Australian Curriculum Mathematics - Measurement and Geometry: Year 3 - Ages 8-9

RIC-6096 4.3/946

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) Published by R.I.C. Publications® 2013 Copyright© Linda Marshall 2013 ISBN 978-1-921750-93-9 RIC– 6096

Titles in this series:

A number of pages in this book are worksheets.

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All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2013.

For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum.

Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors.

Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject.

You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Foundation) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 1) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6)

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

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: MEASUREMENT AND GEOMETRY (YEAR 3) Foreword

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

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the measurement and geometry 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.

Format of this book ................................................. iv – v Using units of measurement .................................... 2–29 • UUM – 1

Location and transformation .................................. 46–71 • L&T – 1

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

Create and interpret simple grid maps to show position and pathways (ACMMG065)

– – – – – –

– – – – – –

Teacher information ............................................................................... 2–4 Hands-on activities ................................................................................. 5–7 Links to other curriculum areas ................................................................... 8 Resource sheets .................................................................................... 9–12 Assessment ........................................................................................ 13–14 Checklist ................................................................................................... 15

Teacher information .................................................................................. 46 Hands-on activities ............................................................................. 47–48 Links to other curriculum areas .................................................................. 49 Resource sheets .................................................................................. 50–56 Assessment ........................................................................................ 57–58 Checklist .................................................................................................... 59

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C.Publ i cat i ons f orr evi ew pur p esonl y• • L&To – 2s • UUM – 2 • Teacher information ........................................................................... 16–17 Hands-on activities ................................................................................... 18 Links to other curriculum areas ................................................................. 19 Resource sheets .................................................................................. 20–25 Assessment ........................................................................................ 26–27 Checklist ................................................................................................... 28

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– – – – – –

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Answers .................................................................................. 29

– – – – – –

Teacher information .................................................................................. 60 Hands-on activities .................................................................................... 61 Links to other curriculum areas .................................................................. 62 Resource sheets .................................................................................. 53–67 Assessment ........................................................................................ 68–69 Checklist .................................................................................................... 70

Answers .................................................................................. 71

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Shape .................................................................... 30–45 • Shape – 1 Make models of three-dimensional objects and describe key features (ACMMG063) – – – – – –

Identify symmetry in the environment (ACMMG066)

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Tell time to the minute and investigate the relationship between units of time (ACMMG062)

Teacher information ........................................................................... 30–31 Hands-on activities ................................................................................... 32 Links to other curriculum areas ................................................................. 33 Resource sheets .................................................................................. 34–39 Assessment ........................................................................................ 40–43 Checklist ................................................................................................... 44

Answers .................................................................................. 45

Geometric reasoning .............................................. 72–82 • GR – 1

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) – – – – – –

Teacher information ........................................................................... 72–73 Hands-on activities ............................................................................. 74–75 Links to other curriculum areas .................................................................. 76 Resource sheets .................................................................................. 77–78 Assessment ........................................................................................ 79–80 Checklist .................................................................................................... 81

Answers .................................................................................. 82

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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FORMAT OF THIS BOOK This teacher resource book includes supporting materials for teaching and learning in all sections of the Measurement and Geometry content strand of Australian Curriculum Mathematics. It includes activities relating to all sub-strands: Using units of measurement, Shape, Location and transformation, and Geometric reasoning. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the proficiency strands have also been included.

Each section supports a specific content description and follows a consistent format, containing the following information over several pages: • teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for • hands-on activities • links to other curriculum areas

• resource sheets • assessment sheets.

• a checklist

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Answers relating to the resource and assessment pages are included on the final page of the section for each sub-strand (Using units of measurement, Shape, Location and transformation, and Geometric reasoning).

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The length of each content description section varies.

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

Sub-strand: Location and transformation— L&T – 1

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.

Create and interpret simple grid maps to show position and pathways (ACMMG065)

RELATED TERMS

TEACHER INFORMATION

Grid maps

What this means

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t 4UVEFOUT DSFBUF TJNQMF HSJE NBQT PG GBNJMJBS QMBDFT F H UIF DMBTTSPPN PS UIF TDIPPM HSPVOET TIPXJOH SFMBUJWF QPTJUJPO PG JUFNT 1SPQPSUJPOBM TDBMF JT OPU FYQFDUFE BU UIJT ZFBS MFWFM UIPVHI TPNF JOUVJUJWF TDBMF NBZ CF FWJEFOU JO TUVEFOUT’ ESBXO NBQT 5IF JEFB PG TDBMF NBZ CF IJHIMJHIUFE CZ BQQSPQSJBUF RVFTUJPOT TVDI BT A*G UIF UFBDIFS’T EFTL UBLFT VQ UIJT NVDI SPPN PO UIF DMBTTSPPN NBQ IPX CJH EP ZPV UIJOL ZPVS EFTL XPVME CF ’

Position

t #FJOH BCMF UP VTF TJNQMF DPPSEJOBUFT GPS EFUFSNJOJOH UIF QPTJUJPO PG BO JUFN PO B HSJE.

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

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C.Publ i cat i ons Teaching points provides a listn of the main teaching •f owhich rr evi ew pur poseso l y • Student vocabulary includes words points relating to the content t TIF MPDBUJPO PG B QMBDF PO UIF NBQ *U NBZ CF EFTDSJCFE BDDPSEJOH UP JUT rFMBUJWF QPTJUJPO UP BOPUIFS QMBDF PS VTJOH DPPSEJOBUFs.

t 4UVEFOUT CFJOH BCMF UP HJWF BOE SFDFJWF EJSFDUJPOT UP EFUFSNJOF MPDBUJPO PS UP HJWF BOE PS GPMMPX EJSFDUJPOT UP NBLF B QBSUJDVMBS DPOTUSVDUJPO

Pathway

Teaching points

t TIF QBUI PS SPVUF VTFE UP HFU GSPN POF QPTJUJPO PO B NBQ UP BOPUIFS.

t TFBDIFS NPEFMT UIF VTF PG BQQSPQSJBUF MBOHVBHF PG MPDBUJPO e.H OPSUI TPVUI FBTU XFTU MFGU SJHIU DMPDLXJTF BOUJDMPDLXJTF CFUXFFO

Coordinates (Cartesian coordinates)

2

t /BUJPOBM UFTUT VTVBMMZ DPOUBJO BU MFBTU POF RVFTUJPO UIBU JOWPMWFT SFBEJOH DPPSEJOBUFs.

west

left

east

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over turn

paces

steps

C

D

E

t 4UVEFOUT XIP DPOGVTF UIF UFSNT MFGU BOE SJHIU BOE DMPDLXJTF BOE BOUJDMPDLXJTF.

right

t 4UVEFOUT XIP BSF OPU GBNJMJBS XJUI EJSFDUJPOT GPS TJNQMF EJTUBODFT e.H GBDF FBTU BOE UBLF UXP TUFQT GPSXBSE UIFO UVSO RVBSUFS PG B UVSO DMPDLXJTF.

forward

under

B

t Students’ VTF PG BQQSPQSJBUF JDPOT UP SFQSFTFOU JUFNT PO NBQT UIFZ IBWF DSFBUFE

north

backwards

A

t 4UVEFOUT XIP BSF OPU BCMF UP HJWF BOE PS GPMMPX EJSFDUJPOT XIFO VTJOH B TJNQMF NBQ.

clockwise

anticlockwise

description.

1

What to look for

Student vocabulary coordinates south

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t 4UVEFOUT XIP XIFO VTJOH DPPSEJOBUFT GPS HSJE SFGFSFODFT VTF UIF WFSUJDBM y BYJT Ăś STU GPMMPXFE CZ UIF IPSJ[POUBM x BYJT JOTUFBE PG UIF PUIFS XBZ BSPVOE. t 4UVEFOUT XIP MBCFM UIF BYJT XJUI UIF [FSP JO UIF JODPSSFDU QMBDe.

Note *O "VTUSBMJB we VTF UIF UFSN ‘aOUJDMPDLXJTF SBUIFS UIBO UIF "NFSJDBO FRVJWBMFOU ADPVOUFSDMPDLXJTF’.

46

Proficiency strand(s): Understanding

Problem solving

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

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

t 4UVEFOUT OFFE UP CF BCMF UP DSFBUF BOE EFTDSJCF EJSFDUJPOT BT XFMM BT JOUFSQSFU UIPTF NBEF CZ PUIFST.

t " QBJS PG OVNCFST PS TZNCPMT UIBU reprFTFOU B QPTJUJPO PO B HSJE 6OEFSTUBOEJOH UIF DPODFQU PG OBNJOH DPPSEJOBUFT JT FTTFOUJBM JO MBUFS ZFBST XIFO VTJOH B HSJE XJUI OFHBUJWF DPPSEJOBUFT BOE UXP PS GPVS RVBESBOUT PS XIFO HSBQIJOH GVODUJPOT JO BMHFCSB BOE USJHPOPNFUSZ #FJOH BCMF UP SFBE rPBE BOE PUIFS NBQT SFMJFT PO BO VOEFSTUBOEJOH PG DPPSEJOBUFs.

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

o c . che e r o t r s super Sub-strand: Location and transformation— L&T– 1

HANDS–ON ACTIVITIES

t 1MBZ UIF Grid moves game )BWF POF Y TRVBSF HSJE GPS FBDI HSPVQ PG PS TUVEFOUT TFF QBHF &BDI TUVEFOU IBT B UPLFO PS DPVOUFS XIJDI UIFZ QMBDF PO B TRVBSF PG UIFJS DIPJDF JO UIF HSJE 5IFZ UBLF UVSOT UP TFMFDU B DBSE GSPN UIF QBDL PG EFTDSJQUPS DBSET TFF QBHF PS UFBDIFS BOE PS TUVEFOUT DSFBUF UIFJS PXO DBSET UIBU BSF GBDF EPXO CFUXFFO UIFN BOE GPMMPX UIF JOTUSVDUJPOT *G UIFJS NPWF UBLFT UIFN Pò UIF HSJE UIFZ BSF ‘PVU’. 5IF MBTU QMBZFS PO UIF HSJE JT UIF XJOOFS *O UIF HSJE CFMPX JG UIF JOTUSVDUJPOT XFSF ‘Move 2 squares to the left and up 3 squares’ BOE JU XBT UIFJS UVSO 1MBZFST PS XPVME CF PVU 1MBZFST BOE DPVME NBLF UIJT NPWF " GBTUFS BMUFSOBUJWF WFSTJPO PG UIJT HBNF JT UIBU all students GPMMPX UIF EFTDSJQUPS DBSET OP NBUUFS XIP UVSOFE JU PWFS

1

4

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.

2

3

t 4UVEFOUT NBLF UIFJS PXO Y HSJET BOE BJN UP Ü OE EJò FSFOU XBZT UP HFU BSPVOE UIF HSJE XJUIPVU DSPTTJOH UIFJS PXO MJOFT 5IFSF BSF NBOZ NPSF BMUFSOBUJWFT UIBO UIF UISFF TIPXO CFMPX

t 4UVEFOUT ESBX B QMBO CJSE T FZF WJFX PG UIF DMBTTSPPN JEFOUJGZJOH UIF LFZ QJFDFT PG GVSOJUVSF %JTDVTT XBZT UP NBSL UIF WBSJPVT PCKFDUT VTJOH JDPOT PS B LFZ "TL RVFTUJPOT BCPVU SFMBUJWF TJ[FT 'PS FYBNQMF Is the bookcase bigger or smaller than the easel? How much bigger is the teacher’s desk than any of the other desks? t 4UVEFOUT SF EP UIF DMBTT NBQ BT BCPWF CVU XJUI DIBOHFT UP CF NBEF GPS SFBSSBOHJOH UIF GVSOJUVSF UP IBWF B DMBTT QBSUZ PS UP JOWJUF HVFTUT JO GPS B DMBTT QMBZ 'PS B DMBTT QMBZ PS TJNJMBS TUVEFOUT XPVME OFFE UP UIJOL BCPVU XIFSF UIF TVSQMVT GVSOJUVSF XPVME CF QVU XIFSF B TUBHF XPVME HP BOE IPX QFPQMF XPVME CF BCMF UP NPWF JO PVU BOE BSPVOE UIF SPPN 'PS B DMBTT QBSUZ DPOTJEFSBUJPO XPVME CF HJWFO GPS BDDFTTJOH UIF UBCMFT XJUI GPPE BOE ESJOLT XIFUIFS UIF TUVEFOUT XPVME TJU BGUFS DPMMFDUJOH UIFJS GPPE BOE JG TP XIFSF UIF DIBJST XPVME HP. t 0ODF UIF TUVEFOUT IBWF IBE QSBDUJDF BU ESBXJOH NBQT TVDI BT UIPTF BCPWF UIF DPODFQU PG HSJE MJOFT DPVME CF JOUSPEVDFE 5IJT DPVME CF EPOF JOJUJBMMZ CZ BEEJOH UIF MJOFT BGUFS UIF NBQ IBT CFFO ESBXO -BUFS TUVEFOUT DPVME VTF DN HSJE QBQFS PO XIJDI UP DSFBUF UIFJS NBQ t 6TF B NBQ PG UIF TDIPPM BEEJOH JG OFDFTTBSy B TJNQMF HSJE PWFSMBZ XJUI MFUUFST PO UIF x BYJT BOE OVNFSBMT PO UIF y BYJT %JTDVTT UIF MPDBUJPO PG UIF DMBTTSPPN VTJOH DPPSEJOBUFT "TL RVFTUJPOT TVDI BT Where is the library? How would you get from the office to the car park? What are the coordinates of the art room? What is the shortest way to get from the canteen to the oval? What other ways could you get there? 4UVEFOUT XBML BSPVOE UIF TDIPPM XJUI UIF QMBO Ü OEJOH FBDI PG UIF QMBDFT UIFZ XBML QBTU PO UIF NBQ QBSUJDVMBSMZ JO UFSNT PG UIFJS DPPSEJOBUFT 4FF B TJNJMBS BDUJWJUZ PO QBHF

t First to ten game: 4UVEFOUT DPOTPMJEBUF UIFJS VOEFSTUBOEJOH PG HSJET BOE DPPSEJOBUFT UISPVHI UIJT HBNF #Z QMBDJOH DPVOUFST PO BYJT QPJOUT TUVEFOUT BUUFNQU UP IBWF UFO DPVOUFST PO UIF HSJE CFGPSF UIFJS QBSUOFS 3VMFT BOE HBNF NBUFSJBMT DBO CF GPVOE PO QBHFT o

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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FORMAT OF THIS BOOK Sub-strand: Location and transformation— L&T – 1

Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English, Information and Communication Technology, Health and Physical Education, History, 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.

