RIC-20176 ACM Measurement and Geometry (Yr 6) Shape 1

©R.I.C. Publications 

Low Resolution Images 

Display Copy

Australian Curriculum Mathematics 

resource book: Measurement and Geometry 

(Year 6) 

Published by R.I.C. Publications ® 2013 

Copyright © Linda Marshall 2013 

RIC– 20176 

Titles in this series: 

Australian Curriculum Mathematics resource book: 

Measurement and Geometry (Foundation) 


Measurement and Geometry (Year 1) 











All material identified by is material subject to 

copyright under the Copyright Act 1968 (Cth) and is owned 

by the Australian Curriculum, Assessment and Reporting 

Authority 2013. 

For all Australian Curriculum material except 

elaborations: This is an extract from the Australian 

Curriculum. 

Elaborations: This may be a modified extract from the 

Australian Curriculum and may include the work of other 

authors. 

Disclaimer: ACARA neither endorses nor verifies the 

accuracy of the information provided and accepts no 

responsibility for incomplete or inaccurate information. In 

particular, ACARA does not endorse or verify that: 

• The content descriptions are solely for a particular year 

and subject; 

• All the content descriptions for that year and subject 

have been used; and 

• The author’s material aligns with the Australian 

Curriculum content descriptions for the relevant year and 

subject. 

You can find the unaltered and most up to date version of 

this material at http://www.australiancurriculum.edu.au/ 

This material is reproduced with the permission of ACARA. 

Copyright Notice 

A number of pages in this book are worksheets. 

The publisher licenses the individual teacher who 

purchased this book to photocopy these pages to hand 

out to students in their own classes. 

Except as allowed under the Copyright Act 1968, any 

other use (including digital and online uses and the 

creation of overhead transparencies or posters) or any 

use by or for other people (including by or for other 

teachers, students or institutions) is prohibited. If you 

want a licence to do anything outside the scope of the 

BLM licence above, please contact the Publisher. 

This information is provided to clarify the limits of this 

licence and its interaction with the Copyright Act. 

For your added protection in the case of copyright 

inspection, please complete the form below. Retain this 

form, the complete original document and the invoice 

or receipt as proof of purchase. 

Name of Purchaser: 

Date of Purchase: 

Supplier: 

School Order# (if applicable): 

Signature of Purchaser: 



Display Copy 

Internet websites 

In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, 

the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class 

teacher checks all URLs before allowing students to access them. 

View all pages online 

PO Box 332 Greenwood Western Australia 6924 

Website: www.ricpublications.com.au 

Email: mail@ricgroup.com.au

Foreword 

AUSTRALIAN CURRICULUM MATHEMATICS 

RESOURCE BOOK: 

MEASUREMENT AND GEOMETRY 

(YEAR 6) 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) 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 .................................................... 2–61 

• UUM – 1 

Connect decimal representations to the metric system (ACMMG135) 

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

– Hands-on activities ................................................................................... 3 

– Links to other curriculum areas ................................................................. 3 

– Resource sheets .................................................................................... 4–6 

– Assessment .......................................................................................... 7–8 

– Checklist ................................................................................................... 9 

• UUM – 2 

Convert between common metric units of length, mass and 

capacity. (ACMMG136) 

– Teacher information ......................................................................... 10–13 

– Hands-on activities ........................................................................... 14–16 

– Links to other curriculum areas ................................................................ 16 

– Resource sheets ................................................................................ 17–25 

– Assessment ...................................................................................... 26–28 

– Checklist .................................................................................................. 29 

• UUM – 3 

Solve problems involving the comparison of lengths and areas 

using appropriate units (ACMMG137) 

– Teacher information ................................................................................ 30 

– Hands-on activities .................................................................................. 31 



– Assessment ...................................................................................... 37–38 

– Checklist .................................................................................................. 39 

• UUM – 4 

Connect volume and capacity and their units of 

measurement (ACMMG138) 





– Assessment ............................................................................................. 46 

– Checklist .................................................................................................. 47 

• UUM – 5 

Interpret and use timetables (ACMMG139) 





– Assessment ............................................................................................. 56 

– Checklist .................................................................................................. 57 

Contents 

Answers ............................................................................................ 58–61 

Shape .................................................................................................. 62–79 

• Shape – 1 

Construct simple prisms and pyramids (ACMMG140) 


