RIC-20164 ACM Measurement and Geometry (Yr 5) Using units of measurement 2

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Australian Curriculum Mathematics 

resource book: Measurement and Geometry 

(Year 5) 

Published by R.I.C. Publications ® 2013 

Copyright © Linda Marshall 2013 

RIC–20172 

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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Foreword 

AUSTRALIAN CURRICULUM MATHEMATICS 

RESOURCE BOOK: 

MEASUREMENT AND GEOMETRY 

(YEAR 5) 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) 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 ......................................................... 2–41 

• UUM – 1 

Choose appropriate units of measurement for length, area, 

volume, capacity and mass (ACMMG108) 

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

– Hands-on activities ................................................................................. 5–8 

– Links to other curriculum areas .................................................................... 9 

– Resource sheets .................................................................................. 10–16 

– Assessment ........................................................................................ 17–18 

– Checklist .................................................................................................... 19 

• UUM – 2 

Calculate the perimeter and area of rectangles using familiar 

metric units (ACMMG109) 

– Teacher information .................................................................................. 20 

– Hands-on activities ............................................................................. 21–22 

– Links to other curriculum areas .................................................................. 23 


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

– Checklist .................................................................................................... 27 

• UUM– 3 

Compare 12- and 24-hour time systems and convert 

between them (ACMMG110) 

– Teacher information ........................................................................... 28–29 

– Hands-on activities .................................................................................... 30 



– Assessment ............................................................................................... 39 

– Checklist .................................................................................................... 40 

Answers .................................................................................. 41 

Shape ........................................................................................ 42–57 

• Shape – 1 

Connect three-dimensional objects with their nets and other 

two-dimensional representations (ACMMG111) 





– Assessment ........................................................................................ 54–55 

– Checklist .................................................................................................... 56 

Answers .................................................................................. 57 

Contents 

Location and transformation .................................................... 58–115 

• L&T – 1 

Use a grid reference system to describe locations. Describe routes 

using landmarks and directional language (ACMMG113) 





– Assessment ............................................................................................... 70 

– Checklist .................................................................................................... 71 

• L&T – 2 

Describe translations, refl ections and rotations of two-dimensional 

shapes. Identify line and rotational symmetries (ACMMG114) 





– Assessment ........................................................................................ 93–94 

– Checklist .................................................................................................... 95 

• L&T – 3 

Apply the enlargement transformation to familiar two-dimensional 

shapes and explore the properties of the resulting image compared with 

the original (ACMMG115) 



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– Resource sheets .............................................................................. 100–110 

– Assessment .................................................................................... 111–112 

– Checklist .................................................................................................. 113 

Answers ........................................................................ 114–115 

Geometric reasoning .............................................................. 116–133 

• GR – 1 

Estimate, measure and compare angles using degrees. Construct angles 

using a protractor (ACMMG112) 

– Teacher information ....................................................................... 116–117 

– Hands-on activities ......................................................................... 118–119 

– Links to other curriculum areas ................................................................ 120 

– Resource sheets .............................................................................. 121–129 

– Assessment .................................................................................... 130–131 

– Checklist .................................................................................................. 132 

Answers ................................................................................ 133 

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) 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. 

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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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. 

iv Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) R.I.C. Publications ® www.ricpublications.com.au

FORMAT OF THIS BOOK 

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

the content description. These are English, Information and Communication Technology (ICT), 

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 

relates 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. These 

support activities in the Hands-on activities 

or resource sheets. 



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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 pages (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 5) R.I.C. Publications ® www.ricpublications.com.au v

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

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) 

RELATED TERMS 

TEACHER INFORMATION 

Perimeter 

• A measure of the distance around the 

boundary of a two-dimensional shape. 

Area 

• The amount of surface covered (i.e. 

2-D; measured in square units). 

Familiar metric units 

• For perimeter, use centimetres, metres 

and kilometres. For area, use square 

centimetres, square metres and square 

kilometres. Large areas of land may 

also be measured in hectares, though 

students would not be expected to 

work with this unit at this year level. 

Student vocabulary 

What does it mean 

• There is no direct relationship between the area and perimeter of 

rectangles. Two rectangles with the same area may have different 

perimeters and two rectangles with the same perimeter may have 

different areas. 