LINKS TO OTHER CURRICULUM AREAS English t 3FBE UIF Once upon a time map book CZ # )FOOFTTZ BOE 1 +PZDe. 5IJT CPPL UBLFT B USJQ UP TJY EJò FSFOU XFMM LOPXO TUPSZ MBOET XJUI NBQT DPPSEJOBUFT SPVUFT IJEEFO PCKFDUT BOE QPJOUT PG JOUFSFTU.

Information and Communication Technology t " GSFF BQQ GPS UIF J1BE™ BOE J1IPOF™ JT B TJNQMF HSJE HBNF DBMMFE 'MPX 'SFF 5IJT HBNF SFRVJSFT TUVEFOUT UP KPJO DPMPVSFE EPUT XIJMF Ü MMJOH UIF XIPMF HSJE t " TJNQMF HSJE HBNF DBO CF GPVOE BU IUUQ BV JYM DPN NBUI LJOEFSHBSUFO MPDBUJPO JO B UISFF CZ UISFF HSJE t ZPP NBQT DBO CF GPVOE BU UIF GPMMPXJOH QMBDFT o 1FSUI ;PP IUUQ XXX QFSUI[PP XB HPW BV WJTJU [PP NBQ o "MNB 1BSL ;PP #SJTCBOF IUUQ XXX BMNBQBSL[PP DPN BV JNBHFT TUPSJFT QEGT BMNB@QBSL@[PP@HVJEF@NBQ QEG o "EFMBJEF ;PP IUUQ XXX [PPTTB DPN BV BEFMBJEF [PP [PP JOGPSNBUJPO [PP NBQ t *OUFSBDUJWF [PP NBQT NBQT DBO CF GPVOE BU UIF GPMMPXJOH QMBDFT o 5BSPOHB 1BSL ;PP IUUQ XXX UBSPOHB PSH BV UBSPOHB [PP NBQ WJTJU QMBOOFS o .FMCPVSOF ;PP IUUQ XXX [PP PSH BV .FMCPVSOF ;PP@.BQ

Health and Physical Education

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

t 1MBZ Indians and tepees GPS QSBDUJDF PG DMPDLXJTF BOE BOUJDMPDLXJTF

4UVEFOUT HFU JO QBJST UIFO GPSN UXP DJSDMFT XJUI POF QBSUOFS JO UIF JOTJEF DJSDMF BOE UIF PUIFS JO UIF PVUTJEF DJSDMF 5IF TUVEFOUT PO UIF JOTJEF DJSDMF UIF A*OEJBOT TJU DSPTT MFHHFE PO UIF ø PPS 5IF TUVEFOUT PO UIF PVUFS DJSDMF UIF A 5FQFFT

TUBOE VQ XJUI UIFJS MFHT BQBSU UP CF UIF AUFQFF EPPS’ "MM TUVEFOUT GBDF UIF DFOUSe. 5IF UFBDIFS DBMMT PVU FJUIFS A*OEJBOT PS A5FQFFT’ *G UIF DBMM JT A*OEJBOT’ UIF TUVEFOUT JO UIF JOOFS DJSDMF EVDL UISPVHI UIF UFQFF EPPS CFUXFFO UIF MFHT PG UIFJS QBSUOFS SVO clockwise BSPVOE UIF DJSDMF BOE UIFO EVDL CBDL UISPVHI UIF EPPS UP TJU DSPTT MFHHFE JO UIFJS PSJHJOBM TQPU *G UIF DBMM JT A5FQFFT’ UIF TUVEFOUT JO UIF PVUFS DJSDMF SVO anticlockwise BSPVOE UIF DJSDMF BOE XIFO UIFZ SFUVSO UP UIFJS TQPU QVU POF IBOE PO UIFJS QBSUOFS’T IFBE BOE SVO JO B TNBMM DJSDMF BSPVOE UIFN FOEJOH CBDL CFIJOE UIFJS QBSUOFS XJUI UIFJS MFHT BQBSU 8IFO SVOOJOH BSPVOE UIF DJSDMF BOZ TUVEFOU XIP XJTIFT UP QBTT BOPUIFS NVTU EP TP PO UIF PVUTJEF XJUI OP KPTUMJOH 5IF A*OEJBO’ PS A5FQFF’ XIP JT UIF MBTU UP HFU CBDL UP UIFJS PSJHJOBM QPTJUJPO MPTFT BOE CPUI QBSUOFST HP BOE TJU JO UIF NJEEMF PG UIF DJSDMFT 0ODF UIFZ IBWF NJTTFE POF UVSO UIFZ DBO SFUVSO UP UIF UXP DJSDMFT (FOFSBMMZ JU JT TVHHFTUFE UIBU FWFSZ PS UVSOT UIF *OEJBOT BOE 5FQFFT JO FBDI QBJS DIBOHF QMBDFT.

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History and Geography t .BQT PG MPDBM BSFBT DBO CF VTFE BT QBSU PG DPNNVOJUZ TUVEJFT.

Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET The new suburb

CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

North

The map is missing some details. Show:

1. Traffic lights at the corner of White and Green Streets 2. A shop at G4

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.

3. A car park east of Black Lane and south of Yellow Rd

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Below is part of a map of a new suburb.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. PublicationsÂŽ www.ricpublications.com.au

Assessment 2

NAME:

Shape—Shape Sub-strand: LocationSub-strand: and transformation— L&T – 1

DATE:

Ring a Toy

4. A park between Green and Yellow Roads, with a slide at B5 and swings at C6

Below is a game used at a school fete. The aim is to throw hoops over the squares and if you land on a toy, you win it.

5. Orange Ave one-way heading west 6. A mail box at K8 and a cafĂŠ at A3

5

7. A building of your choice at F2 and F3.

Assessment pages are included. These Š R. I .

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Pu bl c at i ons support activities included ini the Hands-on activities or resource sheets. •f orr evi ew pur posesonl y•

8. Describe how to get from the mail box to the cafĂŠ.

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1

Checklist

Sub-strand: Location and transformation— L&T – 1

CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

2

Identifies relative positions on a map

Interprets simple grid maps

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A

B

C

D

E

1. What is the toy in D3?

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STUDENT NAME

Creates simple grid maps

Uses simple coordinates

Create and interpret simple grid maps to show position and pathways (ACMMG065)

2. In what square is the fairy doll?

3. The toy in C4 is a

.

4. In what square is the toy train?

5. What is the toy in A5?

6. Draw a toy frog in E2 and a toy of your choice in B1.

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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: Location and transformation

Page 65

L&T – 1

Page 55

Page 56 1.

2.

3.

4.

5.

6.

7.

Assessment 1 – The clothes line

jeans second from the left on the top line skirt 3 4 Teacher check Teacher check

No lines of symmetry

Assessment 1 – Near the school

1.

2.

3.

4.

a swing B7 oval and park (or swing) Arrows showing School Street one-way from west to east. Teacher check.

5. Go left (or west) along Careful Street; turn right (north) into Park Road; first right into School Street and the hospital is on the left.

Page 58

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Answers for resource pages (where appropriate) and assessment pages are provided on the final page of each sub-strand section.

Resource sheet – Transparent mirror activity page

Resource sheet – The new suburb

1.–8. Teacher check

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

1.

2.

3.

4.

5.

6.

Page 66

Resource sheet – Reflections on symmetry

1.–3. Teacher check Page 67 1. (a)

Resource sheet – Symmetry in the garden (b)

(c)

Assessment 2 – Ring a toy

A toy car A2 A (beach) ball C1 A dog Teacher check

(d)

L&T – 2

(e)

(f)

2. Teacher check

Page 63

Resource sheet – Symmetry in shapes

1.

Page 68 1.

(a)

Assessment 1 – Transparent mirror symmetry

(a)

(b)

(c)

(b)

(c) There are an infinite number of lines of symmetry in a circle.

(d) (e)

(d)

(e) (f)

(g) (f)

No lines of symmetry

(h)

2. Teacher check

Page 69

(i)

Assessment 2 – Deb and Tim’s toy shop

1. Teacher check Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. PublicationsÂŽ www.ricpublications.com.au

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

71

v

Sub-strand: Using units of measurement—UUM – 1

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

TEACHER INFORMATION

RELATED TERMS Comparison

What this means

• Relates to making judgements about only two shapes or objects.

The vocabulary of comparison for length are ‘longer’ or ‘shorter’; for mass are ‘heavier’ or ‘lighter’; for capacity are ‘holds more’ or ‘holds less’.

• Up until Year 3, measurements have been made using uniform non-metric units such as counters, blocks, straws, beans etc. This unit introduces metric units for length, mass and capacity.

• Relates to making judgements about three or more shapes or objects. It is also known as seriation. The vocabulary of ordering for length are ‘long’, ‘longer’, ‘longest’ or ‘short’, ‘shorter’, ‘shortest’; for mass are ‘heavy’, ‘heavier’, ‘heaviest’ or ‘light’, ‘lighter’, ‘lightest’; for capacity are ‘holds the most’ or ‘holds the least’.

General • Estimation should be encouraged in all measurement activities.

• The metric units for length are millimetres (mm), centimetres (cm), metres (m) and kilometres (km). For most students in Year 3, millimetres and kilometres would not be considered familiar units.

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Ordering

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• The metric units for mass are grams (g), kilograms (kg) and tonnes (t); and again, tonnes would not be considered familiar units.

• The metric units for capacity are millilitres (mL), litres (L) and kilolitres (kL); with kilolitres not being a familiar unit for Year 3 students.

• Note the use of the upper case ‘L’ for the abbreviation of litres; it is also used for mL and kL. This is to distinguish it from the number 1.

• A gap is always left between the number of units and the abbreviation of the unit; e.g. 5 cm, 8 kg, 375 mL etc. and no full stop used at the end of the abbreviation (unless it is at the end of a sentence).

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C.Publ i cat i ons f orr evi ew pur posesonl y• • The amount of matter• an object contains, commonly measured in grams, kilograms and tonnes.

Weight

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• The force of gravity acting on an object, used to measure mass (actually measured in Newtons).

Note 1: It is correct to use the verb ‘to weigh’.

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Note 2: At this year level, students may use the terms ‘weight’ and ‘mass’ interchangeably, although it is best if the teacher uses the correct terminology.

Capacity

• The amount a container can hold.

Balance scales

• Also known as pan balances and beam balances. These have a pan at either end of a pivoting beam.

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• Abbreviations of metric units never use the ‘s’ at the end; e.g. ‘5 cm’ not ‘5 cms’, ‘8 kg’ not ‘8 kgs’ and ‘375 mL’ not ‘375 mLs’. Of course, if the unit is written in full, the ‘s’ is needed; e.g. ‘5 centimetres’, ‘8 kilograms’ and ‘375 millilitres’.

• Students need to consider what to do when measuring if the units don’t come out even. Judgements about whether to use ‘half units’; ‘a bit more than …’ or ‘a bit less than …’ can be discussed.

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Mass

• Students need to be fluent with conversions of common metric units of measure for length, mass and capacity (see page 3). Discussion could centre on needing to know about multiplying and dividing by ten, or powers of ten. Discuss the meanings of the prefixes such as ‘milli’, ‘centi’, and ‘kilo’.

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• Students need to have had experience measuring with non-metric (uniform, non-standard) units in order to appreciate the need for common metric units. This would involve the communication of measures to another person, with statements such as, ‘the pencil is 17 pebbles long’; ‘the pencil case weighs the same as 12 marbles’ or ‘the cup holds 5 scoops of water’ making little sense, unless access to the pebbles, marbles or cups used is available.