– Hands-on activities ........................................................................... 64–65 



– Assessment ...................................................................................... 76–77 

– Checklist .................................................................................................. 78 

Answers .................................................................................................... 79 

Location and transformation .............................................. 80–113 

• L&T – 1 

Investigate combinations of translations, refl ections and rotations, 

with and without the use of digital technologies (ACMMG142) 





– Assessment ...................................................................................... 95–96 

– Checklist .................................................................................................. 97 

• L&T – 2 

Introduce the Cartesian coordinate system using all four 

quadrants (ACMMG143) 



Display Copy 

– 

– 

– 

– 

– 

– 

Teacher information ......................................................................... 98–99 

Hands-on activities ................................................................................ 100 

Links to other curriculum areas .............................................................. 101 

Resource sheets ............................................................................ 102–108 

Assessment .................................................................................. 109–110 

Checklist ................................................................................................ 111 

Answers ...................................................................... 112–113 

Geometric reasoning ............................................................ 114–131 

• GR – 1 

Investigate, with and without digital technologies, angles on a 

straight line, angles at a point and vertically opposite angles. Use 

results to fi nd unknown angles (ACMMG141) 

– Teacher information ..................................................................... 114–115 

– Hands-on activities ................................................................................ 116 

– Links to other curriculum areas .............................................................. 117 

– Resource sheets ............................................................................ 118–127 

– Assessment ...................................................................................128–129 

– Checklist ................................................................................................ 130 

Answers ................................................................................................. 131 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) 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 

• links to other curriculum areas 

• resource sheets 

• assessment sheets. 

• a checklist 

Answers relating to the 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. 

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. 



Display Copy 

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 resource 

sheets. Where applicable, these will be stated for 

easy reference. 

iv Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) R.I.C. Publications ® www.ricpublications.com.au

FORMAT OF THIS BOOK 

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

the content description. These include Information and Communication Technology, English, 

Science, Languages other than English, History, Geography and the Arts. 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. 

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. Support 

activities are in the hands-on activities or 

resource sheets. 



Display Copy 

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 for resource sheets (where 

appropriate) and assessment pages are 

provided on the final page of each sub-strand 

section. 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) R.I.C. Publications ® www.ricpublications.com.au v

Sub-strand: Shape—Shape – 1 


RELATED TERMS 

TEACHER INFORMATION 

Net 

• A flat two-dimensional pattern that 

can be folded to make a model of a 

three-dimensional object. 

Prism 

• 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 

(below) etc. 

Pyramid 

• A three-dimensional object with a 

polygonal base and the other faces 

triangles with a common vertex 

called the apex. It is named after 

its base; e.g. triangular pyramid, 

square-based pyramid (below) etc. 

What this means 

• The making of models can assist students’ understanding of the 

properties of objects. 

• The use of a variety of materials is important. 

• Students need to de-construct prisms and pyramids as well as 

construct them. 

• Students need experience making nets for themselves using 

equipment such as Geoshapes® and Polydrons. This would come 

before any use of templates. 

• Ready-made templates for nets of three-dimensional objects usually 

only show one way to produce that shape. Particular nets are often 

chosen because they use the least amount of card or because they 

can fit onto a photocopier. However, there are a variety of ways of 

producing nets for any one shape, and students need to be exposed 

to as many of them as possible. For example, the ‘standard’ net for a 

triangular prism (seen in the left column) is shown below left, along 

with a variation that students should be aware of through exploration 

with materials. 

• It is useful for students to produce their own nets and fold and tape 

them together to make their shapes. 

• Students should become familiar with a variety of nets for prisms and 

pyramids. 



Display Copy 

Teaching points 

• Students explore the different ways to make nets for the same shape. 

• There is more than one net for each geometric solid. 

• Students look at nets with different designs on the faces and visualise 

what will be on each face when the solid is constructed. 

• National tests usually have a question that requires students to be able 

to associate three-dimensional objects with their nets. They also have 

questions where students visualise solids and their faces from different 

orientations. 

