EXPLORING MAT HS Vol EXPLORINGume - Blake Education€¦ · These activities encourage your children to think mathematically by exploring, experimenting, being creative and taking

E X P L O R I N G M A T H S

NUMBER Exploring 1-5Exploring 6-10Games and Activities for 0-10Exploring 0-50 NumerationExploring 0-50 Operations

Numbers to 50 Picture PackExploring 0-100 NumerationExploring 0-100 OperationsExploring Calculators Exploring FractionsExploring Money

MEASUREMENTExploring Length/AreaExploring Volume/MassExploring Temperature/Time

EXPLORING VOLUME AND MASS MEASUREMENT LOWER PRIMARY

About the authorOriginally a primary school teacher, Bev Dunbar is now actively involved in teacher education as a Mathematics Consultant and University Lecturer in Mathematics Education.

Bev is a passionate believer in fun, practical resources which help teachers make maths lessons a highlight of the day.

• Seven carefully sequenced units whichdevelop skills in practical measurement

• Over 25 activity-based, easy-to-useteaching ideas

• A sample yearly maths overview • Two sample weekly programs • Useful activity cards for independent

small group work

• An outcome indicators record forassessing individual progress

• Over 50 blackline masters

In fact, almost everything you need to explore volume and mass in your classroom.

Titles in the Exploring Maths series

The Exploring Maths series is designed to provide busy teacherswith practical resources that are mathematically up-to-date, fun andeasy to use. Each book contains a wealth of activities, blackline mastersand assessment tasks for a whole life-time of teaching. These activitiesencourage your children to think mathematically by exploring, experimenting, being creative and taking risks. By asking questions andactive discovery, children learn to enjoy using mathematics as part oftheir everyday lives.

Exploring Volume and Mass includes:


Activities,blackline masters & assessment pages that are fun and

easy to use

BevDunbar

EXPLORINGEXPLORING

VolumeMass

ISBN 1-86509-224-X

9

781865 092249

and

M e a s u r e m e n T L O W E R P R I M A R Y 2

COVER, Volume/Mass 9/30/04 9:08 AM Page 2

Exploring Volumeand Mass

with Lower Primary

Bev Dunbar

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IntroductionExploring Volume and Mass

Measurement is an important aspect of any mathematics program. It is a practical way to apply number skills to solve problems specific to each student’s stage of development. Both the classroom and the playground are utilised and a wide variety of everyday objects can be used as measuring objects.

Exploring Volume and Mass is a companion to the other Measurement books in theExploring Maths series. Volume is a measure of the amount of space occupied bya 3-dimensional object. Capacity relates to containers. It is a measure of theamount of another substance that a container can hold inside it. For example, abrick has a fixed volume but no capacity.

Mass is a measure of the amount of substance in a 3-dimensional object. Itremains the same wherever it is measured. Weight relates to the effect of gravityon a mass. Weight varies depending on where it is measured. For example, inspace you are ‘weightless’ yet your mass is still the same. Most people generallyignore this distinction and talk only about ‘weight’. In this book, the more correctword, ‘mass’, is emphasised.

These particular substrands can easily be neglected in schools because they’reseen as messy, wet or requiring extra equipment. To help inspire you, here areover 30 action-packed ideas for developing skills in exploring, comparing andusing informal units in fun, practical ways. And the activities range from simple to challenging to help you cater for different ability groups.

Making your teaching life easier is a major aim of this series. This book is dividedinto sequenced units, each packed with enough photocopiable discussion andactivity cards for small groups or a whole class to explore, for up to a week at atime. You’ll find easy-to-follow instructions, with assessment help in the form ofclearly stated outcomes linked to a checklist (see p.91).

Each activity is designed to maximise the way in which your students constructtheir own understandings about volume and mass. The activities are generallyopen-ended and encourage each student to think and work mathematically, withan emphasis on practical manipulation of materials and the development of language and recording skills. Look forward now, to exploring these conceptswith your students.

Copyright © Bev Dunbar Maths Matters 2001Reprinted 2004Exploring Volume and Mass ISBN 186509 224 X

Published by Blake EducationLocked Bag 2022Glebe NSW 2037

Series editor: Garda TurnerIllustration and design by Janice Bowles

Printed by Printing Creations The blackline masters in this book may be reproduced by the original purchaser for use with their class(es) only.

9224X_0704R1_title 9/30/04 9:29 AM Page 4

978 1 86509 224 9

Contents

How to use this Book 2

Exploring Volume Language 3

Comparing Volumes 17

Using Informal Volume Units 31

Exploring Displacement 43

Exploring Mass Language 51

Using a Balance 63

Using Informal Mass Units 77

Essential Resources 89

Outcome Indicators Record 91

Sample Yearly Programs 92

Sample Weekly Programs 93

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© Blake Education 978 1 86509 224 9 Exploring Maths - Measurement - Exploring Volume and Mass

Exploring Volume and Mass2

Over 30 Teaching IdeasMore than 30 exciting teaching ideas have been placed into 7 sections to assistyour lesson planning for the whole class or small groups. Each activity hasclearly coded learning outcomes and easy-to-follow instructions. Activities areopen-ended and encourage your students to think for themselves.

Over 50 Blackline MastersThere are 3 types of blackline masters.

How to use this Book

Label cardse.g. p.19 Which is larger?These support free exploration as well as structured activities. Laminate them for reusewith small groups.

Discussion Cardse.g. p.58 Is it heavier?Cut these out, shuffle and use over and overagain for small group games. Photocopy eachset in different colours.

Activity Cardse.g. p.42 BlocksUse these as an additional stimulus for smallgroup work. The language is simple and easy-to-follow. Encourage your students toinvent their own activity cards too. You canlaminate them so that they last for years.

Essential Resources ListsYou’ll find suggestions on pages 89 and 90 forwhat your maths storage supply can look like inreadiness for teaching Volume or Mass with 5-7year olds. Collect these as a whole school and store them centrally.

Outcomes Indicator RecordThe complete list of learning outcomes is available on page 91. Use this to record individual student progress throughout each unit.Try to assess a few students each day.

Sample Weekly ProgramsOn pages 93 and 94 you’ll find examples of how to organise a 5-day selection of activities from Comparing Volumes and Using Informal Mass Unitsfor a whole class.

takes up much less space than

takes up much more space than

takes up a little more space than

takes up about the same space as

takes up a little less space than

Exploring Volume and Mass 19

Exploring Volume and Mass

58

a brick

a bottle of drink

a bed

an apple

a space alien

a kitten

a baby giraffe

a kangaroo

a bunch of celery

a bicycle

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Exploring Volume Language

In this unit, your students will:• Observe, discuss the space occupied by objects (V1-1)

• Fill, empty containers using a variety of materials (V1-2)

• Pack a variety of objects into defined spaces (V1-3)

• Use volume and capacity language, e.g. pack, fit, fill, empty (V1-4)

(The coded outcomes in this section refer to the Outcome Indicators on page 91.)

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How large is it?What are you trying to do?★ Observe, discuss the space occupied by objects (V1-1)

★ Use volume and capacity language (V1-4)

How many can play?★ Whole class

What do you need?★ Balloons★ Blindfold★ Variety of 3D objects, e.g. box, ball, book★ Paper, pencils★ Animal face parts (BLM p.5), scissors, glue

What do you do?★ Discuss the size of objects around you.What’s the largest thing you can see?

What does large mean? e.g. the space taken up by an object. What do youthink is the largest thing in the world? What is the smallest thing?

★ Blow up a balloon. Discuss the idea that large things can also be hollow. Whatcan you see that is about as large as this balloon? Is it hollow also? Does thesize depend on whether it is hollow or not?

★ Blindfold a student. Ask them to feel a variety of objects. Can they identifywhether each object feels large or small or even the same size as anotherobject? How can they tell? e.g. Is this as large as Minh’s backpack?

★ Predict the size of objects using your hands. e.g. Show how big an elephantmight be if it were in the room with us now; show how large Sam’s lunchbox is.Check size estimates wherever possible by comparing with the real objects.

★ Draw pictures of some very large and very small objects. Compare, discuss, display.

Variations★ Blow up balloons to make animal heads. Discuss and compare

the different sizes. Decorate with cut-out animal face parts. Display.

★ Create a class book about the size of objects. Cut out magazine pictures and add drawings and comments from students.