• It is not necessarily the case that, as the perimeter of a rectangle 

is increased or decreased, the area of the rectangle is increased or 

decreased. 

• Students should be led to ‘discover’ the formula for calculating the 

perimeter or area of a rectangle. 

Teaching points 

• Students may measure the lengths of the four sides of a rectangle 

and add them together to obtain the perimeter. They may then 

‘discover’ that a more efficient way to calculate the perimeter is 

to double the lengths of the two different sides and add them 

together. 

• Students will have had experience in finding the areas of 

rectangles by counting squares. The next step is to find the 

number of squares in each row and then work out how many rows 

there are. Students should explore the relationships rather than 

the teacher simply telling them a formula. 

• Teachers need to stress that the formulas for working out the 

perimeters and areas of rectangles only pertain to rectangles and 

are not necessarily appropriate for other shapes. 

• Use the language ‘square centimetres’ not ‘centimetres squared’; 

they mean different things. For example, 2 cm 2 (2 square 

centimetres) means 2 lots of 1 cm x 1 cm squares. Two centimetres 

squared means a square with a length of 2 cm and a width of 2 cm 

(which is actually 4 square centimetres). 



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What to look for 

• Students confused about the difference between perimeter and 

area. 

• Students believing that there is a direct relationship between the 

perimeter and area of a rectangles. 

perimeter 

area 

centimetres 

metres 

kilometres 

square centimetres 

square metres 

square kilometres 

Proficiency strand(s): 

Understanding 

Fluency 

Problem solving 

Reasoning 

20 Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) R.I.C. Publications ® www.ricpublications.com.au


HANDS-ON ACTIVITIES 

• Students construct rectangles on 1 cm 2 grid paper (see page 11). They record the size of the length and widths and add 

them together to determine the perimeter. Students can be ‘led’ to realise that if they double the size of the length and 

the size of the width, then add those two figures together, they have found an efficient way to calculate the perimeter 

of a rectangle. Another method for calculating the perimeter of a rectangle is to add the size of the length and width 

together and double the result. 

3 cm 

5 cm 

The length of the rectangle 

is 5 cm, the width is 3 cm. 

• Students investigate how to calculate the perimeter of a square, which is a ‘special’ type of rectangle. They could use the 

above method, but may realise that as all four sides of a square are equal, they only need to work out the length of one 

side and multiply it by four. 

• Find the perimeter of Geoboard shapes. These do not need to be just one rectangle or square, but can be combinations, 

as below. 

The perimeter is 

8 units 



• Use eight squares and investigate how many different shapes can be made. Some examples are shown below. Discuss 

which shape has the longest perimeter. Why are some of the perimeters different if all the shapes are made with eight 

squares? What types of shapes have the longer/shorter perimeters? 

3 cm 

The perimeter is 5 + 5 + 3 

+ 3, which is 16 cm. This is 

the same as 10 cm (2 x 5) 

+ 6 cm (2 x 3). 





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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) R.I.C. Publications ® www.ricpublications.com.au 21

HANDS-ON ACTIVITIES (CONTINUED) 


• Students work out the area of a rectangle by counting the total number of squares, one at a time. Next, they count 

the number of squares in one row and work out how many rows there are altogether. Students then investigate any 

relationship between the sets of figures. To assist in this, a table could be drawn up. 

Rectangle 

Rectangle 

Number of squares in 

each row (length) 

Number of rows 

(width) 

Total area 

1 5 3 15 cm 2 

2 

3 

Number of squares in 

each row (length) 

Number of rows 

(width) 

Perimeter 

Total area 

1 5 3 10 + 6 = 16 cm 15 cm 2 

2 

3 

Area of each row of the 

rectangle is 5 cm 2 

There are 3 rows; so the area 

of the rectangle is 15 cm 2 

• Students may use a similar format to the one above, but include a column for calculating and recording the perimeters. 

• Using a Geoboard, students investigate area and perimeter of various shapes. 



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The perimeter is 8 

units and the area is 

3 square units. 

The perimeter is 12 

units and the area is 6 

square units. 

