Australian Curriculum Mathematics - Measurement and Geometry: Year 2 - Ages 7-8

RIC-6095 5.8/945

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) Published by R.I.C. Publications® 2013 Copyright© Linda Marshall 2013 ISBN 978-1-921750-92-2 RIC– 6095

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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.

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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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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: MEASUREMENT AND GEOMETRY (YEAR 2) Foreword Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the 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.

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

Shape ........................................................................................ 54–75

Using units of measurement ........................................................ 2–53

• Shape – 1

• UUM – 1

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

Teacher information ............................................................................... 2–3 Hands-on activities ................................................................................. 4–6 Links to other curriculum areas .................................................................... 7 Resource sheets .................................................................................... 8–12 Assessment ........................................................................................ 13–14 Checklist .................................................................................................... 15

• UUM – 2

Teacher information ........................................................................... 16–17 Hands-on activities .................................................................................... 18 Links to other curriculum areas .................................................................. 19 Resource sheets .................................................................................. 20–23 Assessment ............................................................................................... 24 Checklist .................................................................................................... 25

• UUM – 3

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Tell time to the quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039) – – – – – –

Teacher information ........................................................................... 26–27 Hands-on activities .................................................................................... 28 Links to other curriculum areas .................................................................. 29 Resource sheets .................................................................................. 30–36 Assessment ........................................................................................ 37–40 Checklist .................................................................................................... 41

• UUM – 4

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Teacher information .................................................................................. 42 Hands-on activities .................................................................................... 43 Links to other curriculum areas .................................................................. 44 Resource sheets ......................................................................................... 45 Assessment ............................................................................................... 46 Checklist .................................................................................................... 47

• UUM – 5 Use a calendar to identify the date and determine the number of days in each month (ACMMG041) – – – – – –

• Shape – 2

Describe the features of three-dimensional objects (ACMMG043) – – – – – –

Teacher information .................................................................................. 66 Hands-on activities .................................................................................... 67 Links to other curriculum areas .................................................................. 68 Resource sheets .................................................................................. 69–71 Assessment ........................................................................................ 72–73 Checklist .................................................................................................... 74

Answers .................................................................................. 75

Location and transformation .................................................... 76–112 • L&T – 1 Interpret simple maps of familiar locations and identify the relative position of key features (ACMMG044) – – – – – –

Teacher information .................................................................................. 76 Hands-on activities .................................................................................... 77 Links to other curriculum areas .................................................................. 78 Resource sheets .................................................................................. 79–82 Assessment ........................................................................................ 83–84 Checklist .................................................................................................... 85

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Name and order months and seasons (ACMMG040) – – – – – –

Teacher information ........................................................................... 54–55 Hands-on activities ............................................................................. 56–57 Links to other curriculum areas .................................................................. 58 Resource sheets .................................................................................. 59–62 Assessment ........................................................................................ 63–64 Checklist .................................................................................................... 65

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Compare masses of objects using balance scales (ACMMG038) – – – – – –

– – – – – –

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– – – – – –

Describe and draw two-dimensional shapes, with and without digital technology (ACMM042)

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

Teacher information .................................................................................. 48 Hands-on activities .................................................................................... 49 Links to other curriculum areas .................................................................. 49 Resource sheets ......................................................................................... 50 Assessment .................................................................................................51 Checklist .................................................................................................... 52

Answers .................................................................................. 53

• L&T – 2

Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045) – – – – – –

Teacher information .................................................................................. 86 Hands-on activities .................................................................................... 87 Links to other curriculum areas .................................................................. 88 Resource sheets .................................................................................. 89–95 Assessment ........................................................................................ 96–98 Checklist .................................................................................................... 99

• L&T – 3 Identify and describe half and quarter turns (ACMMG046) – – – – – –

Teacher information ....................................................................... 100–101 Hands-on activities .................................................................................. 102 Links to other curriculum areas ................................................................ 103 Resource sheets .............................................................................. 104–107 Assessment .................................................................................... 108–109 Checklist .................................................................................................. 110

Answers ........................................................................ 111–112

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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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, and Location and transformation. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the proficiency strands have also been included.

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

• resource sheets • assessment sheets.

• a checklist

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

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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.

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

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

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

description.

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

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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

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

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

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

FORMAT OF THIS BOOK Sub-strand: Using units of measurement—UUM – 4

Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English, Information and Communication Technology (ICT), Health and Physical Education, History, Geography, the Arts, Science 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 A Year on our farm CZ 1 .BUUIFXT BOE " .D-FBO 5IJT CPPL JT POF PG GFX UIBU JMMVTUSBUFT UIF NPOUIT PG UIF ZFBS BOE UIF GPVS TFBTPOT JO B EJTUJODUMZ "VTUSBMJBO TFUUJOH SBUIFS UIBO TIPXJOH GPS FYBNQMF TOPX JO %FDFNCFS

Information and Communication Technology t 6TF UIF JOUFSOFU UP JOWFTUJHBUF UIF WBSJPVT TFBTPOT XJUIJO EJò FSFOU QBSUT PG "VTUSBMJB 5IJT DBO CF GPMMPXFE CZ BO JOWFTUJHBUJPO PG UIF TFBTPOT VTFE CZ *OEJHFOPVT "VTUSBMJBO QFPQMF BOE IPX UIFTF DPNQBSF UP UIPTF VTFE JO WFTUFSO TPDJFUZ 'VSUIFS JOWFTUJHBUJPO DPVME JOWPMWF MPPLJOH BU TFBTPOT JO UIF /PSUIFSO )FNJTQIFSF F H DPNQBSJOH UIF UJNJOH PG PVS TFBTPOT XJUI UIPTF JO /PSUI "NFSJDB PS UIF 6, PS OFBS UIF FRVBUPS F H JO 4JOHBQPSF PS *OEPOFTJB

t 6TF UIF JOUFSOFU UP JOWFTUJHBUF UIF TFBTPOT VTFE CZ *OEJHFOPVT "VTUSBMJBO QFPQMF 4PNF QFPQMFT TVDI BT UIF YPMOHV BOE /PPOHB QFPQMFT IBWF TJY TFBTPOT PUIFST POMZ UXP t 5IF "VTUSBMJBO (PWFSONFOU #VSFBV PG .FUFPSPMPHZ IBT B TJUF UIBU DPNQBSFT UIF TFBTPOT PG Ü WF EJò FSFOU HSPVQT PG *OEJHFOPVT "VTUSBMJBOT UP UIF WFTUFSO GPVS TFBTPOT XJUI UIF OBNFT BOE NPOUIT PG FBDI PG UIFN IUUQ XXX CPN HPW BV JXL DMJNBUF@DVMUVSF *OEJH@TFBTPOT TIUNM

History and Geography t 5IF EJò FSFOU TFBTPOT BOE UIF DPSSFTQPOEJOH XFBUIFS GPS WBSJPVT DPVOUSJFT DPVME CF JOWFTUJHBUFE BT JO *$5 BCPWF 5IFTF DPVME CF DPOOFDUFE UP DPVOUSJFT PG PSJHJO JG UIFSF BSF TUVEFOUT JO UIF DMBTT XIP BSF OPU PSJHJOBMMZ GSPN "VTUSBMJB

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

The Arts t 4UVEFOUT JMMVTUSBUF B QPTUFS PG UIF TFBTPOT UP IJHIMJHIU UIF EJò FSFOU UZQFT PG XFBUIFS UZQJDBMMZ FYQFSJFODFE JO FBDI PG UIFN t *OWFTUJHBUF *OEJHFOPVT "VTUSBMJBO BSU UIBU JT DPOOFDUFE UP TFBTPOT VTJOH BO JOUFSOFU TFBSDI FOHJOF t WaUDI BOE MJTUFO UP UIF :PV5VCF WJEFP Months of the year song IUUQ XXX ZPVUVCF DPN XBUDI W FO%3S8Z9BX

Languages

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t 4UVEFOUT MFBSO UIF OBNFT PG UIF NPOUIT PG UIF ZFBS BOE TFBTPOT JO BOPUIFS MBOHVBHF VJTJU BMNPTUø VFOU DPN UJNFEBUFT BOE TFBTPOT JO GSFODI UP Ü OE UIF TFBTPOT JO 'SFODI t 4UVEFOUT JOWFTUJHBUF BOE MFBSO TPNF PG UIF OBNFT HJWFO UP UIF TFBTPOT CZ *OEJHFOPVT "VTUSBMJBOT

Science

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

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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Assessment pages are included. These Š R. I .

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

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: Using units of measurement

(c)

UUM – 1 Page 9

Answers will vary Page 10

(d)

2. 6 5. 4

Page 12

3. 6 6. 5

Page 40

Resource sheet – Shell ruler

3. fish

starfish

Page 13

octopus

shark

Assessment 1 – Snakes alive

UUM – 4

Page 14

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Assessment 2 – Tropical islands

1. Teacher check 2. Answers in table will vary according to chosen unit.

3. Island 2 is the biggest.

UUM – 2 Page 23

(b) 10:45 (e) 1:15 (h) 3:15

Page 24

Assessment 1 – Comparing masses

Assessment 1 – In the year Month

Season

January

Summer

February

Summer

March

Autumn

April

Autumn

May

Autumn

June

Teacher check

UUM – 3 Assessment 1 – Quarter past nine

Winter

July

Winter

August

Winter

September

Teacher check

October Page 38

(c) 7:45 (f ) 4:45

Resource sheet – Which is heavier?

Teacher check

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

Assessment 4 – Draw the times – 2

(a) 2:30 (d) 6:15 (g) 6:30

Answers will vary according to the unit chosen.

Page 37

(h)

Resource sheet – Model building

1. 3 4. 4

1.–2.

(g)

Resource sheet – Triangle puzzle

Spring Spring

Assessment 2 – Match the times

(a)

9:45

ON

November

Spring

December

Summer

OFF

GIGA-BLASTER

UUM – 5 (b)

4:15

ON

OFF

Page 50

Resource sheet – Calendar activities

GIGA-BLASTER

(c)

2:15

ON

OFF

GIGA-BLASTER

(d)

11:45

ON

OFF

GIGA-BLASTER

Page 39

Assessment 3 – Draw the times – 1

(a)

(e)

(b)

(f )

1. (a) Teacher check (b) five (5) 2. (a) Thursday (b) five (5) 3. (a) Mondays (b) Thursdays 4. Answers should indicate that the calendar would need an extra row to have it after the 29th.

5. (a) Teacher check (b) 4th, 6th, 11th, 13th, 18th, 20th, 25th, 27th Page 51

Assessment 1 – Calendar questions

1. (a) Thursday (b) Sunday 2. (a) 1st, 8th, 15th, 22nd, 29th (b) 6th, 13th, 20th, 27th 3. (a) five (5) (b) four (4) 4. (a) Teacher check (b) 31st

(c) Friday

(c) four (4) (c) 25th

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) R.I.C. PublicationsÂŽ www.ricpublications.com.au

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

RELATED TERMS

TEACHER INFORMATION What does it mean

Comparison

• Relates to making judgements about only two shapes or objects. The vocabulary of comparison for length are ‘longer’ or ‘shorter’; for area and volume are ‘bigger’ or ‘smaller’; for capacity are ‘holds more’ or ‘holds less’.

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Teaching points

• Estimation should be encouraged in all measurement activities.

• Comparisons of length may be made by holding the two items directly alongside each other, making sure they are lined up at the same base point. Comparison can also be made using uniform units and counting how many of each unit it takes to cover the length of each item, and looking at the difference.

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• Refers to units that are all the same size, but not standard (metric) units.

For example, shells are non-standard units but are not uniform as they may vary in size. Paperclips are a nonstandard unit, but if they are all the same size—e.g. all small ones—then they would be considered uniform units.

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• The amount of space an object takes up.

• The amount a container can hold.

An example of this difference is if you consider an esky™. The amount of room it takes up in a cupboard is its volume.

The amount it can hold is its capacity.

• Comparisons of area may be made by placing one item directly on top of the other and using the visual difference. Comparisons may also be made using uniform units and counting how many of each unit it takes to cover each item, and considering the difference. A third method of comparing the area of two items is to cut one shape to fit inside the other; this may require several pieces of the first shape to be cut and placed over the second piece so that as much of the second piece is covered as possible.

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Uniform unit

• To compare and order the capacities of containers, use various containers of different sizes (heights and widths) and shapes.

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• Relates to making judgements about three or more shapes or objects.

It is also known as seriation. The vocabulary of ordering for length is ‘long’, ‘longer’, ‘longest’ or ‘short’, ‘shorter’, ‘shortest’; for area and volume – ‘big’, ‘bigger’, ‘biggest’ or ‘small’, ‘smaller’, ‘smallest’; for capacity – ‘holds the most’ or ‘holds the least’.

