minus 14. The number is

1. (a) 31 (e) 15 (i) 19

When a number is subtracted from 62, the answer is the same as 33 plus 7. The number is

The number is

When a number is added to 49, the answer is the same as 105 minus 24. The number is

Page 78 1. (a) 11 (e) 37

It’s a balancing act (b) 55 (f ) 41

(d) 18 (h) 50

Page 76

(b) 7 (f ) 17 (j) 28

(d) 16 (h) 34 (l) 37

I seek a draw – the perfect cricket scores (b) 328 (f ) 181 (j) 274

w ww

1. (a) 265 (e) 324 (i) 358

Balance scale word problems – who am I?

. te

(d) 144 (h) 264 (l) 299

m . u

Page 75

The number is

ew i ev Pr

When a number is added to 29, the answer is the same as 71 minus 15.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Number and Algebra (Year 4)

R.I.C. Publications®

www.ricpublications.com.au

197