stage 3a – unit 46 measurement volume and capacity entry...

Maths K–6Stage 3A

P/M 3A 43827 Centre for Learning Innovation

Stage 3A – Unit 46

Measurement

Volume and CapacityEntry 1: Rectangular Prisms

This booklet includes:

• Teacher notes (to be detached before sending to the student and supervisor)

• Supervisor notes

• Student and supervisor guide

Number: 43827 Title: Using Maths Tracks Stage 3A Unit 46

All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.

Published byCentre for Learning Innovation (CLI)51 Wentworth RdStrathfield NSW 2135________________________________________________________________________________________________Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction ortransmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited withoutthe written authority of the Centre for Learning Innovation (CLI).

© State of New South Wales, Department of Education and Training 2006.

This publication is copyright New South Wales Department of Education and Training (DET), however it may containmaterial from other sources which is not owned by DET. We would like to acknowledge the following people andorganisations whose material has been used:

Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002 Teacher notespp 1, 5;Supervisor notes p 3

Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by TrishLeigh and Jennifer Vincent.Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh andJennifer Vincent.The copyright in the Maths Tracks material is vested in the publisher, ReedInternational Books Australia Pty Ltd, trading as Harcourt Education Australia.Maths Tracks for NSW has been published under the Rigby imprint and the seriescovers seven stages from Early Stage 1 to Stage 3B. Each stage has a Teacher’sResource Book, Student Book and Homework Book.For professional development and support, view online atwww.rigby.com.au/pd/event.asp

Supervisor notespp 5, 6;Student sheet 1a p17

Microsoft screen shots reprinted with permission from Microsoft Corporation. Student andSupervisor guidep 12, 13

COMMONWEALTH OF AUSTRALIA

Copyright Regulations 1969

WARNING

This material has been reproduced and communicated to you on behalf ofthe

New South Wales Department of Education and Training(Centre for Learning Innovation)

pursuant to Part VB of the Copyright Act 1968 (the Act).

The material in this communication may be subject to copyright underthe Act. Any further reproduction or communication of this material by

you may be the subject of copyright protection under the Act.

CLI Project Team acknowledgement:

Writer: Helen Richards

Using Maths Tracks, Stage 3A, Unit 46 � Teacher notes© NSW DET 2006


These Teacher notes support ‘Using Maths Tracks’. The teacher should detach them before sending the Supervisor notes and the Student and supervisor guide to the supervisor and student. They contain:

• Student outcomes• Prior knowledge• Language• What is needed• Preparation• Interactivity• Resources (including websites)• Returns• Checking up answers• Assessment record

Student outcomes

Outcomes from the Mathematics K–6 Syllabus, © Board of Studies NSW 2002

MeasurementMS3.3 Measurement Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms

Working MathematicallyWMS3.2 Applying Strategies Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations WMS3.3 Communicating Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions

WMS3.5 Reflecting Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content

Students will learn about:• constructing rectangular prisms using cubic centimetre blocks and counting to

determine volume• estimating then measuring the capacity of rectangular containers by packing with

cubic centimetre blocks

Prior knowledge

• Constructing rectangular prisms using cubic centimetre blocks and counting to determine volume

• Multiplying three-digit numbers by two-digit numbers

Language

volume, capacity, measuring, dimensions, rectangular prism

Using Maths Tracks, Stage 3A, Unit 46 2 Teacher notes© NSW DET 2006

What is needed

Introduction• 1 litre milk carton• 200 mL glass• measuring jug• MAB minis

Activity 1• sticky tape• MAB minis

Activity 2 • rectangular prism food containers of different sizes• MAB minis• ruler

Activity 3• Maths Tracks Student Book Stage 3A, page 116• MAB minis



Activity 6• Microsoft Word

Maths Tracks Homework Book Stage 3A, page 29 (if you are using it)

Preparation

Select the activities you think suitable for the student by ticking the boxes beside the activity numbers in the Student and supervisor guide.