Capacity

• The lengths of items can be compared and ordered using units such as pencils, finger lengths, paperclips, craft sticks or lengths of string.

• To compare and order items according to area, use handprints or objects such as counters, pattern blocks, plastic shapes, etc.

Ordering

Volume

• Whenever the curriculum mentions ‘shapes’ it is referring to two dimensions; when it mentions ‘objects’ it is referring to three dimensions.

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• Comparisons of volume may be made by building objects with cubes and counting how many cubes were used for each object.

• Comparisons of capacity may be made by pouring from one container directly into another container. Comparisons may also be made by counting how many of a designated unit—e.g. eggcups—are needed to fill each container, and using the count to work out which holds more or less.

• Ordering items according to their length, area, volume or capacity would be similar to the above comparisons but use three or more shapes or objects.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

TEACHER INFORMATION (CONTINUED) Student vocabulary

• Students line up objects along the same base when comparing the length of two objects, or ordering three or more objects by length.

tall

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taller than tallest long

• Same-sized (uniform) units are used when making comparisons.

• Students counting uniform units to make comparisons; or to place objects in order of length, area, volume or capacity.

• Students realising that the smaller the unit, the more needed; the larger the unit, the fewer needed.

longer than

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longest

What to look for

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the same length as short

shorter than shortest

covers more (as in area) covers less

covers most

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holds more than hold less than

holds the most holds the least

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holds the same as

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

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

HANDS-ON ACTIVITIES Estimate before measuring in all these activities Length • Students are each given pieces of string of different lengths. They are asked to try to find another student with a piece of string that is the same length as theirs; then another that is longer than theirs, and another that is shorter. Move into groups of five or six and arrange the pieces of string from the shortest to the longest.

• Students choose an object—for example, a craft stick or pencil—and try to find things in the classroom that are the same length as it; then items that are longer or shorter than their object. Students then use their chosen object as a unit and find out how many of their units are needed to measure the length of items in the room, such as the whiteboard, a cupboard, a desk etc. Students write the names of five objects of their choice, and place them in order from the shortest to the longest. Discuss the results, and then ask the students to write a sentence explaining why they chose to put objects in their particular order. Hopefully the number of units they needed to measure each object would be mentioned in their reasoning. Discuss whether they could compare one student’s list with another student’s list if they used different units; e.g. if one used a straw as the unit, and the other used a Base Ten long.

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beanbag

chair

desk

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In our classroom

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• Objects within the classroom can be measured using paper tape. These lengths of tape can then be labelled (e.g. width of teacher’s desk, height of bookcase), lined up from shortest to longest and glued onto a chart as a permanent record of the lengths. The teacher needs to ensure that the pieces of tape are lined up from the same base point.

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Hand ruler

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• Students measure the same object using different units, and discuss (or write about) their findings. For example, ‘It took 23 buttons to go across the paper. It took 18 paperclips to go across it. It took 4 straws to go across it. It took 4 pencils to go across it. It took more buttons because they are smaller than the straws. It took 4 straws and 4 pencils because they are the same length’.

• Students cut a paper strip the same length as their hands; i.e. from their wrist to the tip of their middle finger. They then cut another paper strip the length of their waists, and use their hand ruler to find out how may of these units make the length of their waist. Use the hand ruler to measure their arm lengths etc.

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• The teacher asks the students how they could compare the lengths of two objects that are not close together; for example, the height of a bookcase and the length of the teacher’s desk. Students discuss the different ways they could be compared, and decide on the unit they wish to use to make the comparison. Have available a variety of materials the students could use, such as string, wool, counters, paper tape, sticks, shells, craft sticks etc. After the students have measured the two lengths and decided which one is longer, discuss the different results achieved using the different units.

• Have a collection of different materials for students to sort using the Sorting labels on page 8.

longer than

4

same length as

shorter than

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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

HANDS-ON ACTIVITIES (CONTINUED) Area

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• Students make a simple triangle puzzle, folding and cutting their own puzzle with instructions from the teacher, or use the template on page 9. Rearrange the pieces to form different shapes. Discuss what happens to the area of the rearranged shapes. Some students may not understand the concept of conservation of area; that the area of each new shape made with the four pieces has not changed because nothing has been added or taken away, and there are no overlaps. They may need plenty of experiences of this type before they come to this realisation.

• On blank paper, students draw around one hand with their fingers held together; then cut this out. Using their handprint, find others in the class whose hands are the same size as theirs; then look for people whose handprints are larger or smaller than theirs. Move into groups of 5 or 6 and arrange the handprints from smallest to largest (using the attribute of area – taking up more paper). Students then use their handprint as a unit, and measure the area of various items in the classroom; for example, it takes 5 of my handprints to cover the book. This can lead to discussion of why it takes, for example, 8 of Josh’s handprint but 6 of Natalie’s handprints.

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Volume

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• Use informal uniform units to cover various shapes. Suitable materials to use as units are: counters, blocks, beans, shells, gumnuts, square tiles, cubes, leaves of similar size, handprints, footprints etc. The teacher may try to lead students to look at which units work best and why. Discuss the gaps that are left when using some units, such as counters or beans. Discussion could also take place about why the units used to measure the area of an object should be uniform.

For example, if using leaves, rocks or shells, each piece needs to be a similar size so that comparisons can be made. We cannot make a valid comparison of the area of two shapes if large rocks are used to measure one, and smaller rocks used for the other; or if there is a different mix of large and small rocks.

• Students build various shapes using cubes. Discuss which shapes have the biggest volume. Students build different shapes that have the same base; for example, a 3 x 4 base (12 cubes). Give a maximum height; for example, 3 blocks high. Look at how many different models can be built, and what the volumes are of each model.

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• Build model buildings from the plans on page 10 using cubes. Discuss the volume (the number of cubes) in each building. Discussion can also take place about the height of each building, how many blocks were used on the base of each one, and which one was the tallest, shortest, widest etc. Also look at which two buildings used the same number of cubes (i.e. had the same volume), and discuss why they can look quite different. Finally, students order the buildings from the biggest volume to the least volume. Note: Twice there will be two buildings with the same volume.

• Ask the students to make their own set of buildings, each with a volume, for example, of five cubes. How many different buildings can they make? Check for buildings that are reflections or rotations of another.

• Collect a number of different sized boxes; e.g. cereal boxes, savoury biscuit boxes, ice-cream cone boxes. Discuss the different heights of the boxes and ask if the boxes with the same heights have the same volume. How can they find out?

Order the boxes according to their volumes.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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

HANDS-ON ACTIVITIES (CONTINUED) Capacity: • Have four or five of the same containers; e.g. yoghurt containers. Students leave one empty, fill one completely, then put different amounts of water or sand in the others so that they can line them up in order from ‘holding the least’ to ‘holding the most’.

• Use sand, water, beans or similar to measure the capacities of different containers. Ideally try to find containers that have different heights, widths, shapes etc. so it is not immediately obvious which container hold the most, least etc.

Sort the containers according to their capacity. Use labels to show the order of the containers’ capacities (See page 11).

holds the same as

holds more than

holds the most

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holds the least

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

• Students estimate the capacities of four or five different containers, and then measure by filling them using a uniform unit such as beans, cubes, rods, rocks etc. Alternatively, they can fill them with water or sand, using the one item such as a cup, beaker or eggcup as a unit to fill them, and counting the number needed. After the first container has been filled and measured, allow the students to revise their estimates of the other containers in the light of finding out how much the first container held. Students make a table of their results.

Container

My estimate

Measure

cup

10 eggcups

6 eggcups

ice-cream bucket

30 20 eggcups

15 eggcups

jar

21 14 eggcups

10 eggcups

vase

15 12 eggcups

12 eggcups

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• Compare and order the capacities of different containers using the same unit to measure; e.g. using a cup to fill several containers with water, and place them in order from the one that holds the most to the one that holds the least. Discuss what happens if the container being measured is smaller than the unit used; e.g. using a cup as the unit to compare the capacities of a ladle and a yoghurt container.

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• Students make simple pictographs using a drawing of the unit used, to show the capacities of a set of containers.

Discuss the results, using language such as ‘holds the most’, ‘holds the least’ and ‘holds the same as’. Then look at how you would line the containers up from the one/s that hold the least to the one/s that holds the most.

o c . che e r o t r s super milk carton

jar

jug

juice bottle

• Students pour two cupfuls of liquid into a tall, thin glass; then pour another two cupfuls of liquid into a short, fat glass.

Get them to estimate which glass will hold more before pouring. Discuss the result. Which glass did you think would hold more? Is that the one that did hold more? This experience is similar to Piaget’s Conservation Task where a child was shown two identical glasses, both with blue liquid in them. The child confirmed that both of the glasses held the same amount. The child was then asked to pour the liquid from one of the glasses into a longer, thinner glass. When asked if there was the same amount of liquid in these two glasses, a student who understands about conservation of volume would answer ‘Yes’; if not able to conserve volume, the student would answer ‘No’.

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

LINKS TO OTHER CURRICULUM AREAS English • Read the story Knee high Nigel by L Anolt. This story tells of five giants, one of whom, though still a giant, is much smaller than the other four.

• Read Big and small by J Pipe. This book looks at ‘big’, ‘bigger’, ‘biggest’; ‘small’, ‘smaller’, ‘smallest’; and ‘growing’.

Health and Physical Education • In groups of about six students, in a designated area—e.g. a wet area—students estimate how many strides it will take for one student to cross to the other side. Then all the students count out loud as the student strides across the area. If the student’s estimation is correct, he or she chooses the type of moves the next student in line will take. If the estimation is not correct, the student whose turn it is next decides on the moves. Suggestions for the moves could be long strides, bunny hops, walking backwards, shuffling sideways, jumping, running etc.

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• Have the students throw a beanbag as far as they can; both overarm and underarm. (This is better than throwing a ball, where it may bounce further than the initial throw.) Who could throw it the furthest?

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• Around the time of sports days, look at different lengths students achieve in the long jump and high jump. Who jumped the furthest or highest?

The Arts

• Students decorate paper to cover the area of a given object; for example, cover a jar or tin with triangles or squares or circles to make a pencil holder. Discuss which of the shapes made the best cover; i.e. covered the area most closely.

Look at whether the different shapes produce gaps or overlaps.

• Students make print patterns to cover a sheet of paper, using cut vegetables such as carrots, potatoes etc. Students could look at how many apple prints filled the paper compared to another student’s carrot prints on a same-sized sheet of paper. Also students could use strips of coloured paper to make a border or frame for the print. Discuss the length of the frame. This helps students form the initial concepts of area and perimeter.

Science

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• Make jelly, measuring how many cups of water are needed. Compare the jelly crystals to the finished jelly.

Languages

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• Students learn the words for long, longer, longest; short, shorter, shortest; the same length as, holds more than, holds less than, holds the most, holds the least, holds the same as in another language.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

RESOURCE SHEET

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o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

m same length as the .

longer than

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T ach shorter e than er

Sorting labels for length

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

RESOURCE SHEET Triangle puzzle

1. Cut along the lines so you have one big, one middle-sized and two small triangles.

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

2. What shapes can you make using all four pieces?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

RESOURCE SHEET Model building

1. Make each building below.

2. Write how many blocks you used for each model.

Teac he r I used

3.

blocks.

I used 4.

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blocks.

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I used 5.

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I used

10

blocks.

I used 6.

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I used

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

blocks.

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

2.

1.

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

RESOURCE SHEET

holds the least

holds the most

holds the same as

holds less than

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Teac holds more than he r

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

Sorting labels for capacity

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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11

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

RESOURCE SHEET Shell ruler

1. Cut strips of paper as long as each of the four sea creatures.

2. Use the shell ruler below and your strips of paper to order the sea creatures from the shortest to the longest. fish r o e t s Bo r e p ok u S

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3. Write the names in order. (shortest)

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

shark

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Teac he r

starfish

Assessment 1

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

NAME:

DATE: Snakes alive

1. Choose a unit to compare the lengths of the four snakes.

2. Complete the table.

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Sean snake

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Teac he r

Sandy snake

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

Sammy snake

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shortest

longer

even longer

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

longest

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Assessment 2

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

NAME:

DATE: Tropical islands

This map shows three tropical islands.

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. ttable to show how many units covered eachoisland.

2. Complete the e c . c e r Myh estimate Measure er o st super Island 1 Island 2 Island 3 3. Complete the sentence.

Island 14

is the biggest.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

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

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Teac he r

1. Choose some units to cover each island to help you decide which is the smallest and which is the largest.

Checklist

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

Can compare and order the volume and capacity of shapes using uniform units

Can compare and order the areas of shapes using uniform units

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

ew i ev Pr

Teac he r

STUDENT NAME

Can compare and order the lengths of shapes using uniform units

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

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o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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15

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

Compare masses of objects using balance scales (ACMMG038)

TEACHER INFORMATION

RELATED TERMS

What does this mean Mass

• 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’.