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How full is it?What are you trying to do?★ Fill, empty containers

using a variety of materials (V1-2)

★ Pack a variety of objects into defined spaces (V1-3)


How many can play?★ Small groups, whole class

What do you need?★ Empty cartons, boxes, containers★ Packing materials, e.g. blocks, marbles, dried beans★ Funnels, plastic tubing, cups, spoons★ Sieves, e.g. milk cartons cut down with different size holes in the base★ Pouring materials, e.g. water, rice, pasta, seeds★ How full is it? activity cards (BLMs pp.7,8)★ How full is it? worksheet (BLM p.9)

How do you play?★ Close your eyes. Imagine your hands are full of chocolates. What do you mean

when you say something is full?

★ Imagine you are thirsty and you ask someone for a cup of water. How do youknow if your cup is full or not? Demonstrate by filling a cup with water. Is it full to thebrim or does it have a small gap left?

★ Discuss what happens when you open a carton of milk. Where does the milk comeup to inside? Why? e.g. When you are packing liquids you usually want a gap atthe top of the container to prevent spills.

★ What about a full packet of biscuits? ... a tub of ice-cream? ... a box of apples?e.g. You usually mean full to the brim when packing solid objects into a container.

★ What happens if you add more to a container that is already full? e.g. Fill a boxwith marbles, then predict what will happen if you add more.

★ Walk around your environment, inside and outside, looking for examples ofcontainers. Predict whether they are empty, half full or full before you check thecontents of each one.

Variations★ Use the How full is it? activity cards in small groups. You need a partner for each

activity. Explore different ways to fill your containers. Experiment with differentpacking materials too. Remember to use water only in suitable wet areas.

★ Fill in the worksheet. Call out instructions for each container. e.g. Draw a line toshow where the milk is in the carton if it is half full.

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You need cups, funnels, plastic

tubes, containers and water.

Find different ways to fill your

container to the top.

What makes some containers

easier to fill than others?

Which filling devices are easier

to use?

You need empty containers and

packing materials.

Find different ways to pack your

container to the top.

What makes some containers

easier to pack than others?

What makes some materials easier

to pack?

Pack it in

Fill it up

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You need sieves and packing orpouring materials, e.g. marbles,rice, water.Find different ways to fill your sieveto the top.What makes some sieves more difficult to fill than others?What makes some materials difficult to hold?

You need cups, funnels, plastictubes, containers.You need pouring materials too,e.g. rice, shells, pasta.Find different ways to fill your container to the top.What makes some containers easier to pour into than others?What makes some materials easierto pour?

Pour it in

Can it hold it?

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How full is it?

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Will they fit?What are you trying to do?★ Observe, discuss the space occupied by objects (V1-1)




What do you need?★ An example of a very large shoe★ A paper bag or small box and some oranges★ Will they fit? discussion cards A (BLM p.11 - copied onto yellow paper)★ Will they fit? discussion cards B (BLM p.12 - copied onto blue paper)★ Will they fit? activity cards (BLM p.13)

How do you play?★ What size foot do you need to fit into this shoe? How many of your feet do you

think could fit inside it?

★ Discuss the fact that some things can be too large or too small to be a perfectfit. Identify some things that you know are a good fit, e.g. a hand and a glove, adress on your big sister. Tell me some things you know are not a good fit. e.g. Ourgarage is built for 2 cars but we own only 1 car - there is lots of space left over.

★ Demonstrate how to pack objects neatly into a container. How many do youguess will fit inside? Is there any space left over? e.g. I guess you need 6 orangesto fill that bag.

★ Shuffle the sets of cards into two separate piles. Turn and read out the top cardin each pile. Imagine the situation and discuss it together. Estimate the size of theitems on each card. Will they fit together?

e.g. Could 8 grandmas fit inside your teacher’s car?

★ Can you think of any special circumstance when they will fit? e.g. 4 whales anda shopping trolley - perhaps they are only toy whales.

Variations★ Create your own set of Will they fit? discussion cards for another class to discuss.

★ Use the Will they fit? activity cards. Explore different ways to make a containerwith an exact fit for each set of objects.

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your feet 2 cats

3 cars 4 whales

8 grandmas 10 students

15 cans 20 fish

50 beetles 100 people


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a jar your dad’s shoes

a cardboard box

a medium size aquarium

a shopping trolley

your teacher’s car

your garage

a swimming pool

your lounge room

an aeroplane


9224X_0704R1_p3-50 10/18/04 10:59 AM Page 12


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9224X_0704R1_p3-50 10/18/04 10:59 AM Page 13



Tip it outWhat are you trying to do?★ Observe, discuss the space occupied

by objects (V1-1)

★ Fill and empty containers using a variety of materials (V1-2)



How many can play?★ Small groups

What do you need?★ Sand, water, small cups, moulds★ Prepared jelly mixture, jelly moulds, access to a fridge★ Plaster, plaster moulds★ Prepared cake or muffin mix, cake trays, access to an oven★ Tip it out activity cards (BLMs pp.15,16)

How do you play?★ Imagine you are in a shop. Where do you find things packed into a

container? e.g. biscuits in a tin, groceries in a shopping bag, soap powder ina box. If you open the container and tip out the contents, what happens?e.g. Biscuits are loose and can be put into a jar.

★ Sometimes the contents of a container are solid. When you open the container you can tip out the inside and it stays the same shape as it waswhen it was inside. List objects that you know like this, e.g. a toy car, a cakeof soap, some cans of pet food.

★ Discuss what happens to water in a container. e.g. If you spill a glass ofwater, the water goes everywhere. If you freeze water to make an ice-block,then the water stays the same shape when you tip it out.

★ Identify things in your environment which would stay the same shape if youtipped them out from a container. e.g. A bag of marbles would spill out ontothe floor but a box of books would stay the same shape if you removed thecardboard box.

Variation★ Use the Tip it out activity cards. Explore different ways to pack your

containers and investigate the shapes made when you tip them out. e.g. Trydry sand, damp sand then really wet sand. What do you notice when you tipout the shapes each time?

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Explore different ways to make shapes from jelly.Put them in a fridge to set.Predict what each shape will look like when you tip it out.What makes some shapes easier to tip out than others?Make one huge jelly shape together.

Explore different ways to make shapes made from sand. Predict what each shape will look like when you tip it out.What makes some shapes easier to tip out than others? What’s the largest shape you canmake? ... the smallest?Make one huge sand shape together.

Sand

Jelly

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Explore different ways to makeshapes from cake mix.Put them in an oven to cook.Predict what each shape willlook like when you tip it out.What makes some shapeseasier to tip out than others?Make one huge cake shape together.

Explore different ways to make shapes from plaster.Leave them to set.Predict what each shape willlook like when you tip it out.What makes some shapes easier to tip out than others?Make one huge plaster shape together.

Plaster

Cake

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ComparingVolumes

In this unit, your students will:

• Compare, describe 2 or more volumes, capacities (V2-1)

• Identify objects with the same volume, capacity (V2-2)

• Understand that objects with same volume,capacity may have a different shape (V2-3)

• Order 3 or more volumes, capacities (V2-4)

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Which is larger?What are you trying to do?★ Compare, describe 2 or more

volumes, capacities (V2-1)

How many can play?★ Whole class, pairs

What do you need?★ Objects around the classroom★ Which is larger? label cards (BLM p.19)★ Workbook, pencils★ Which is larger? discussion cards (BLM p.20)

How do you play?★ What’s the largest thing in this room? How do you know? What’s the smallest

thing you can see in this room?

★ Hold up 2 objects at random. Which one is larger? What clues do you use tojudge size? How do you know just by looking? Discuss ideas together.

★ Discuss the 5 label cards. Demonstrate how to place objects on either side ofeach label to record your decisions.

e.g.takes up much more

space than

★ Walk around with a partner. Find pairs of objects to label. Record 2 of your favourites in a workbook.

★ Class challenge.Name two objects, e.g. a giraffe and a hippo. Which one islarger? Compare pairs of objects which are quite different in size, as well asobjects that are very similar in size.

Variations★ Shuffle the discussion cards. Select any 2 cards. Think about how large each

object might be in real life. Which of the 2 objects would be larger? Considerdifferent possibilities, e.g. a cricket ball is only small but a beach ball can bevery large.

★ Invent 10 more discussion cards for another team to try.