Introduction (explicit teaching) – for all studentsActivity 1 (beginning) – can provide extra supportActivity 2 (additional assistance) – can provide extra supportActivity 3 (consolidating) – for all studentsActivity 4 (establishing) – for all studentsActivity 5 (problem solving) – can provide extra challengeReflection–forallstudentsChecking up – for all studentsNote: most activities require MAB minis.

Interactivity

Activity 2: Students should have an opportunity to use MAB minis to calculate the volume of rectangular prism containers. They will not have enough MAB minis in their maths kit to do this. During classroom experience or a satellite lesson, students could estimate volumes and the teacher could place MAB minis in containers to test.


Resources

Teaching measurement Stage 2 and Stage 3. Volume and capacity lesson ideas. Curriculum K-12 directorate. NSW Department of Education and Training. 2004

Addanyothersyoufindsuitable.

Websites [accessed 9/6/06]

Check all websites before recommending them to students.

Online maths dictionary: http://www.teachers.ash.org.au/jeather/maths/dictionary.html

Returns

Student sheet 1b – Estimating capacity – Activity 1

Student sheet 2 – Capacity of containers – Activity 2

Checking up sheet

personaltapeorrecording–Reflection

Supervisor and Student Feedback sheets

this guide (if you ask for it) t t

Checking up answers

1 b Possible rectangular prisms with 24 MAB minis.

length = 24 cm; width = 1 cm; height = 1 cm



All volumes = 24 cm3

2

The capacity of the container is 48 cm3.

It would hold 48 MAB minis. It would hold 48 mL of water.

volume = 48 cm3

8 c

m

3 cm 2 cm



Using Maths Tracks, Stage 3A, Unit 46 � Teacher notes© NSW DET 2006

Indicator Activity Comment

• constructs rectangular prisms using cubic centimetre blocks and counting to determine volume (MS3.3)

• estimates then measures the capacity of rectangular containers by packing with cubic centimetre blocks (MS3.3)

• explains that objects with the same volume may have different shapes (WMS3.3, WMS3.5)

• explains why particular three-dimensional objects are used in the built environment or appear in the natural environment (WMS3.3, WMS3.5)

• constructs different rectangular prisms that have the same volume (WMS3.2)

1, 3, 4

Introduction, 1, 2, 3, 4

1, 2, 3, 4, Reflection,

Checking up

Reflection

5, 6, Checking up

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Assessment record

Using Maths Tracks, Stage 3A – Unit 46Measurement: Volume and Capacity Entry 1: Rectangular Prisms

Circle the numbers of the activities the student was asked to complete.

1 2 3 4 5 6

The student:

Maths K–6

P/M 3A 43827 Centre for Learning Innovation

Supervisor notesand

Student and supervisor guide


Measurement

Volume and CapacityEntry 1: Rectangular Prisms

Number: 43827 Title: Using Maths Tracks Stage 3A Unit 46

All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.

Published byCentre for Learning Innovation (CLI)51 Wentworth RdStrathfield NSW 2135________________________________________________________________________________________________Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction ortransmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited withoutthe written authority of the Centre for Learning Innovation (CLI).

© State of New South Wales, Department of Education and Training 2006.

This publication is copyright New South Wales Department of Education and Training (DET), however it may containmaterial from other sources which is not owned by DET. We would like to acknowledge the following people andorganisations whose material has been used:

Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002 Teacher notespp 1, 5;Supervisor notes p 3

Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by TrishLeigh and Jennifer Vincent.Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh andJennifer Vincent.The copyright in the Maths Tracks material is vested in the publisher, ReedInternational Books Australia Pty Ltd, trading as Harcourt Education Australia.Maths Tracks for NSW has been published under the Rigby imprint and the seriescovers seven stages from Early Stage 1 to Stage 3B. Each stage has a Teacher’sResource Book, Student Book and Homework Book.For professional development and support, view online atwww.rigby.com.au/pd/event.asp

Supervisor notespp 5, 6;Student sheet 1a p17

Microsoft screen shots reprinted with permission from Microsoft Corporation. Student andSupervisor guidep 12, 13

COMMONWEALTH OF AUSTRALIA

Copyright Regulations 1969

WARNING

This material has been reproduced and communicated to you on behalf ofthe

New South Wales Department of Education and Training(Centre for Learning Innovation)

pursuant to Part VB of the Copyright Act 1968 (the Act).