• Comparisons of mass may be made by placing one object in the pan on one side of the pan balance and the other object in the pan on the other side. Students then look at which pan is lower, signifying that this is the heavier object. Alternatively, one object may be placed in the pan on one side of the pan balance, and units such as marbles, counters, blocks etc, placed in the other pan.

Students make a count of how many of their units were needed to balance the beam. They then remove these, place the second object in one side of the pan balance, and use the same units in the other pan to balance the beam, again counting how many were needed. These counts are then compared to determine which is the heavier object.

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.

• The teacher should ensure that the pan balance is set so that, when empty, the beam is horizontal. Most pan balances have an adjustable sliding weight that can be moved to ensure the device is balanced when empty.

Balance scales

Teaching points

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

• Estimation should be encouraged in all measurement activities.

• The amount of matter, commonly measured in grams, kilograms and tonnes.

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• Relates to making judgements about only two objects. The terms of comparison for mass are ‘light’ and ‘lighter’; ‘heavy’ and ‘heavier’.

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• Hefting is a good way to encourage students to compare the masses of two objects. Students do this by holding one object in one hand, and the second object in the other hand. Students can move their hands up and down to simulate a pan balance. To check if they are happy with their estimations, have the students change which object is in each hand and heft again.

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Comparison

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Weight

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• Weighing is an activity that is active. It involves students picking up the objects; simply looking at an object will not usually tell you how heavy or light it is.

• Try to have some of the objects to be weighed of the same size and shape, but with different masses. For example, use two lidded tins, or yoghurt containers and fill each one with a different substance such as polystyrene beads and stones.

• Students need to discuss what it means when the pan on one side of the pan balance is lower than the pan on the other side.

• The materials chosen as non-standard units—e.g. marbles, blocks etc.—need to be of a mass that, when a number are placed in one pan to balance an object, that number will be within the students’ counting capabilities.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

Compare masses of objects using balance scales (ACMMG038)

TEACHER INFORMATION (CONTINUED) Student vocabulary

• Students who are unsure of whether the object in the pan that is lower weighs more or less than the object in the other pan.

light lighter heavy heavier

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

weighs more than weighs less than

weighs the same as

• Students keeping count of the number of units they use to balance the masses of each of the two objects being compared.

• Students who use a variety of items to measure against their object to be compared; e.g. some shells, cubes, counters and marbles.

• Students who do not use uniform units to compare; e.g. using big and small marbles.

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Teac he r

What to look for

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

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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17

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

HANDS-ON ACTIVITIES Estimate before measuring in all these activities Hefting • Students have two objects or containers for weighing. Encourage them to heft the two objects to estimate which of the two is heavier. They can then be placed on either side of a pan balance to determine which is heavier. Use the Mass labels on page 20 to record the results.

Pan balance activities

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

• The above activity could be done, but instead of putting the objects on either side of the pan balance, students put one object on one side and balance the object by placing units such as marbles, blocks, pebbles etc. and take note of the number of units needed. They then remove the object and units from the pan balance and put the second object to be compared into one pan, and count how many of the units are needed to balance it. Students then use the counts to determine which of the two objects is the heavier. Students record their results by writing about their findings, and by drawing a simple table. They could also use the Mass labels on page 20.

Teac he r

• Use sets of prompts on cards for students to follow. See pages 21 and 22 for some examples.

ew i ev Pr

• Students make a shape such as a ball with plasticine or similar material, and put it on one side of a pan balance. Then place units such as marbles or blocks in the other pan and count how many are needed to balance their shape. The student removes the shape and units from either side of the pan balance and make their shape into another form; e.g. snake shaped. They then predict how many of the units they think will be needed to balance this new shape when they put it back in the pan balance. This changing of the shape of the object, but understanding that the mass stays the same, is the concept of conservation of mass.

• Students could gain a deeper understanding of how a pan balance works by making a small seesaw with a ruler or larger piece of wood with a pencil or cotton reel as the fulcrum. For an even smaller model, students may use a craft stick and pencil. Students experiment by putting small objects on either side of the fulcrum to make the seesaw balance; or by adding items to one side to see what happens. Students need to be aware that as one side has more mass added to it, it will go down, and the more that is added, the lower it will go (although with most of these models, there’s not a lot of scope for going down far). Discuss what the seesaw will look like when there are objects of equal mass on each side, or when one object has more mass than the other. Also discuss what happens when one object is moved closer to the fulcrum. Modern playground seesaws use spring devices to avoid the old hazard of one child getting off unexpectedly and the child on the other side jolting to the ground. This means that ideas about having people of different masses on each side and the effect that has on the balance, or the effect of one person moving closer to the fulcrum are rarely experienced.

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• Teacher prepares a set of containers that are all the same size—e.g. yoghurt containers—but with different masses; include some containers that are about the same mass. Students are asked to find two containers that weigh about the same, or two containers where one is heavier than the other. Students record their results in a way of their choice, or they may use the Mass labels on page 20.

• Students could become involved in filling some containers to be weighed. This may help them realise that the samesized container could hold some materials that will be light and other materials that make them heavy.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

LINKS TO OTHER CURRICULUM AREAS English • Read Who sank the boat by Pamela Allen. This book looks at the idea of balance, and the fact that as each animal jumps into the boat, it sits a little lower in the water. It is the smallest animal that finally sinks the boat.

• Read Elephee’s walk by H Nakao. The idea of mass is highlighted, where again the smallest creature is the one that finally causes the downfall.

Health and Physical Education

Science

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Teac he r

• Ask the students to throw balls of different masses and sizes to see which they can throw the furthest before they bounce. Compare by throwing other suitable materials such as beanbags.

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• Students compare items collected from the outside environment for mass; e.g. two gumnuts or rocks.

• Students learn the words for ‘heavy’, ‘heavier’, ‘light’ and ‘lighter’ in another language.

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Languages

o c . che e r o t r s super

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

RESOURCE SHEET Labels for mass comparison

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weighs more than

has more mass than

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o c . c e herthe samest r weighs as o super

has the same mass as

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Compare masses of objects using balance scales

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has less mass than

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

RESOURCE SHEET Mass comparison cards –1

Card 1

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Teac he r

Find an object that has the same mass as your ruler.

Find an object that has more mass than a pair of scissors.

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CONTENT DESCRIPTION: Compare masses of objects using balance scales

Card 3

What can you find that has less mass than a tennis ball?

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Find two books that have the same mass.

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

RESOURCE SHEET Mass comparison cards – 2

Card 5

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Teac he r

Find an object that weighs the same as a basketball.

Find an object that has less mass than a whiteboard marker.

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What can you find that has more mass than your pencil case?

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Find two containers that weigh the same.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Compare masses of objects using balance scales

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Card 7

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

RESOURCE SHEET Which is heavier?

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Teac he r

Tick the one in each pair that is heavier. Using a pan balance will help.

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CONTENT DESCRIPTION: Compare masses of objects using balance scales

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Assessment 1

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

NAME:

DATE: Comparing masses

1. Circle the one in each pair that is heavier.

(b)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

CONTENT DESCRIPTION: Compare masses of objects using balance scales

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2. Circle the hand that holds the object with the greater mass.

Checklist

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

Uses the language of heavy/heavier or light/ lighter

Compares the masses of two objects by hefting

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

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Teac he r

STUDENT NAME

Uses a pan balance to determine the heavier of two objects

Compare masses of objects using balance scales (ACMMG038)

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o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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25

Sub-strand: Using units of measurement—UUM – 3

Tell time to the quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039)

RELATED TERMS

TEACHER INFORMATION What does it mean

Analogue clock

• 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, though at this year level it would not be needed.

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

• 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.

O’clock

• The use of the term ‘quarter to’ is the only time that students read times as ‘to’ the hour. When they learn to read and say times to the nearest 5 minutes and beyond, we use the digital method of saying times such as ‘three forty’ or ‘six thirty-eight’, rather than ‘twenty to four’ or ‘twenty-two minutes to seven’.

• Using an analogue clock, students recognise that at 12:00, the minute (big) hand and the hour (small) hand are both pointing to the 12. At any other o’clock time, the hour hand points to the hour, and the minute hand points to the 12. Also, students recognise that when the time is ‘half past’ the hour, the big hand points to the 6 and the small hand points halfway between two numbers on the dial; that when the time is ‘quarter past’ the hour, the big hand points to the 3 and the small hand points a quarter of the way between two numbers on the face; and when the time is ‘quarter to’ the hour, the big hand points to the 9, and the small hand points three-quarters of the way between the two numbers.

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Digital clock

• Students need to have a basic understanding of the fractions half and quarter.

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• Students understand that there are 60 minutes in an hour, that half an hour is 30 minutes and a quarter of an hour is 15 minutes.

• Students should be able to count by 5s to 60.

• Literally means ‘of the clock’.

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• Students recognise the features of an analogue clock: it is often circular; has a small hand for the hour, a large hand for the minutes, and many analogue clocks also have a longer, thinner hand for the seconds; the 12 is located at the top of the clock, the 6 at the bottom and the 3 and 9 on either side. For students of this age, a clock that shows all twelve digits is preferable. Try to avoid clocks that use Roman numerals.

• Students recognise that the hour hand on an analogue clock travels slowly and its movement cannot be seen; the minute hand travels more quickly and can sometimes be seen moving; if the clock has a second hand, it moves quite quickly and its movement can easily be seen.

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• 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, 7:15, the hour hand will be a quarter of the way between the 7 and the 8. As the minute hand on the clock is moved from 7:00 to 7:15, 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 3 to show quarter past the hour times, the hour hand does not move. This may be confusing for some students.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Using units of measurement—UUM – 3

Tell time to the quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039)

TEACHER INFORMATION (CONTINUED) Student vocabulary o’clock

• Classrooms should have both an analogue clock and a digital clock, preferably side-by-side. Regularly seeing the two different displays for the same time of day helps students realise that 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.

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

half past

quarter past quarter to

xx:15 (e.g. 3:15) xx:45 (e.g. 3:45) clockwise

What to look for

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

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Teaching points (continued)

• Students can make the connection between times to the hour, half hour and quarter hour shown on an analogue clock and the same times shown on a digital clock.

• On an analogue clock, students mixing up where the minute and hour hands point, e.g. showing 4:15 with the hour hand pointing to the 3 and the minute hand pointing to the 4.

• Students confusing ‘quarter past’ and ‘quarter to’.

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• Students not making the connection between ‘quarter past’ (e.g. quarter past 4) and xx:15 (e.g. 4:15); and not making the connection between ‘quarter to’ (e.g. quarter to 7) and xx:45 (6:45).

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• Confusion with the hour when reading or writing ‘quarter to’; e.g. that ‘11:45’ and ‘quarter to 12’ is the same time.

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Sub-strand: Using units of measurement—UUM – 3

HANDS-ON ACTIVITIES Discuss time incidentally • The teacher should take the opportunity to discuss what time it is whenever appropriate. For example, ‘It is playtime, half past 10, so the big hand is on the 6 and the small hand is just half way between the 10 and 11’; or ‘It is nearly home time, so the big hand is on the 9 and the small hand is nearly on the 3; it is quarter to three’. The teacher also discusses the corresponding time display on the digital clock.

Clock bingo

Using clocks

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• Play Clock bingo (Boards on pages 30–32; with a blank bingo board on page 33). Students have bingo boards showing analogue times, digital times, or a mixture of both. The teacher or person in charge has a set of time cards (various times on pages 34–35 [to be enlarged]; with a blank time cards sheet on page 36). The teacher turns over and holds up a time card for the students to see. If using only analogue times on the bingo boards, the teacher’s cards should show digital times, and vice versa. If students have a clock on their bingo board that matches the time shown on the teacher’s card, the student covers the time with a counter. The first student to cover all the clocks on their board is the winner. Note: Time cards have not been made for all of the appropriate times between 1:00 and 12:45; only the times used in the bingo boards. Blank bingo cards are provided on page 33 if other times are required.

• Students have their own analogue clocks, either ones they’ve made themselves or commercial ‘toy’ clocks. The teacher holds up a digital time card from page 35, or uses the blank time cards on page 36, enlarged. Alternatively, the teacher could call out a time. Students show that time on their clocks and hold them up for the teacher to see.

• Commercial clocks can be bought where both the analogue and digital times can be displayed. These may come with a smaller desk-sized version where students can turn the hands, and write the digital time. The teacher could then hold up a time card, or call out a time, and the students make that time on both the analogue and digital section of the clock.