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 18


takes up much less space than

takes up much more space than

takes up a little more space than

takes up about the same space as

takes up a little less space than


9224X_0704R1_p3-50 10/18/04 10:59 AM Page 19


a wombat

a pumpkin

a puppy

a rooster

a koala

a television set

a carton of milk

a ball

a rock

a baby

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Which holds more?What are you trying to do?★ Compare, describe 2 or more

volumes, capacities (V2-1)

★ Identify objects with the same volume, capacity (V2-2)

★ Order 3 or more volumes, capacities (V2-4)

How many can play?★ Whole class, pairs, small groups

What do you need?★ Various plastic bottles, sponges, buckets, boxes ★ Water, balls, blocks★ Which holds more? label cards (BLM p.22)★ Which holds more? discussion cards (BLM p.23)★ Which holds more? activity cards (BLMs pp.24,25)

How do you play?★ List at least 10 containers you use in daily life, e.g. a can of pet food.

★ Why do you need containers? e.g. To store things in; to carry things from oneplace to another.

★ What can you put in a container? e.g. I pack all my clothes in a large suitcasewhen I travel.

★ How can you compare containers? e.g. You can sometimes tell just by looking.How can you check which one holds more? e.g. You can pour things from onefull container to another to see whether it overflows.

★ Take 2 containers, e.g. 2 cans. Demonstrate how to check which one holdsmore marbles. Discuss the 5 label cards. Demonstrate how to use them forrecording your discoveries.

★ Find a partner. Find pairs of containers to compare, check then label.

★ Finish with the Which holds more? discussion cards. Take any 2 cards. Decidewhich one holds more. Justify why you think this. Try to put three or more inorder from the thing that holds the least to the thing that holds the most.

Variation★ Use the Which holds more? activity cards in small groups.

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holds much less than

holds much more than

holds a little more than

holds about the same as

holds a little less than


9224X_0704R1_p3-50 10/18/04 10:59 AM Page 22


a garbage truck

a school bag

a paper bag

a pelican’s beak

a refrigerator

a storeroom

a bookshelf

a shopping trolley

a wheelbarrow

a bicycle carry basket

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You need 2 sponges.Which one holds more water?Guess first, then check.Find another sponge you thinkholds even more. Check. Mix up the 3 sponges. Ask a friend to put them in order from the one that holds the least,to the most.

You need 2 bottles.Which one holds more water?Guess first, then check.Find another container you thinkholds even more. Check. Mix up the 3 containers. Ask a friend to put them in order from the one that holds the least,to the most.

Bottles

Sponges

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You need 2 boxes.Which one holds more blocks?Guess first, then check.Find another box you think holdseven more. Check. Mix up the 3 boxes. Ask a friend to put them in order from the one that holds the least,to the most.

You need 2 buckets.Which one holds more balls?Guess first, then check.Find another container you thinkholds even more. Check. Mix up the 3 buckets. Ask a friend to put them in order from the one that holds the least,to the most.

Buckets

Boxes

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 25



Find a pairWhat are you trying to do?★ Identify objects with the same

volume, capacity (V2-2)

★ Understand that objects with the same volume or capacity may have a different shape (V2-3)

How many can play?★ Small groups, pairs

What do you need?★ Milk cartons, boxes, bottles, cans★ Water, rice, marbles, blocks★ Scissors, paste, cellotape, plasticine★ Find a pair activity cards (BLM p.27)

How do you play?★ Do all things that hold the same amount have to be the same shape?

Discuss different views together.

★ Demonstrate how a full carton of water can be poured into a second carton to exactly the same level. They are the same shape and hold thesame amount of water or milk.

★ What if the container was a different shape? Can you find another container that holds exactly the same amount of water as the milk carton?Check then discuss your results together.

★ Demonstrate how to make a small container from plasticine. Fill it with water. Make a second container that is a different shape, e.g. it is longerand narrower. Check the size by pouring the water from one container to another.

★ Work with a partner. Find pairs of containers that hold about the sameamount as each other but have a different shape.

★ Discuss some of the solution strategies together. e.g. I cut down this container until it held the same amount of rice as that one.

Variation★ How can you make your own containers? e.g. Cut up boxes or bottles.

Use the Find a pair activity cards. Compare and discuss the different shapesyou discover or make. Look at the size of each one in your pair. What doyou notice?

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 26


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9224X_0704R1_p3-50 10/18/04 10:59 AM Page 27



Race awayWhat are you trying to do?★ Order 3 or more volumes, capacities (V2-4)


What do you need?★ Bowls of water, cups, large containers, funnels★ Long plastic tubes, e.g. 2 metres★ Thick sponges★ Flat trays★ Race away activity cards (BLMs pp.29,30)

How do you play?★ What’s the fastest way you can fill a container with water? e.g. Use a

funnel and a cup. Discuss different possibilities.

★ How can you quickly fill a can with loose marbles? e.g. Use your hands.Discuss different possibilities.

★ Discuss the fastest ways to fill a bookcase with books. e.g. First stack allthe same size books together.

★ How can these ideas for filling containers be used for team races? Discuss suggestions.

★ Try out one of the examples shown on the Race away activity cards forstarters. Collect the equipment you need. Discuss the rules behind eachrace.

Variation★ Invent more races like this. e.g. Pack old clothes into a suitcase, lunch

boxes into a basket, books into a box.

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 28



Race away 1(like Tunnel Ball)

Line up in teams, with a cup and a bowl of water in front

of each team and a container and a funnel next to the

last person in each team.

Race to fill the cup with water then pass it under all the legs to the

last person, who pours the water into the container.

The last person races to the front with the empty cup and the

whole process starts again.

Which team has collected the most water at the end of the race?

Race away 2Line up in teams with water, a long plastic tube, a cup

and a funnel in front of each team and a container

and a funnel next to the last person in each team.

Race to pour a cup of water into the tube then manipulate it

over the shoulders of each person and into the container

for the last person.

The last person races to the front and the whole process

starts again.


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Race away 3(like Captain Ball)

Line up in teams with water and a thick sponge

at the start of each team and a funnel and a container at a 10

metre line in front.

The first person fills the sponge with water, races to the line and

squeezes as much water as possible into the funnel. The first person

then runs back, passes the sponge to the next person and goes to

the back. The whole process starts again.


Race away 4(a shuttle relay)

Line up in teams with water, a waiter’s tray and a cup at the

start of each team and a funnel and a container at a 10 metre line

in front of each team.

The first person races to fill the cup with water, place it on the tray,

run to the 10 metre line and pour the water into the container.

The first person then runs back, passes the cup and the tray to the

next person, then goes to the back of the team.

The whole process starts again.


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Using Informal Volume Units

In this unit, your students will:• Use informal units to estimate, measure volume, capacity (V3-1)

• Record volume, capacity measurements using tallying (V3-2)

• Build, compare 3D models using informal units (V3-3)

• Understand that different shapes can have the same volume (V3-4)

• Order 3 or more volumes, capacities using informal units (V3-5)

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How many ...?What are you trying to do?★ Use informal units to estimate,

measure volume, capacity (V3-1)

★ Record volume, capacity measurements using tallying (V3-2)

How many can play?★ Whole class, small groups

What do you need?★ Water, cups, containers★ Packing materials, e.g. blocks,

marbles, lunch boxes, books★ How many? discussion/activity cards (BLM p.33)★ Workbook, pencils

How do you play?★ Why would you need to know which of two or more containers is the larger?

e.g. To hold the most drink for a picnic lunch.

★ How do we know which container holds the most? Discuss suggestions for comparing2 containers. e.g. I can tell by looking, that this one is larger.

★ What if the two containers look similar? Discuss the idea of counting up how manysmaller containers you need to fill each of the containers. Demonstrate by filling oneof the containers with cups of water. How will you keep count? e.g. Make tally markson paper. How many cups do you need to fill the second container? Estimate thencheck. Compare tally counts.

★ What else can we measure this way? e.g. How many oranges will fill a bag? How many buckets of water will fill a bath? How many people will fill a car?

★ Work in small groups. Explore the How many? cards. Collect the equipment youneed. Estimate how many of each unit you will use. Discuss with your partners at leasttwo ways to check. Find another container that holds the same amount. Record some of your discoveries. Make up more questions to explore.

★ Discuss discoveries and any problems together.

Variation★ At home, how many cans fit in a cupboard? How many towels? How many

saucepans? Look for items around your home that you can count. Compare yourresults with friends back at school.

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How many cups of water in a saucepan?

How many blocks in a box?

How many cups of water in a teapot?

How many lunch boxes in a basket?

How many pencils in a pencil case?

How many marbles in a bag?

How many books in a school bag?

How many cans of water in a bucket?