The material in this communication may be subject to copyright underthe Act. Any further reproduction or communication of this material by

you may be the subject of copyright protection under the Act.

CLI Project Team acknowledgement:

Writer: Helen Richards

Using Maths Tracks, Stage 3A, Unit 46 1 Supervisor notes© NSW DET �006


These Supervisor notes support the Student and supervisor guide for ‘Using Maths Tracks’. The supervisor should detach them before giving the guide to the student. They contain information on:

• How to use this unit• Support and extension• Answer guide• Feedback• Checking up.

How to use this unit

Read with your student:• What you’ll do• What you need• Words you need to know.

Your student’s teacher may have selected the appropriate activities from 1 to 6 by ticking them in the list of What you’ll do. See also Support and extension.

The boxes on the right-hand side of the pages in the Student and supervisor guide contain information and suggestions to help you support your student. There is also space for you to make notes about how your student managed. You can use your notes to help you fi ll in the Feedback sheet at the end of the unit.

An icon shows when to refer to the Maths Tracks Student Book pages.

After completing the unit, ask your student to complete the Checking up sheet independently and return it to the teacher. Complete the supervisor side of the Feedback sheet. Discuss the student side of the Feedback sheet and help your student complete it.

Support and extension

The activities following the Introduction are at different levels. Your student’s teacher may have selected the activities for your student. If activities have not been selected in the guide, choose activities as below:

Introduction – for all students Activities 1 and 2 – can provide extra support Activities 3 and 4 – for all students Activities 5 and 6 – can provide extra challenge Refl ection and Checking up – for all students.

An icon shows when to refer to the

page x

Using Maths Tracks, Stage 3A, Unit 46 � Supervisor notes© NSW DET �006

Answer guide

This guide helps you give your student feedback on questions and tasks in the unit or the Maths Tracks Student Book, especially where answers will vary.

Activity 4 – Maths Tracks Student Book Stage 3A, page 117

4 Suggested answers: Box for 36 chocolates. 4 cm x 3 cm x 3 cm 9 cm x 2 cm x 2 cm 6 cm x 3 cm x 2 cm

Activity 5 – Maths Tracks Student Book Stage 3A, page 118

1 30 cm x 15 cm x 12 cm = 5400 cm3

Reflection

Suggested answers to questions:

What is your definition of capacity? Capacity is how much a container will hold.

What is your definition of volume? Volume is how much space something takes up.

Can objects with the same volume have different shapes? Explain. Objects can have the same volume but different shapes as long as the three dimensions of length, width and height multiply together to give the same volume.

How could it be useful to measure the volume of an object or the capacity of a container in everyday life? For example, if you know the capacity of your car’s petrol tank, you know how much petrol your car needs if it is showing empty or showing half full. You can estimate how many litres of petrol are needed to fill it up.


Feedback

Supervisor

The feedback you provide will help teachers assess your student’s progress and plan future learning experiences. Please mark the scale and comment on the activities that your student completed.

• construct rectangular prisms using cubic centimetre blocks and counting to determine volume (MS3.3)

1, 3, 4

Introduction, 1, 2, 3, 4

Reflection

5, 6, Checking up

(Tick along line)with with independentlydifficulty help

Did your student: Activity

• estimate then measure the capacity of rectangular containers by packing with cubic centimetre blocks (MS3.3)

Student’s name

Date

• explain that objects with the same volume may have different shapes (WMS3.3, WMS3.5)

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• construct different rectangular prisms that have the same volume (WMS3.2)


Feedback

Student

In this unit I learnt __________________________________________________________________

_______________________________________________________________________________________.

My favourite activity for this unit was __________________________________________ because

_______________________________________________________________________________________.

I had to work hard at __________________________________________________________ because

_______________________________________________________________________________________.

Help your student to give feedback on their learning for completed activities.


