RIC-20153 ACM Measurement and Geometry (Yr 3) Geometric reasoning

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Australian Curriculum Mathematics 

resource book: Measurement and Geometry 

(Year 3) 

Published by R.I.C. Publications ® 2013 

Copyright © Linda Marshall 2013 

RIC– 20153 

Titles in this series: 

Australian Curriculum Mathematics resource book: 

Measurement and Geometry (Foundation) 


Measurement and Geometry (Year 1) 











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Curriculum. 

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AUSTRALIAN CURRICULUM MATHEMATICS 

RESOURCE BOOK: 

MEASUREMENT AND GEOMETRY 

(YEAR 3) 

Foreword 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) is one in a series of seven teacher resource books that support 

teaching and learning activities in Australian Curriculum Mathematics. The books focus on the measurement and geometry content strands of the 

national maths curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and assessment 

activities, along with links to other curriculum areas. 

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

Using units of measurement .................................... 2–29 

• UUM – 1 

Measure, order and compare objects using familiar metric units of 

length, mass and capacity (ACMMG061) 

– Teacher information ............................................................................... 2–4 

– Hands-on activities ................................................................................. 5–7 

– Links to other curriculum areas ................................................................... 8 

– Resource sheets .................................................................................... 9–12 

– Assessment ........................................................................................ 13–14 

– Checklist ................................................................................................... 15 

• UUM – 2 

Tell time to the minute and investigate the relationship between units 

of time (ACMMG062) 

– Teacher information ........................................................................... 16–17 

– Hands-on activities ................................................................................... 18 

– Links to other curriculum areas ................................................................. 19 

– Resource sheets .................................................................................. 20–25 

– Assessment ........................................................................................ 26–27 

– Checklist ................................................................................................... 28 

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

Shape .................................................................... 30–45 

• Shape – 1 

Make models of three-dimensional objects and describe key 

features (ACMMG063) 


– Hands-on activities ................................................................................... 32 

– Links to other curriculum areas ................................................................. 33 


– Assessment ........................................................................................ 40–43 

– Checklist ................................................................................................... 44 

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

Contents 

Location and transformation .................................. 46–71 

• L&T – 1 

Create and interpret simple grid maps to show position and 

pathways (ACMMG065) 

– Teacher information .................................................................................. 46 

– Hands-on activities ............................................................................. 47–48 

– Links to other curriculum areas .................................................................. 49 


– Assessment ........................................................................................ 57–58 

– Checklist .................................................................................................... 59 

• L&T – 2 

Identify symmetry in the environment (ACMMG066) 

– Teacher information .................................................................................. 60 

– Hands-on activities .................................................................................... 61 



– Assessment ........................................................................................ 68–69 

– Checklist .................................................................................................... 70 



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

Geometric reasoning .............................................. 72–82 

• GR – 1 

Identify angles as measures of turn and compare angle sizes in 

everyday situations (ACMMG064) 


– Hands-on activities ............................................................................. 74–75 



– Assessment ........................................................................................ 79–80 

– Checklist .................................................................................................... 81 

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

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

FORMAT OF THIS BOOK 

This teacher resource book includes supporting materials for teaching and learning in all sections of the Measurement and Geometry content strand of 

Australian Curriculum Mathematics. It includes activities relating to all sub-strands: Using units of measurement, Shape, Location and transformation, 

and Geometric reasoning. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the 

proficiency strands have also been included. 

Each section supports a specific content description and follows a consistent format, containing the following information over several pages: 

• teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for 

• hands-on activities 

• resource sheets 

• a checklist 

• links to other curriculum areas 

• assessment sheets. 

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

Shape, Location and transformation, and Geometric reasoning). 

The length of each content description section varies. 

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. 

Student vocabulary includes words which 

the teacher would use—and expect the 

students to learn, understand and use—during 

mathematics lessons. 

The proficiency strand(s) (Understanding, 

Fluency, Problem Solving solving or Reasoning) relevant 

to each content description are listed. shown in bold. 