How many spoons of rice in a cup?

How many matches in a matchbox?


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GroceriesWhat are you trying to do?★ Use informal units to estimate,



How many can play?★ Whole class, small groups, pairs

What do you need?★ Grocery items, e.g. cans, packets, tubes★ Empty boxes, crates, shopping bags★ Workbooks, pencils★ Groceries discussion cards (BLM p.35)

How do you play?★ Why do you need shopping bags? e.g. To help carry things to the car without

spilling them everywhere.

★ How many groceries can you fit inside a shopping bag? Discuss different possibilities. What if all the items were the same, e.g. cans of cat food? How many cans do you estimate would fit inside?

★ What if you need to know how many cans would fit altogether, yet you onlyhave one can? e.g. Estimate the space one can takes up and keep mentallyadding spaces until you’ve ‘filled’ the whole bag.

★ Explore stacking and packing in groups. Investigate how many of each itemyou’d need to fill a crate, a bag or a box. Are some items easier to pack thanothers? What about how heavy they feel? Can you still carry them safely eventhough they fill the container?

★ Record some of your discoveries.

Variations★ Shuffle the discussion cards. Read out the top card. Discuss the size and shape

of the container you’d need to hold this set of grocery items. Demonstratewith your hands. Discuss different possibilities. Justify why you selected this sizeand shape.

★ What sized container would you need to hold 4 dogs? ... 3 kittens? ...10 mice?Discuss. Demonstrate with your hands.


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15 tubes of toothpaste

3 boxes of soap powder

2 bags of chips

5 packets of cheese

4 apple pies

10 packets of biscuits

20 cans of soup

8 bottles of drink

18 yoghurt containers

13 loaves of bread

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OrangesWhat are you trying to do?★ Use informal units to estimate,



★ Order 3 or more volumes, capacities using informal units (V3-5)


What do you need?★ Oranges, cardboard box★ Lemon squeezers, plastic knives, potato peelers★ Funnels, containers, cups★ Oranges activity cards (BLMs pp.37,38)★ Oranges recipes, utensils and ingredients (BLMs pp.39,40)

How do you play?★ What’s the largest orange you’ve ever seen? ... the smallest?

Demonstrate with your hands.

★ Investigate a pile of oranges. What’s the largest orange you can see?Put them in order from the smallest to the largest.

★ How many oranges would you need to fill a bag? ... a box? Estimatefirst, then find a way to check. What happens if the oranges are all different sizes?

★ Break into small groups with an Oranges activity card for each group.Collect all the equipment you need. Think of other Oranges activitiesyou could try in your group.

★ Discuss any discoveries or problems together.

Variations★ Follow up with small group cooking tasks. Collect your own recipes or

use the Oranges recipes provided here.

★ Explore volume activities with other fruits and vegetables. e.g. Howmany apples do you need to make a cup of juice?

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OrangesHow much juice is in one orange? Estimate

first then check. Do all oranges give the same

amount of juice? What’s the largest amount

in any one orange? ... the smallest amount?

OrangesHow many oranges make one cup of juice?

Estimate first then check. How many oranges

would you need to make a jug of juice?

How many oranges would you need if 10

children wanted a cup of juice each?

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Oranges

What’s the longest orange peel you can

make from one orange? Estimate first then

check. Does the largest orange have the

longest peel? Does the smallest orange

have the shortest peel?

Oranges

What’s the heaviest orange you can find?

Is the largest orange also the heaviest?

Is the smallest orange also the lightest?

Does the heaviest orange have the

most juice? Does the

lightest orange have

the least juice?

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What do you need?1 ripe banana 1 cup of plain yoghurt1 cup of orange juice1 tablespoon of honey

1 mixing bowl1 wooden spooncups

What do you need?3/4 cup butter1/2 cup honey 1/2 cup milk1/2 cup coconut 1/2 cup chopped raisins1/2 cup wheatgerm1/2 cup lecithin meal1 teaspoon grated orange rind

1 wooden spoon1 saucepan1 greased tray

What do you do?Melt butter and honey in saucepan over low heat.Mix in other ingredients, except milk and coconut.Stir in enough milk to make a firm mixture. Roll this into small balls. Roll each ball in coconut.Place on tray.Put in fridge to set.

Orange Fruit Balls

Orange Fruit Shake

What do you do?Mash the banana with the spoon.Mix this with the honey and yoghurt.Stir in the orange juice.Blend. Pour into cups and drink.

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What do you need?1 cup of self-raising floura pinch of salt1 dessertspoon of butter1 teaspoon grated orange rind1 tablespoon of orange juice4 tablespoons of milk

mixing bowlwooden spoongreased traydessertspoonplastic knifepaintbrush

Orange FacesWhat do you need?1 cup of butter1 cup of sugar2 eggs1 teaspoon grated orange rinda few drops of vanilla2 cups self-raising flour

1 cup cream cheese1 tablespoon honeyorange food colouringSmarties

1 large bowlwooden spoonrolling pinplastic knifegreased tray

What do you do?Preheat oven to 180 C. Beat butter and sugar in bowl until creamy. Beat in eggsone at a time. Add orange rind and vanilla. Stir in flour. Mix to a light dough. Roll on floured surface until thin. Cut out oval face shapes. Put on greased tray.Bake about 10 minutes, then cool. Mix cream cheese, honey and orange colouringto make icing. Cover top of each biscuit with icing. Create face with Smarties foreyes and nose.

What do you do?Preheat oven to 240 C. Mix flour and salt in bowl. Rub in butter with fingertips.Pour in orange juice and most of milk. Mix quickly to a soft dough with knife. Place dough on a floured surface. Knead lightly. Press out to a thick, flatter shape.Cut out small triangle shapes. Paint tops with remaining milk. Place on tray. Bake about 10 minutes until brown.

Orange Triangles

o

o

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BlocksWhat are you trying to do?★ Build, compare 3D models

using informal units (V3-3)

★ Understand that different shapes can have the same volume (V3-4)


What do you need?★ Stacking boxes or blocks,

e.g. multilinks, wooden cubes★ Paper, pencils★ Blocks copy cards (BLM p.42)

How do you play?★ Imagine you had to design a toy made from 2 blocks. How many different ways can you

arrange them? e.g. beside each other, on top.

★ How many different ways can you arrange 3 blocks? Discuss various possibilities together.

★ Imagine you had to design a toy made from 4 blocks. What are possible shapes it couldlook like? How many different shapes can you discover?

★ What if there were 5 blocks? 10 blocks? 20 blocks?

★ Class challenge - Imagine you had to design a box to hold and transport 5 large TV sets.What could it look like? Is one shape more suitable than another? Why? How muchspace would it take up in the room? Ask your friends to think of other size challenges.

Variations★ Draw your favourite 4-block model. Can your partner build an identical copy based on

your drawing?

★ Build models identical to those shown on the copy cards. How many other ways can youbuild a model with 8 blocks?

★ Race your friends to build a model from blocks in a given time, e.g. 1 minute. Who hasbuilt the largest model? How can you check?

★ Play a packing game with blocks, dice and an identical empty box for each player.Throw the dice, take the matching number of blocks and pack them into your box.Who is the first player to fill their box? Or race to fill a bucket with cups of water according to the throw of the dice.

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Exploring Displacement

In this unit, your students will:• Compare volumes by water displacement (rising levels) (V4-1)

• Compare volumes by water displacement (overflow) (V4-2)

• Compare volumes by water displacement (falling levels) (V4-3)

• Understand that volumes stay the same when broken into smaller parts (V4-4)

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Drop it inWhat are you trying to do?★ Compare volumes by water

displacement (rising levels) (V4-1)

★ Compare volumes by water displacement (overflow) (V4-2)

★ Understand volumes stay the same when broken into smaller parts (V4-4)


What do you need?★ Clear containers, water, objects,

overflow trays or bowls, marker pens★ Interlocking bricks (e.g. DUPLO),

plasticine★ Drop it in activity cards (BLMs pp.45,46)

How do you play?★ When you have a bath, how do you know how much water to put in?

e.g. Just enough to cover your body. What happens to the water level whenyou get in completely? e.g. It goes up. What happens to the water level whenyou get out of the bath? e.g. It goes down again.

★ Imagine you have a new aquarium full of water. What will happen if you putin one large fish? Where should you fill it to so the water doesn’t spill over?

★ What else do we use in our daily life that involves water this way? e.g Addingice cubes to a drink, adding potatoes to a pot of water.