62 Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) R.I.C. Publications ® www.ricpublications.com.au 

ISBN 978-1-921750-96-0



Student vocabulary 

net 

cube 

prism 

triangular prism 

rectangular prism 

pentagonal prism 

hexagonal prism 

octagonal prism 

pyramid 

square-based pyramid 

tetrahedron 

pentagonal pyramid 

hexagonal pyramid 

octagonal pyramid 

faces 

vertices (one vertex) 

edges 

TEACHER INFORMATION (CONTINUED) 

What to look for 

• Students confused about the difference between a pyramid and a 

prism. 

• Students limited to being able to find only one or two different nets for 

any shape. 

• Students being given a net for a geometric solid and having difficulty 

visualising what the shape will look like when completed. 

• Students unable to visualise and draw models from different 

orientations. 

• Students having difficulty drawing three-dimensional objects on 

isometric dot paper. 



Display Copy 

Proficiency strand(s): 

Understanding 

Fluency 

Problem solving 

Reasoning 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6) R.I.C. Publications ® www.ricpublications.com.au 63 

ISBN 978-1-921750-96-0


HANDS-ON ACTIVITIES 

• Students identify and describe the differences between prisms and pyramids. 

• Students classify prisms according to the face at each end; and pyramids according to their base. 

• It is worth pointing out to students that most diagrams and texts show 

the ends of prisms as regular polygons or rectangles. However, if the 

faces are congruent and irregular, and connected by rectangles, the 

shape is still a prism. In the diagram (right), we would classify the object 

as an octagonal prism, even though it does not look like the usual 

octagonal prism we see, which has a regular octagon at each end. 

• Students use open construction materials such as straws, toothpicks or 

skewers, and blu-tac or plasticine to make various prisms and pyramids. There 

are open construction sets are available commercially. 

• Students use Polydrons or Geoshapes® to construct prisms and pyramids. The advantage of using this manipulative is 

that students can undo some of the joins and reconnect them in different ways to investigate the various nets that can 

be made for the shapes. 

• Students draw their prisms and pyramids from different orientations. 

Model Top Front Back Right Left 

• Students use isometric dot paper as well as 1 cm 2 grid paper as another form of recording the models they make. 

Students may need to be shown the best way to use isometric dot paper; for example, the paper should be used in 

landscape rather than portrait orientation. 



Display Copy 

• Students investigate the number of different nets that can be made for a cube, drawing them onto 1 cm 2 grid paper. 

There are 11 different possibilities. To assist in this process, students could use Geoshapes® or Polydrons and join six 

squares together, then ‘unjoin’ some of the edges and rejoin them in different ways. Once students have found all 11 

nets, they could cut them out, fold them and check that each of them does indeed make a cube. 

Note: There are other ways to join six squares together, but no others will fold to make a cube. One example is shown 

below. 


ISBN 978-1-921750-96-0


HANDS-ON ACTIVITIES (CONTINUED) 

• An extension of the investigation on the previous page is for students to use some (or 

all) of the nets made; and try to work out where the numbers 1–6 would go in order to 

turn them into dice. Students need to know that the sum of the numbers on opposite 

faces of a dice is always 7. They can then check if their predictions on where the numbers 

sit on their cubes actually work by cutting them up and folding them into cubes. 

• Students investigate the number of edges, faces and vertices on a range of different prisms and pyramids. The teacher 

can ‘lead’ the students to Euler’s law: that for all polyhedra, the number of vertices plus the number of faces is equal to 

the number of edges plus two (V + F = E + 2). 

Pentagonal prism 

V + F = E + 2 

10 + 7 = 15 + 2 

Information and Communication Technology 

Pentagonal pyramid 

V + F = E + 2 

6 + 6 = 10 + 2 

LINKS TO OTHER CURRICULUM AREAS 

• Printable nets for different solids can be found at Note that only one 

version of a net is shown for each solid, so students would still need to see other variations. 

• An animated display of nets and their solids can be found at Again, there is only one version of each net shown. 

• A similar website to the one above, but for pyramids, can be found at 

• The illuminations website has an interactive website where different solids can be selected and rotated, and their 

nets displayed. It still has the same problem as the sites above. It can be found at 

• Another website for looking at nets of solids can be found at 

• A short quiz where students match a net with the solid can be found at 

History and Geography 

• Discuss the historical significance of pyramids in different cultures around the world. Students could research their use, 

and the range of building materials and possible techniques used in their construction. They could also investigate the 

ways they were decorated inside. 

The Arts 

• Students make various prisms and pyramids using light cardboard, and decorate them in different ways. 