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• To assess student knowledge of time, ask students to draw their own analogue clock ‘from scratch’. To successfully read and write times with ‘quarter to’ and ‘quarter past’, students will need to know: – the sequence of numbers from 1 to 12

– the correct placement of those numbers on a circle – where the minute (big) hand points when showing ‘quarter to’ (pointing to the 9) and ‘quarter past’ (pointing to the 3) – where the hour (small) hand points when showing ‘quarter to’ (pointing almost to the next hour) and ‘quarter past’ (pointing to just past the hour).

• Take note of how they deal with the four points above. This initial sample of work may be dated and kept to be used as a benchmark. Later in the year, a second clock may be drawn and comparison made between the first and second clocks.

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Sub-strand: Using units of measurement—UUM – 3

LINKS TO OTHER CURRICULUM AREAS English • Read The Bad tempered ladybird by Eric Carle. In this book a ladybird works it way through different times of the day. The times are shown on analogue clocks.

• Learn the rhyme Hickory dickory dock. For full verses for times from 1–12, see <www.enchantedlearning.com/ Hickorydickory.html>

Information and Communication Technology • Have analogue clock faces and digital clocks on the interactive whiteboard. Students match each analogue time with the digital equivalent.

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Health and Physical Education

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• Play a variation of What’s the time, Mr Wolf? Instead of calling out a time on the hour, allow only times with ‘quarter past’ or ‘quarter to’. Students still go forward the number of steps for the hour—e.g. if quarter past three is called out, the students may walk forward three steps—but if quarter to three is called, the students need to know that the ‘hour’ shown on an analogue clock would only be past the two (although nearer the three, it is not there yet), so they may only take two steps forward.

The Arts

• Students make their own paper plate clocks; folding to find the correct position for the 12, 6, 3 and 9, then put in the other digits. Use split pins or similar for the hour and minute hands.

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RESOURCE SHEET Student bingo boards – 1

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RESOURCE SHEET

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Sub-strand: Using units of measurement—UUM – 3

RESOURCE SHEET

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CONTENT DESCRIPTION: Tell time to the quarter hour, using the language of ‘past’ and ‘to’

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Assessment 1

Sub-strand: Using units of measurement—UUM – 3

NAME:

DATE: Quarter past nine

1. Draw the shape of a large clock face.

2. Write the numbers 1 to 12.

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3. Draw hands to show quarter past nine.

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Assessment 2

Sub-strand: Using units of measurement—UUM – 3

NAME:

DATE: Match the times

Draw a line from each analogue clock to the digital clock that shows the same time.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

CONTENT DESCRIPTION: Tell time to the quarter hour, using the language of ‘past’ and ‘to’

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Assessment 3

Sub-strand: Using units of measurement—UUM – 3

NAME:

DATE: Draw the times – 1

Draw the hands on the clocks for each time. (a)

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Assessment 4

Sub-strand: Using units of measurement—UUM – 3

NAME:

DATE: Draw the times – 2

Show the correct times on the clocks. (a)

(e) quarter or e st B : er : past 1 o p ok u S ON

OFF

quarter to 11

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quarter to 8

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CONTENT DESCRIPTION: Tell time to the quarter hour, using the language of ‘past’ and ‘to’

half past 2

Checklist

Sub-strand: Using units of measurement—UUM – 3

Can convert time to the quarter hour from analogue to digital and vice versa

Can tell time to the quarter hour on a digital clock

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STUDENT NAME

Can tell time to the quarter hour on an analogue clock using the language of ‘past’ and ‘to’

Tell time to quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039)

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Sub-strand: Using units of measurement—UUM – 4

Name and order months and seasons (ACMMG040)

RELATED TERMS

TEACHER INFORMATION What does this mean

• Relates to making judgements about three or more shapes or objects. It is also known as seriation. In this context, ordering months or seasons means simply naming them in the correct order.

• Students know there are twelve months in the year.

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• Students become fluent in reciting the months of the year.

• Students need to be aware of the abbreviation used for each month.

• Students know the names of the seasons.

• Students recognise the typical weather patterns associated with each of the seasons.

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Ordering

• There is a need to acknowledge the local situation regarding seasons.

Teaching points

• Students know that there are twelve months in a year and can name the months in the correct order.

• Students know there are about four weeks in a month.

• Students (in most areas) know there are four seasons in the year, and can name them; although students in some areas such as tropical regions may know that they have only two seasons (the wet and the dry).

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Student vocabulary Months of the year: January

• Students not being able to recite the months of the year in the correct order.

March April

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August

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• Students not being conversant with the seasons for their region, and the months that correspond with those seasons.

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• Students not aware of the differences in weather that are typical for each of the seasons.

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Seasons: spring summer autumn winter

the wet season the dry season

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Using units of measurement—UUM – 4

HANDS-ON ACTIVITIES Months of the year card mix up • In pairs, one student cuts out the months of the year (page 45), mixes them up, and the partner puts them into the correct order.

What month is missing?

• Using the cards on page 45 after mixing up the order of the months, one student removes and hides the label for one of the months and the partner works out which month is missing.

Birthday month sort

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• Sort students’ birthdays into months; then into seasons. Make a class graph of how many students have birthdays in each month. Discuss which month or which season has the most or least birthdays.

The seasons

Spring

Summer

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• Make posters of the types of weather that typically occur in each season, and the types of clothing that we would use for each. The students can draw the illustrations, or make a collage of pictures from magazines to glue onto the posters.

Autumn

Winter

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• Discussion could arise on the types of weather in different countries, particularly if some students come from overseas.

This could include the fact that the seasons in the Northern Hemisphere are at opposite times of the year from the seasons in Australia. Also some regions may experience snow while others may have tropical weather, including cyclones.

• Make a mobile showing the four seasons. Use a strip of card, staples and fishing line or string. Fold the paper strip into 4 equal sections. The students label each of the segments, and illustrate each season on the mobile. The card can then be stapled to make a loop, and suspended using the fishing line or string.

ING Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Using units of measurement—UUM – 4

LINKS TO OTHER CURRICULUM AREAS English • Read A Year on our farm by P Matthews and A McLean. This book is one of few that illustrates the months of the year and the four seasons in a distinctly Australian setting, rather than showing, for example, snow in December.

Information and Communication Technology • Use the internet to investigate the various seasons within different parts of Australia. This can be followed by an investigation of the seasons used by Indigenous Australian people, and how these compare to those used in Western society. Further investigation could involve looking at seasons in the Northern Hemisphere (e.g. comparing the timing of our seasons with those in North America or the UK), or near the equator (e.g. in Singapore or Indonesia).

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• Use the internet to investigate the seasons used by Indigenous Australian people. Some peoples such as the Yolngu and Noonga peoples have six seasons, others only two.

History and Geography

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• The Australian Government Bureau of Meteorology has a site that compares the seasons of five different groups of Indigenous Australians to the Western four seasons, with the names and months of each of them <http://www.bom. gov.au/iwk/climate_culture/Indig_seasons.shtml>

• The different seasons and the corresponding weather for various countries could be investigated, as in ICT above. These could be connected to countries of origin if there are students in the class who are not originally from Australia.

The Arts

• Students illustrate a poster of the seasons to highlight the different types of weather typically experienced in each of them.

• Investigate Indigenous Australian art that is connected to seasons using an internet search engine.

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• Watch and listen to the YouTube video Months of the year song <http://www.youtube.com/watch?v=5enDRrWyXaw>

Languages

• Students learn the names of the months of the year and seasons in another language. Visit <almostfluent.com/timedates-and-seasons-in-french/> to find the seasons in French.

Science

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• Students investigate and learn some of the names given to the seasons by Indigenous Australians.

• Select animals of student choice and research their behaviour during different seasons. Plants may also be studied in the same way.

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET

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Assessment 1

Sub-strand: Using units of measurement—UUM – 4

NAME:

DATE: In the year

Below are the months of the year, but not all of the letters in the words have been written. Write in the rest of the word and then put the season next to it. Use the words Spring, Summer, Autumn or Winter.

Month

Season

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CONTENT DESCRIPTION: Name and order months and seasons

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Checklist

Sub-strand: Using units of measurement—UUM – 4

Knows the names and order of the seasons

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STUDENT NAME

Knows the names and order of the months of the year

Name and order months and seasons (ACMMG040)

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Sub-strand: Using units of measurement—UUM – 5

Use a calendar to identify the date and determine the number of days in each month (ACMMG041)

RELATED TERMS

TEACHER INFORMATION

Calendar

What does this mean

• A chart showing the days, weeks and months of the year. Usually it spans January to December, although July of one year to June of the next may be shown.

• Students need to be aware that calendars have a variety of ways in which the months are arranged (one to a page, several to a page, all twelve months on one page; reading across, reading down) and in which the days of the weeks are written (usually either across the top row, or down the left-hand column).

Leap year

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• A year in which there are 366 days.

This normally occurs every 4 years, and occurs whenever the year is divisible by 4, other than century years. The length of a solar year (the amount of time it takes for the earth to orbit the sun, on which the length of the year is based) is just under 365¼ days, so every four years an extra day is needed to balance this. However, to correct the fact that this is very slightly over the days required, the century years are only leap years if they are divisible by 400.

• Some calendars have different ways of dealing with months where more than five rows are used; e.g. there may be situations where the last day/s of the month are shown at the start of the month rather than in their correct chronological place at the end of the month.

• Students know the number of days in each month.

• The use of ‘st’ (as in 1st), ‘nd’ (as in 2nd), ‘rd’ (as in 3rd) and ‘th’ (as in 4th) when writing the date is no longer encouraged. The date should be written as, for example, 4 July 2013.

Teaching points

• Students find a given date on a calendar and are able to determine on what day of the week it occurs.

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• All the months of the year have 28, 29, 30 or 31 days. February is the most problematic month because it usually has 28 days, but 29 in a leap year.

What to look for • Students unable to recall how many days there are in each month.

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• Students unable to use a calendar to find a specific date, or unable to determine the day of the week on which it occurs.

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

Student vocabulary days of the week

Understanding Fluency Problem solving Reasoning

months of the year leap year

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Sub-strand: Using units of measurement—UUM – 5

HANDS-ON ACTIVITIES Daily dates • As part of the daily routine, the teacher talks about what the date is each day. This would include the day of the week, the date of the month and the month of the year. Discuss what month it is, what the month before was, what the next month will be.

Number tracks • Number tracks can be made for any particular month, and students use them to determine that day’s date. The number track could have the day of the week included, as well as space to record any important events that will occur that month.

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1 Thur.

2

3

4

5

Fri.

Sat.

Sun.

Mon.

Using a calendar

...

29

30

Thur.

Fri.

Holiday

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Ben’s birthday

...

• Teacher gives the students specific dates to find in the calendar. Questions could include: On what day of the week does Anzac Day fall this year? In what month is Easter this year? Is that the same as last year? How many months is it until we start swimming lessons in November?

• Write onto a calendar some specific events for a month; e.g. mark in music lessons that occur every Wednesday.

• Investigate and discuss culturally-specific days, particularly where they relate to students who come from another culture.

Learn the days of the months rhyme

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• Students learn a rhyme for the number of days in each month. There are two main variations: Thirty days hath September, Thirty days has September, April, June and November.

April, June and November.

All the rest have thirty-one February has twenty-eight; Excepting February alone.

And thirty-one the others date.

It has twenty-eight days clear, But if a leap year to assign And twenty-nine in each leap year.

Then February twenty-nine.

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LINKS TO OTHER CURRICULUM AREAS

31 days 30 days or less

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• Knuckles can also be used to help remember the number of days in each month. Both fists are clenched alongside each other, and the knuckles and gaps can be used, as in the diagram.

J M MJ

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Information and Communication Technology

• Students investigate the number of different types of calendars they can find on the internet.

• Students use the internet to determine the origins of the names of the months.

• View and listen to the days in the month song on YouTube <http://www.youtube.com/watch?v=drH3_Flt85g>

The Arts • Students make a calendar, or download one from the internet, and then illustrate it as a present for a family member.

Languages • Students learn the names of the months of the year in another language.

Civics and Citizenship • Investigate culturally significant events in the local community and link them to the calendar.

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Sub-strand: Using units of measurement—UUM – 5

RESOURCE SHEET Calendar activities

Tues.

Wed.

Thur.

Fri.

Sat.

Sun.

1

2

8

9

31 3 10

5

11

12

7

25

26

27

28

29

1. Music lessons are on Mondays. (a) Colour them in red on the calendar. (b) How many Mondays are there in this month?

16 23

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13o 14 15 r e t s B r e oo p 18 u19 20 21 22 k S

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4

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C.Publ i cat i ons •f orr evi ew pur posesonl y• What day of the week is that?

2. The class item for Assembly is on the 20th of this month. (a)

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(b) If the class practises every Monday and Thursday, how many

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practices can they fit in this month before Assembly?

3. Underline the correct day.

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o c . (b) There are less Thursdays/Saturdays than Sundays. che e r o t r s up er 4. Why is the 31st shown at the s start of the month? (a) There are more Mondays/Fridays in this month.