★ Form small groups with an activity card for each group. Find the equipmentyou need. Explore different ways to solve your problem. Think of extra activitieson the same topic.

★ Discuss problems. e.g. How many different ways can you place an object intothe water? ... with a piece of string tied around it ... just by pressing down withyour fingers.

★ Discuss discoveries. e.g. How does the overflow method help us measure size?e.g. You can measure the amount of water in the overflow tray - the largestobject spills the most water.

Variation★ Explore ways to compare the size of large objects (e.g. balloons) using bins or

large buckets of water.


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Drop it in 1Find 3 objects that you think are close in size.

Estimate which one is the largest.

Partly fill a clear container with water.

Mark the water level. Predict what will

happen when you drop an object in and

then remove it.

How can you use this to measure size?

From the results place your objects in order.

Check your estimate.

Drop it in 2Find 3 objects that you think are close in size.

Estimate which one is the largest.

Place a small bucket in a larger empty

bowl. Fill the bucket to the brim with water.

Predict what will happen when you place

an object in the bucket.

How can you use this to measure size?

From the results place the objects in order.

Check your estimate.

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Drop it in 3Make a model from 6 interlocking blocks.Partly fill a clear container with water. Mark the water level. Predict what willhappen when you drop your model in.Predict what will happen when you drop6 loose bricks in. Compare results.

Drop it in 4Make a large model from plasticine.

Place a small bucket in a larger empty bowl.

Fill the bucket to the brim with water. Predict

what will happen when you drop your

model in. Break your model into small

pieces. Predict what will happen when you

drop all these pieces in.

Compare results.

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Take it outWhat are you trying to do?★ Compare volumes by water displacement

(falling levels) (V4-3)


What do you need?★ A box of cornflakes, a bottle of soft drink★ Clear containers, water, objects, marker pens★ Take it out activity cards (BLMs pp.48,49)★ Take it out discussion cards (BLMs p.50)

How do you play?★ Imagine you are setting up a small aquarium. You arrange some rocks in the bottom

and fill it up with water. What will happen if you decide to remove the rocks? What will happen to the water level now?

★ Imagine you are given a large gift-wrapped box as a birthday present. When youopen it up, it is full of shredded paper with your present hidden in the middle.What happens when you remove your present? e.g. The height of the paper goesdown to fill the space where the present was.

★ Imagine you have a new box of cornflakes. You decide to eat a cupful for breakfast.What happens to the height of the cornflakes in the box when you remove a cupful?Estimate first, then check how many cupfuls there are in one box.

★ Imagine you are planning a party. You need enough drink for 10 people. How manypeople would one bottle serve? How many bottles will you need to buy? Estimate first,then find a way to check. e.g. Pour out a cupful for each person.

★ Form small groups with an activity card for each group. Discuss activities briefly. Findthe equipment you need. Remember to select objects that can get wet without anydamage. Explore different ways to solve your problem. Think of extra activities on thesame topic.

★ Discuss problems and discoveries.

Variation★ You need a bucket, water and the top 6 discussion cards. Turn over the top card,

e.g. 5 saucepans. Where will the water come up to in the bucket when it holds thatamount? Estimate by pouring water into the bucket to a level you think matches the amount shown on the card. Check by taking out the amounts one by one. e.g. Remove 5 saucepans full of water. How close was your estimate?Repeat using the bottom 4 cards for rice.

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Take it out 1You need a clear open container, 3 objectsand water. Place an object in the bottom ofyour container. Fill it with water until the objectis completely covered. Mark the water level.Predict what will happen when you take theobject out. How can you use this to measure size? Place your objects in order of size using theresults. Do your estimates get more accurate?Try this again with completely different objects.

Take it out 2You need 3 large objects, a box and somefoam pellets or shredded paper. Place an object in the bottom of the box. Fill the box with pellets or paper. Predict what will happen when you take theobject out. How can you use this to measure size? Place your objects in order of size using theresults. Do your estimates get more accurate? Try this again with completely different objects.

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 48



Take it out 3You need a full container of rice anda cup. Guess how many cups ofrice there are altogether. Predict thenew level when you pour out onecup of rice each time. Do it again.Do your estimates getmore accurate? Try this again with different shapedcontainers.

Take it out 4You need a cup and a full bottle ofwater. Predict the new level whenyou pour out one cup of water. Do it again.Do your estimates get more accurate? Try this again with different shapedbottles.

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 49



6 cups

3 ice-cream tubs

5 saucepans

8 margarine tubs

10 spoons

4 bowls

2 jugs

1 small bottle

15 matchboxes

6 bags

9224X_0704R1_p3-50 10/18/04 10:59 AM Page 50



Exploring MassLanguage

In this unit, your students will:• Push, pull or carry to compare 2 or more masses (M1-1)

• Use mass language, e.g. heavy, light (M1-2)

• Heft to compare 2 or more masses (M1-3)

• Understand that size is not always related to mass (M1-4)

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Too heavyWhat are you trying to do?★ Push, pull or carry to compare 2 or more masses (M1-1)

★ Use mass language, e.g. heavy, light (M1-2)

★ Understand that size is not always related to mass (M1-4)


What do you need?★ Heavy objects, e.g. bricks, rocks, boxes, bins★ Ropes★ (Optional) Trolley, wheelbarrow★ Too heavy label cards (BLMs pp.53,54)

How do you play?★ What’s the heaviest thing you can think of?

What’s the lightest thing? Discuss ideas together.

★ How do we know how heavy something is? e.g. You can sometimes tell just by looking.

★ How can you take a heavy object from one place to another? Discuss.

★ Walk around your environment together. Identify heavy objects that you mightbe able to move. Can you carry them with one hand? ... with two hands?Can you push them? Can you pull them? Investigate different ways to check ifyou were correct. e.g. Tie a rope around very heavy objects and then try to pullthem. Do you need more than one person? Remember to consider safety factors!

★ How might a wheelbarrow or a trolley help you?

★ Identify the 3 heaviest items you discovered that you could still push or pull.Identify 3 objects that were too heavy to push, or too heavy to pull. Were thelargest objects always the heaviest?

★ Find a way to record your discoveries.

Variations★ Use the label cards to identify pairs of objects around the room or on a display.

e.g.

★ Identify objects around your home that are too heavy for you to push, pull or carrybut not too heavy for an adult to push or pull.

is hard to push

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 52



is easy to push

is easy to pull

is easy to carry

is hard to push

is hard to pull

is hard to carry

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 53



is a lot heavier than

is a little bit heavier than

is as heavy as

is as light as

is a little bit lighter than

is a lot lighter than

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 54


Is it heavier?What are you trying to do?★ Use mass language, e.g. heavy, light (M1-2)

★ Heft to compare 2 or more masses (M1-3)



What do you need?★ A collection of objects (with obviously different masses)

for each group★ An ice-cream container with a lid, a collection of smaller

objects that can each fit inside★ Is it heavier? activity cards (BLM pp.56,57)★ Is it heavier? discussion cards (BLM p.58)

How do you play?★ How accurate are you at estimating heaviness? Ask a friend to place 5 objects on a

table. Without first touching these objects, tell this person how to put the objects intoorder by heaviness.

★ How can you check your guesses? e.g. Place an object in each hand and say whichfeels heavier. This is called ‘hefting’. Does closing your eyes make hefting any easier?Does swapping the objects from one hand to another?

★ Discuss the idea that hefting is only a rough way to check. Sometimes the differencesare so small it is difficult for our hands to feel the difference.

★ Form small groups with an activity card for each group. Collect the equipment you need.

★ Discuss problems and discoveries.

★ Class challenge - Guess what’s inside.

★ Pass around 5 different objects for everyone to feel. Which object is the heaviest? ... the lightest? Secretly place one of these objects into a container and put the lid on.Pass the container around the group. Can everyone guess what’s inside just by feelinghow heavy it is?

Variations★ Shuffle the discussion cards. Turn over the top two cards. Discuss how heavy each

object might feel. Which one is the heavier of the two? Try to find different possibilities.e.g. What if the baby giraffe was a toy? Is it possible to check your estimate?

★ Sort 3 or more discussion cards into order by heaviness.Make up your own set of Is it heavier? discussion cards.


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Is it heavier? 1Tell a friend how to sort some objects

from lightest to heaviest without

touching them.

Check your guesses by hefting.

Try this again with another set

of objects.

Is it heavier? 2Find objects which look as though

they are the same size.