Make sure your student completes this work independently for return to the teacher.

Checking up

Using Maths Tracks, Stage 3A – Unit 46Measurement: Volume and CapacityEntry 1: Rectangular Prisms

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1 a If you had 24 MAB minis and you made a rectangular prism, what could the three dimensions measure?

Length = _______________________________________________

Width = _______________________________________________

Height = _______________________________________________

Volume = _______________________________________________

b Draw your rectangular prism in the box below.

Your student can use MAB blocks to make a model if they need to.


2 Look at the following rectangular prism containers. Which one has a volume of 48 cm3? Colour the correct container red.

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What is that container’s capacity? __________________

How many MAB minis would it hold? __________________

How much water would it hold? __________________

6 c

m

4 cm5 c

m8 c

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4 cm5 c

m

6 c

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3 cm 4 cm

8 c

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3 cm 2 cm

Using Maths Tracks, Stage 3A, Unit 46 i Student and supervisor guide© NSW DET 2006


Student and supervisor guide

Unit contents

About this unit .................................................................................... ii What you’ll do ................................................................................ ii What you need .............................................................................. iii Words you need to know .......................................................... iii Icons .................................................................................................. iv Using this guide ............................................................................ iv Returns ............................................................................................. iv

Introduction .......................................................................................... 1

Activity 1 ................................................................................................. 6

Activity 2 ................................................................................................. 7

Activity 3 ................................................................................................. 9

Activity 4 .............................................................................................. 10

Activity 5 .............................................................................................. 11

Activity 6 .............................................................................................. 12

Refl ection ............................................................................................. 14

Checking up ....................................................................................... 15

Student sheets ................................................................................ 17

Using Maths Tracks, Stage 3A, Unit 46 i Student and supervisor guide

................................................................................ ................................................................................

.............................................................................................. 12

............................................................................................. 14

....................................................................................... 15

................................................................................ 17

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.............................................................................................

.......................................................................................

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Using Maths Tracks, Stage 3A, Unit 46 ii Student and supervisor guide© NSW DET 2006

About this unit

What you’ll do

Introduction• discuss the terms volume and capacity• investigate the volume and capacity of different containers• estimate and calculate the capacity of a milk carton

Activity 1• estimate and then calculate the capacity of containers• fi nd the volume of containers using MAB minis Activity 2• choose three containers and place them in ascending order of

capacity by estimating• draw the containers• estimate the number of MAB minis that would fi t into each

container• use a ruler to calculate the capacity of each container• calculate the volume of each container

Activity 3• use MAB minis to construct rectangular prisms • calculate the volume of rectangular prisms• calculate the capacity of boxes• write measurements in their abbreviated form Activity 4• use MAB minis to construct models• compare volumes of models• use measurements of rectangular prisms to calculate their capacity• design a box that will fi t 36 chocolates, given the volume of one

chocolate

Activity 5• calculate the number of MAB minis that would fi t inside a shoe box• make different prisms with the same volume

Activity 6• use Microsoft Word drawing tools to draw different prisms with the

same volume

Refl ection• discuss defi nitions for capacity and volume• discuss why it would be useful to measure the volume of an object

or capacity of a container in everyday life

Checking up• calculate the possible dimensions of a rectangular prism, given its

volume• draw the rectangular prism• calculate the volume and capacity of a rectangular prism, given its

dimensions

√

√

√

Using Maths Tracks, Stage 3A, Unit 46 iii Student and supervisor guide© NSW DET 2006

What you need

Introduction• 1 litre milk carton• 200 mL glass• measuring jug• MAB minis

Activity 1 • sticky tape• MAB minis

Activity 2 • rectangular prism food containers of different sizes• MAB minis• ruler

Activity 3 • Maths Tracks Student Book Stage 3A, page 116• MAB minis



Activity 6• Microsoft Word

Words you need to know

volume capacity measuring dimensions rectangular prism

Using Maths Tracks, Stage 3A, Unit 46 iv Student and supervisor guide© NSW DET 2006

Icons

Record this for the teacher.