• Students need to develop ‘referents’ for length, mass and capacity. For example, students being aware that their little finger is approximately one centimetre in width and that a big stride is about a metre long. For mass, when holding an item to be estimated, most people mentally compare the item to something they know such as a tub of butter or a bag of sugar.

Capacity is often problematic because of marketing, where a 2-litre cool drink bottle looks as if it holds more than a 2-litre tub of ice-cream.

• Students need to know which units are appropriate for measuring different items. For example, we would not usually measure the length of a room in millimetres, the mass of a balloon in kilograms or the capacity of a bucket in millilitres.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement—UUM – 1

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

TEACHER INFORMATION (CONTINUED) Conversions Length

• Ideally, students should be the ones to choose the tools and units when measuring. However, they will need a lot of guidance in this at first.

10 mm = 1 cm 100 cm = 1 m

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1000 mm = 1 m 1000 m = I km Mass

Capacity

1000 mL = 1 L

• National tests usually have a question that requires students to interpret simple scales in length, mass and capacity.

Length • There are two types of rulers: dead-end (where the ‘zero’ is level with the end of the ruler) and waste-end (where the ‘zero’ is situated a little way in from the end of the ruler).

Dead end

1 cm

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1000 g = 1 kg

• Students need experiences actually doing the measuring, not just watching someone else do it.

Waste end

0 1 cm

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• Students may need specific teaching on how to use a ruler; we cannot assume they know. For example, they should have their non-writing hand spanned out so the ruler is more stable and won’t move easily; they line up the item to be measured with the ‘zero’ on the ruler and read along to the end of item.

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• Ensure that all students’ rulers are in centimetres and millimetres, not inches.

• Drawing a line of a particular length is a different skill to measuring a line of a particular length.

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Mass • When estimating and measuring mass, the teacher needs to ensure that the masses of the items to be measured are not always obvious (i.e. that students cannot determine comparisons simply by looking). To do this, you need items that have similar masses but different volumes; e.g. a golf ball and a tennis ball, and items that are the same size but have different masses; e.g. lidded tins filled with materials of different masses.

• When using metric units for mass, students may use either a pan balance and weights or kitchen scales. Kitchen scales may have a dial or a digital readout. It is a useful skill to be able read a dial, although students may need some assistance with this at first. (See activity on page 11.)

• Measuring the mass of an item using scales with a digital readout requires no actual measuring skills, only the ability to read numbers.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

3

Sub-strand: Using units of measurement—UUM – 1

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

TEACHER INFORMATION (CONTINUED)

Student vocabulary centimetres metres grams kilograms millilitres litres

Capacity • Students may need help with strategies for measuring capacity, such as marking off levels (an elastic band on a container is a good way) and reading a graduated scale on a measuring jug.

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• Measuring capacity can be done directly, by pouring from one container to another and seeing which one is left with some in it; by using a unit such as a scoop to compare capacities; or by marking levels of a container showing the height of the contents. (See activity on page 13.)

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long longer longest short shorter shortest

heavy heavier heaviest light lighter lightest

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What to look for

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holds more holds less holds the most holds the least

• Students unsure of what attribute to measure; i.e. length, mass or capacity.

• Students using inappropriate units of measure.

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• Students using inappropriate tools to measure; e.g. using a ruler to measure the length of a basketball court, bathroom scales to weigh a pencil case or a medicine measure to calculate the capacity of a bucket.

• Students using a tool incorrectly; e.g. not making sure a trundle wheel is at zero before measuring length; not levelling the horizontal arm on a pan balance before filling them up to measure mass; not filling measuring spoons, cups or jugs to the correct level when measuring capacity.

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES Estimate before measuring in all these activities

Length • Students cut a piece of paper tape that is the same length as their stride. They use this to determine how many of their strides will be needed to go across a room, the playground etc. Compare this to their count when they actually stride out the length of the room, playground etc. Students then compare the number of strides they used to other students’ counts. Discuss the differences in the number of strides needed and the consequent need for a common measurement unit such as a metre.

• Use a 10-centimetre orange rod or Base Ten long as a measuring unit (it’s actually a decimetre, though we don’t often label it that). This has the advantage of being easily compared to centimetres and metres, and needs less counting of units to determine length. Students can measure the lengths of their arms, desks, chairs, bookcase etc. using this unit.

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• Students are usually interested in finding out their own heights, but be aware that a particularly short or tall student may be very sensitive to having this displayed. Other body measurements such as head circumference, arm length or hand span can be compared by students making paper tape graphs.

Chris

Bonnie Ian Karen 1

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The length of our hand spans

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Centimetres • Students make their own metre strip rulers using paper tape, string or similar. Use these to find things in the classroom or outside that are close to a metre, less than a metre and more than a metre in length. They then make a table of their results. These metre strip rulers may also be used to measure longer distances such as the length of a path or the distance between the library and the drink fountain. Students could put their findings into a table and then order the distances from shortest to longest. Trundle wheels could then be introduced as an easier way to measure distance with instruction on how to start at zero. Students measure the same distances with the trundle wheel as they had with their paper metre strip rulers and see if there are any differences. Discuss why this may be so.

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• Measuring the length of straight and curved items (See pages 9 and 10). Students use pieces of string to determine the lengths of objects that cannot be measured directly using a ruler and then straighten the string out against a ruler or metre stick to obtain a measurement in millimetres or centimetres.

• Using a metre stick or trundle wheel, students can measure longer lengths such as the width of a room or the distance between the classroom and the canteen. Discuss what to do when the distance is not in exact metres: use half units, or terms such as ‘a bit more than …’, ‘a bit less than …’, ‘nearly …’ etc.

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• Mystery object: The teacher chooses an item in the classroom that is about 30 centimetres long. Groups of students are asked to make a list of as many items in the room that are around that length. Each group then reports back with their list; other groups are invited to comment about whether they agree with all the items being around 30 centimetres.

Then the teacher reveals what the mystery object is. This could be done with different lengths and students could take turns in choosing the mystery object.

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• Students look at relationships between the ‘long’ in Base Ten Blocks (MAB), an orange coloured (Cuisenaire™) rod and a metre. Ask questions such as: How many Base Ten longs (or orange coloured rods) can you fit along the metre stick? How many centimetres is each of these items? How can we use this to work out how many centimetres in a metre?

• The one-metre race: A game played in pairs. For this game, you will need one 10-sided dice for each pair of students, a set of coloured (Cuisenaire™) rods and a metre ruler or a strip of paper tape that is one metre long. Players take turns to roll the dice and place the appropriate length of rod along the metre ruler. The second player then has a turn and places the appropriate length of rod along the opposite side of the metre ruler. The winner is the first to make a full metre. An extension to this game would be to exchange smaller rods for orange rods whenever possible during the game.

1 metre

• Students consolidate their understanding of using informal and formal methods of measuring length by completing the appropriate sections of the worksheets on pages 12 and 13.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

5

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES (CONTINUED) Estimate before measuring in all these activities

Mass • Have four or five objects of quite different masses for students to compare. Students heft the items two at a time (hold one in each hand and estimate which is the heavier object) to decide which two of the objects has the heavier mass, then use a pan balance to check. Students do this with the objects, two at a time. They then place all the four or five items in what they estimate to be the correct order from lightest to heaviest. Discuss the results; were they what the students expected?

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• Use a uniform unit to make comparisons. For example, use a pan balance to find how many blocks are needed to balance a pair of scissors.

Then do the same for several other items, determining how many blocks are need to balance a book, pencil case, lunch box etc. Students estimate the number of blocks needed before measuring. Once the first item has been weighed, students may revise their other estimations in the light of this new knowledge (having a referent). Students make a table of their results and then put the items in order from lightest to heaviest.

Item

My estimate

scissors book Pencil case Lunch box

5 blocks 8

12 blocks

6 15 blocks 8

13 blocks

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• Using supermarket catalogues, students cut out a number of items of different masses (where they were given in the catalogue) and glue onto a page in order from the lightest to the heaviest. Discuss how big each of the items would be; would they fit in your hand, in an ice cream-container, in a plastic bag? Then try to find items that are the same (or similar) masses. Discuss whether they look about the same size, or is there a noticeable difference?

Actual mass 14 blocks 18 blocks

16 blocks 22 blocks

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C.PPencil ubl i cat i ons Lunch box case scissors book Lightest •f orr ev i ew pur posesonl yHeaviest •

• Students complete a similar activity to above, but estimate and measure in grams rather than non-standard units.

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• Cooking may provide opportunities to measure in grams, although often measures of capacity are used in recipes; e.g. 375 grams of flour or ½ cup of sugar.

• Some students may be sensitive to having their mass disclosed. For this reason, it is preferable to weigh other items such as a class pet. Weekly records of its mass can be kept and the results graphed. However, to be able to measure in kilograms, heavier items may be needed. Students could use kitchen or bathroom scales to weigh filled boxes, cartons, buckets and other larger containers, again estimating their masses at the start, weighing the first item, revising their other estimates based on this new knowledge, weighing the rest of the items and ordering the items from lightest to heaviest.

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• Collect items that have the same mass; e.g. 500 gram bag of flour, 500 gram box of biscuits, 500 gram bag of potatoes.

Discuss the comparative sizes of the items.

• Set up a class shop with various items that need to be purchased by weight such as nuts in shells, or students can make fruit and other items from plasticine or clay for sale by grams or kilograms.

• Students consolidate their understanding of using informal and formal methods of measuring mass by completing the appropriate sections of the worksheets on pages 12 and 13.

Estimate before measuring in all these activities

Capacity • Using supermarket catalogues, students cut out a number of items of different capacities (where they were given in the catalogue) and glue onto a page in order from the one that holds the least to the one that holds the most. Discuss how big each of the items would be; would they fit in your hand, in an ice cream-container, in a plastic bag? Then try to find items that are the same (or similar) capacities. Discuss whether they look about the same size, or is there a noticeable difference?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES (CONTINUED)

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• Have four or five objects of different capacities for students to compare. Students estimate which of the containers will hold the most sand/water/beans etc. and which will hold the least.

They then fill the first container, counting the number of cups or scoops needed to fill it. Based on this knowledge, students revise their other estimates, then measure the other containers.

Finally the containers are put in order from the one that holds the least to the one that holds the most.

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• Students complete a similar activity to above, but estimate and measure in millilitres rather than non-standard units.

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• Students compare two different-shaped containers by trying to decide which one will hold the nearest to 500 millilitres (500 mL). They then measure each container to see if their estimation was correct. This activity could be extended to three or more containers, with the students making judgements about which will hold nearest to 375 millilitres (375 mL), 750 millilitres (750 mL), 1 litre (1 L) etc.

• Cooking can be a good context for measuring capacity. Look for recipes that use millilitres rather than spoonfuls, cupfuls etc.

• Use a large, clear unmarked container to display the amounts of water, sand etc. other containers hold.

Stick masking tape on one side to record the amounts, or use sticky notes at the different levels. From this information, place all the containers in order from the one that holds the least to the one that holds the most.

Students draw pictures of their findings.

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• Students look at different containers and compare their heights and capacities. This could be connected to a task used to determine if students understand about conservation of capacity, where they measure the capacities of a tall thin glass and a short fat glass and find that the taller glass may not hold as much liquid as the short glass.

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• Finding containers to give students experience with litres is a little more problematic; however, different sized buckets, soft drink bottles and ice-cream containers could be used.

• Students make their own measuring jug by taking a large unmarked glass container with masking tape on one side. They then use a measure such as 20 mL and fill the container, marking the level of each 20 mL on the masking tape.

800mL

700mL

600mL

• The above activity could be completed using a ready-made graduated jug and elastic bands or sticky notes to show the amounts that the different containers hold.

Students then record their results and place the containers in order.

500mL

400mL

300mL

200mL

100mL

• Students consolidate their understanding of using informal and formal methods of measuring capacity by completing the appropriate sections of the worksheets on pages 12 and 13.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

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Sub-strand: Using units of measurement—UUM – 1

LINKS TO OTHER CURRICULUM AREAS English • Read Knee high Nigel by L Anolt. This is the story of five giants, one of whom, though still a giant, is considerably smaller than the others. They argue over the building of castles and go their separate ways with unsuccessful results.

• Read Six feet long and three feet wide by J Billington and N Smee. This story illustrates the need for standard units.

• A similar story to the one above is How big is a foot? by R Myller.

• Read Actual size by S Jenkins. This book has fantastic drawings of animals in actual size (large and small). Make sure to get the English edition in centimetres.

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Information and Communication Technology

• A website with measures of length, mass, volume and capacity can be found at <http://www.bgfl.org/bgfl/custom/ resources_ftp/client_ftp/ks2/maths/measures/index.htm>

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• A website that simulates weighing in grams on a pan balance can be found at <http://www.teacherled.com/resources/ oldscales/oldscalesload.html>

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• A website that gives students practice in reading a kitchen scale can be found at <http://www.crickweb.co.uk/ ks1numeracy.html#simplescales2>

History and Geography

• The understanding that the metric units of measure we use are based on the SI (International System of Units; from the French name Système internationale d’unités).

The Arts

• Measure and construct frames for pictures, using millimetres and centimetres.

Science

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• Measure the length of shadows. Discuss the different lengths at various times of the day.