Check how heavy each one feels.

Put them into order by heaviness.

Can you find 2 objects with the same

size but one is much heavier than

the other?

Explain your discoveries.

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 56



Is it heavier? 3Select an interesting toy.

Feel how heavy it is. Without touching

them, select objects you think are

heavier than this toy.

Then select objects you think are lighter

than this toy.

Find a way to check your guesses.

Try this again with another toy.

Is it heavier? 4Point to two objects that you think

are as heavy as each other.

Check your guesses.

Can you find 2 objects that are as

heavy as each other but one is

much larger?

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 57



a brick

a bottle of drink

a bed

an apple

a space alien

a kitten

a baby giraffe

a kangaroo

a bunch of celery

a bicycle

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 58



Mystery parcelsWhat are you trying to do?★ Use mass language, e.g. heavy, light (M1-2)

★ Heft to compare 2 or more masses (M1-3)



What do you need?★ Mystery parcels for each group (see Mass Resources p.90)★ Mystery parcels activity cards for each group (BLM p.60)

How do you play?★ Think about your birthday. What’s the heaviest present you’ve ever

received? ... the lightest?

★ Discuss the mystery parcels. Imagine you were given one for your birthday.What might there be inside?

★ Pass the parcels around the class. Heft, shake or rattle each one in turn.What do you notice? e.g. Even though two parcels are the same size, theyare not always the same heaviness. They don’t always have the same mass.

★ How do you know if two parcels have the same mass? e.g. They feel thesame when you heft them on either hand.

★ Form pairs within small groups, with either the bottles, margarine tubs, ice-cream tubs or yoghurt mystery parcels. Shuffle the activity cards. Pass them around to each pair.

★ Swap cards within each group. Can you think of other activities too?

★ Discuss the results together. Which parcel in each set is the heaviest? ... the lightest?

Variation★ Class challenge - Use the Is it heavier? discussion cards (from p.58). Name 3

things in real life that are just a little bit heavier than the object on eachcard. Name 3 things a lot heavier than... a bit lighter than ... much lighterthan each object. Discuss suggestions together.

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 59



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9224X_0704R1_p51-90 10/18/04 11:53 AM Page 60



Does large mean heavy?What are you trying to do?★ Heft to compare 2 or more masses (M1-3)



What do you need?★ A balloon, a beach ball, a cricket ball★ Workbooks, pencils★ Activity cards (BLM p.62)

How do you play?★ Which is heavier - a beach ball or

a cricket ball? Why?

★ Blow up the balloon until it is as large as possible. Which of the 3 objects is the heaviestnow? Which object is the largest? Does a large size always mean heavy? Why?

★ Challenge the class to find objects, from around the room, that are large but light.

★ Pass the objects around so that you can feel and compare them. Who has the largestobject? Who has the lightest object?

★ Challenge everyone to now find an object from around the room that is small but heavy.

★ Pass the objects around so that you can feel and compare them. Who has the smallestobject? Who has the heaviest object?

★ Discuss your results together.

★ Record your favourite discoveries.

Variations★ Work in small groups or pairs with an activity card each. Collect the equipment you

need. Discuss your results and compare objects together.

★ Make a class display or book about your results. Challenge everyone to add changes tothe book as a new item that fits the criteria is discovered. Collect examples from aroundthe home too.

9224X_0704R1_p51-90 10/18/04 11:53 AM Page 61



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Using a Balance

In this unit, your students will:• Use an equal arm balance to compare masses (M2-1)

• Predict, interpret actions of an equal arm balance (M2-2)

• Order 3 or more masses by hefting, check using a balance (M2-3)

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Make a balanceWhat are you trying to do?★ Use an equal arm balance to

compare masses (M2-1)

★ Predict, interpret actions of an equal arm balance (M2-2)

★ Order 3 or more masses by hefting, check using a balance (M2-3)


What do you need?★ Plank, heavy cylinder, e.g. a car wheel, an empty oil drum ★ Dowel, rulers, coat hangers, buckets, ice-cream/yoghurt tubs, paper/foam

cups, string, cotton, scissors★ A pan, bucket and rocker balance★ Make a balance examples (BLMs pp.65,66)★ Make a balance activity cards (BLM p.67)

How do you play?★ What does it mean when you say something balances? What uses this idea?

e.g. Circus performers, someone riding a bicycle.

★ Discuss seesaws in a playground or park. What do they look like? What dothey do?

★ Discuss the pan, bucket and rocker balances. What can you do with one ofthese? Where do you find them in daily life? e.g. In a grocery or fruit shop.

★ What are other ways to make a balance? Discuss suggestions.★ Form small groups. Challenge each group to design and make their own

balance. The sample cards show 4 different ideas.

★ Explore what happens if you rearrange items on your balance. e.g. Move onepan closer to the centre, add extra masses (... Blu-Tack) on one side.

★ How can you test each balance for accuracy? e.g. Place identical objects ineither side and watch what happens.

Variations★ Use the activity cards in small groups.

★ Make a list or a class book about uses of mass measurers in daily life, e.g. kitchen scales, bathroom scales, spring balances.

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Bucket balance

Ice-cream tub balance

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Coat hanger balance

Yoghurt tub balance

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Grocery detectiveWhat are you trying to do?★ Predict, interpret actions of an

equal arm balance (M2-2)



What do you need?★ Grocery items, e.g. cans, bottles, boxes★ Balances★ Blindfolds★ Grocery pictures (BLM p.69)★ Workbook, pencils, scissors, paste

How do you play?★ What do you think is as heavy as this can? Why?

★ Pass around a range of grocery items. Which one feels the heaviest? Whichone feels the lightest? Do any items feel as heavy as each other?

★ Are you a successful grocery detective? In turn, put on the blindfold and place3 groceries in order from lightest to heaviest just by hefting.

★ Remove your blindfold. Check what happens when you use the balance tocompare your groceries.

★ Try this again using more than 3 groceries. How many different items can you successfully place into order by heaviness?

★ Record your discoveries by drawing pictures to show your final order.

Variation★ Instead of drawing, cut out grocery pictures which represent the items you

hefted. Paste these into order of heaviness in a workbook.

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Vegetable detectiveWhat are you trying to do?★ Predict, interpret actions of an equal

arm balance (M2-2)



What do you need?★ Vegetables, e.g. potatoes, carrots, pumpkin★ Balances, blindfolds★ Vegetable pictures (BLM p.71)★ Workbook, pencils, scissors, paste★ Classroom pictures (BLM p.72)

How do you play?★ What do you think is heavier - this potato or this carrot? What makes you

think that?

★ Pass around a range of vegetables. Which one feels the heaviest? Which onefeels the lightest? Do any items feel as heavy as each other?

★ Are you a successful vegetable detective? In turn, put on the blindfold andplace 3 vegetables in order from lightest to heaviest just by hefting.

★ Remove your blindfold. Predict then check what happens when you use thebalance to compare your vegies.

★ Try again using more than 3 vegetables. How many different ones can you successfully place into order by heaviness?

Variations★ Record your discoveries by drawing pictures to show your final order. Or cut out

the vegetable pictures which represent the items you hefted and paste theseinto order in a workbook.

★ Repeat the above activities using objects from around your classroom. Use thecut-out pictures, or draw your own, to record some of your discoveries.

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What balances it?What are you trying to do?★ Use an equal arm balance to

compare masses (M2-1)

★ Predict, interpret actions of an equal arm balance (M2-2)


What do you need?★ Balances★ Collections of light to heavy objects★ Containers of informal mass units★ Paper or workbooks, pencils★ What balances it? activity cards (BLM p.74)★ What balances it? recording sheets (BLMs pp.75,76)

How do you play?★ How do you know if 2 things balance each other?

★ Revise how to test an empty balance for accuracy. Demonstrate how to make eachside equal, e.g. pull one bucket closer to the centre.

★ Find 2 objects you think have the same mass, e.g. a toy and a book. Predict, thencheck what happens to each side when you use a balance.

★ What lighter objects balance one of these objects? e.g. How many bolts balancethe toy? How many shells? Guess first then check.

★ What if you have 4 pine cones in one side? What will balance these? Guess first thencheck, e.g. 14 pencils.

★ Form small groups with an activity card for each group. Check your balances foraccuracy.

★ Rotate activities after a time limit.

★ Record your favourite discoveries.

Variation★ Use the What balances it? recording sheets. Predict first then check.


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What balances it?