5. Mum comes to help in the class every Tuesday and Thursday. (a) Circle the days she helps. (b) Write all the dates she helps if this month is August.

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CONTENT DESCRIPTION: Use a calendar to identify the date and determine the number of days in each month

Mon.

Assessment 1

Sub-strand: Using units of measurement—UUM – 5

NAME:

DATE: Calendar questions Mon.

6

Tues.

Wed.

Thur.

Fri.

Sat.

Sun.

1

2

3

4

5

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12

7

13

27

28

29

9

30

10

31

1. What day of the week is:

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2. What are the dates of: (a) all the Wednesdays?

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CONTENT DESCRIPTION: Use a calendar to identify the date and determine the number of days in each month

(a) the 16th?

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20

8

(b) all the Mondays?

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Wednesdays are in this month? ch e r e o t r s Mondays are in thiss month? uper

3. How many: (a) (b)

(c) Sundays are in this month?

4. (a) Circle Bella’s birthday, which is on the last Friday. (b) What is its date? (c) Bella is having her birthday party on the Saturday before her birthday. What is the date of her party?

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Checklist

Sub-strand: Using units of measurement—UUM – 5

Knows the number of days in each month

Is able to determine the day of the week of a given date using a calendar

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STUDENT NAME

Is able to identify specific dates on a calendar

Use a calendar to identify the date and determine the number of days in each month (ACMMG041)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Answers

Sub-strand: Using units of measurement

UUM – 1 Page 9

(c)

(g)

(d)

(h)

Resource sheet – Triangle puzzle

Answers will vary Page 10

Resource sheet – Model building

1. 3 4. 4

2. 6 5. 4

Page 12

3. 6 6. 5

Page 40

Resource sheet – Shell ruler

3. fish

starfish

Page 13

(a) 2:30 (d) 6:15 (g) 6:30

shark

Answers will vary according to the unit chosen.

UUM – 4

Page 14

Page 46

Assessment 2 – Tropical islands

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January February March

Resource sheet – Which is heavier?

April

Teacher check

May

Assessment 1 – Comparing masses

June July

Assessment 1 – Quarter past nine

Teacher check Page 38

9:45

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(c)

ON

OFF

GIGA-BLASTER

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UUM – 5

4:15

Autumn

Autumn Autumn Winter

Winter

August

Winter

September

Spring

October

Spring

November

Spring

December

(d)

2:15

11:45

OFF

ON

OFF

ON

OFF

GIGA-BLASTER

Assessment 3 – Draw the times – 1

(a)

(e)

(b)

(f )

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Summer

Resource sheet – Calendar activities

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GIGA-BLASTER

GIGA-BLASTER

Page 39

Summer

Assessment 2 – Match the times

(a)

(b)

Summer

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Teacher check

UUM – 3

Season

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Page 37

Assessment 1 – In the year

Month

UUM – 2

(c) 7:45 (f ) 4:45

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1. Teacher check 2. Answers in table will vary according to chosen unit.

3. Island 2 is the biggest.

1.–2.

(b) 10:45 (e) 1:15 (h) 3:15

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octopus

Assessment 1 – Snakes alive

Page 23

Assessment 4 – Draw the times – 2

1. (a) Teacher check (b) five (5) 2. (a) Thursday (b) five (5) 3. (a) Mondays (b) Thursdays 4. Answers should indicate that the calendar would need an extra row to have it after the 29th.

5. (a) Teacher check (b) 4th, 6th, 11th, 13th, 18th, 20th, 25th, 27th

Page 51

Assessment 1 – Calendar questions

1. (a) Thursday (b) Sunday 2. (a) 1st, 8th, 15th, 22nd, 29th (b) 6th, 13th, 20th, 27th 3. (a) five (5) (b) four (4) 4. (a) Teacher check (b) 31st

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

(c) Friday

(c) four (4) (c) 25th

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Sub-strand: Shape—Shape – 1

Describe and draw two-dimensional shapes, with and without digital technology (ACMM042)

RELATED TERMS

TEACHER INFORMATION What does it mean

Classification

• Involves deciding which things belong in a group and which do not.

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Two-dimensional shapes; Threedimensional objects

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• Attributes of the shape to be described could include straight or curved lines, the number of sides, the number of corners etc.

Teaching points

• Students look at the attributes of familiar two-dimensional shapes, classifying them according to their corners, number of straight sides, curves etc.

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• Whenever the curriculum mentions ‘shapes’ it is referring to two dimensions; when it mentions ‘objects’ it is referring to three dimensions.

Note: All two-dimensional shapes we use with students have a third dimension of depth, but we generally accept that paper shapes and manipulatives such as pattern blocks and Attribute Blocks can be used to represent two-dimensional shapes.

• Students use different methods to construct two-dimensional shapes; e.g. folding and/or cutting

• ‘Families’ of shapes can be identified; particularly the ‘quadrilateral’ family. There are many different common shapes that fit into this ‘family’. These include squares, rectangles, kites, and rhombuses; also trapeziums, parallelograms and the less commonly used chevron or arrowhead. Any other, non-regular, four-sided shape also fits into the quadrilateral ‘family’. This understanding that there are a number of different shapes that fit into the quadrilateral ‘family’ would lead to discussions about what are the special features or attributes of each of the types of common quadrilaterals. For example, describe what the difference is between a square and a rectangle. (Note: A square can be classified as a special type of rectangle, but a rectangle may not necessarily be a square.)

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• Any four-sided shape. This includes squares, rectangles, kites, rhombuses etc.

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• There is a slight difference in definition between a rectangle and an oblong. A rectangle can be defined as a quadrilateral with all angles right angles (90°). An oblong is a rectangle that is not a square. It would not be necessary to discourage students’ use of the word ‘oblong’, but it would be better to use the term ‘rectangle’ with the students.

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Quadrilateral

• Suggested two-dimensional shapes include squares, rectangles, triangles, kites, rhombuses and circles.

• Teacher models the use of the appropriate language of comparison, such as ‘belongs with’, ‘is bigger than’, ‘has three straight sides’, ‘is different from’, ‘has more corners’, ‘has curved sides’ etc.

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• The real world functions of familiar shapes can be discussed; e.g. triangles used as part of the roof support of an undercover area, or squares and/or rectangles used as windows and doors.

• Students need to be able to know and use the correct names for shapes and objects. Note: A square turned on one of its corners is not a ‘diamond’, it is still a square. There is no mathematical term ‘diamond’; if it is not a square, then it is a rhombus (below).

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Shape—Shape – 1

Describe and draw two-dimensional shapes, with and without digital technology (ACMM042)

TEACHER INFORMATION (CONTINUED) Student vocabulary

What to look for • Students using the correct names for shapes.

square

triangle kite

rhombus

sides

corners curves

straight lines

• Students are able to classify shapes and describe the reasons for their classification.

• Students are able to identify particular shapes in the environment; e.g. triangles in building structures, squares and rectangles in windows and doors.

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circle

• Students are able to draw squares, rectangles, triangles, kites, triangles, rhombuses and circles, and that their drawings are reasonably accurate. (Note: The use of compasses to construct circles would not be expected at this stage. Students could trace around circular objects or templates of various-sized circles.)

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rectangle

• Students are able to correctly identify the number of corners and sides (edges) on common two-dimensional shapes.

belongs with

goes together because

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

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Sub-strand: Shape—Shape – 1

HANDS-ON ACTIVITIES Folding and cutting squares and rhombuses • Students fold and cut squares of paper in different ways. Can you do one straight fold/cut to make two rectangles? Can you do one straight fold/cut to make two triangles? Can you do two straight folds/cuts to make four triangles? Two straight folds/ cuts to make four squares? Two straight folds/cuts to make four rectangles? What other shapes can you make with full folds on a square of paper? Can you make the same shapes if you start with a rectangular sheet of paper instead of a square one?

Are there other shapes you can make from this shape?

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fold

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• Students construct squares by taking a rectangular piece of paper and folding from one corner until the side touches the adjacent side. Then fold the leftover rectangle across the base of the triangle that has been formed, and cut that section off along the fold. Open out and a square will have been produced.

• Another way students can construct a square from a rectangular piece of paper is to fold the paper in half, and then fold from one corner of the fold until the side touches the adjacent side on both sides. Open up that fold and do the same the other way. When the paper is opened up, a square will have been formed on a diagonal in the centre.

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• To construct a rhombus from either a square or rectangular piece of paper, fold it in half and half again. Using a ruler, from any point on one of the folded edges, draw a line to the top of the opposite folded edge. Cut along the line and open out.

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fold

fold

Geoboards • Use Geoboards and elastic bands or string to make different shapes such as triangles, rectangles and squares. Look at the different shapes of all the triangles the students have made. What is the same about them all? What is different? Look at the different squares that have been made. What is the same about them all? What is different? Look at the different rectangles. What is the same about them all? What is different? Make a rhombus and a square on the Geoboard. What is the same about the squares and rhombuses; and what is different? (They both have four equal sides, but the square has four right angles, whereas a rhombus simply has two pairs of opposite equal angles. Students sometimes describe a rhombus as being like a square that has been pushed over.) Make a kite on the Geoboard. What is the same about the kite and the square, and what is different? (They both have four sides, but the square has four equal sides and four right angles, whereas a kite has two shorter adjacent congruent sides and two longer adjacent congruent sides [in adultspeak].) Ask, Can you make a circle on your Geoboard? Why/Why not? What is the closest you can get to a circle?

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Sub-strand: Shape—Shape – 1

HANDS-ON ACTIVITIES (CONTINUED) Cut and fold kites • Students, with the teacher’s help, investigate making a kite by folding and cutting. Fold a rectangular piece of paper in half. Using a ruler, draw a line from one corner on the fold side to the edge, and then do the same from the other corner.

Cut along the two folds and open out.

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Shape posters

fold

• Shape puzzles – 1 on page 59 requires students to solve simple shape puzzles that describe shapes according to their particular attributes.

• Play Guess my shape. In groups, students create a set of shape clues for other groups to solve. For example, I have straight sides. There are two long sides and two . Once the shorter sides. I have four corners all the same size. I am a clues have been solved, students draw their shape to make an information page for display.

Folding and cutting shapes from circles

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• Make a class poster of the different shapes created by folding and cutting coloured paper. Label each different shape.

Discuss what is the same about the shapes and what is different. Question why we can’t make a circle by cutting and folding.

Guess my shape

I have straight sides.

There are 2 long sides and 2 shorter sides.

I have 4 corners all the same size.

I am a rectangle.

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• Investigate the shapes that can be made by folding and cutting paper circles. (See page 61)

draw and cut

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fold

fold

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– To make a square, fold a circle of paper in half and half again, then use a ruler to draw a line from one outer point to the other. Cut along this line and open out.

– To make a rhombus, fold a circle of paper in half and half again, then use a ruler to draw a line from one outer point to a point on the other fold. Cut along this line and open out.

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fold

fold

– To make a kite, fold a circle of paper in half, then make another fold at right angles to the first fold, but less than half way up. Open up the circle, and, using a ruler, draw a line from one outer point to the next, and so on around the circle. Cut along these lines and open out.

draw and cut

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Sub-strand: Shape—Shape – 1

LINKS TO OTHER CURRICULUM AREAS English • Read The greedy triangle by Marilyn Burns. This book looks at the attributes of different shapes, some of which may be beyond the students’ experience; e.g. pentagons and hexagons. However, it is a nice shape story that describes some real life uses of some two-dimensional shapes.

• Read Harry and the dinosaur have a very busy day by I Whybrow and A Reynolds. Students make the shapes with their hands as the teacher reads the story.

Information and Communication Technology

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• Students make Guess my shape posters as described on page 57 using ICT.

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• Use Word draw and the Formatting palette to create two-dimensional shapes. Circles and rectangles can be drawn straight from the menu. The only triangles that can be made from the menu are equilateral, isosceles and right-angled.

To make a square, students will need to go to Format AutoShape and tick the box for ‘Lock aspect ratio’. Then if they increase or decrease the dimensions of the shape, it will remain a square. Note: There is no diagram readily available in the menu to create a kite.

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Note: The activities below use quite sophisticated terminology that would not be expected from Year 2 students. For example, the teacher would describe the hypotenuse of a right-angled triangle as the ‘long side’.

• Using Word draw and the Formatting palette investigate how to make different shapes using only triangles.

– A square can be made by constructing two congruent rightangled isosceles triangles. One triangle is rotated, and then the two are joined along the hypotenuse.

– A kite can be made by constructing two isosceles triangles with the same sized base but different heights. One triangle is rotated, and then the two are joined along the equal sides.

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– A rhombus can be made by constructing two congruent equilateral triangles. One triangle is rotated 60°, and then the two are joined along one side. However, this one is quite difficult to achieve.