• Cooking activities where students weigh ingredients using grams and measure capacities using millilitres.

Civics and Citizenship

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• Make cakes, biscuits etc. as a fundraiser for a community event or charity.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Which is the longest? – 1 Measure each of the items below, then order them from shortest to longest, writing the letters in the boxes.

1.

Shortest

Longest

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C

mm

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Shortest

Longest

B

mm

mm

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2.

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CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

A

C

. te mm o 3. Draw four lines below in order of length from shortest to longest. Make c . c e the lines 16 cm, 145 17.5 cm and 100 mm. r hmm, er o st super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

9

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Which is the longest? – 2 Use a length of string to measure each of the items below. Order them from shortest to longest, writing the letters in the boxes.

1.

Shortest

Longest

A

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mm

C

3.

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Shortest

Longest

Shortest

mm

mm

mm

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mm

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Longest

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mm

mm

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

mm

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2.

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mm

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Reading scales 1. Work out the mass on each of the scales below.

2

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6 7 4 5 KG

200

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50 100

450 grams

400 350

C

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500

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GRAM

150

200 0 300 25

mL

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C.P ubl i cat i ons •f orr evi ew pur posesonl y• 2. Work out the capacity show on each of the containers below.

6 mL

50 mL

40

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40 30 20

30 20

10

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2000

mL

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100

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CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

A

600

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10

1800 1600

350

1400

300

E

250 200 150

1200 1000 800

D

100

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

600 400 200

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

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Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Measure hunt 1. Find items that would belong in each of the boxes below. (a) Length Between 20 cm and 80 cm

Between 80 cm and 1½ metres

(b) Mass

Between 1 gram and 10 grams

Between 20 grams and 80 grams

Between 80 grams and 1½ kilograms

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o c . cheBetween 20 mL and r e Between 80 mL and o t r Between 1 mL and 10 mL s sup r e 80 mL 1½ litres

(c)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

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Between 1 cm and 10 cm

Assessment 1

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Measurement tasks

1. Find three (3) things in the classroom that are about 20 cm long.

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C.Publ i cat i ons 3. Measure the heights ofe your and to nearest half •f o r r evi wchair pu r pdesk os ethe so nl y •a centimetre.

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chair:

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CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

2. Draw pictures for three items from the classroom that are longer than your arm.

4. Find three (3) things in the classroom that weigh about 300 grams.

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o c . che e r o t r s super 6. Find three (3) containers in the classroom that have a capacity of about

5. Find four (4) items of different masses in the classroom. Weigh them and list them in order from lightest to heaviest.

350 millilitres.

7. Find four (4) items of different capacities in the classroom. Measure them and list in order from holding the least to holding the most.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

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Assessment 2

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Length, mass or capacity?

(b)

(a)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Measure, order and compare objects using familiar metric units of length, mass and capacity

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1. Below are some tools that are used to measure objects. Under each picture, write what they are called and what they are used for: measuring length, mass or capacity.

Checklist

Sub-strand: Using units of measurement—UUM – 1

Measure, order and compare objects using familiar metric units of length, mass and capacity

Understands the difference between length, mass and capacity.

Measures, orders and compares capacity in millilitres and litres.

Measures, orders and compares mass in grams and kilograms.

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STUDENT NAME

Measures, orders and compares length in millimetres, centimetres and metres.

(ACMMG061)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

15

Sub-strand: Using units of measurement—UUM – 2

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

RELATED TERMS

TEACHER INFORMATION What this means

• A clock with some or all of the digits from 1 to 12. These clocks have at least two hands: an hour hand and a minute hand. Many analogue clocks also have another hand—a second hand—at this year level this would be useful.

• Students need to be able to skip count by 5s to at least 60.

Digital clock

• Students begin by telling the time to the nearest 5 minutes before proceeding to tell the time to the nearest minute.

• Students recognise that there are 60 minutes in an hour and 60 seconds in a minute.

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• A clock that displays the time using only digits, with the digit for the hour separated from the digits for the minutes by a colon; e.g. 3:24.

Geared clock

• A model of a clock where as one hand moves, the other moves a proportional distance. Thus the hands move in the same way that working analogue clocks do.

• There is an expectation that students can tell the time to the nearest quarter hour on both analogue and digital clocks and that they know half an hour is 30 minutes and a quarter of an hour is 15 minutes.

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Analogue clock

• Students are aware that when the minute hand has moved once all the way around the clock, the hour hand will have moved between one digit representing the hour and the next digit around the clock.

They also recognise that when the minute hand moves part of the way around the clock, the hour hand will move a small distance between two digits on the clock.

• Students recognise that when the second hand has moved once all the way around the clock, one minute has passed. The movement of the minute hand may not be obvious, but if the clock has gradations between each of the digits (i.e. it shows all 60 minutes around the dial), then they will see that the minute hand has moved forward one place.

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of time

60 seconds = 1 minute 60 minutes = 1 hour

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30 minutes = half an hour

15 minutes = quarter of an hour

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12 hours = from midnight to noon

12 hours = from noon to midnight 24 hours = 1 day

• If using a model of an analogue clock, it is preferable to have a geared clock, so that as the minute hand moves, the hour hand moves a proportional distance. This means that when the time is, for example 9:25, the hour hand will be nearly half of the way between the 9 and the 10. As the minute hand on the clock is moved from 9:00 to 9:25, the hour hand slowly moves too. With a non-geared clock, the hour and minute hands are moved independently so, as the minute hand is moved from the 12 to the 5 to show twenty-five minutes past the hour times, the hour hand does not move. This may be confusing for some students.

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Relationships between units

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• Classrooms should have both an analogue and a digital clock, preferably side-by-side. Regularly seeing the two different displays for the same time of day helps students realise there are two equally valid ways to read the time. There are some large clocks available commercially that clearly show the time in both formats.

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• Incidental references to the time of day should occur whenever possible. A balance should be struck between reading and recording times in written form and oral discussion, so students who are uncertain will gain assistance and positive reinforcement.

16

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement—UUM – 2

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

TEACHER INFORMATION (CONTINUED) Student vocabulary o’clock half past

• It is generally recommended that ‘quarter to an hour’ is the only instance where students deal with times to the next hour. For example, we would use 5:52 rather than 8 minutes to 6. These times ‘to’ an hour may be dealt with informally as the need arises.

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quarter past quarter to

xx:25 (e.g. 3:25) xx:52 (e.g. 3:52) clockwise

• The spoken time reflects the written digital time; e.g. 11:28 would be said as eleven twenty-eight, not twenty-eight minutes after/ past eleven. The time 7:31 would be said as seven thirty-one, not twenty-nine minutes to 8 or thirty-one minutes after/past seven. With times such as 3:05, whether we say oh instead of zero, or whether we verbalise the initial zero at all, depends on community practice.

However, the zero must be used in the written form. The time 3:05 makes sense—3:5 does not.

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Teaching points

• Students begin by telling the time to the nearest 5 minutes before proceeding to tell the time to the nearest minute.

• National tests always have a question that relates to telling the time using analogue and digital clocks as well as a question where students calculate simple time differences.

© R. I .

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

• If students draw or make their own analogue clocks, they put the 12 at the top of the clock, the 6 at the bottom and the 3 and 9 on either side.

• Students can make the connection between times shown on an analogue clock and the same times shown on a digital clock.

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• On an analogue clock, students mixing up where the minute and hour hands point; e.g. showing 2:38 when the hour hand points to just past the 7 and the minute hand points to the 2.

• For times other than on the hour (o’clock), students incorrectly showing the hour hand directly pointing to the hour digit rather than between it and the next digit; e.g. for showing 6:20, the hour hand pointing to the 6 rather than nearly half way between the 6 and 7.

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• Students being able to associate the ‘5’ on a time with an interval of 5 minutes; e.g. 1:05 means 5 minutes after one o’clock.

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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17

Sub-strand: Using units of measurement—UUM – 2

HANDS–ON ACTIVITIES

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• Regularly ask students at different time intervals to tell you the time orally. This will assist with assessment of individual student’s ability to read clocks, if you consider rostering your questions to ensure you are able to ask each student to read the clock over a short period. This could be done at the beginning and end of a teaching period dedicated to teaching clock-reading skills. Teacher observations of student’s abilities could be made on a before/after criterion based checklist.

• Students have a model analogue clock (either a commercial version, or students make their own from a paper plate with cardboard hands held in place by a split pin). In pairs, students take turns to make a time on the clock and their partner tells the time orally and then writes it in digital form. Encourage students to start with times to 5 minutes, then when ready, move on to times to the minute. Later, reverse the activity, by starting with a time given orally which the partner has to show on the model analogue clock.

• Students arrange cards that show different analogue clock times to 5 minutes, in order. (See page 20) • Later, students can place cards that show different analogue clock times to the minute, in order. (See page 21) • Make a number line to 60 on a strip of light card, marking only by 5s. Discuss where the zero would go, and why it is shown as ‘00’. Also discuss the fact that each of the marks on the line is 5 higher than the previous mark. Make the connection to the times on an analogue clock. Count along the strip by fives. Discuss the fact that on an analogue clock, all the hour times, and therefore all the digits, only go to 12, that there is no zero and single digits do not have a lead zero (e.g. not 05). With a digital clock, the hours are shown the same as the hours (digits) on an analogue clock, but the minutes go to 60 and the single digits have a lead zero.

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• The number line could be joined into a loop, with the digits on the inside, 1 9 either by stapling or using glue or a paper clip. This could then be laid 2 over a similar-sized picture of an analogue clock with the digits 1–12 on 8 3 it so that students can see the relationships. Students could use a large 7 and small pencil as hands for the clock or the analogue clock could have 4 6 5 moveable hands (e.g. using a split pin) so students can represent different times.

• Later, the same or a similar number line could be made, but this time all the digits to 60 would be shown. The numbers from ‘00’ to ‘09’ would all have zero as the lead digit. Again, this could be turned into a loop and placed on top of an analogue clock face to show the relationship between the hour and the minute hands.

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• Once students can read and show the time to the minute, discuss the concept of rounding to the nearest 5 minutes, so 7:42 is close to 7:40 and 7:48 is close to 7:50. Discuss when it is necessary to tell time to the minute (and even to the second and hundredths of a second in sport) and when it is good enough to give the time to the nearest 5 minutes.

• Time dominoes: A game for 2–4 players. (Laminate the dominoes on pages 22–23) Rules: The dominoes are placed face down on the table and seven are given to each player. Each player looks at their dominoes and the person with the latest time double piece places that domino face up on the table. If no player has a double domino, the player with the latest time starts the play. Players take turns playing one domino at a time, by matching one of their pieces with either end of the string of dominoes. New pieces can only be placed at either end of the string of dominoes. The string can be turned to fit onto the playing surface, but the line can only be built on at the two ends. When a player cannot match one of the ends of the string, they take another domino from the pack that is face down on the table. This becomes the end of their move, even if their new card will match one of the ends. If there are no pieces left, the player misses a turn. Play ends when one player has no dominoes left or when no further moves can be made. The winner is the player with no dominoes left or if no further moves can be made, the player with the least number of dominoes left. In the case of two players having the same number of dominoes left, the player with the earliest time left on their remaining dominoes wins.

• Discuss what the time will be 5 minutes later than any given time (see page 24). Extend to 30 minutes, or 10 or 23 (or whatever amount) of minutes later, with different starting times. Do the same for 5, 30, 13 or 42 etc. minutes earlier than any given times.

• Collect jewellery catalogues or pages from department store catalogues showing watches and clocks. Students cut out the pictures and arrange them in order from the earliest to latest times displayed. This also offers the opportunity to discuss the different shapes, sizes and layouts of time pieces, hopefully both digital and analogue.

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• Blank analogue and digital clock faces have been provided on page 25 for teacher use.

18

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Sub-strand: Using units of measurement —UUM – 2

LINKS TO OTHER CURRICULUM AREAS Number • When dealing with half past, quarter to and quarter past, there is a link to fractions. See (Model and represent unit fractions including ½, ¼, 1⁄3, 1⁄5 and their multiples to a complete whole [ACMNA058] )

English • Read Clocks and more clocks by Pat Hutchins. This book takes a humorous look at reading the time.

• Read The bad tempered ladybird by Eric Carle. In this book a ladybird works its way through different times of the day.

The times are shown on analogue clocks.

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

• Look at Tick tock by James Dunbar. This book provides an opportunity to talk about units of time in seconds, minutes, hours, days, weeks, months, years, decades and seasons. It is not a storybook, more a stimulus book for discussion about time periods.

• Read Just a minute by T Slater.

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Information and Communication Technology

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• A website which shows five analogue clocks and five digital clocks showing the same times but in a different order (which are to be matched), can be found at <http://resources.oswego.org/games/stoptheclock/sthec4.html>. This site shows times to the nearest minute.

• A website which has moving hour and minutes hands where the students can press a ‘Stop the clock’ button to digitally record the time display can be found at <http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/time/ index.htm>. This site, however, seems to stop the clock only on the 5 minute marks and the recording of the time has to have four digits; e.g. 08:45.