Teacher information includes background information relating to the content description, as well as 

related terms, desirable student vocabulary and other useful details which may assist the teacher. 

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

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

RELATED TERMS 

Grid maps 

vever 

 

s. 

w 

(x 

ver(y 

Position 

T 

 

r 

s. 

Pathway 

T 

. 

Coordinates (Cartesian 

coordinates) 

 

repr 

 

 

 

 

 

 

r 

s. 

Student vocabulary 

coordinates 

north 

south 

east 

west 

clockwise 

anticlockwise 

right 

left 

forward 

backwards 

over 

under 

turn 

paces 

steps 

Notewe 

‘a 

 

’. 

TEACHER INFORMATION 

What this means 

 

 

 

’ 

 

’ 

’ 

 

. 

 

 

 

Teaching points 

T 

e. 

 

 

. 

5 

 

4 

x 

y 3 

 

2 

 

1 

s. 

A B C D E 

What to look for 

 

. 

Students’ 

 

 

. 

 

e. 

. 

 

yx 

. 

e. 

Proficiency strand(s): 

Understanding Problem solving 

F 

 

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

What this means provides 

a general explanation of the 

content description. 

Teaching points provides 

a list of the main teaching 

points relating to the content 

description. 

What to watch look for for suggests any any 

difficulties and misconceptions 

the students might encounter or 

develop. 



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

HANDS–ON ACTIVITIES 

Grid moves game 

 

 

‘’. 

‘Move 2 squares to the left and up 3 squares’ 

all 

students 

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. 

1 

4 

2 

3 

 

 

 

Is the bookcase bigger or smaller 

than the easel? How much bigger is the teacher’s desk than any of the other desks? 

 

 

 

 

. 

 

 

 

yxy 

Where is the library? How would you get 

from the office to the car park? What are the coordinates of the art room? What is the shortest way to get from the canteen to 

the oval? What other ways could you get there? 

 

 

First to ten game: 

 

 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. Publications ® www.ricpublications.com.au 47 

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

(c) 

(e) 

(a) 

(d) 

(f) 

(b) 

No lines of symmetry 

There are 

an infinite 

number 

of lines of 

symmetry in 

a circle. 

No lines of symmetry 

(d) 

(a) (b) (c) 

(f) 

(h) 

(g) 

(e) 

(i) 

FORMAT OF THIS BOOK 

Links to other curriculum areas includes activities in other curriculum areas which support 

the content description. These are English, Information and Communication Technology, Health 

and Physical Education, History, Geography, the Arts and Languages). This section may list many 

links or only a few. It may also provide links to relevant interactive websites appropriate for the 

age group. 

Cross-curricular links reinforce the knowledge that mathematics can be found within, and relate 

to, many other aspects of student learning and everyday life. 

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




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

STUDENT NAME 

RESOURCE SHEET 

The new suburb 

Below is part of a map of a new suburb. 

The map is missing some details. Show: 

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

2. A shop at G4 

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

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

at C6 

5. Orange Ave one-way heading west 

6. A mail box at K8 and a café at A3 

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

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

Uses simple 

coordinates 

Creates simple grid 

maps 

Interprets simple 

grid maps 

North 

Checklist 

Identifies relative 

positions on a map 

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. 

Assessment pages are included. These 

support activities included in the Hands-on 

activities or resource sheets. 

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. 


English 


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

NAME: 

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

Sub-strand: Location and transformation 

L&T – 1 

Page 55 Resource sheet – The new suburb 

1.–8. Teacher check 

Page 56 Assessment 1 – The clothes line 

1. jeans 

2. second from the left on the top line 

3. skirt 

4. 3 

5. 4 

6. Teacher check 


Ring a Toy 

Page 65 

DATE: 

Below is a game used at a school fete. The aim is to throw hoops over the 

squares and if you land on a toy, you win it. 