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– A rectangle can be made by constructing two congruent rightangled scalene triangles. One triangle is rotated, and then the two are joined along the hypotenuse.

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• Print the shapes made above and use them to create posters with the names of the shapes clearly labelled.

• An internet search for “Geometric shapes” will uncover a number of sites and images that can be used in the classroom.

Health and Physical Education • In groups, students arrange themselves in poses to make different shapes with their bodies. How many students do you need to make a square? What about a triangle or a rectangle? How many students do you need to make a circle?

The Arts • Use multiples of the shapes made by students on pages 56–57 to create pictures and designs of the students’ choice.

Use coloured paper and ask students to add features with markers.

Languages • Learn the names of the shapes in another language.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET Shape puzzles – 1

Solve the puzzles below by drawing and naming the shapes under each clue. Use the shapes at the bottom to help you.

1. I have 4 equal sides and no right angles. What am I?

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no right angles. What am I?

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5. I have no angles and am made up of one long line that joins up.

What am I?

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4. I have 4 equal sides and all my angles are equal. What am I?

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

3. I have 4 sides; 2 of them are long and 2 of them are short. I have 4 right angles. What am I?

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r o e t s Bo r e p ok 2. I have 4 sides;u 2 of them are long Sare short. I have and 2 of them

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6. I have 3 sides and 3 angles.

What am I?

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET Shape puzzles – 2

The puzzles below show trees in a park.

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1.

(a) How many trees are in the square and the circle, but not in the kite?

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2.

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square?

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(a) How many trees are in the rhombus and the circle and the rectangle? (b) Write about the shapes where you can find 4 trees.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

(b) How many trees are in the kite and the circle, but not in the

Sub-strand: Shape—Shape – 1

RESOURCE SHEET Polygons from circles

1. Follow the instructions to make polygons from circles.

You will need: • 3 paper circles • large sheet of paper

• glue • pencil

fo l

d

d

l fo

draw and cut

Diagram 2

Polygon 2 (a) Fold a circle in half and half again. (b) Fold it in half a third time. (c) Rule a line like Diagram 2. (d) Cut along the line and open up the shape. (e) Glue it onto your sheet of paper.

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Diagram 1

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Polygon 1 (a) Fold the circle in half and half again. (b) Rule a line like Diagram 1. (c) Cut along the line and open up the shape. (d) Glue it onto your sheet of paper.

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Polygon 3 (a) Fold a circle in half and half again. (b) Rule a line like in Diagram 3. (c) Cut along the line and open up the shape. (d) Glue it onto your sheet of paper.

d

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

• ruler

Diagram 3

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1

/2 way

point

draw and cut

2. Choose the label that belongs to each shape and write it underneath. octagon (8 sides)

square (4 equal sides and 4 right angles)

rhombus (4 equal sides) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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61

Sub-strand: Shape—Shape – 1

RESOURCE SHEET Shapes with string

Use a length of string to make the shapes below. Then draw a picture of each shape and write what is special about it.

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circle

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triangle

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rhombus

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

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square

Assessment 1

Sub-strand: Shape—Shape – 1

NAME:

DATE: Match the shapes

Draw a line from each shape to its name. (a)

square

circle

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(d)

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

(c)

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(b)

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(f)

rhombus

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Assessment 2

Sub-strand: Shape—Shape – 1

NAME:

DATE: Special shapes

1. Name the shapes below.

2. Write two things you know about each shape.

r o e t s Bo r e This is a p This is a . o u k S What I know: What I know:

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This is a

What I know:

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What I know:

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.

What I know:

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

This is a

.

What I know:

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CONTENT DESCRIPTION: Describe and draw two-dimensional shapes, with and without digital technology

(d)

.

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(c)

(b)

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(a)

Checklist

Sub-strand: Shape—Shape – 1

Can use ICT to draw common 2-D shapes

Can describe and draw rhombuses and kites

Can describe and draw circles

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STUDENT NAME

Can describe and draw squares, rectangles and triangles

Describe and draw two-dimensional shapes, with and without digital technology (ACMM042)

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Sub-strand: Shape—Shape – 2

Describe the features of three-dimensional objects (ACMMG043)

TEACHER INFORMATION

RELATED TERMS Three-dimensional objects

What does this mean

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

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

Face

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• A two-dimensional region of a threedimensional object.

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

Edge

• where two faces of a three-dimensional object meet.

Prism

Teaching points

• Provide opportunities for students to work with three-dimensional objects in free play and in directed situations. These may include stacking, constructing, modelling and moving. This helps students develop an awareness of the attributes of the objects.

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Corner (vertex [vertices; plural])

• Features of three-dimensional objects would include the number of faces, vertices (corners) and edges; they may also include whether they can roll, stack, etc.

• Students look at the attributes of familiar three-dimensional objects, classifying them according to their corners, edges, faces, etc. Also look at attributes such as do they roll, can you stack them, etc., and why/why not.

• Cylinders and cones are special types of prisms and pyramids. They are not considered polyhedra as they have curved surfaces that are generally not considered to be faces.

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Pyramid

Cylinder

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• A three-dimensional object with a polygonal base and the other faces triangles with a common vertex called the apex.

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• A special type of prism with circular ends.

Cone

• A special type of pyramid with a circular base.

• Discuss the difference between a prism and a pyramid. (The pyramid comes to an apex; the prism doesn’t. The pyramid has all 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.)

• Students look for similar objects to ones described, e.g. Can you find something in the classroom that is the same shape as this cube?

Also, students could suggest uses for familiar objects, e.g. What could a cylinder be used for?

m . u

• 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.

• Students compare their objects to those of other students, and ask questions such as, Whose sphere (ball) is heavier, yours or your partner’s?

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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 to’, ‘has more edges’, etc.

What to look for

• Students are using the correct names of the three-dimensional objects.

• Students are able to describe the reasons for their classifications.

Student vocabulary sphere

cube

cone

cylinder

prism

pyramid

edges

faces

corners

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• Students are able to identify particular objects in the environment, e.g. six-sided dice as cubes.

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

Proficiency strand(s): Understanding Problem solving

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Sub-strand: Shape—Shape – 2

HANDS-ON ACTIVITIES Find the object • Have a collection of three-dimensional objects and pictures of each of them. (You could enlarge and use the pictures on page 69). Hold up a picture and the students decide which of the objects it shows. This requires the students to connect the physical with the symbolic.

• Students use labels such as those on page 72 and glue them onto a sheet. They then draw a picture of each of them.

Have models of the shapes available for the students to refer to as needed.

• Students find objects in and out of the classroom that are the same as the three-dimensional objects on their sheet from the above activity. Discuss why a particular three-dimensional object would be used for each purpose; e.g. Why is a (traffic) witch’s hat a cone shape?

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Build with 3-D objects

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• Students use blocks of different shapes to build a town, showing buildings, roads, park with playground equipment etc.

Students record (tally) the different three-dimensional objects used. Discuss why they chose each particular object for its purpose.

Explore the features of 3-D objects

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• Discuss the pros and cons of using different three-dimensional objects in construction. Can you use a cone at the base of your building? What happens if you put the cylinder on its side instead of on it base? Where could you use the pyramid?

Which shape would be best as a base for the tower? Where in the building could a triangular prism be used?

• Have a collection of three-dimensional objects. Students discuss which of them has the greatest number of edges, faces and/or corners (vertices). Does the piece with the most edges also have the most faces? Do any of the pieces have the same number of edges, faces and corners? Why is this the case? What is the same about them? What is different? How many of the faces on your cube can you see without picking it up? What about the pyramid?

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• Using the table on page 71, students explore different features of six 3-D objects. In the ‘Other features’ column students may suggest how each object moves, stacks etc.

• Have a collection of three-dimensional objects for the students to see. Remove them all from sight and, without the students seeing, put one object in a drawstring bag. One student puts their hand into the bag and feels the object without being able to see it. They describe what they can feel (the attributes of it) and then try to determine the name of the object.

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Guess the object

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• Use ready-made three-dimensional objects such as wooden models of a cube, triangular prism and square-based pyramid. To help students determine the number of faces on their object, have them cut out different-coloured pieces of paper to put on each of the faces of their object, counting as they go. If they use only water on their paintbrush rather than glue, the paper will stick for a short while but should come off quite easily. To help determine the number of corners, use small balls of plasticine, play dough or Blu-tack®, and place one on each of the corners, counting as they go. The same could be done to count the number of edges, with the plasticine, play dough or Blu-tack® going in the middle of each edge.

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• Teacher describes a three-dimensional object, and the students have to guess what it is. Once they have tried this a few times, a student could describe the object to be found, and the other students have to guess what it is. Aim to discover the name of the object with as few clues as possible.

Make patterns with 3-D objects

• Arrange a small set of three-dimensional objects in a row, and have the students try to replicate the pattern with their set of objects. Students could take it in turns to display a pattern that the rest of the group has to replicate.

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Sub-strand: Shape—Shape – 2

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • The illuminations website has a tool that allows students to learn about various three-dimensional solids and their properties. The solids can be manipulated to help explore the number of faces, edges and corners. Visit <http://illuminations.nctm.org/ActivityDetail.aspx?ID=70> and <http://www.learner.org/interactives/geometry/> to investigate them.

The Arts

r o e t s Bo r e p ok u S My robot used: 1 prism 1 cube 4 cylinders 1 cone 3 triangles

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• Have a collection of cardboard boxes, including small triangular prisms, tubes and other objects for students to build models. The students make lists of the three-dimensional objects used.

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• 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?

• Learn the names of common objects in another language.

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Languages

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Matching the objects

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Draw a line to match the two pictures of the same object.

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CONTENT DESCRIPTION: Describe the features of three-dimensional objects

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Name the objects

1. Name the shapes in each building.

2. Write how many of each shape have been used.

This building has:

(b)

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This building has:

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This building has:

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3. Draw your own building using 3 cylinders, 2 cubes and 1 square-based pyramid.

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CONTENT DESCRIPTION: Describe the features of three-dimensional objects

(c)

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Features of 3-D objects

Draw a picture of each object and complete the table.

Name of object

Other features

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sphere

Number of Number of Number of faces corners edges

cube

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CONTENT DESCRIPTION: Describe the features of three-dimensional objects

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prism

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cone

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Assessment 1

Sub-strand: Shape—Shape – 2

NAME:

DATE: Matching labels

Draw a line from the picture of each object to its name. (a)

prism

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(b)

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sphere

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pyramid

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(f)

cube

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Describe the features of three-dimensional objects

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(d)

Assessment 2

Sub-strand: Shape—Shape – 2

NAME:

DATE: Special objects

1. Name the objects.

2. Write two things you know about each one. (a)

(b)

r o e t s Bo This is a r . e p o u k I know: What I know: What S

(c)

(d)

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This is a

This © R. I .

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CONTENT DESCRIPTION: Describe the features of three-dimensional objects

w ww (e)

.

What I know:

What I know:

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.

o c . c This is e her r o t s super a This is a (f)

.

.

What I know:

What I know:

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Checklist

Sub-strand: Shape—Shape – 2

Describe the features of three-dimensional objects (ACMMG043) Can recognise and describe the features of ...

Pyramids

Cones and cylinders

Spheres

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Teac he r

STUDENT NAME

Prisms and cubes

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

Answers

Sub-strand: Shape

Shape – 1 Page 59

Shape – 2 Resource sheet – Shape puzzles – 1

Page 69

Resource sheet – Matching the objects

1. rhombus 2. kite 3. rectangle 4. square 5. circle 6. triangle Teacher check all drawings Page 60

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Resource sheet – Shape puzzles – 2

Teac he r Page 61

Resource sheet – Polygons from circles

1. Teacher check 2. Polygon 1 – square Polygon 2 – octagon Polygon 3 – rhombus

Page 70

Resource sheet – Name the objects

1.–2. (a) 1 cylinder, 1 cube, 1 cone (b) 2 cubes, 2 cylinders, 1 triangular prism (c) 2 cubes, 3 cylinders 3. Teacher check Page 71

Resources sheet – Features of 3-D objects

Assessment 1 – Match the shapes

Name of objects

Number of edges

Other features

1

0

0

answers will vary

6

8

12

answers will vary

5

6

sphere

(a) square

cube

(b) circle

prism triangular rectangular

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(d) triangle (e) kite

rhombus

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pyramid triangular

4

12

4

6

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(b) circle (e) rectangle

(c) triangle (f ) kite

answers will vary

answers will vary

8

5

8

2

0

0

answers will vary

2

1

1

answers will vary

5

rectangular

9

8

5

5

square

Assessment 2 – Special shapes

1. (a) square (d) rhombus 2. Teacher check

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(c) rectangle

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Number of corners

Number of faces

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Page 63

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1. (a) 6 (b) 2 2. (a) 3 (b) in the rectangle and the circle, but not the rhombus or in the rhombus but not in the rectangle or circle

cylinder

cone

Page 72

Assessment 1 – Matching labels

(a) cone (d) sphere Page 73

(c) pyramid (f ) cylinder

Assessment 2 – Special objects

1. (a) cube (d) pyramid 2. Teacher check

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

(b) cube (e) prism

(b) cylinder (e) prism

(c) cone (f ) sphere

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

Interpret simple maps of familiar locations and identify the relative position of key features (ACMMG044)

RELATED TERMS

TEACHER INFORMATION

Location

What does this mean

• Identifying a specific place. It is the ‘where’ of the Geometry strand.