• Another interactive website where students can stop the clock can be found at <http://resources.oswego.org/ games/BangOnTime/clockwordres.html>. This site shows times ‘to’ the hour, such as ‘ten to 3’, rather than the digital equivalents.

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• The Clockworks website has three levels of time-telling problems. Some of the questions require students to tell the time, while others pose questions such as, ‘What will the time be in 4 hours and 30 minutes?’ This site can be found at <http://www.bbc.co.uk/bitesize/ks1/maths/telling_the_time/play/>.

Languages

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• Learn to say the time in a different language.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

19

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Five-minute time cards

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

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Cut out the time cards below and place them in the correct order. Write the times on each card to help you.

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET One-minute time cards

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CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

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Teac he r

Cut out the time cards below and place them in the correct order. Write the times on each card to help you.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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21

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Time dominoes–1

3:45

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

3:05

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Time dominoes–2

3:45

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CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

23

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Five minutes later Fill in the missing clocks for each of the times below, but make it show five (5) minutes later.

Digital clock

ON

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

10:00

Analogue clock

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET

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CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

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Blank clock templates

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

25

Assessment 1

Sub-strand: Using units of measurement—UUM – 2

NAME:

DATE: Digital and analogue

Fill in the matching time in the clocks below.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Tell time to the minute and investigate the relationship between units of time

:

Analogue clock

Assessment 2

Sub-strand: Using units of measurement—UUM – 2

NAME:

DATE: Read and write the time

Below are some different clocks. Either draw in the hands to show the correct times given or write the correct time for the clocks with the hands showing.

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Checklist

Sub-strand: Using units of measurement—UUM – 2

Tells the time to the nearest minute

Tells the time to the nearest 5 minutes

Knows 60 seconds = 1 minute

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STUDENT NAME

Knows 60 minutes = 1 hour

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

Answers

Sub-strand: Using units of measurement

Page 24

UUM – 1 Page 9

Resource sheet – Which is the longest? – 1

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Assessment 2 – Length, mass or capacity?

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C = 200 g C = 20 mL

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B = 150 grams B = 40 mL E = 1000 mL

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(d)

12

9

4:31

(b)

11 10 9

11 10

2

1

7 6 5

2 3

12 3

4

9 6

5:43

8:07

(h) 11 10

2 3

12 1

2 3

9

4

4

8 7

(j)

6

5

12:18

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Sub-strand: Shape—Shape – 1

Make models of three-dimensional objects and describe key features (ACMMG063)

TEACHER INFORMATION

RELATED TERMS Three-dimensional objects

What does it mean

• An object having the dimension of depth, as well as height and breadth.

• Whenever the curriculum mentions ‘objects’, it is referring to threedimensions.

Face

• Familiar three-dimensional objects may include spheres, cubes, prisms, pyramids, cylinders and cones.

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

Corner (vertex [plural vertices])

• Where three or more faces or edges of a three-dimensional object meet.

Edge

• Where two faces of a threedimensional object meet.

Prism

• Key features of three-dimensional objects include the number of faces, vertices (corners) and edges. Other features can include whether they can roll, stack etc.

• Students make models of objects using paper folding (origami) and other methods.

Teaching points

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• A two-dimensional (having height and width) region of a three-dimensional object.

• Students look at the key features of familiar three-dimensional objects, classifying them according to their corners, edges, faces etc. They also look for features such as ‘If they roll, can they be stacked?’ etc. and discuss why/why not.

• Cylinders and cones are special types of prisms and pyramids.

They are not considered polyhedra as they have curved surfaces (generally not considered to be faces).

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Pyramid

• A three-dimensional object that has a polygonal base with the other faces triangles with a common vertex called the apex. The shape of the base names the pyramid; e.g. square-based pyramid, pentagonal pyramid

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Cylinder

• A special type of prism with circular ends.

• Discuss the difference between a prism and a pyramid (the pyramid comes to an apex, the prism doesn’t; the pyramid has all faces but the base as triangles, although that too may be a triangle; the prism has all but the ends as rectangles, although they too may be rectangles).

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• A three-dimensional object with parallel and congruent end faces, with the other faces rectangles. The shape of the pair of congruent end faces names the prism; e.g. rectangular prism, triangular prism.

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• Teacher models the correct names of the objects and uses the appropriate language of comparison, such as ‘comes to an apex’, ‘belongs with’, ‘is bigger than’, ‘has six faces’, ‘is different from’, ‘has more edges’.

• Students use a range of construction materials to make a variety of different three-dimensional objects.

• Students investigate changes of shape using modelling materials such as plasticine, play dough or clay. This also offers the opportunity to look at cross-sections of these objects.

• Other materials for construction could include pipe cleaners, straws, cardboard, paper, craft sticks, wire and string or wool.

• National tests often have pictures of familiar objects shown from different orientations. Students need to be familiar with this concept. They also test students’ knowledge of the names and features of common shapes and objects.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Shape—Shape – 1

Make models of three-dimensional objects and describe key features (ACMMG063)

Cone

• A special type of pyramid with a circular base.

TEACHER INFORMATION (CONTINUED) What to look for • Students using the correct names of the three-dimensional objects.

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• Students know the difference between a prism and a pyramid, and between a cone and a cylinder.

• Students are able to correctly identify and name the corners, edges and faces of common three-dimensional objects.

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• Students are able to identify particular objects in the environment; e.g. soft drink cans as cylinders, balls as spheres.

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Student vocabulary sphere cube cone cylinder

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prism pyramid edges faces corners apex base

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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31

Sub-strand: Shape—Shape – 1

HANDS–ON ACTIVITIES • Students construct models using milk cartons, cereal boxes, empty tins with lids, savoury biscuit boxes, paper towel tubes etc. (See page 36.) These can be constructed according to a theme; e.g. robots or towns. Students then tally the number of different types of objects used; e.g. four rectangular prisms, five cylinders, etc. This data may be made into a graph using sticky dots. It is often helpful to have horizontal lines drawn in so the students can line up the dots evenly. This makes comparison of the number of dots for each object easier to see.

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• Specific constructions could be made according to instructions (e.g. shape cities) where all the pieces are triangular prisms, or a village where all ‘houses’ are different-based and different-sized pyramids.

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From the left

Model

From the right

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• Teacher makes a three-dimensional model using wooden cubes that the students copy. They then draw the model from different positions; for example, from above, from the left, from the front. Grid paper could be used to help the students draw their models. Later, the students can make their own designs from the cubes and draw them from different perspectives.

From above

From the front

• Students look at supermarket pamphlets for different shaped packages. They cut out a selection and make a chart of the different shapes found. (See page 34.) Discuss why the particular shapes would have been chosen for each of the products.

• Use pictures of three-dimensional objects (or provide actual objects), and ask students to visualise and draw what these would look like when viewed from different angles and positions. The teacher could present different views of similar objects and the students work out which one represents the chosen object. (See page 35.)

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• Use toothpicks or small straws and Blu-tac®, plasticine or play dough to make ‘skeletal’ three-dimensional objects such as prisms, cubes and pyramids. The number of pieces of Blu-tac® needed to join the toothpicks or straws is the number of corners (vertices) the object has and the number of toothpicks or straws is the number of edges. To work out the number of faces on the object, pieces of paper could be cut to size and attached to flat surfaces of the object and counted as they are attached.

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My cylinder

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• Students use plasticine or play dough to make models of other three-dimensional objects such as spheres, cones and cylinders. They can then draw their model from different viewpoints. The teacher can ask what it look likes from on top, from the side or from the front. Discuss the features of the object; for example, the cylinder looks the same from the top and the bottom (a circle); it looks the same if you look at it from the front, the back or from either side (a rectangle).

Encourage students to lift their models up to eye level to investigate the views from the top, bottom, all sides, and front and back.

o c . che e r o t r s super From the top

From the side

From the front

From the bottom

• Students look at various shapes in the environment, both human-made and natural (maybe on a class walk). Keep a record of the different shapes seen (e.g. cylinder, cubes, prisms, etc.) and what their purposes are. Discuss the differences in the shapes and sizes of each of them and why the items may have been a particular shape.

• What am I? – Memory game: Use the cards on page 38, enlarged and laminated. Students place the cards face down on the desk and, in turns, turn over two cards. If they match, the player keeps the cards. The player with the most cards at the end is the winner. There are two cards left blank for any additional shapes the teacher or students may want to add.

• Use construction material such as Geoshapes™ or Polydrons to make prisms, cubes and pyramids. This would lead to the idea of the nets of the objects. (See page 37.)

Cube

Net of a cube

• Students can consolidate their understanding of the features of 3-D objects by completing the table on page 39.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Shapeâ&#x20AC;&#x201D;Shape â&#x20AC;&#x201C; 1

LINKS TO OTHER CURRICULUM AREAS English â&#x20AC;˘ Read Mummy math: An adventure in geometry by C Neuschwander. This book looks at different three-dimensional objects.

Information and Communication Technology â&#x20AC;˘ For instructions on how to make an origami open box, see <http://www.origami-fun.com/origami-box.html> â&#x20AC;˘ There is a YouTubeâ&#x201E;˘ video on how to make an origami pentagonal prism, which is not as difficult as it sounds (and not as difficult as many other origami sites). It can be found at <http://www.youtube.com/watch?v=i6fcvrTLqRg>

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â&#x20AC;˘ From the same source, simple instructions on how to construct an origami triangular prism can be found at <http:// www.youtube.com/watch?v=KHP9Aw3a3Dc> â&#x20AC;˘ An origami triangular pyramid is constructed by a child in the following YouTubeâ&#x201E;˘ site <http://www.youtube.com/watc h?v=C3LOUE8GsVQ&feature=related>

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â&#x20AC;˘ YouTubeâ&#x201E;˘ video on how to make an origami cube can be found at <http://www.youtube.com/watch?feature=endscre en&v=Sy3t8ogJYls&NR=1>. This is fairly complicated.

The Arts

â&#x20AC;˘ Have a collection of cardboard boxes, tubes and other objects such as Tobleroneâ&#x201E;˘ boxes (triangular prisms). Students build models from the â&#x20AC;&#x2DC;junkâ&#x20AC;&#x2122; and make lists of the three-dimensional objects used. Students decorate their models.

: in used My tra JXODU SULVPV DQ Â&#x2021; UHFW Â&#x2021; FXEH LQGHUV FO Â&#x2021; F\ HV Â&#x2021; FRQ HV DU Â&#x2021; VTX XODU SULVP QJ Â&#x2021; WULD OH Â&#x2021; FLUF

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â&#x20AC;˘ Students make different three-dimensional objects using plasticine or play dough. Discuss the difference and similarities of each one; e.g. What is the same about the cylinder and the cone? What is different?

Languages

â&#x20AC;˘ Learn the names of common objects in another language.

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33

Sub-strand: Shape—Shape – 1

RESOURCE SHEET Name the 3-D objects 1. Below are some items found at the shops. Name the shape of each of them. cube

sphere

prism

(a)

cylinder

cone

pyramid

(g) YUM !

YUM !

(c)

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(b)

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(j)

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(e)

(f)

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(d)

(k)

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2. Draw your own pictures of each of these shapes: cube 34

sphere

prism

cylinder

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

cone

pyramid

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET Front view 1. Use blue coloured rods (Cuisenaire™) to build each of the models below.

Circle the picture of each model that shows it as if you’re looking at it from the front (front view).

(b)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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(a)

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2. Make your own model and draw it in the blank box (e) above.

Next to it, draw your model from the front view.

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35

Sub-strand: Shape—Shape – 1

RESOURCE SHEET Junk models 1. Below are some models that have been made from packaging. Name all the shapes you can find in them and how many there are of each one.

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(a) Junk city

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(b) Junk martian

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2. Now draw your own junk model on the back of this sheet and list all the shapes you used.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET Pick the nets 1. Below are nets of some three-dimensional objects. Decide what objects they would make. cube

sphere

cylinder

cone

pyramid

(b)

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(c)

(d)

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(a)

prism

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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2. Enlarge the nets onto cardboard and make your own models.

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37

Sub-strand: Shape—Shape – 1

RESOURCE SHEET What am I? Memory cards

I am made up of 6 squares

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I am made up of 1 square and 4 triangles

I have a triangle at each end and 3 rectangles joining them

I am made up of 2 circles and 1 rectangle

I am made up of 4 triangles

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o c . che e Ir am made up of 6 o r st rectangles super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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I have a circle at one end and come to a point at the apex

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET 3-D shapes

(b)

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(f)

faces

edges

corners

Name of 3–D shape:

faces

edges

faces

edges

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(d)

(e)

Name of 3–D shape:

corners

Name of 3–D shape: © R. I .

C.P ubl i cat i ons •f orr evi ew p ur pose sonl ycorners • faces edges

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

(c)

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1. Trace around the dotted lines to draw each 3-D shape. Then complete the table. cube pentagonal pyramid triangular prism triangular pyramid octagonal prism square-based pyramid (a) Name of 3–D shape:

o c . che Name of 3–D shape: e r o t r s super

corners

corners

Name of 3–D shape:

faces

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

edges

corners

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39

Assessment 1

Sub-strand: Shape—Shape – 1

NAME:

DATE: Different views

1. Pictures are shown below of different objects. Circle which of the options is the same object seen from a different viewpoint. (a)

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(b)

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(c)

(d)

(f)

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YUM !