5 

4 

3 

2 

1 

1. What is the toy in D3? 

2. In what square is the fairy doll? 

3. The toy in C4 is a . 

4. In what square is the toy train? 

5. What is the toy in A5? 

LINKS TO OTHER CURRICULUM AREAS 

Once upon a time map booke. 

. 

Information and Communication Technology 

 

 

 

Z 

 

 

 

 

 

 

Health and Physical Education 

Indians and tepees 

 

 

’e. 

’’ 

clockwise 

’anticlockwise 

’ 

 

’’ 

 

. 

History and Geography 

. 

A B C D E 

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



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Answers 

Resource sheet – Transparent mirror 

activity page 

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


Answers for resource pages (where 

appropriate) and assessment pages are 

provided on the final page of each sub-strand 

section. 

Page 57 Assessment 1 – Near the school 

1. a swing 

2. B7 

3. oval and park (or swing) 

4. Arrows showing School Street one-way from west to 

east. Teacher check. 

5. Go left (or west) along Careful Street; turn right 

(north) into Park Road; first right into School Street 

and the hospital is on the left. 

Page 58 Assessment 2 – Ring a toy 

1. A toy car 

2. A2 

3. A (beach) ball 

4. C1 

5. A dog 


L&T – 2 

Page 63 Resource sheet – Symmetry in shapes 

1. 

Page 66 Resource sheet – Reflections on symmetry 

1.–3. Teacher check 

Page 67 Resource sheet – Symmetry in the garden 

1. 

(a) (b) (c) 

(d) (e) (f ) 


Page 68 Assessment 1 – Transparent mirror 

symmetry 

1. 


Page 69 


Assessment 2 – Deb and Tim’s toy shop 


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

Sub-strand: Geometric reasoning—GR – 1 

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

RELATED TERMS 


Angle 

• Two lines with a common end point 

called a vertex, or the extent of 

rotation about a point. 

Right angle 90° 

• Exactly 90°. 

Acute angle 

• An angle less than 90°. 

Obtuse angle 

• Greater than 90° but less than 180°. 

Straight angle 

• Exactly 180°. 

One rotation 

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

Degree 

• A unit of measure of an angle, based 

on there being 360° in a circle. 

• Students need to be aware that 

degrees are also used to measure 

temperature, but this is not the same 

as the measure for angle. 

What this means 

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

recognise. 

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

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

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

• Students are developing an awareness and understanding of 

the movement that relates to how angles are formed and to the 

measurement of angles. 

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

Teaching points 

• Angles are classified by their size in their relationship to the right angle 

(90°). (Refer to related terms.) 

• Right angles are used extensively in most buildings. For example, where 

walls meet the floor and the ceiling, the corners of rooms and most of 

the angles in the construction of cupboards. Books and paper mostly 

have 90° angles. 

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

about 90°. 

• Make links to the unit on time (UUM – 2) looking at the hands on an 

analogue clock as they turn in a clockwise direction. 

• Also make links to the unit on location and transformation (L&T – 1) 

where quarter and half turns are used, along with ideas about the four 

cardinal compass points (north, south, east and west) and left/right and 

clockwise/anticlockwise. 

• Students can get an intuitive idea of the size of angles when making 

comparisons. For example, that the size of the angles on the hexagon 

piece of pattern blocks are greater than a right angle (90°) and also 

much bigger than the size of the angles on the triangular block, which 

are less than a right angle. At this stage, they do not need to measure 

the angles on the two pieces. 



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• Show right angles in different orientations. This should help avoid a 

common misconception that we can have right angles and ‘left angles’. 

Student vocabulary 

right angle 

acute angle 

obtuse angle 

straight angle 

degrees 

rotation 

arms (of an angle) 

• It is important to make angles with different arm lengths so students 

realise that the length of the arms does not affect the size of an angle. 

• National tests often include a question on angles, where students 

identify the largest or smallest angles from a set of angles that have 

different arm lengths. 

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




What to look for 

• Students know the properties of a right angle (90°) and can represent 

them without the use of a protractor. (Note: Protractors are not 

encouraged at this year level). 