Return this to the teacher.

Use the page in the Maths Tracks Student Book.

Use a computer for this activity.

Using this guide

The boxes on the right-hand side of pages in the Student and supervisor guide contain information and suggestions for the supervisor.

After each activity, circle the face that shows how you feel about your work.

Returns



Checking up sheet

personal tape or recording – Refl ection

Supervisor and Student Feedback sheets

this guide (if your teacher asks for it)

Record this for the teacher. Record this for the teacher.

Return this to the teacher. Return this to the teacher.

Use the page in the Use the page in the

Page x

Use a computer for this activity. Use a computer for this activity. Use a computer for this activity.



Checking up sheet Checking up sheet

personal tape or recording – Refl ection personal tape or recording – Refl ection

Supervisor and Student Feedback sheets Supervisor and Student Feedback sheets

this guide (if your teacher asks for it) this guide (if your teacher asks for it)

Using Maths Tracks, Stage 3A, Unit 46 iv Student and supervisor guide

Using Maths Tracks, Stage 3A, Unit 46 1 Student and supervisor guide© NSW DET 2006

Introduction

In this unit, you will learn about measuring the volume and capacity of rectangular prisms. For this activity, you will need an empty 1 litre milk carton, a 200 mL glass or cup and a measuring jug.

Can you remember what the terms volume and capacity mean?

If you are not sure, you could look them up on the online maths dictionary:

http://www.teachers.ash.org.au/jeather/maths/dictionary.html Complete the following sentences:

Volume is _____________________________________________

_________________________________________________________.

Capacity is ___________________________________________

_________________________________________________________.

Volume is the amount of space occupied by an object.

It is different to capacity, which is the amount that a container can hold.

A milk carton has both volume and capacity, since it takes up space and can hold stuff.

___________________________________________

_________________________________________________________.

Volume is the amount of space occupied by an

It is different to capacity, which is the amount

1 L

Using Maths Tracks, Stage 3A, Unit 46 1 Student and supervisor guideUsing Maths Tracks, Stage 3A, Unit 46 1 Student and supervisor guideUsing Maths Tracks, Stage 3A, Unit 46 1 Student and supervisor guide


Look at the glass below. The glass is empty.

The volume of water that the glass could hold is 200mL.So the capacity of the glass is 200 mL.

Now look at the container below. The container can hold 1 litre (1000 mL) of water. So it has a capacity of 1 litre.

However, the container is only half full of water.So the volume of water in the container is 500 mL.

Find a milk carton like the one above.What do you think the capacity of the milk carton might be?

What does it say on the side of the carton?

Open your milk carton up completely to form a rectangular prism.Find a cup or glass and use it to fi ll the milk carton with water until you reach the new top of the carton. Count how many glasses of water you used.

If you do not have a milk carton, substitute with another rectangular prism container such as a take-away carton.Make sure it is empty and washed out with water.

The glass should measure 200 mL. You may want to check, using a measuring jug.

Now look at the container below.


How many glasses did the milk carton hold?

The actual capacity of a milk carton, when opened up to form a rectangular prism, is ____________ glasses.

Milk cartons are sold with 1 litre of milk in the carton, but they can actually hold around 1200 mL of milk.

Find a MAB mini. It has three dimensions (length, width and height). It is 1 cm high, 1 cm wide and 1 cm long. The volume of a MAB mini, or the amount of space it takes up, is:1 cm x 1 cm x 1 cm = 1 cm3

Estimate how many MAB minis will fi t into your milk carton. Remember, 1 mL equals 1 cm3.

Its actual capacity is around 6 glasses of water, which is approximately 1200 mL.

There are not enough MAB minis to fi ll the carton, so estimation is important. Your student should estimate around 1200 MAB minis which is 1200 cm3.

Using Maths Tracks, Stage 3A, Unit 46 3 Student and supervisor guide

Did you know that 1 cm3 = 1 mL. So, 1200 cm3 = 1200 mL!

Its actual capacity is Its actual capacity is Its actual capacity is Its actual capacity is

1 L

? ? ? ?