5 bolts

10 matchsticks

6 buttons

1 toy

4 blocks

What balances it?

12 pieces of chalk

9 shells

14 tiles

1 pine cone

7 cotton reels

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2 cups of rice

1 tub of pasta

3 eggcups of water

5 lidfuls of water

10 spoons of beans

1 rock

4 small books

7 pencils

11 buttons

15 paperclips

What balances it?

What balances it?


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Using Informal Mass Units

In this unit, your students will:• Use informal units to estimate, measure mass (M3-1)

• Select an appropriate informal unit to measure mass (M3-2)

• Record mass measurements using tallying (M3-3)

• Order 3 or more masses using informal units (M3-4)

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Balance itWhat are you trying to do?★ Use informal units to estimate,

measure mass (M3-1)

★ Select an appropriate informal unit to measure mass (M3-2)

★ Record mass measurements using tallying (M3-3)

How many can play?★ Pairs

What do you need?★ A balance★ A small toy★ Bottle tops★ Dice

How do you play?★ How do you know when something feels as heavy as another thing? How can

you check? e.g. You can heft, then check using a balance.

★ How heavy does this toy feel? e.g lighter than that book, heavier than a pair ofscissors. How heavy is a handful of counters? Estimate how many counters you’llneed to balance the toy.

★ Revise how to check a balance for accuracy.

★ Place the toy in one side of the balance.

★ In turn, throw the dice, add the numbers on your dice and place a matchingnumber of counters into the other pan.

★ The winner is the player whose counters finally balance the toy.

★ How many counters balanced the toy altogether? Count and record by tallying.Compare this result with your estimate.

Variations★ Place a large heavy object in one side of a bucket balance. Select small heavy

objects to add to the other side after each dice throw, e.g. a brick and bolts.

★ Place a light object in one side of a rocker balance. Select light objects to add tothe other side after each dice throw, e.g. a pair of scissors and buttons.

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How many ...?What are you trying to do?★ Use informal units to estimate, measure mass (M3-1)

★ Select an appropriate informal unit to measure mass (M3-2)

★ Record mass measurements using tallying (M3-3)


What do you need?★ Balances★ Informal mass units, e.g. large shells, marbles, paddle-pop sticks★ Small, medium, large objects★ Pencils, workbooks★ Informal units cards copied onto red paper (BLM p.80)★ Objects cards copied onto yellow paper (BLM p.81)

How do you play?★ One way to measure the heaviness of an object is to find out how many smaller

objects balance it.

★ How many shells do you think will balance this book? Discuss then check.

★ What else could you try to balance the book with? Could you try buttons? e.g. They may be too light, you might need too many. Could you try rocks? e.g. They may be too heavy. Justify your suggestions. When you measure themass of an object try to use a suitable smaller object as a unit.

★ Revise how to use tally marks to keep count of your units.

★ Form small groups. Explore different ways to measure the mass of an objectusing informal units. e.g. Group A may use heavy objects and a bucket balance. Group B may use very light objects and a rocker balance. Group Cmay use medium objects. Group D may explore continuous materials like cupsof water or rice to balance an object.

★ Discuss discoveries and problems together. Record your most interesting ones.

Variations★ Shuffle the Units cards and turn over the top card. Shuffle the Objects cards

and turn over the top card, e.g. rocks and an apple. Are rocks suitable units?Why? Why not? Estimate how many units you will need to balance the object.

★ Make your own cards, based on objects available in your classroom.

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large wooden blocks

different size rocks

bathroom tiles

bottle tops

paperclips

marbles

cotton reels

shells (different sizes,shapes)

pine cones

building blocks

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apple

school cap

banana

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book

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Unit detectivesWhat are you trying to do?★ Select an appropriate informal unit to measure mass (M3-2)

★ Order 3 or more masses using informal units (M3-4)


What do you need?★ Balances★ Objects, e.g. classroom items, fruit, vegetables★ Four sets of informal units, e.g. bottle tops, pebbles, bolts, shells★ Unit detectives recording sheets (BLM p.83)

How do you play?★ How does comparing the number of informal units used to balance an object, allow

you to order objects by mass?

★ Discuss the 4 available units to use as mass measures, e.g. bottle tops are light, boltsare quite heavy.

★ Check your balances for accuracy.

★ In your group, work with a partner. Select 4 different items to measure. How heavydoes each object feel?

★ Select one item and a unit to measure it with, e.g. an apple and pegs. Estimatehow many of this unit you’ll need to balance your object then check using theselected unit.

★ Repeat using a different object and a different unit each time.

★ Record your discoveries on the worksheet.

★ You’re now ready to become a Unit Detective. Ask all the other pairs in your groupto reveal their records. Select one of the units used, e.g. bottle tops. Try to work outthe order of heaviness of the objects measured with bottle tops, just by looking atthe written results.

★ Check using a balance pan.

Variations★ Estimate then measure a variety of objects with the same unit. Do your estimates

get closer with practice?

★ Class challenge: Who is the Champion Estimator? Are you better at estimating withlight, medium or heavy units?

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Unit detectives

My object My unit My estimate The actual measure

Unit detectives

My object My unit My estimate The actual measure

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Kangas What are you trying to do?★ Record mass measurements using tallying (M3-3)

★ Solve problems using mass concepts★ Use informal mass units in a game


What do you need?★ Animal sanctuary playing board (BLM p.85)★ Kangas spinners (BLM p.86)★ Dice, pencils, paper, counters

How do you play?★ Which Australian animal would be the heaviest? Which one would be

the lightest? Why?

★ Imagine your family has built an animal sanctuary. What type of animalscould you collect there?

★ You’ve decided to find the mass of each animal using a special unitcalled a ‘kanga’. How heavy might this be? Discuss suggestions.

★ You can play an animal sanctuary game using kangas. The playing board shows you how many kangas balance each animal you’d like tocollect. Spin the spinner and keep a tally of how many kangas you havealtogether. When you have enough to match an animal, you can circle it.That means you’ve added this animal to your sanctuary.

★ You can collect more than one of each animal.

★ At the end of the game, discuss your results. Who has the sanctuary withthe most animals? Which player’s animals have the most mass altogether?

Variation★ Invent your own informal mass units. Make up a different game using

these in some way.


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5 kangas

1 kanga

30 kangas

10 kangas

40 kangas

5 and a half kangas

8 kangas

1 and a half kangas1 and a half kangas

echidna wombat koala

platypus snake tasmanian devil

bandicoot kangaroo possum

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kangasCopy onto cardboard,cut out, place matchthrough centre.

Copy onto cardboard,cut out, place matchthrough centre.

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Fat catsWhat are you trying to do?★ Solve problems using mass concepts★ Work cooperatively as a team

How many can play?★ Pairs or small groups

What do you need?★ Fat cats problem (BLM p.88 - cut into 6 strips)

How do you play?★ Discuss your pets. Would your pet be the heaviest? Why?

Whose pet would be the lightest? Why?

★ Imagine you are a vet. You have to give medicine according to howheavy each animal is. A customer comes in with four very fat cats.How could you put them in order according to heaviness? Discuss suggestions.

★ Look at the Fat cats problem. The strips tell you a story. Discuss theproblem in your own words. How can you work out your answer?

★ Work together to find a solution. What different strategies do you use?

★ Check your solution against each statement.

★ When you are convinced your solution is correct, see if you can discover another possibility.

Variation★ Invent your own problem about heavy animals for another team

to solve. Try to make it have more than one solution.

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There are four fat cats.

The cats’ names are Tom, Ming, Sam and Puss.

Tom is heavier than Ming.

Puss is not the lightest.

Sam is lighter than Ming.

Which cat is the heaviest?

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Essential Volume ResourcesBoxes/cartonsAbout 30 mixed size, shape boxes stored in a large, clearly labelled,plastic container that can be carried by 2 students,e.g. cereal packets, matchboxes, chocolate boxes, shoe boxes,milk cartons.

ContainersAbout 30 mixed size, shape containers in a large, clearly labelled,plastic container that can be carried by 2 students,e.g. drink bottles, shampoo/detergent bottles, washing-up bowls,buckets, pots and pans.

Measuring equipmentIn a large, clearly labelled, plastic container,e.g. funnels, plastic tubing, sponges, sieves, cups, spoons (teaspoons, tablespoons), scoops.

Packing resources, informal volume unitsIn a large clearly labelled, plastic container,e.g. large, small foam blocks, balls, building blocks (e.g. multilink, wooden cubes, DUPLO 4-stud bricks), dried beans,rice, pasta.