• Students are aware that a straight angle is 180° (which is two right 

angles) and a full rotation is 360° (which is four right angles). 

• Students confused by the length of the arms of an angle, thinking that 

an angle with short arms is less than an angle of lesser degrees but 

with longer arms. Students with this misconception would judge that 

the first angle below is wider than the second because of the length of 

the arms. In fact, the second angle is larger. 



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Proficiency strand(s): 

Understanding 

Fluency 

Problem solving 

Reasoning 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) R.I.C. Publications ® www.ricpublications.com.au 73


HANDS–ON ACTIVITIES 

• In this unit, students will mostly compare angles to the right angle (90°). This would involve recognising that a straight 

angle is two right angles (180°) and a full turn is four right angles (360°). Discuss the idea that right angles occur all 

around us, including the corners of pieces of paper, books, corners in rooms etc. 

• One method of introducing 

students to the idea of angles is 

to get them to (very carefully) 

trace the cutting edge of an 

open pair of scissors. 

• Students make an angle demonstrator (see page 77). They use these to show various angles such as 90°, an angle 

less than 90°, an angle greater than 90°, a straight angle and a full turn. Students find ways to record their results. Play 

games where the teacher (or a student) calls out an angle size (from the five mentioned above) and the students make 

that angle with their angle demonstrator and hold it up for the teacher to check. 

• Students make an angle unit measure that can be 

used as a non-standard unit. One version of this is to 

cut a sharp angle from a piece of cardboard. Allow the 

students to decide on how ‘pointy’ the angle is, but 

‘quite pointy’ would be the instruction. Students then 

use their angle unit measures to measure different 

angles. Note that as the students have each decided 

on the ‘pointiness’ of their angle unit measure, there 

will be a variation of results for the same measuring 

activity, as there is when measuring the length of a 

table using the non-standard unit of hand spans. 

• Another way to compare angles without a 

protractor is for students to make a different type 

of angle unit measure. This involves using a circle 

of light card. Students fold the circle in half, in half 

again, a third time, and finally a fourth time. When 

this is opened out, there are 16 equal (or very nearly 

equal) segments that become the units of the 

angle unit measure. Students then can use these to 

measure the size of angles in terms of the number 

of segments needed on their angle unit measure. 

Students may make the link to the fact that four of 

these angle unit segments make a right angle (90°). 

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

My angle unit 

measure 



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I needed 4 of my angle unit segments to be 

the same as the corner of my book. 



HANDS–ON ACTIVITIES (CONTINUED) 

• Students look for objects that can rotate through a full turn, such as a rotary clothesline, helicopter rotors, windmills, 

wheels on any vehicles or the hands on a clock. Describe this as a ‘full turn’, which can then be related to 360°. 

• Students look for objects that can rotate through part of a full turn, such as doors, the tray on a tip truck, pages in a 

book, swings or scissors. Encourage the use of the terms ‘less than a full turn’, ‘half turn’, ‘quarter turn’ and ‘three-quarter 

turn’. These terms can then be related to 180° for a half turn and 90° for a quarter turn. Relating a three-quarter turn to 

270° would not be expected at this year level. 

• Opening doors partially or fully gives an idea of angles. Many doors open to 180°, though if near a corner, they may only 

open to about 90°. Students could draw what the angle looks like at different points of turn. 

• The hour and minute hands on a clock make angles as they turn. Students could discuss what angle is formed at certain 

times; e.g. 3 o’clock, 9:15, 12 o’clock, 9 o’clock or 12:07. This may link with the unit on time (UUM – 2). 

• Links could also be made to the unit on location and transformation (L&T – 1) where quarter and half turns are used, 

along with ideas about the four cardinal compass points (north, south, east and west) and left/right and clockwise/ 

anticlockwise. 

• Students use their arms to demonstrate angles. One arm remains out straight from their body (parallel to the ground); 

the other arm can be turned slowly to show a right angle, an angle less than a right angle, an angle greater than a right 

angle, a straight angle and a full turn. 