YUM !

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Draw your own object, and show 3 different views of it

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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Assessment 2

Sub-strand: Shape—Shape – 1

NAME:

DATE: Top view

1. Build each of the models below. Circle the picture of each model that shows it as if you’re looking down on it (top view). (a)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

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2. Make your own model and draw it in the blank box (e) above.

Next to it, draw your model from the top view.

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41

Assessment 3

Sub-strand: Shape—Shape – 1

NAME:

DATE: Edges, faces and corners

(a)

Number of cubes

Number of edges

Number of faces

Number of corners

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Number of corners

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C. Publ i ca t i ons Number of Number of Number of faces corners •f orr evi ewedges pur pose sonl y •

Number of cubes

Number of edges

Number of faces

Number of cubes

Number of edges

Number of faces

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Number of corners

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Number of corners

2. What do you notice about (c) and (d)? Write about it.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

(d)

Number of faces

Number of cubes

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(c)

Number of edges

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Number of cubes

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1. The models below have been built using cubes glued together. Name how many edges, faces and corners are in each model. Use cubes to help.

An example has been done for you.

Assessment 4

Sub-strand: Shape—Shape – 1

NAME:

DATE: Making faces

1. Below are pictures of some 3-D objects and some 2-D faces that may belong to them. Circle the 2-D shapes that are needed for each object and write how many of each will be needed. (a)

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CONTENT DESCRIPTION: Makes models of three-dimensional objects and describe key features

(c)

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(f)

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Checklist

Sub-strand: Shape—Shape – 1

Make models of three-dimensional objects and describe key features (ACMMG063) Makes models of and describes the key features of … cubes

pyramids

cones & cylinders

spheres

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STUDENT NAME

prisms

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44

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Answers

Sub-strand: Shape

Shape – 1 Page 34

Resource sheet – Name the 3-D objects

1. (a) prism (d) cylinder (g) prism (j) cube 2. Teacher check Page 35

(b) (e) (h) (k)

sphere sphere pyramid cone

(c) (f ) (i) (l)

cone prism cylinder cube

Page 40 1. (a) (b) (c) (d)

(e) (f ) Teacher check

Resource sheet – Front view

1. (a)

Assessment 1 – Different views

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Assessment 2 – Top view

1. (a)

(b) (c)

(d) 2. Teacher check

(c)

Page 42

(d) (e) Teacher check

1.

Edges

Faces

Corners

12

6

8

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

4 (a)

(b)

Resource sheet – Pick the nets

1. (a) pyramid (tetrahedron; triangular-based pyramid) (b) cube (square prism) (c) prism (rectangular prism) (d) pyramid (square-based pyramid) (e) cone (f ) cylinder 2. Teacher check Page 39

Cubes

Resource sheet – Junk models

1. (a) Junk city: 3 cylinders, 1 cone, 2 spheres 2 cubes, 6 rectanglar prisms (b) Junk martian: 7 cylinders, 1 cone, 4 cubes, 2 spheres, 1 rectangular prism, 4 triangular prisms 2. Teacher check

Page 37

Assessment 3 – Edges, faces and corners

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3

(c)

3 (d) 2. Teacher check

18

12

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Resource sheet – 3-D shapes

triangular pyramid: 4 faces, 6 edges, 4 corners octagonal prism: 10 faces, 24 edges, 16 corners cube: 6 faces, 12 edges, 8 corners triangular prism: 5 faces, 9 edges, 6 corners square-based pyramid: 5 faces, 8 edges, 5 corners (f ) pentagonal pyramid: 6 faces, 10 edges, 6 corners

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8

12

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(b)

6

8

Assessment 4 – Making faces

(a)

6

0

0

3

0

2

3

0

2

1

4

0

0

2

1

0

4

0

(b)

(c)

(d)

(e)

(f)

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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45

Sub-strand: Location and transformation— L&T – 1

Create and interpret simple grid maps to show position and pathways (ACMMG065)

RELATED TERMS

TEACHER INFORMATION

Grid maps

What this means

• Maps that have both vertical and horizontal lines dividing the page and use coordinates. Simple grid maps would use, for example, letters along the horizontal (x-axis) and numerals along the vertical (y-axis).

• Students create simple grid maps of familiar places; e.g. the classroom or the school grounds, showing relative position of items.

Proportional scale is not expected at this year level, though some intuitive scale may be evident in students’ drawn maps. The idea of scale may be highlighted by appropriate questions such as, ‘If the teacher’s desk takes up this much room on the classroom map, how big do you think your desk would be?’

Position

• Being able to use simple coordinates for determining the position of an item on a grid.

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• The location of a place on the map.

It may be described according to its relative position to another place or using coordinates.

Pathway

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• Students being able to give and receive directions to determine location, or to give and/or follow directions to make a particular construction.

Teaching points

• The path or route used to get from one position on a map to another.

Coordinates (Cartesian coordinates)

• Teacher models the use of appropriate language of location; e.g. north, south, east, west, left, right, clockwise, anticlockwise, between.

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Student vocabulary coordinates

north

south west

east clockwise

anticlockwise left

right forward

backwards

over

under

turn

paces

steps

5 • When using coordinates for grid references, name the horizontal 4 (across), (x-axis) first followed by the vertical (up/down), (y-axis). So the 3 is at (B,4), not (4,B).

• National tests usually contain at least one question that involves reading coordinates.

What to look for

2 1

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• A pair of numbers or symbols that represent a position on a grid.

Understanding the concept of naming coordinates is essential in later years when using a grid with negative coordinates and two or four quadrants or when graphing functions in algebra and trigonometry. Being able to read road and other maps relies on an understanding of coordinates.

• Students need to be able to create and describe directions as well as interpret those made by others.

A

B

C

D

E

• Students who are not able to give and/or follow directions when using a simple map.

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• Students’ use of appropriate icons to represent items on maps they have created.

• Students who confuse the terms left and right and clockwise and anticlockwise.

• Students who are not familiar with directions for simple distances, e.g. face east and take two steps forward, then turn quarter of a turn clockwise.

• Students who, when using coordinates for grid references, use the vertical (y-axis) first followed by the horizontal (x-axis) instead of the other way around.

• Students who label the axis with the zero (0) in the incorrect place.

Note: In Australia, we use the term ‘anticlockwise’, rather than the American equivalent ‘counterclockwise’.

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Proficiency strand(s): Understanding

Problem solving

Fluency

Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Location and transformation— L&T – 1

HANDS–ON ACTIVITIES • Play the Grid moves game. Have one 8 x 8 square grid for each group of 3 or 4 students (see page 50). Each student has a token or counter which they place on a square of their choice in the grid. They take turns to select a card from the pack of descriptor cards (see page 51, or teacher and/or students create their own cards) that are face down between them and follow the instructions. If their move takes them off the grid, they are ‘out’. The last player on the grid is the winner. In the grid below, if the instructions were ‘Move 2 squares to the left and up 3 squares’, and it was their turn, Players 1 or 3 would be out. Players 2 and 4 could make this move. A faster alternative version of this game is that all students follow the descriptor cards, no matter who turned it over.

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2

3

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4

• Students make their own 5 x 5 grids and aim to find different ways to get around the grid without crossing their own lines. There are many more alternatives than the three shown below.

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• Students draw a plan (bird’s-eye view) of the classroom, identifying the key pieces of furniture. Discuss ways to mark the various objects using icons or a key. Ask questions about relative sizes. For example: Is the bookcase bigger or smaller than the easel? How much bigger is the teacher’s desk than any of the other desks?

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• Students re-do the class map, as above, but with changes to be made for rearranging the furniture to have a class party or to invite guests in for a class play. For a class play or similar, students would need to think about where the surplus furniture would be put, where a stage would go and how people would be able to move in, out and around the room.

For a class party, consideration would be given for accessing the tables with food and drinks, whether the students would sit after collecting their food, and if so, where the chairs would go.

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• Once the students have had practice at drawing maps such as those above, the concept of grid lines could be introduced. This could be done initially by adding the lines after the map has been drawn. Later, students could use 1 cm2 grid paper on which to create their map.

• Use a map of the school, adding, if necessary, a simple grid overlay with letters on the x-axis and numerals on the y-axis.

Discuss the location of the classroom, using coordinates. Ask questions such as: Where is the library? How would you get from the office to the car park? What are the coordinates of the art room? What is the shortest way to get from the canteen to the oval? What other ways could you get there? Students walk around the school with the plan finding each of the places they walk past on the map, particularly in terms of their coordinates. (See a similar activity on page 55.)

• First to ten game: Students consolidate their understanding of grids and coordinates through this game. By placing counters on identified coordinate cells, students attempt to have ten counters on the grid before their partner. Rules and game materials can be found on pages 52–54.

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Sub-strand: Location and transformationâ&#x20AC;&#x201D; L&T â&#x20AC;&#x201C; 1

HANDSâ&#x20AC;&#x201C;ON ACTIVITIES (CONTINUED) â&#x20AC;˘ Students create a map of a treasure island on grid paper and then write directions about how to get to the buried treasure. The first direction would start with a coordinate, then directions could be given according to moving a specific number of squares in different directions. Students try to make the directions interesting rather than just finding the shortest route.

H

edge of the world

START HERE

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Mt Explosion

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Bigboulders Beach

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TREASURE

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6 P 7 b 8l 9 t 10o 11s 12 Š4R. I C. u i ca i n Start at Fishermans point (1,H) and head south 3 squares, then east 1 square to Seal Beach.

3â&#x20AC;˘ squares toe Spotty Lighthouse.

3u squares to e Darkly f osouth rr vi e wp r peast os sforest. onl yâ&#x20AC;˘ 4 squares north and 1 square east to Pirate Cove. 1 square south to the summit of Mt Explosion.

1

2

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Then east 4 squares to the base of the Dusty Mountains.

3 squares south to the secret treasure spot (near Bigboulders Beach)

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â&#x20AC;˘ Provide a simple grid map of places of interest to the students, like a place where the students will have an excursion. Before the excursion discuss how the map may be of use, what can be found at certain points on the map, where lunch might be taken, or where free play time can occur. In groups, students plan routes for the trip, making sure all the points of interest are visited. Discuss the pros and cons of each of groupâ&#x20AC;&#x2122;s planned routes. Many places of interest have their maps available as an app for phones or handheld tablets.

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â&#x20AC;˘ Another activity which encourages students to interpret directional language can be found on page 55.

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â&#x20AC;˘ Ask students to draw a map of bedroom or lounge room over the weekend and bring it to class. Discuss what their maps show in terms of the layout of furniture, sizes of items and walkways in and out of the room. â&#x20AC;˘ Introduce the cardinal compass points of north, south, east and west. Signs could be put up on the classroom walls showing these directions. Ask students to turn in various directions, such as: Face north, turn clockwise 90°. Where are you now facing? Now turn 180°. Where are you facing now? Can you show this in some way on paper? â&#x20AC;˘ Students use â&#x20AC;&#x2DC;junkâ&#x20AC;&#x2122; items to build a city (see Shape â&#x20AC;&#x201C; 1), then draw a map of the city onto grid paper. They could then use both the map and the model to describe how to get from one place in the city to another. The lines on the grid paper become a way of referencing places on the map, and coordinates on each of the axes can be added to enable communication of the particular places. To organise a similar effect, lines of string could be laid out over the â&#x20AC;&#x2DC;junkâ&#x20AC;&#x2122; city corresponding to the lines on the grid map.

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Sub-strand: Location and transformation— L&T – 1

LINKS TO OTHER CURRICULUM AREAS English • Read the Once upon a time map book by B Hennessy and P Joyce. This book takes a trip to six different well-known story lands with maps, coordinates, routes, hidden objects and points of interest.

Information and Communication Technology • A free app for the iPad™ (and iPhone™) is a simple grid game called Flow Free. This game requires students to join coloured dots, while filling the whole grid.

• A simple grid game can be found at <http://au.ixl.com/math/kindergarten/location-in-a-three-by-three-grid>

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• Zoo maps can be found at the following places: – Perth Zoo <http://www.perthzoo.wa.gov.au/visit/zoo-map/> – Alma Park Zoo (Brisbane) <http://www.almaparkzoo.com.au/images/stories/pdfs/alma_park_zoo_guide_map.pdf> – Adelaide Zoo <http://www.zoossa.com.au/adelaide-zoo/zoo-information/zoo-map>

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Health and Physical Education • Play Indians and tepees (for practice of clockwise and anticlockwise):

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• Interactive zoo maps maps can be found at the following places: – Taronga Park Zoo <http://www.taronga.org.au/taronga-zoo/map-visit-planner> – Melbourne Zoo <http://www.zoo.org.au/Melbourne/Zoo_Map>

Students get in pairs, then form two circles with one partner in the inside circle and the other in the outside circle. The students on the inside circle (the ‘Indians’), sit cross-legged on the floor. The students on the outer circle (the ‘Tepees’), stand up with their legs apart to be the ‘tepee door’. All students face the centre. The teacher calls out either ‘Indians’ or ‘Tepees’. If the call is ‘Indians’, the students in the inner circle duck through the tepee door (between the legs of their partner), run clockwise around the circle and then duck back through the door to sit cross-legged in their original spot.