The perimeter is 18 units and 

the area is 9 square units. 



LINKS TO OTHER CURRICULUM AREAS 

Information and Communication Technology 

• Students can calculate the perimeters of shapes on the website 

• A shape surveyor that looks at area and perimeter of rectangles can be found at 

• The Shape Explorer can be found at You can choose 

to have only rectangular shapes for this activity. It also has the option of looking at the areas and perimeters of the 

shapes students have worked with in table format. 

• A catchy YouTube song on perimeter and area can be found at 

It goes straight to multiplication for working out the area of a rectangle, so this could be used after students have 

‘discovered’ how the formula works. 

• A perimeter rap song can be found on YouTube at It shows some of the measurements in inches and others in centimetres. 

• An activity where students use perimeter and area to launch a ship can be found at The instructions are a little unclear, but students will soon get the hang of it. 

• A Design a Party planning activity where students look for particular rectangles with given areas and perimeters can be 

found at 



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Materials: 

8 square tiles 

1 cm 2 grid paper 

(a) 

(b) 

(c) 

(d) 

(e) 

Examples: 

RESOURCE SHEET 

Area the same 

• This square is 1 unit long and 1 unit wide. 

Its perimeter is 4 units. 

• Tina the tiler has 8 tiles. She must use all the tiles 

so she always has an area of 8 square units. 

• She has arranged her tiles like this 

to get a perimeter of 12 units. 


1. Do the same with your tiles. Make a copy of Tina’s floor on your grid paper. 

Shape Area Perimeter 

8 square units 12 units 

8 square units 





1 unit 



2. Help Tina by making these 5 different floors, using all 8 tiles for each one and copy 

each floor on grid paper. 

(a) 

(b) 

(c) 

a perimeter of 12 units (different from the one above) 

a perimeter of 14 units 

a perimeter of 16 units 

(d) and (e) two different floors with a perimeter of 18 units. 

1 unit 

1 unit 

1 unit 


Write the area and perimeter next to each shape and complete the table to show your 

results. 

3. Write about your results. 



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CONTENT DESCRIPTION: Calculate the perimeter and area of rectangles using familiar metric units 



RESOURCE SHEET 

Perimeter the same 

Materials: 

Examples: 


8 square tiles 

1 cm 2 grid paper 

• This square is 1 unit long and 1 unit wide. 

Its perimeter is 4 units. 

• Arrange 8 tiles like this. 

• The area is 8 square units 

The perimeter is 12 units. 

1. Do the same with your tiles. Make a copy of this floor on your grid paper. 

2. Make the perimeter stay at 12 units by removing different numbers of tiles, then 

copy each floor on grid paper: 

(a) 

(b) 

(c) 

(a) 

(b) 

(c) 

1 tile 

2 tiles 

3 tiles 

Write the area and perimeter next to each shape and complete the table to show your 

results. 

Shape Area Perimeter 

3. Write about your results. 


1 unit 



1 unit 

1 unit 


8 square units 12 units 




1 unit 



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Assessment 1 Sub-strand: Using units of measurement—UUM – 2 

NAME: 

DATE: 

Twelve squares 

1. (a) Find the area and perimeter of each shape below. 

(b) 

(c) 

Which shapes have the same perimeter? 

Which shapes have the same area? 

(i) (ii) (iii) 

(iv) 

P = 

cm 

A = cm 2 P = cm 

A = cm 2 P = cm 

P = 

cm 

(v) 

A = cm 2 P = cm 

2. (a) What is the perimeter of this rectangle? 

(b) 

What is its area? 

3. Materials: 12 square tiles 

(a) 

(b) 

(c) 

A = cm 2 

Make the three different rectangles that are possible with 12 tiles. 

Draw the rectangles in the first column of the table. 

Complete the table. 

Sketch of rectangle Length Width Perimeter Area 

4. Write about what you found. 

12 units 1 unit 26 units 

A = cm 2 



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12 square 

units 




Checklist 

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) 

STUDENT NAME 

Understands how to 

calculate the perimeter 

of rectangles 

Understands how to 

calculate the area of 

rectangles 

Compares area and 

perimeter of rectangles 



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Sub-strand: Using units of measurement 

Answers 

Area 

UUM –1 

3. The perimeters are all the same (12 units), but the 

areas are different. 