• Interpreting simple maps would involve recognising some of the more common representations used in them; for example, the icon to represent a public phone, or to represent an airport.

Relative position

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Coordinates (Cartesian coordinates)

• 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 four quadrants, or when graphing functions in algebra and trigonometry. Being able to read road and other maps relies on an understanding of coordinates.

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

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

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• The location of one place in relation to another. At this stage students would refer to ‘under’, ‘next to’, ‘behind’, ‘on top of’ etc.

• Relative position of key features involves being able to simply describe where one thing is compared to another; for example, the library is between our classroom and the office.

Teaching points

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

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

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• When using coordinates for grid references, name the across (x-axis) first, followed by the up/down (y-axis). So the below; not (2,B)

is at (B,2)

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Student vocabulary coordinates

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north

south

east

west

clockwise

anticlockwise

right

left

forwards

backwards

over

under

next to

in front of

behind

on top of

below

turn

paces

steps

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

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A

B

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C

D

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• Students who are not able to give and/or follow simple directions, either when using a simple map, or when giving or receiving directions for making a construction or arrangement.

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

• Students who are not familiar with directions for simple distances; e.g. face east and take two steps forward.

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

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

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

HANDS-ON ACTIVITIES Follow directions • Follow directions on where to turn. Students stand up and the teacher tells them to turn; for example, make a threequarter turn clockwise, make a half turn anticlockwise, turn to face south etc. Later, students can take turns giving the directions.

Robot path • The teacher (or a student) stands at the front and gives instructions to a student (the Robot) on how to move around the classroom; for example, from the teacher’s desk to the bookcase. Once this has been tried a few times, the robot could be blindfolded. The other students can call out ‘yes’ or ‘no’ for each of the moves the robot makes. This can also be done in an outdoors area in a similar way, or the students could do the activity in small groups.

Simple maps

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Teac he r

• Students are given a simple map of the school grounds, and keep a record of where they walk within a day/week. They draw the paths onto the map and, at the end of the time, compare their maps and the routes travelled.

Space monster game

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• Discuss the fact that streets are numbered with all odd numbers on one side and even numbers on the other. Give students simple ‘maps’ or drawings of a street with questions to highlight this convention, as in the Postman activities on page 79.

• Students get a copy of a ‘Space monster’ computer game screen (page 80). The space monster’s aim is to capture and eat each of the bugs. After it catches each bug, it takes it back to its dump to eat it, before starting out again to capture the next bug. The teacher asks directional questions about how the monster gets to each of the bugs. The students can also be asked to add extra bugs according to simple directions given by the teacher. Teacher questions may include:

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– What is the shortest way for the space monster to get to bug 1?

– Describe a different way for the monster to get back to its dump after capturing bug 1.

– Describe the longest way for it to get to bug 4.

– How many streets would the monster use to get to bug 5?

Following directions

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– What if the monster started at the bottom left corner of the screen, where bug 6 is currently. What would be the closest bug for it to capture? What would be the furthest?

• Students have a number of 2-cm wooden cubes. The teacher gives directions on how to build a particular model, using 5 or 6 cubes, which the students must follow. Later, a student can build a model which is unseen by the other students, and then give directions to the other students for them to make the same model.

Barrier games

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• Students use wooden cubes, pattern blocks or other manipulative materials. One student builds a simple model or makes a pattern behind a barrier (such as a book) so that is hidden from their partner. To start with, limit the number of pieces to be used to 6–8. They then describe the model, piece by piece, so that their partner can build it. One level of difficulty is if the ‘describer’ can see their partner constructing the model and therefore can correct them as they go; the more difficult level is if the ‘describer’ cannot see the result of their instructions, and so doesn’t see their partner’s model until it is finished.

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

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Download simple maps of familiar locations; e.g. the school grounds, a venue for a class excursion such as an animal sanctuary etc. Use these maps for class discussion about moving around the area to get to a particular site.

Health and Physical Education • Play the game ‘Follow the leader’.

• Play the ‘Four corners’ game. Use a square or rectangular room, or an outside area where there are four obvious corners.

Each of the corners is given a number from 1 to 4. The person who is designated ‘It’ stands in the middle of the area with their hands over their eyes, and counts to 10. During this time, all the students run to stand in their choice of one of the corners; making sure they’re stopped by the time ‘It’ stops counting. Then ‘It’ calls out a number from 1–4.

All the students in that corner are then ‘out’, and come to the middle and sit down. ‘It’ again covers their eyes and the remaining students run to their choice of another corner, or stay where they are while ‘It’ counts to 10. They repeat the process until there is only one student remaining; and that student becomes the new ‘It’.

• Sing and dance to the Hokey pokey, making all the movements.

You put your right hand in You put your right hand out You put your right hand in And you shake it all about You do the hokey pokey and you turn around That’s what it’s all about.

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• Repeat the whole song but sing the ‘left hand’, instead of the ‘right hand’; then sing verses using the right foot, left foot and whole self.

Languages

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• Learn the words for north, south, east and west in another language.

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

RESOURCE SHEET The postman’s job

The map below shows part of the road the postman rides.

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SALE

Answer the following.

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5

1. Joe lives next door to house 1. What number is his house?

. tat the house across the road from house o 2. Mary livese 6. c .

What numberc is her house? e her r o st super 3. Which houses are at the end of the street?

4. James lives in the furthest house from the garage.

What is his house number?

5. When the postman rides from the shop to house 7, what direction does he turn?

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

RESOURCE SHEET Space monsters

Below is the computer screen for a space monster game. The monster has to catch each of the bugs for food. When it has caught a bug, it takes it back to its dump and eats it. Then it goes looking for the next bug.

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BUG 1

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BUG 3

BUG 4

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BUG 6

See page 77 for suggestions on using this page.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Interpret simple maps of familiar locations and identify the relative position of key features

MON DUSMTER’S P

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

RESOURCE SHEET My family room

Use the drawing of my family room below to answer the questions.

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2. What is between the couch and the TV?

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1. What is to the west of the couch?

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1

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3. If I do a quarter-turn anticlockwise when I enter the room, what will be in front of me?

4. What is north of the pot plant?

5. Describe how you would get from the door to the pot plant.

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

RESOURCE SHEET Ring a teddy bear

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

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. te bear wearing in (D, 2)? o 1. What is the teddy c . che e r o t r s super 2. What is different about the teddy bear in (A, 3)?

3. The teddy bear in (B, 4) is wearing

.

4. Colour the outfit of the teddy bear in (C, 1) blue.

5. Draw your own teddy bear in (C, 3).

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CONTENT DESCRIPTION: Interpret simple maps of familiar locations and identify the relative position of key features

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Assessment 1

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

NAME:

DATE: My park

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CONTENT DESCRIPTION: Interpret simple maps of familiar locations and identify the relative position of key features

Look at the map of a park.

1. Park Street is the road between the toilets and the oval. Label it on the map.

. te to show how you would get from the playground o 2. Draw arrows to the c . che cafe. e r o t rwalk s up er 3. If you leave the cafe ands towards the oval, then turn first right, what is on your right?

4. Draw a slide at the western end of the playground and swings at the eastern end.

5. Draw a dotted line to show how you would get from the swings to the toilets.

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Assessment 2

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

NAME:

DATE: Stickers

Look at the stickers below.

2

A

B

C

D

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.

4. Where is the hat sticker?

5. Draw: • a cat sticker in (D, 4).

• your own sticker in (B, 3).

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CONTENT DESCRIPTION: Interpret simple maps of familiar locations and identify the relative position of key features

3

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Checklist

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

Identifies relative positions on map

Can find features on a map

Can use simple coordinates

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STUDENT NAME

Understands the directions north, south, east and west

Interpret simple maps of familiar locations and identify the relative position of key features (ACMMG044)

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

Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045)

RELATED TERMS

TEACHER INFORMATION What does this mean

Slide (the correct mathematical term is translation)

• Students start off looking at the transformations of slides (translations) and flips (reflections) informally.

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• One step: A one-step move means that the object or shape only moves in one direction within the transformation. In later years, students will investigate multistep transformations.

• The movement of an object or shape which changes position in a given direction. It remains oriented the same way. The shape and size of the object or shape do not change.

Flip (the correct mathematical term is reflection)

• The mirror image of an object or shape so that each point of the object or shape is the same distance from the mirror line (or plane of symmetry with a threedimensional object) as the same point on the image.

Teaching points

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• Students need to have experience transforming or moving real objects and shapes before doing so using digital technologies.

• When an object or shape undergoes either a slide or flip transformation, its size, shape and features do not change.

• A slide transformation can be done in any direction, but without turning (rotating) the object or shape.

• Slide transformations can be the basis of tessellations where the same shape is repeated without gaps or overlaps to create a pattern.

• A flip transformation is performed around a ‘mirror’ line, which is generally drawn in for clarity.

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• When the object or shape has been transformed by a flip, the mirror line indicates a line of symmetry, where any point on one side of the line is the same distance from the line as the equivalent point in the reflection. This is different to finding any line/s of symmetry within a shape, where the shape can be folded in half to show the line of symmetry.

• The end result of a slide or flip to a shape that has more than one line of symmetry can appear the same.

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• The covering of a surface with one or more shapes without gaps or overlaps. In this context, the same shape would be used, thereby performing a series of slides of the shape to create a tessellating or tiling pattern.

Student vocabulary slide flip mirror line no gaps no overlaps tessellate

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Tessellations

Mirror line

• The end result of a slide or flip to a shape that has either one or no lines of symmetry will appear different.

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What to look for

• Students who alter the shape or size of the object or shape as part of their transformation.

• Students who move their shape or object beyond the transformation to be performed; e.g. rotating a shape while sliding it.

• Students who are unaware that their shape has changed in some way after a flip and need to flip it back to check.

• Students who leave gaps when tessellating multiples of the same shape, or who overlap their shapes.

Proficiency strand(s): Understanding

Fluency

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

Problem solving

Reasoning

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

HANDS-ON ACTIVITIES Jigsaw puzzles • The use of jigsaw puzzles often requires students to slide or flip pieces to fit into a particular spot.

Pattern blocks • Using manipulatives such as pattern blocks, students choose one piece and trace around it on paper. They then slide the shape in any direction and draw around it again. Discuss what has happened to the shape. What has changed? What has stayed the same? How can we record this on the paper?

• In pairs, using pattern blocks, one student creates a pattern or design with about 6–8 pieces. Their partner now has to create the same pattern, but reflected about a line. A drinking straw could be used to designate the mirror (symmetry) line. Discuss the fact that the pattern or design has now been flipped. What has changed? What has stayed the same?

How can we record this on the paper? Pages 91 and 92 may also be used for the latter activity.

Tessellations

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• Use templates of a tessellating shape—e.g. rectangle or square—trace around it, slide it in a straight line without rotating it in any way, until it joins one side of the original, and then trace around it again. Repeating this process will produce a tessellating (tiling) pattern. Discuss the slides that have been made to produce the design.

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• Students use a transparent mirror (also known as a Mira or Georeflector) to look for lines of symmetry in shapes. These lines of symmetry are a line about which half of the shape is reflected.

The transparent mirror can then be used to complete half pictures as on pages 94–95 by flipping the shapes.

• Students could investigate what happens to upper case letters when reflected horizontally using a transparent mirror.

Some letters, such as A, will look the same, while others, such as F, will look quite different. Discuss the fact that when the letters look the same after a flip, this means the letter’s shape is symmetrical about a vertical line (mirror line). In these cases, the flip has the same effect as a slide.

o c . che e r o t r sF F up A As Aer

• When any of the letters of the alphabet are flipped (reflected) vertically, they will almost all look different from the original. Discuss which letters still look the same. Note, only H, I, O and X still look the same (as if they had undergone a slide). Each of these four letters has symmetry about a horizontal line (mirror line).