?


Since a rectangular prism has three dimensions (length, width and height), its volume is measured in cubic units – litres (L), millilitres (mL) or cubic centimetres (cm3). Place the milk carton on top of a MAB fl at.

Calculate the area of the carton’s base:7 cm x 7 cm = 49 cm2. The area of the base of the carton is the length and width multiplied together. Now use a ruler to measure the height of the container. This should measure around 24 cm. The volume of the milk carton equals the area of the base x the height. So, 49 cm2 x 24 cm = 1176 cm3.

7 cm 7 cm

20.5

cm


Feedback:

lots of some nohelp help help

The capacity of the milk carton when fi lled with MAB minis is approximately __________ cm3 or __________ mL

Provide feedback for this activity on the Feedback sheet.

The milk carton has a volume of 1200 cm3 and can hold 1200 mL – that’s its capacity.

I have 20 litres capacity.


Activity 1

Capacity and volume of rectangular prisms

Find Student sheet 1a. Cut out each 2D shape, then fold them along the lines to make rectangular containers. Use sticky tape to tape them together.

Find Student sheet 1b and write your estimations for the capacity of each container in cm3.

Fill each container with MAB minis. Then tip each container over to see how many MAB minis your container could hold. For each 3D shape, count the number of MAB minis that it could hold. This is their capacity in cubic centimetres. It is equivalent to (or the same as) their volume. Calculate the volume of each container by multiplying: length x width x height.

Write the capacity and volume of each container on Student sheet 1b.

Answer the question on Student sheet 1b.

Feedback:


prisms

Find Student sheet 1a. Cut out each 2D



Activity 2

Capacity and volume of rectangular prisms

Find a collection of rectangular prism food containers of different sizes. These might include cereal boxes, biscuit containers and video containers.

Choose three containers and place them in order of capacity from smallest to largest, by estimating their capacities.

Find Student sheet 2 and draw your containers in the boxes provided.

Estimate how many MAB minis would fi t into each container. Write your capacity estimations on Student sheet 2.

Can you think of another way to measure the capacity of each container? Tell your supervisor.

Use a ruler to measure the length, width (breadth) and height of each container. Then calculate the capacity of each container and write it on Student sheet 2. For example, 15 cm x 5 cm x 5 cm = 375 cm3.

As you won’t have enough MAB minis to actually fi t into the containers, your student’s estimation is important.

Your student might know to use their ruler to measure length, width and height and then calculate the capacity by multiplying the three dimensions together. Alternatively, they might place MAB minis on the bottom layer, measure the area of the base and then multiply this by the height.

Find a collection of rectangular prism food


Feedback:


Was your estimate close to the actual capacity for each container?

What is the capacity of each container in millilitres (mL)? In other words, how much water could each container hold?Use a measuring jug and measure in millilitres (mL). Write your answers on Student sheet 2.

What is the volume of each container? Measure in cubic centimetres (cm3). Write your answers on Student sheet 2.

You will need to check your student’s answers as they will vary.Provide feedback for this activity on the Feedback sheet.


Feedback:


Activity 3

Find page 116 in the Maths Tracks Student Book.

1 Use MAB minis to construct these rectangular prisms. Don’t worry about comparing your models with a partner.

2 For each model, count how many MAB minis you used. Then write the volume of each prism that you constructed.

3 Calculate how many MAB minis will fi t inside each box. Then write their capacity in cubic centimetres (cm3).

4 Write the measurements in their abbreviated form.

Mark your answers for this page at the back of the Maths Tracks Student Book. Have another try if you went off the track.

Help your student read and interpret the instructions.

Check your student’s models.

Discuss possible reasons for different answers and praise successes. Provide feedback for this activity on the Feedback sheet.

Page 116


Activity 4

Feedback:



1, 2 Use MAB minis to construct the models. Then calculate the volume of each model (volume = length x width x height)

3 Calculate the capacity of each rectangular prism.

4 You should start by calculating the volume of the chocolate box.



Check your student’s models.