If the call is ‘Tepees’, the students in the outer circle run anticlockwise around the circle, and when they return to their spot, put one hand on their partner’s head and run in a small circle around them, ending back behind their partner with their legs apart. When running around the circle, any student who wishes to pass another must do so on the outside, with no jostling. The ‘Indian’ or ‘Tepee’ who is the last to get back to their original position loses, and both partners go and sit in the middle of the circles. Once they have missed one turn, they can return to the two circles. Generally, it is suggested that, every 2 or 3 turns, the Indians and Tepees in each pair change places.

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• Maps of local areas can be used as part of community studies.

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History and Geography

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Sub-strand: Sub-strand:Location Locationand andTransformation—UUM transformation— L&T – 41

RESOURCE SHEET Grid moves - Game grid

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You will need: • 1 grid per group of 3–4 students • 1 counter for each player (a different colour for each player) • 1 set of Grid moves – Game cards (see page 51)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET Grid moves – game cards

Move right 3 squares and down 2 squares

Move left 3 squares and down 1 square

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Move left 4 squares and up 2 squares

Go right 1 square and down 2 squares

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Move left 1 square and up 2 squares

Go left 2 squares and down 3 squares

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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C.Publ i cat i ons Go right 2 squares Move 2 squares to Move 1 square right rr evi e wleftp ur seson l y • up and• upf 2o squares the and upp 3o squares and 1 square

Go 4 squares right and 2 squares down

Go left 5 squares and up 3 squares

Move 2 squares to the right and 2 squares down

Move left 4 squares and 1 square down

Go right 5 squares and 1 square up

Go 1 square to the left and 1 square down

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Location and transformation—L&T – 1

RESOURCE SHEET First to ten game A game for 2 or 3 players.

You will need: • 1 grid per group • 10 counters for each player (a different colour for each player) • A set of letter cards in one colour and numeral cards in another colour (see pages 53-54)

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Rules: Players take it in turns to turn over one letter card and one numeral card. Place a counter on that square on the grid. If any player already has a counter in that square, the player misses that turn. The first player to have 10 counters of his or her colour on the grid is the winner. Alternative: If a player lands on a square already occupied by a counter, he or she ‘bumps’ it off, returns that counter to its owner and puts his or her counter in the square.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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Sub-strand: Location and transformation—L&T – 1

RESOURCE SHEET

A

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First to ten – letter cards

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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F

E

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(Copy onto a different coloured card to the numeral cards on the following page.)

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET First to ten – numeral cards

1

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(Copy onto a different coloured card to the letter cards on the previous page.)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET The new suburb

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Below is part of a map of a new suburb.

North

The map is missing some details. Show:

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1. Traffic lights at the corner of White and Green Streets

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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2. A shop at (G,4)

. te Green and Yellow Roads, with a slide ato 4. A park between (B,5) and swings c . at (C,6) che e r o t r 5. Orange Ave one-way heading s suwest per 3. A car park east of Black Lane and south of Yellow Road

6. A mail box at (K,8) and a café at (A,3) 7. A building of your choice at (F,2) and (F,3).

8. Describe how to get from the mail box to the café.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET The clothes line

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Below are two clothes lines with some washing hanging on them.

. te o c 1. What item is second from the right on the top line? . che e r o 2. Where you can find the T-shirt? t r s super 3. What item is second from the left on the lower line?

4. How many items are to the right of the socks?

5. How many items are to the left of the black jeans?

6. Draw your favourite piece of clothing so that it is second from the left on the top line.

7. Draw a jumper at the far right end of the bottom line.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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

CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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Assessment 1

Sub-strand: Location and transformation— L&T – 1

NAME:

DATE: Near the school

Below is a map of the streets around a school.

8 7

Park Road

4

School Street

Oval and Park

North

3 2

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Day care centre

Class Road

Busy Street

6 5

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School Careful Street

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1. What is at (H,5)?

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2. What are the coordinates of the post box?

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Shops

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1

o c . e what is on yourc left? her r o t s sup er 4. Use arrows to show that School Street is one-way from west to east.

3. If you leave the café and head east along Busy Street, then turn first right,

5. A hospital is going to be built just north of the school, with its entrance opposite the school’s entrance. Mark it on the map and describe how would you get from the shops to the hospital.

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Assessment 2

Shape—Shape Sub-strand: LocationSub-strand: and transformation— L&T – 1

NAME:

DATE: Ring a toy

Below is a game used at a school fete. The aim is to throw hoops over the squares and if you land on a toy, you win it.

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2. In what square is the fairy doll?

3. The toy in (C,4) is a

.

4. In what square is the toy train?

5. What is the toy in (A,5)?

6. Draw a toy frog in (E,2) and a toy of your choice in (B,1).

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Create and interpret simple grid maps to show position and pathways

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Checklist

Sub-strand: Location and transformation— L&T – 1

Identifies relative positions on a map

Interprets simple grid maps

Creates simple grid maps

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STUDENT NAME

Uses simple coordinates

Create and interpret simple grid maps to show position and pathways (ACMMG065)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Location and transformation— L&T – 2

Identify symmetry in the environment (ACMMG066)

TEACHER INFORMATION

RELATED TERMS Symmetry (reflectional or

What this means

bilateral symmetry)

• Students identify symmetry in the natural and built environment.

• The correspondence in size, form and arrangement, of parts on opposite sides of a line, point or plane; e.g. the butterfly below is symmetrical about the vertical line.

• Students look for symmetry in Aboriginal rock carvings and art.

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• We say that a shape that has no lines of symmetry is asymmetrical.

• Symmetry seems to be a concept that pleases the eye and is achieved naturally by most students (and adults) when using equipment such as pattern blocks or construction material in free play.

Teaching points

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vertical line of symmetry

• With two-dimensional shapes, folding and cutting are common ways to determine reflectional symmetry about a line.

Transparent mirror

(also known as a mira or georeflector) • A clear plastic tool used with symmetry; it has the reflective quality of a mirror, but can also be seen through, so that it reflects the front side of the shape onto the other side.

• Transparent mirrors may also be used to determine whether threedimensional objects are symmetrical about a plane.

• Students may need to be shown the correct way to handle a transparent mirror. Directions for this can be found on page 64.

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• Symmetry often occurs in the natural environment; e.g. pine cones, reflections of the landscape in a lake, many leaves and plants etc.

• National tests usually include at least one question about symmetry. Students need many experiences folding and cutting shapes to be able to visualise the results of these actions.

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• This applies to three-dimensional objects where half of the object corresponds in size, form and arrangement to the other half on the opposite side of a plane. For example, the cube below, has nine planes of symmetry, one of which is shown below.

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Student vocabulary

What to look for • Students are able to identify lines of symmetry in given situations, are able to identify more than one line of symmetry, where appropriate, and are able to identify shapes and objects with no lines of symmetry (i.e. they are asymmetrical).

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Plane symmetry

• Transparent mirrors are useful tools for this purpose.

• Students are able to identify planes of symmetry in threedimensional objects.

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• Students correctly holding and using a transparent mirror.

symmetry symmetrical line of symmetry plane of symmetry asymmetrical reflection transparent mirror

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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Sub-strand: Location and transformation—L&T – 2

HANDS–ON ACTIVITIES • Students investigate lines of symmetry in letters of the alphabet (choose a font for upper case letters that best suits this activity). For this activity, it may be useful to introduce the transparent mirror (see page 64).

I O

A B One line of symmetry

N J

Two or more lines of symmetry

No lines of symmetry

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Vertical line of symmetry

Horizontal line of symmetry

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• Symmetrical letters could also be classified according to the direction of the line(s) of symmetry.

Both horizontal & vertical

• As a follow-up to the activities above, students look to identify symmetry in words, using a transparent mirror. (See the activity on page 66.) Students could then make their own list of simple words that have line symmetry, using the letters identified as symmetrical in the activity above. Note: The way the words are written will make a difference to whether they may be considered symmetrical or not. For example, the word ‘HAT’ below, when written horizontally, is not symmetrical, but when written vertically, there is a line of symmetry that can be drawn through it. That is because all three letters have a vertical line of symmetry, but the ‘A’ and ‘T’ do not have a horizontal line of symmetry, only the ‘H’.

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• Students look in magazines for pictures that are symmetrical and make a ‘Symmetry book’, which may also include their own pictures and designs. Students can draw the lines of symmetry onto the pictures.

• Students collect pictures of symmetrical objects according to themes. For example, look for pictures of buildings, plants, art works, furniture or toys that are symmetrical. A related activity can be found on page 67.

• Investigate the number of lines of symmetry in each piece of a set of pattern blocks. Either the students could trace around each of the shapes, cut them out and then fold them to find the lines of symmetry, or they could use a transparent mirror (see pages 63–64 for similar activities). Note: All of the blocks are symmetrical, with the number of lines of symmetry shown below.

1 line of symmetry

2 lines of symmetry

3 lines of symmetry

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

4 lines of symmetry

6 lines of symmetry

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Sub-strand: Shape—Shape – 1

Sub-strand: Location and transformation— L&T – 2

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Symmetrical images of Indigenous art can be found through a simple internet search.

• Five pieces of symmetrical art work by Aboriginal artist Clifford Possum can be found at <http://prezi.com/exjkcnjshj_p/ copy-of-symmetry-examples-in-aboriginal-art/>. Note, however, that two of the artworks show rotational symmetry rather than reflectional symmetry.

• There is a simple symmetry ‘game’ that can be found at <http://www.innovationslearning.co.uk/subjects/maths/ activities/year3/symmetry/shape_game.asp>. What is good about this game is when you (deliberately) get a question wrong, the explanation as to why the answer is incorrect is very good, showing the shape folding on itself.

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• A series of symmetry activities with three levels of difficulty can be found at <http://www.haelmedia.com/ OnlineActivities_txh/mc_txh4_001.html> • A large number of different activities about symmetry can be found at <http://greatmathsgames.com/Symmetry/index. htm>

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• A simple activity where a series of dots are joined to make half a pattern so students fill in the other half can be found at <http://www.softschools.com/math/geometry/symmetry_game/>. Note: Each line section has to be made by clicking on two dots and cannot be done continuously by assuming that it will join to the dot just used.

Health and Physical Education

• Students create symmetrical shapes with their bodies that their partners try to reproduce. For example, a student may hold both arms out from his or her body at about the same angle.

• Mirrors: similar to the above activity, with partners facing each other. One student makes a shape or does a particular movement with his or her body (symmetrical or asymmetrical) and the partner must mirror it; so if the student raises his or her left leg, the partner raises his or her right leg, as would appear in a mirror.

The Arts

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• Students’ early experiences with symmetry comes about with ‘blob’ pictures, where blobs of paint are placed on paper, then the paper folded in half and pressed down. When opened out, the paint design will be symmetrical about the fold (the line of symmetry). Students can decorate these ‘blob’ pictures to make animals or other designs.

Science

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• Students look for symmetry in nature; e.g. flowers such as asters, banksias or bottlebrush. Also look for items in nature that are asymmetrical, such as kangaroo paws and emu bushes. Students could go for a bush walk to look at the different types of species in their area and which ones have symmetrical flowers.

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Symmetrical

Asymmetrical

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Symmetrical

Asymmetrical

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Symmetry in shapes

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(b)

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1. Trace the shapes below and cut them out. Try folding each one in two, so that each side of the fold is exactly the same. This is a line of symmetry.

Some of these shapes have one line of symmetry, some have more than one and some have no lines of symmetry. How many can you find? Mark any lines of symmetry on the shapes below. (a)

(c)

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CONTENT DESCRIPTION: Identify symmetry in the environment

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2. Make your own shapes and find lines of symmetry in them. Glue all your shapes onto paper and mark in all the lines of symmetry.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Using a transparent mirror

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1. Hold the transparent mirror on your desk, as shown in the picture. There is a ‘right’ and ‘wrong’ side for looking through the mirror. The ‘right’ side has a slanted edge which is placed face down on the paper. In this position, the mirror’s slanted edge will be touching the desk. You can move it to the mirror’s line of symmetry to show you a reflection.

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3. Now use the mirror to check for lines of symmetry in the shapes on the page 65. Some will have one line of symmetry, some will have more than one line of symmetry and some may have no lines of symmetry. Mark in all the lines of symmetry and write ‘Not symmetrical’ if the shape is asymmetrical (has no lines of symmetry).

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CONTENT DESCRIPTION: Identify symmetry in the environment

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2. Place the mirror on the picture of the butterfly below. Try to move the page rather than the mirror; move it until one half of the figure reflects onto the other half. Draw along the ridge with your pencil to mark in the line of symmetry.

Sub-strand: Location and transformation— L&T – 2 Shape—Shape –1

RESOURCE SHEET Transparent mirror activity page

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Draw in all the lines of symmetry you can find. Try making some different shapes of your own.

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CONTENT DESCRIPTION: Identify symmetry in the environment

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Reflections on symmetry 1. Put a transparent mirror on the dotted lines below. What did you notice?

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M A .te o c B OX . che e r o t r s super T 2. Make up some more ‘mirror words’.