A A

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

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • An animated display that explains flips and slides (and also turns or rotations) can be found at <http://www.learnalberta.ca/content/me5l/html/math5.html> • There is an interesting tessellating program at <http://www.pbs.org/parents/education/math/games/first-second-grade/tessellation/> • Another website for tessellations is <http://nlvm.usu.edu/en/nav/frames_asid_163_g_2_t_3.html?open=activities> • The Illuminations site for tessellating shapes can be found at <http://illuminations.nctm.org/ActivityDetail.aspx?ID=27>

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• A similar site to the one above, again from Illuminations, can be found at <http://illuminations.nctm.org/ActivityDetail.aspx?ID=35>

The Arts

• Students could design their own paving or wall tiles using various aspects of slides and flips.

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• There are many opportunities to integrate this unit with art projects. Making wrapping paper using slides (translations) of a particular shape is an interesting and useful activity. A similar use could be made of reflections of shapes to make wrapping paper.

• Stained glass windows. Students choose a shape that will tessellate—for example a quadrilateral (square, kite, rectangle, rhombus) or triangle—and trace around it a number of times onto coloured cellophane paper. Cut these out and join them together by using strips of black cardboard and glue. The cardboard can also be used to frame their window. Compare student made artwork to images of actual stained glass windows.

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• Students could make half pictures (similar to those on pages 94 and 95) and either complete the other half using a transparent mirror, or exchange their pictures with a partner and complete each other’s half pictures.

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

RESOURCE SHEET Slide or flip?

The shapes below have been moved. For each shape, decide if the movement has been a slide or a flip. Circle the correct word.

slide

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2.

3.

or

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

RESOURCE SHEET Making patterns

1. Choose one of the shapes below.

2. Trace around it onto cardboard to make a template and cut it out.

Example

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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3. Now trace around the shape many times on a sheet of paper, with each new drawing touching the previous shape so that there are no gaps or overlaps. An example of a finished pattern is shown below.

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

RESOURCE SHEET Finish the pattern – 1

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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The pattern below has been made with pattern blocks. The dotted line represents a mirror. Use pattern blocks to show it flipped over the mirror line, then trace around the new shapes.

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mirror line Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

RESOURCE SHEET Finish the pattern – 2

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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The pattern has been made with pattern blocks. The dotted line represents a mirror. Use pattern blocks to show it flipped over the mirror line, then trace around the new shapes.

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

RESOURCE SHEET Make and finish the pattern

1. Make a pattern below with pattern blocks that touches the dotted mirror line.

2. Ask your partner to use pattern blocks to complete the pattern by flipping it over the mirror line.

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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3. Trace around all the shapes.

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

RESOURCE SHEET Finish the picture – 1

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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Below is half of a picture. Use a transparent mirror to complete the other half of the picture.

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

RESOURCE SHEET Finish the picture – 2

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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Below is half of a picture. Use a transparent mirror to complete the other half of the picture.

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Assessment 1

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

NAME:

DATE: Sliding shapes

The shapes below have been moved. Circle the picture of each that shows a slide.

2.

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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Assessment 2

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

NAME:

DATE: Make a fish

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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The design below has been made with pattern blocks. The dotted line represents a mirror. Use pattern blocks to show it flipped over the mirror line, then trace around the new shapes. Do you think it looks like a fish?

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Assessment 3

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

NAME:

DATE: Flipped shapes

The shapes below have been moved. Circle the picture of each that shows what each shape looks like after it has been flipped.

2.

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CONTENT DESCRIPTION: Investigate the effect of one-step slides and flips with and without digital technologies

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Checklist

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

Can tessellate shapes

Can identify flips

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STUDENT NAME

Can identify slides

Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045)

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Sub-strand: Location and transformation—L&T – 3

Identify and describe half and quarter turns (ACMMG046)

TEACHER INFORMATION

RELATED TERMS Turn (the correct mathematical term is rotation)

• The process by which an object or shape changes position by rotating through a given angle.

Half turn

• Flips, slides and turns (reflections, translations and rotations) are the three forms of transformations where the shapes or objects do not change size, shape or proportion. This unit deals with the third of these transformations: rotation or turns.

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Quarter turn

• A turn of 90°.

• Rotations or turns can be of any size from less than 1° through to 360° (a full turn), where the object or shape ends back where it started. This unit only deals with quarter turns (90°) and half turns (180°).

Teaching points

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• A turn of 180°.

What does this mean

• When an object or shape undergoes a turn (rotation) transformation, its size, shape and features do not change.

• There are an infinite number of degrees of turn that can be produced; however this unit only looks at half turns (180°) and quarter turns (90°).

Clockwise

• A turn of 360° takes the shape or object back to where it started.

• A turn in the direction that the hands on a clock move.

• In most cases, a turn of 90° clockwise leaves an object in a very different position from a turn of 90° in an anticlockwise direction; in fact it is a half-turn (180°) different between the two turns.

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C.Publ i cat i ons • A turn that is in the opposite direction • omove. rr evi ew pur posesonl y• to the way that hands on f a clock Note: In Australia, we use the term ‘anticlockwise’, rather than the American equivalent ‘counterclockwise’.

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• If a shape with at least two lines of symmetry is turned exactly 180°, it produces the same effect as when it is flipped (reflected). If the shape or object does not have two or more lines of symmetry, it will be upside down after a flip of 180°.

turn (rotation)

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flip (reflection)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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Sub-strand: Location and transformation—L&T – 3

Identify and describe half and quarter turns (ACMMG046)

TEACHER INFORMATION (CONTINUED) Student vocabulary

What to look for • Students who confuse half and quarter turns.

turn half turn

clockwise

anticlockwise

slide

• The shape, size and proportions of the shape do not change when a turn is made.

• When a shape or object is turned 180° (a half turn), it will be upside down.

• Students who do not recognise the pattern when a shape is turned 90° or 180° several times, or who are unable to continue the pattern by drawing the next one or two elements.

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upside down flip

• Students who confuse the directions of clockwise and anticlockwise.

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quarter turn

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Sub-strand: Location and transformation—L&T – 3

HANDS-ON ACTIVITIES Pattern blocks • Make patterns using shapes or manipulatives such as pattern blocks that are turned (rotated). Students can construct a simple design for which their partner builds the same pattern except turned 90° or 180°.

Investigating symmetrical and asymmetrical shapes • Students investigate what happens to different shapes when they are turned, as opposed to being flipped or slid.

This may involve using shapes that are asymmetrical, have only one line of symmetry, or have more than one line of symmetry. As a class, or in groups, collate the results into a table like the one below.

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Robot path (See also page 77)

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Turn 180°

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• The teacher (or a student) stands at the front and gives instructions to a student (the robot) on how to move around the classroom; for example, from the teacher’s desk to the bookcase. Once this has been tried a few times, the robot could be blindfolded. The other students can call out ‘yes’ or ‘no’ for each of the moves the robot makes. This can also be done in an outdoors area in a similar way, or the students could do the activity in small groups. To enhance the link to this unit, moves would require either quarter or half turns, with the use of the language of ‘clockwise’ and ‘anticlockwise’.

Simon says • Students stand, and play the game of Simon says, but with directions being only ‘turn a quarter turn clockwise’ or ‘turn a quarter turn anticlockwise’ and the same for ‘half a turn’. Any students who turn in the wrong direction, or for the incorrect amount of turn, are ‘out’. The last student standing is the winner.

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Sub-strand: Location and transformation—L&T – 3

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • The web links recommended in the previous unit (L&T–2) are also appropriate for this unit, as they all include turns (rotations), as well as flips (reflections) and slides (translations).

Health and Physical Education • Students play games where they are required to run in clockwise and anticlockwise directions.

The Arts

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• Make rotating paper pinwheels. You will need a piece of coloured paper about 10 cm by 10 cm, a dressmakers pin, a plastic drinking straw, a small piece of Blu-tack® or plasticine, a ruler and pencil.

1. On the paper draw two diagonal lines using a ruler.

2. Mark 1 cm from the centre on each of the diagonals.

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3. Mark in a dot in the centre, and one in one corner of the four triangles, as in the picture below.

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4. Use the pin to make a small hole on each of the dots, wiggling it to make the hole a bit larger than the shaft of the pin. Or a sharp pencil could be used to make the holes, but make sure the holes are not too big.

5. Cut along the diagonals from the corner to the mark that is 1 cm from the centre. Do not cut through to the very centre.

6. Match up the hole in each triangle to the hole in the centre.

7. Push the dressmakers pin through the holes, and through to the drinking straw. Place a piece of Blu-tack® or plasticine on to the point of the pin. You now have a rotating pinwheel.

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Sub-strand: Location and transformation—L&T – 3

RESOURCE SHEET What comes next?

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The shapes below have been turned either a half or quarter turn. In the boxes, draw what the next turn of the shape would look like.

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Sub-strand: Location and transformation—L&T – 3

RESOURCE SHEET Finish the patterns

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The shapes below have been turned. Draw the next two shapes to finish each pattern.

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RESOURCE SHEET Rotating pattern – 1

1. Place pattern blocks over the shapes below.

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2. Complete the pattern by turning the shapes around the line (not by flipping them).

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3. Trace the new part of the pattern.

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Sub-strand: Location and transformation—L&T – 3

RESOURCE SHEET Rotating pattern – 2

1. Place pattern blocks over the shapes below.

2. Continue the pattern by turning the shapes around the next quarter.

Trace the new part of the pattern.

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3. Repeat for quarters C and D.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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107

Assessment 1

Sub-strand: Location and transformation—L&T – 3

NAME:

DATE: Quarter turn or half turn?

The shapes below have been turned. How far has each shape has been turned? Write ‘quarter turn’ or ‘half turn’ in the boxes.

1.

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4.

w ww 5.

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o c . che e r o t r s super

6.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

CONTENT DESCRIPTION: Identify and describe half and quarter turns

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m . u

3.

Teac he r

2.

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

Assessment 2

Sub-strand: Location and transformation—L&T – 3

NAME:

DATE: Next turn

Imagine that each picture below has been turned either a quarter turn or half turn. In the box draw what each one would look like after the turn.

r o e t s Bo r e p ok u S half turn anticlockwise

ew i ev Pr

Teac he r

quarter turn clockwise

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m . u

w ww

CONTENT DESCRIPTION: Identify and describe half and quarter turns

© R. I .

C .P ub l i cat i ons half turn clockwise •f orr evi ew pur posesonl y• quarter turn anticlockwise

o c . che quarter turn r e o t r s s r u e p anticlockwise half turn clockwise

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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109

Checklist

Sub-strand: Location and transformation—L&T – 3

Can identify a quarter turn

Can identify a half turn

Can describe a quarter turn

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

ew i ev Pr

Teac he r

STUDENT NAME

Can describe a half turn

Identifies and describes half and quarter turns (ACMMG046)

w ww

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110

m . u

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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

Answers

Sub-strand: Location and transformation

L&T – 1 Page 79

Resource sheet – My family room

chair 1 (or lamp) a table chair 1 (or lamp) a bookcase head east, north, east, south

Page 94

Resource sheet – Finish the picture – 1

Page 95

Resource sheet – Finish the picture – 2

ew i ev Pr

Assessment 1 – My park

Teacher check Teacher check flowerbeds Teacher check Teacher check

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Page 84

Page 96

a cupcake a frog a crown (A, 4) Teacher check

L&T – 2

Page 89

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2. flip 5. slide

3. flip

4.

Resource sheet – Making patterns

Teacher check Page 91

2.

Resource sheet – Slide or flip?

1. slide or flip 4. flip Page 90

Assessment 1 – Sliding shapes

1.

Assessment 2 – Stickers

w ww

1.

2.

3.

4.

5.

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

a hat teddy is wearing boots a jacket/coat/shirt Teacher check Teacher check

Page 83 1.

2.

3.

4.

5.

Resource sheet – Make and finish the pattern

Resource sheet – Ring a teddy bear

Teac he r

Page 82 1.

2.

3.

4.

5.

Page 93

Resource sheet – The postman’s job

3 5 houses 7 and 8 8 right

Page 81 1.

2.

3.

4.

5.

Resource sheet – Finish the pattern – 2

m . u

1.

2.

3.

4.

5.

Page 92

5.

Resource sheet – Finish the pattern – 1 Page 97

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

Assessment 2 – Make a fish

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111

Answers Page 98

Sub-strand: Location and transformation

Assessment 3 – Flipped shapes

Page 106

Resource sheet – Rotating pattern – 1

Page 107

Resource sheet – Rotating pattern – 2

1.

2.

3.

ONE WAY

ON E WAY

YA W E N O

ONE WAY

5.

r o e t s Bo r e p ok u S Page 108

Page 104

Page 105

Resource sheet – What comes next?

half turn quarter turn quarter turn half turn half turn quarter turn

Page 109

Assessment 2 – Next turn

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Resource sheet – Finish the patterns

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1.

2.

3.

4.

5.

6.

ew i ev Pr

Teac he r

L&T – 3

Assessment 1 – Quarter turn or half turn?

m . u

4.

o c . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2)

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