Science 



Display Copy 

• Students investigate crystals. 

• A website that offers information on crystals can be found at 

• Another website from the same source, which explains how to make rock candy using crystals, can be found at 


ISBN 978-1-921750-96-0


RESOURCE SHEET 

Net for a cube 



Display Copy 

This is only one of many nets that can be made for a cube. How many others can you find? 

CONTENT DESCRIPTION: Construct simple prisms and pyramids 


ISBN 978-1-921750-96-0



Net for a rectangular prism 




Display Copy 

This is only one of many nets that can be made for a rectangular prism. How many others can 

you find? 


ISBN 978-1-921750-96-0



Net for a square-based pyramid 



Display Copy 

This is only one of many nets that can be made for a square-based pyramid. How many others can 

you find? 



ISBN 978-1-921750-96-0



Net for a tetrahedron 




Display Copy 

This is one of two nets that can be made for a tetrahedron. Can you find the other one? 


ISBN 978-1-921750-96-0



Net for a triangular prism 



Display Copy 

This is only one of many nets that can be made for a triangular prism. How many others can you 

find? 



ISBN 978-1-921750-96-0



Net for a pentagonal prism 




Display Copy 

This is only one of many nets that can be made for a pentagonal prism. How many others can 

you find? 


ISBN 978-1-921750-96-0



Net for a pentagonal pyramid 



Display Copy 

This is only one of many nets that can be made for a pentagonal pyramid. How many others 

can you find? 



ISBN 978-1-921750-96-0



Net for a hexagonal pyramid 




Display Copy 

This is only one of many nets that can be made for a hexagonal pyramid. How many others can 

you find? 


ISBN 978-1-921750-96-0



Net for a hexagonal prism 



Display Copy 

This is only one of many nets that can be made for a hexagonal prism. How many others can 

you find? 



ISBN 978-1-921750-96-0



Dicey dice 

1. Study the net of each dice and answer the question. If you are not sure of the answer, cut it 

out and construct the cube. 

(a) What is opposite the ♥ on this dice? 


(b) What symbol is on the bottom of this dice? 

(c) Kim folds this net to make a cube. 

What face is opposite the ➢? 

(d) This net is folded to make the cube below. What shapes would be 

on the top and bottom of the cube? 

(e) Draw a different net for a dice. Construct the cube to check that the net is correct. 

Draw the net again and add a design to each face. 

♣ 

♦ 

✢ 



Display Copy 

Challenge a partner to work out the position of each face on the constructed dice. 


ISBN 978-1-921750-96-0

Assessment 1 Sub-strand: Shape—Shape – 1 

NAME: 

DATE: 

Prisms and pyramids 

Write everything you know about prisms. 

Draw three different prisms. 

Write everything you know about pyramids. 

Draw three different pyramids. 



Display Copy 



ISBN 978-1-921750-96-0

Sub-strand: Shape—Shape – 1 Assessment 2 

NAME: 

DATE: 

Prism and pyramid nets 

• Match the nets in the left-hand column to the prisms and pyramids in the middle column. 

Write the matching letter in the box. 

• In the right-hand column, draw a different net for each 3-D shape in the middle column. 

Net 1 Geometric solid Net 2 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 



Display Copy 

A 

B 

C 

D 

E 

F 

G 

H 


ISBN 978-1-921750-96-0

Checklist Sub-strand: Shape—Shape – 1 


STUDENT NAME 

Knows the 

features of 

prisms and 

pyramids 

Constructs 

prisms from 

nets 

Constructs 

pyramids from 

nets 



Display Copy 


ISBN 978-1-921750-96-0


Shape – 1 

Answers 

Page 75 

Resource sheet – Dicey dice 

1. (a) (b) ♥ 

(c) (d) and 

(e) Teacher check 

Page 76 Assessment 1 – Prisms and pyramids 

Teacher check 

Page 77 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

Assessment 2 – Prism and pyramid nets 

Net 1 Geometric solid Net 2 

F 

G 

E 

C 

A 

H 

A 

B 

C 

D 

E 

F 

Teacher check 



Display Copy 

8. 

B 

G 

D 

H 


ISBN 978-1-921750-96-0

RIC-20176 ACM Measurement and Geometry (Yr 6) Shape 1

Create successful ePaper yourself

Delete template?

Save as template?