Page 10 Resource sheet – Paperclip chains 

Page 26 Assessment 1 – Twelve squares 

Teacher check 

1. (a) (i) P = 12 cm A = 6 cm 2 (ii) P = 16 cm A = 9 cm 2 

Page 12 Resource sheet – Ambitious areas 

(iii) P = 18 cm A = 8 cm 2 (iv) P = 12 cm A = 5 cm 2 

1.–2. Teacher check 

(v) P = 12 cm A = 8 cm 2 

3. Bird: 19.5 squares Rabbit: 26 squares 

(b) (i) (iv) (v) (c) (iii) (v) 

2. (a) 22 units (b) 10 square units 

Page 13 Resource sheet – Boxes of eight 

3. (a) Teacher check 

Teacher check 

(b)–(c) 

Page 14–15 Resource sheet – Mystery tour 

Sketch Length Width Perimeter 

3 5 cm 4 cm 2 cm 40 cm 3 80 cm 2 (g) 7:14 am 

(h) 4:21 pm 

You will be taken to the zoo. 

12 square 

12 units 1 unit 26 units 


Page 16 Resource sheet – Units of length 

12 square 

6 units 2 units 16 units 


1. (a) tape measure (b) 30 cm ruler 

(c) tape measure (d) tape measure or 1 m ruler 

12 square 

4 units 3 units 14 units 


(e) trundle wheel (f) 30 cm ruler 

(g) trundle wheel (h) pedometer 

4. The areas are the same for all of the rectangles, but 

the perimeters are different. The longer and thinner 

2. Teacher check 

the shape, the greater the perimeter. 

Page 17 Assessment 1 – Units of length 

UUM – 3 

Teacher check 

Page 33 Resource sheet – The 24-hour clock 

Page 18 Assessment 2 – Boxes and more boxes 

1. (a) 0400 (b) 1400 

1. (a) Teacher check (b) 24 cm 3 

(c) 1200 (d) 2400 

(c) Their volume is the same, but their shapes are 

(e) 1223 (f) 0525 

different. 

(g) 2115 (h) 0420 

2. (b) 

Surface 

Prism Length Width Height Volume 

area 2. (a) 1:48 pm (b) 3:44 am 

1 3 cm 3 cm 3 cm 27 cm 3 54 cm 2 

(c) 10:15 pm (d) 6:05 pm 

2 2 cm 2 cm 1 cm 4 cm 3 16 cm 2 

(e) 11:11 am (f) 10:22 pm 

UUM – 2 

(c) Teacher check 

Page 24 Resource sheet – Area the same 


2. a perimeter of 12 units P = 12; A = 8 

a perimeter of 14 units P = 14; A = 8 




3. The areas are all the same (8 square units), but the 

perimeters are different. 

Page 25 Resource sheet – Perimeter the same 


2. (a) 1 tile P = 12; A = 7 

(b) 2 tiles P = 12; A = 6 

(c) 3 tiles P = 12; A = 5 

Page 39 Assessment 1 – It’s about time 

1. 10:49 am is 1049. The bus leaves at 1137. 1049 until 

1100 is 11 minutes, plus the extra 37 minutes until 

1137 gives 48 minutes. Answer: 48 minutes 

2. 2:00 is 1400. The trip takes 32 minutes, so the latest 

bus she could take would be 1328 (1400–32 minutes). 

The bus that leaves just before 1328 is the 1305 bus. 

Answer: The 1305 bus 

3. 7:30 am is 0730. An hour later it would be 0830. The 

closest bus to that time is the 0837 bus. 


4. 10:30 am is 1030. The trip takes 32 minutes, so the 

latest bus she could take would be 0958. The bus that 

leaves just before 0958 is the 0955 bus. 


5. 3:45 pm is 1545. The next bus is at 1604. It is 15 

minutes from 1545 until 1600; add on the extra 4 

minutes until 1604, and the wait is 19 minutes. 

Answer: The 1604 bus. A 19 minute wait 



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RIC-20164 ACM Measurement and Geometry (Yr 5) Using units of measurement 2

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