• Play ‘Simon says’, with the teacher calling out various angle sizes and the students making the nominated angle with 

their arms. Terms such as ‘right angle’, ‘90°’, ‘less than 90°’, ‘more than 90°’, ‘straight angle’, ‘180°’, ‘full turn’ and ‘360°’ could 

be used. ‘Clockwise’ and ‘anticlockwise’ could also be used to indicate the direction of the turn. If students do not show 

the correct angle and/or direction, they sit down. The last one standing is the winner. 

• Students use two craftsticks, straws or similar to make different types of angles: right angle, an angle less than a right 

angle, an angle greater than a right angle, a straight angle and a full turn. The sticks do not need to be joined; one may 

just overlay the other. 

• Students identify different angles in the room and in the outside environment. Try to find examples of right angles, 

angles less than 90° and angles larger than 90°. Students could look for pictures that illustrate the different angles. 



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

straight angles and a full turn. 

staight 

angle 

180° 

right 

angle 

360° 



LINKS TO OTHER CURRICULUM AREAS 

English 

• Make vocabulary cards with drawings and definitions for new words associated with angles. For example, ‘right angle’, 

‘straight angle’ and ‘full turn’. Each of the cards could also make mention of degrees of turn; e.g. 90°, 180° and 360°. 

Information and Communication Technology 

• A website that asks students to decide whether the angles shown are greater than a right angle, exactly a right angle 

or less than a right angle can be found at . 

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

Health and Physical Education 

• Students make angles using their arms, as described earlier. The teacher, or a student, could make an angle with his or 

her arms that the other students copy and describe. The person out the front could call out a type of angle for the other 

students to make with their arms. 



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Make and use an angle demonstrator 

• Make two (2) circles about the same size as the one below; one in a light 

colour, the other in a darker colour. Carefully cut a line to the centre as 

shown below. 

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



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• Place one circle inside the other as shown. You can now turn one circle of 

your angle demonstrator within the other to show different angles. 

• Use your angle demonstrator to show a right angle (90°), an angle less than 

90° and a straight angle (180°). Draw these onto a sheet of paper. How can 

you show a full turn? 




Mix and match angles 

Cut out the 12 cards below. Mix them up and try to put them back in the 

correct groups. 

right 

angle 

straight 

angle 

90° 

180° 

full turn 360° 



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Sub-strand: Geometric reasoning—GR – 1 Assessment 1 

NAME: 

DATE: 

What’s my angle? 

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

Bend your object to make the angle below. 

Call this the ‘angle unit’. 


1. Now use this to find out if the angles below are bigger, smaller or the same 

as your angle unit. Write it under each of the angles. 

(a) 

(c) 

2. How many of your angle units will fit in each of the angles below? 

Describe what type of angle each one is. 

(a) 

(b) 



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Number = Number = 

(d) 

(b) 


Assessment 2 Sub-strand: Geometric reasoning—GR – 1 

NAME: 

DATE: 

What do you know about angles? 

Write what you know about each of the types of angles below. Draw an 

example of each one. 

(a) Draw any angle (what does an 

angle measure?) 

(b) A right angle 

(c) A straight angle (d) A full turn 



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STUDENT NAME 

Recognises right angles 

Recognises angles greater 

than and less than 90° 

Recognises a straight 

angle 

Recognises a full turn 



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Sub-strand: Geometric reasoning 

GR – 1 

Answers 

Page 79 

1. 

Assessment 1 – What’s my angle? 

(a) 

smaller 

(c) 

bigger 

(b) 

bigger 

(d) 

the same size 

2. 

(a) 

Page 80 

3 angle units. The angle is 

greater than a right angle (90°) 

It is an obtuse angle. 

Assessment 2 – What do you know 

about angles? 

Teacher check 

(b) 

2 angle units. The angle is 

less than a right angle (90°). 

It is an acute angle. 



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RIC-20153 ACM Measurement and Geometry (Yr 3) Geometric reasoning

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