Discuss possible reasons for different answers and praise successes. Provide feedback for this activity on the Feedback sheet.

Discuss possible reasons for different answers and praise

models.models.

11 cm 11 cm

8 c

m

Find page 117 in the

1, 2Page 117


Feedback:


Activity 5

Problem-solving


1 Don’t forget, volume = height x length x width.

2 If you have 36 MAB minis, build as many different rectangular prisms as you can. How many did you make? If you don’t have 36 MAB minis, then you will need to think of three numbers that, when multiplied together, make 36 cm3. (Remember, volume = height x length x width). If you removed 2 cm3, what would the new volume be? Use the problem-solving framework on the page to help you.



Refer to the Answer guide in the Supervisor notes.

Discuss possible reasons for different answers and praise successes.Provide feedback for this activity on the Feedback sheet.

1 volume = height x length x width.

2

Problem-solvingProblem-solving

15 cm

30 cm

12 c

m

Page 118


Activity 6

Making rectangular prisms

• Open a Word document

• Use the Drawing tool to draw a 1 cm square, using the screen rulers to measure the sides

• Use the 3D Style 4 graphic from the drawing tool bar to turn your square into a cube

• Copy your cubic centimetre 11 times, to make 12 cubic centimetres in total. Move each copy to its own space on the screen

• Arrange your cubes to form a rectangular prism. When you have made a rectangular prism, write its volume next to it

• Repeat, arranging the 12 cubic centimetres to make a different rectangular prism

Step 1Draw a square.

Screen

Click 3D Style 4

Drawing tools

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Feedback:


• How many different rectangular prisms can you make with 12 cubic centimetres? Include three on your page

• Write a sentence underneath your prisms, explaining what you found out

Print out this page and return it to your teacher.

Arrange your cubic centimetres to make different rectangular prisms.

Check your student’s rectangular prisms.


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Feedback:


Feedback:


Refl ection

Record your answers to the following questions for your teacher.

What is your defi nition of capacity?What is your defi nition of volume?Can objects with the same volume have different shapes? Explain.How could it be useful to measure the volume of an object or the capacity of a container in everyday life?

Stop recording now.

Refer to the Answer guide in the Supervisor notes for suggested answers to questions. Provide feedback for this activity on the Feedback sheet.

I am now going to measure two cups of sugar with this measuring jug.

I think you’ll fi nd that the capacity of the jug is only 1 cup!

Record your answers to the following questions

I think you will fi nd that the ute will only hold 36 bales. I can fi t 12 on the bottom layer and two more layers on top.

I want you to stack 50 bales on the ute.


Checking up

Complete the Checking up sheet without any help from your Supervisor.

After you have fi nished the Checking up sheet, fi ll in the student side of the Feedback sheet. You may need to look back at the smiley faces you circled to remind yourself how you felt about each activity.

Feedback:


The Checking up sheet and Feedback sheet are near the back of the Supervisor notes for this unit. Make sure your student works on this assessment task independently, with your assistance to read and interpret the instructions. Return the Checking up sheet to the teacher unmarked.

Using Maths Tracks, Stage 3A, Unit 46 17 Student sheet 1a© NSW DET 2006

Estimating Capacity Activity 1

Cut out the shapes carefully.

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Using Maths Tracks, Stage 3A, Unit 46 19 Student sheet 1b© NSW DET 2006

Estimating Capacity Activity 1

Student's name:

Container Estimated capacity

Capacity Volume

a

b

c

d

What do you notice about the volume and capacity of each box?

Using Maths Tracks, Stage 3A, Unit 46 21 Student sheet 2© NSW DET 2006

Capacity of containers Activity 2

Student's name:

Draw your containers in the boxes below. Your drawings do not need to be to scale.

Container a

Container b

Container c

Container Estimated capacity,

in cm3

Capacity,in cm3

Volume,in cm3

Capacity,in mL

a

b

c

What did you find out?

Centre for Learning InnovationNSW Department of Education and Training

51 Wentworth RoadStrathfield NSW 2135

stage 3a – unit 46 measurement volume and capacity entry...

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