3. Try cutting out some symmetrical letters from newspapers and magazines. Can you find any full words that have a line of symmetry?

Make a poster of what you find.

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CONTENT DESCRIPTION: Identify symmetry in the environment

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Symmetry in the garden 1.

Use a transparent mirror to find out if these objects have symmetry. Draw or cross

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in each box. Show any lines of symmetry.

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Choose •two f o rr e vi e wcould pufir pino eso nl yone •that is

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CONTENT DESCRIPTION: Identify symmetry in the environment

symmetrical and one that does not have symmetry (is asymmetrical).

Draw the line(s) of symmetry.

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Assessment 1

Sub-strand: Location and transformation— L&T – 2

NAME:

DATE: Transparent mirror symmetry

1. Use a transparent mirror to find which of these shapes have lines of symmetry, then draw them all in. Some may have one, some more than one and some have no lines of symmetry (they are asymmetrical). (b)

(c)

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2. Now draw some shapes of your own that have reflectional symmetry.

Draw in all the lines of symmetry for each one.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Identify symmetry in the environment

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Assessment 2

Sub-strand: Location and transformation— L&T – 2

NAME:

DATE: Deb and Tim’s toy shop

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TOY

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1. Use a transparent mirror to find and mark all the lines of symmetry in the words and objects in the picture below.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Checklist

Sub-strand: Location and transformation— L&T – 2

Uses a transparent mirror correctly

Identifies symmetry in natural environments

Identifies symmetry in human-made environments

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STUDENT NAME

Identifies symmetry in artwork

Identify symmetry in the environment (ACMMG066)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Answers

Sub-strand: Location and transformation

Page 65

L&T – 1 Page 55

Resource sheet – Transparent mirror activity page

Resource sheet – The new suburb

1.–8. Teacher check Page 56

jeans far left on the top line skirt 3 4 Teacher check Teacher check

Page 57

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Assessment 1 – Near the school

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a swing (B,7) oval and park (or swing) Arrows showing School Street is one-way from west to east. Teacher check.

5. Go left (or west) along Careful Street; turn right (north) into Class Road; first right into School Street and the hospital is on the left.

Page 58 1.

2.

3.

4.

5.

6.

Resource sheet – Reflections on symmetry

1.–3. Teacher check Page 67 1.

Resource sheet – Symmetry in the garden

(a)

Assessment 2 – Ring a toy

A toy car (A,2) A (beach) ball (C,1) A dog Teacher check

(b)

(c)

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L&T – 2

(e)

(f)

2. Teacher check

Page 63

Resource sheet – Symmetry in shapes

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(a)

(b)

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Assessment 1 – The clothes line

(c)

o c . che e r o t r s super There are an infinite number of lines of symmetry in a circle.

(d)

(e)

(f)

(g)

(f)

no lines of symmetry No lines of symmetry

2. Teacher check

(h)

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(i)

Assessment 2 – Deb and Tim’s toy shop

1. Teacher check Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Geometric reasoning—GR – 1

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

TEACHER INFORMATION

RELATED TERMS Angle

What this means

• Two lines with a common end point called a vertex, or the extent of rotation about a point.

• Right angles (those of approximately 90°) are ones that students should recognise.

Right angle 90°

• Knowledge that an obtuse angle is between 90° and 180°.

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• Knowledge that a full turn is the same as 360° and that half a turn is 180°.

Acute angle

• An angle less than 90°.

Obtuse angle

• Greater than 90° but less than 180°.

Straight angle

• Students are developing an awareness and understanding of the movement that relates to how angles are formed and to the measurement of angles.

• The use of a protractor is not encouraged at this stage.

Teaching points

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• Exactly 90°.

• Angles are classified by their size in their relationship to the right angle (90°). (Refer to related terms.)

• Right angles are used extensively in most buildings. For example, where walls meet the floor and the ceiling, the corners of rooms and most of the angles in the construction of cupboards. Books and paper mostly have 90° angles.

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• Many doors open to 180°, though if near a corner, they may only open to about 90°.

• Make links to the unit on time (UUM – 2) looking at the hands on an analogue clock as they turn in a clockwise direction.

One rotation

• A full turn to end up at the start (360°).

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• A unit of measure of an angle, based on there being 360° in a circle.

• Students need to be aware that degrees are also used to measure temperature, but this is not the same as the measure for angle.

Student vocabulary

• Also make links to the unit on location and transformation (L&T – 1) where quarter and half turns are used, along with ideas about the four cardinal compass points (north, south, east and west) and left/right and clockwise/anticlockwise.

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• Exactly 180°.

Degree

• Knowledge that an acute angle is less than 90°.

• Students can get an intuitive idea of the size of angles when making comparisons. For example, that the size of the angles on the hexagon piece of pattern blocks are greater than a right angle (90°) and also much bigger than the size of the angles on the triangular block, which are less than a right angle. At this stage, they do not need to measure the angles on the two pieces.

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• Show right angles in different orientations. This should help avoid a common misconception that we can have right angles and ‘left angles’.

right angle acute angle obtuse angle straight angle degrees rotation arms (of an angle)

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• It is important to make angles with different arm lengths so students realise that the length of the arms does not affect the size of an angle.

• National tests often include a question on angles, where students identify the largest or smallest angles from a set of angles that have different arm lengths.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Geometric reasoning—GR – 1

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

TEACHER INFORMATION What to look for • Students know the properties of a right angle (90°) and can represent them without the use of a protractor. (Note: Protractors are not encouraged at this year level).

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• Students confused by the length of the arms of an angle, thinking that an angle with short arms is less than an angle of lesser degrees but with longer arms. Students with this misconception would judge that the first angle below is wider than the second because of the length of the arms. In fact, the second angle is larger.

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• Students are aware that a straight angle is 180° (which is two right angles) and a full rotation is 360° (which is four right angles).

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Sub-strand: Geometric reasoning—GR – 1

HANDS–ON ACTIVITIES • In this unit, students will mostly compare angles to the right angle (90°). This would involve recognising that a straight angle is two right angles (180°) and a full turn is four right angles (360°). Discuss the idea that right angles occur all around us, including the corners of pieces of paper, books, corners in rooms etc.

• One method of introducing students to the idea of angles is to get them to (very carefully) trace the cutting edge of an open pair of scissors.

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My angle demonstrator is showing a straight line, which is 180°.

• Students make an angle unit measure that can be used as a non-standard unit. One version of this is to cut a sharp angle from a piece of cardboard. Allow the students to decide on how ‘pointy’ the angle is, but ‘quite pointy’ would be the instruction. Students then use their angle unit measures to measure different angles. Note that as the students have each decided on the ‘pointiness’ of their angle unit measure, there will be a variation of results for the same measuring activity, as there is when measuring the length of a table using the non-standard unit of hand spans.

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• Students make an angle demonstrator (see page 77). They use these to show various angles such as 90°, an angle less than 90°, an angle greater than 90°, a straight angle and a full turn. Students find ways to record their results. Play games where the teacher (or a student) calls out an angle size (from the five mentioned above) and the students make that angle with their angle demonstrator and hold it up for the teacher to check.

My angle unit measure

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• Another way to compare angles without a protractor is for students to make a different type of angle unit measure. This involves using a circle of light card. Students fold the circle in half, in half again, a third time, and finally a fourth time. When this is opened out, there are 16 equal (or very nearly equal) segments that become the units of the angle unit measure. Students then can use these to measure the size of angles in terms of the number of segments needed on their angle unit measure.

Students may make the link to the fact that four of these angle unit segments make a right angle (90°).

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I needed 4 of my angle unit segments to be the same as the corner of my book.

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Sub-strand: Geometric reasoning—GR – 1

HANDS–ON ACTIVITIES (CONTINUED) • Students look for objects that can rotate through a full turn, such as a rotary clothesline, helicopter rotors, windmills, wheels on any vehicles or the hands on a clock. Describe this as a ‘full turn’, which can then be related to 360°.

• Students look for objects that can rotate through part of a full turn, such as doors, the tray on a tip truck, pages in a book, swings or scissors. Encourage the use of the terms ‘less than a full turn’, ‘half turn’, ‘quarter turn’ and ‘three-quarter turn’. These terms can then be related to 180° for a half turn and 90° for a quarter turn. Relating a three-quarter turn to 270° would not be expected at this year level.

• Opening doors partially or fully gives an idea of angles. Many doors open to 180°, though if near a corner, they may only open to about 90°. Students could draw what the angle looks like at different points of turn.

• The hour and minute hands on a clock make angles as they turn. Students could discuss what angle is formed at certain times; e.g. 3 o’clock, 9:15, 12 o’clock, 9 o’clock or 12:07. This may link with the unit on time (UUM – 2).

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• Links could also be made to the unit on location and transformation (L&T – 1) where quarter and half turns are used, along with ideas about the four cardinal compass points (north, south, east and west) and left/right and clockwise/ anticlockwise.

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• Students use their arms to demonstrate angles. One arm remains out straight from their body (parallel to the ground); the other arm can be turned slowly to show a right angle, an angle less than a right angle, an angle greater than a right angle, a straight angle and a full turn.

• Play ‘Simon says’, with the teacher calling out various angle sizes and the students making the nominated angle with their arms. Terms such as ‘right angle’, ‘90°’, ‘less than 90°’, ‘more than 90°’, ‘straight angle’, ‘180°’, ‘full turn’ and ‘360°’ could be used. ‘Clockwise’ and ‘anticlockwise’ could also be used to indicate the direction of the turn. If students do not show the correct angle and/or direction, they sit down. The last one standing is the winner.

• Students use two craftsticks, straws or similar to make different types of angles: right angle, an angle less than a right angle, an angle greater than a right angle, a straight angle and a full turn. The sticks do not need to be joined; one may just overlay the other.

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• Students identify different angles in the room and in the outside environment. Try to find examples of right angles, angles less than 90° and angles larger than 90°. Students could look for pictures that illustrate the different angles.

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• Mix and match angles game. The cards on page 78 can be used to reinforce students’ recognition of right angles, straight angles and a full turn.

staight angle

180°

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

360°

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Sub-strand: Geometric reasoning—GR – 1

LINKS TO OTHER CURRICULUM AREAS English • Make vocabulary cards with drawings and definitions for new words associated with angles. For example, ‘right angle’, ‘straight angle’ and ‘full turn’. Each of the cards could also make mention of degrees of turn; e.g. 90°, 180° and 360°.

Information and Communication Technology • A website that asks students to decide whether the angles shown are greater than a right angle, exactly a right angle or less than a right angle can be found at <http://au.ixl.com/math/year-3/angles-greater-less-or-equal-to-right-angle>.

The explanation when an incorrect answer is entered is very good.

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Health and Physical Education

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• Students make angles using their arms, as described earlier. The teacher, or a student, could make an angle with his or her arms that the other students copy and describe. The person out the front could call out a type of angle for the other students to make with their arms.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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Sub-strand: Geometric reasoning—GR – 1

RESOURCE SHEET Make and use an angle demonstrator

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CONTENT DESCRIPTION: Identify angles as measures of turn and compare angles in everyday turns

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• Make two (2) circles about the same size as the one below; one in a light colour, the other in a darker colour. Carefully cut a line to the centre as shown below.

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Place one circle inside the other as shown. You cane now turn one circle of c h r your angle demonstrator within the other tot er o different angles. sshow super

• Use your angle demonstrator to show a right angle (90°), an angle less than 90° and a straight angle (180°). Draw these onto a sheet of paper. How can you show a full turn?

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Sub-strand: Geometric reasoning—GR – 1

RESOURCE SHEET Mix and match angles Cut out the 12 cards below. Mix them up and try to put them back in the correct groups.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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CONTENT DESCRIPTION: Identify angles as measures of turn and compare angles in everyday turns

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right angle

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Assessment 1

Sub-strand: Geometric reasoning—GR – 1

NAME:

DATE: What’s my angle?

You will need a wire, bread tie or a pipe cleaner.

Bend your object to make the angle below.

Call this the ‘angle unit’.

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CONTENT DESCRIPTION: Identify angles as measures of turn and compare angles in everyday turns

(a)

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Describe what type of angle each one is.

Number =

(a)

Number =

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Assessment 2

Sub-strand: Geometric reasoning—GR – 1

NAME:

DATE: What do you know about angles?

Write what you know about each of the types of angles below. Draw an example of each one. (b) A right angle

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(d) A full turn

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CONTENT DESCRIPTION: Identify angles as measures of turn and compare angles in everyday turns

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(a) Draw any angle (what does an angle measure?)

Sub-strand: Geometric reasoning—GR – 1

Recognises a full turn

Recognises a straight angle

Recognises angles greater than and less than 90°

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STUDENT NAME

Recognises right angles

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

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Answers

Sub-strand: Geometric reasoning

GR – 1 Page 79

Assessment 1 – What’s my angle?

1. (a) smaller (c) bigger

(b) bigger 2.

(b) 2 angle units. The angle is less than a right angle (90°).

It is an acute angle.

Assessment 2 – What do you know about angles?

Teacher check

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3 angle units. The angle is greater than a right angle (90°) It is an obtuse angle.

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(d) the same size

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3)

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