Other resourcese.g. balloons, plasticine, playdough,washing-up bowls, buckets.

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Essential Mass ResourcesInformal mass units(in clear plastic containers with lids)e.g. Light paddle-pop sticks buttons cotton balls

bottle tops tiny shells dried beans pastametal washers beads paperclips

Medium small shells pegs marbles plastic cubespebbles cotton reels bear counters farm animals

Heavy bolts blocks large shells large tilespine cones rocks ball bearings

Grocery items(in a large storage box)e.g. cans, bottles, jars, cartons, boxes ...

Mystery parcelsTo use as informal masses - up to 30 of each, filled with non-perishable items,e.g. sand, pebbles, bottle tops, wrapped in second-hand birthday paper andsecurely fastened with tape.2 litre ice-cream containers, with lids(in 100 gram multiples from 100 g to 1000 g)e.g. 100 g 200 g 300 g

Margarine containers, with lids (in 50 gram multiples from 50 g to 500 g)e.g. 50 g 100 g 150 g

Yoghurt containers, with lids (in 50 gram multiples from 50 g to 500 g)e.g. 50 g 100 g 150 g

Extra heavy objectse.g. brickswooden offcuts

Commercial balancesrocker balancespan balancesbucket balances

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Exploring Volume

V1-1 Observes, discusses the space occupied by objects

V1-2 Fills, empties containers using a variety of materials

V1-3 Packs a variety of objects into defined spaces

V1-4 Uses volume and capacity language e.g. pack, fill, empty

V2-1 Compares, describes 2 or more volumes, capacities

V2-2 Identifies objects with the same volume, capacity

V2-3 Understands that objects with same volume,

capacity may have a different shape

V2-4 Orders 3 or more volumes, capacities

V3-1 Uses informal units to estimate, measure volume, capacity

V3-2 Records volume, capacity measurements using tallying

V3-3 Builds, compares 3D models using informal units

V3-4 Understands that different shapes can have the same volume

V3-5 Orders 3 or more volumes, capacities using informal units

V4-1 Compares volumes by water displacement (rising levels)

V4-2 Compares volumes by water displacement (overflow)

V4-3 Compares volumes by water displacement (falling levels)

V4-4 Understands that volumes stay the same when

broken into smaller parts

Exploring Mass

M1-1 Pushes, pulls, or carries to compare 2 or more masses

M1-2 Uses mass language e.g. heavy, light

M1-3 Hefts to compare 2 or more masses

M1-4 Understands that size is not always related to mass

M2-1 Uses an equal arm balance to compare masses

M2-2 Predicts, interprets actions of an equal arm balance

M2-3 Orders 3 or more masses by hefting, checks using a balance

M3-1 Uses informal units to estimate, measure mass

M3-2 Selects an appropriate informal unit to measure mass

M3-3 Records mass measurements using tallying

M3-4 Orders 3 or more masses using informal units

Outcome IndicatorsRecord SheetEXPLORING VOLUME

NA

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capacity may have a different shape

broken into smaller parts

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Mathematics Topics for 5 year oldsWeek Term 1 Term 2 Term 3 Term 41 Prenumber Exploring 5 Chance/Data Chance/Data2 Prenumber Length Exploring 9 Early Fractions3 Space: 3D Exploring 6 Space: Position Length4 Exploring 1 Time Exploring 0 Early +/-5 Space: 3D Exploring 7 Space: 3D Area6 Exploring 2 Mass Space: 2D Time7 Space: 2D Temperature Time Mass/Volume8 Exploring 3 Exploring 8 Exploring 10 Space: Position9 Space: 2D Money Volume Number Revision

10 Exploring 4 Revision Revision Measurement Revision

Mathematics Topics for 6 year oldsWeek Term 11 Revisiting 0-92 3D Space3 Length4 Exploring +/-5 2D Space6 Volume7 Exploring 10-908 Mass9 Time

10 Revision

Sample Yearly Mathematics Topics

Term 2 Term 3 Term 4Exploring 11-19 Revision 0-20 Exploring 0-503D Space 2D Space 3D SpaceLength Area Chance/DataExploring +/- Exploring +/- Exploring +/-Money Position 2D SpaceVolume Time PositionExploring x Exploring x Exploring ÷Mass Temperature Measurement RevisionFractions Fractions Number RevisionRevision Revision Space Revision

Mathematics Topics for 7 year oldsWeek Term 1 Term 2 Term 3 Term 41 Revisiting 0-20 Exploring 0-99 Exploring 0-99 Exploring 1002 3D Space 3D Space 2D Space Time3 Exploring +/- Exploring +/- Exploring +/- Exploring +/-4 Length Area Length 2D Space5 2D Space Fractions Exploring x Exploring x6 Volume Mass Temperature Volume7 Revisiting 10-90 Exploring x Exploring ÷ Exploring ÷8 Time Money Chance/Data Measurement Revision9 Exploring x Position Fractions Number Revision

10 Revision Revision Revision Space Revision

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kes

upm

uch

less

sp

ace

than

.

• Re

cord

in w

orkb

ooks

.

• W

hole

cla

ss:

D

iscu

ssio

n ca

rds

(e

.g.

wom

bat/

roos

ter)

.

• W

hole

cla

ss:

W

hich

hol

ds m

ore?

Dis

cuss

con

tain

ers

and

how

muc

h th

eyca

n ho

ld.

• Pa

ir ac

tivity

:

Labe

l obj

ects

aro

und

room

, e.

g. h

olds

abo

utas

muc

h as

.

• Re

cord

in w

orkb

ooks

.

• W

hole

cla

ss:

D

iscu

ssio

n ca

rds

(e.

g.sc

hool

bag

/pap

er b

ag).

• W

hole

cla

ss:

W

hich

hol

ds m

ore?

Dis

cuss

way

s to

pla

ce 3

cont

aine

rs in

ord

er.

• Ro

tatin

g gr

oup

act

iviti

es:

Whi

ch h

olds

mor

e?

A:

Bott

les

B:

Sp

onge

s

C:

Buck

ets

D

: Bo

xes

• W

hole

cla

ss:

D

iscu

ssio

n ca

rds

(e

.g.

stor

eroo

m/t

ruck

).

• W

hole

cla

ss:

Fi

nd a

pai

r.

Dis

cuss

con

tain

ers

whi

chlo

ok d

iffer

ent

but

hold

the

sam

e am

ount

.

• Ro

tatin

g gr

oup

act

iviti

es:

Find

a p

air.

A

: Ri

ce

B: M

arbl

es

C:

Wat

er

D:

Bloc

ks

•W

hole

cla

ss:

D

iscu

ssio

n ca

rds.

LAN

GU

AG

E•

this

tak

es u

p a

litt

le m

ore

spac

e th

an .

.. •

this

tak

es u

p m

uch

less

sp

ace

than

...

• th

is h

olds

as

muc

h as

...

• th

is is

larg

er t

han

...

• th

is is

sm

alle

r th

an .

.. •

this

is t

he la

rges

t, s

mal

lest

9224X_0704R1_p91-94 10/18/04 12:11 PM Page 93



•

Revi

se w

eek’

s ac

tiviti

es.

•

Che

ck b

alan

ces

for

accu

racy

.

•

Gro

up a

ctiv

ity:

U

nit

dete

ctiv

es.

•

Estim

ate,

mea

sure

, co

mp

are

mas

s of

obj

ects

usi

ng

info

rmal

uni

ts.

•

Reco

rd o

n w

orks

heet

.

•

Cla

ss c

halle

nge:

W

ho is

the

bes

t es

timat

or u

sing

in

form

al u

nits

? -

light

, m

ediu

m,

heav

y.

RES

OU

RC

ES

Vario

us b

alan

ces

Dic

e, in

form

al u

nits

, obj

ects

Wor

kboo

ks

Vario

us b

alan

ces

Info

rmal

mas

s un

its

Smal

l, m

ediu

m, l

arge

obj

ects

Vario

us b

alan

ces

Info

rmal

mas

s un

its

Smal

l, m

ediu

m,

larg

e ob

ject

sBL

Ms

pp.8

0,81

Vario

us b

alan

ces

Info

rmal

mas

s un

its

Frui

t, v

eget

able

s

Vario

us b

alan

ces

Info

rmal

mas

s un

its

Frui

t, v

eget

able

sBL

M p

.83

Sam

ple

Wee

kly

Prog

ram

STR

AN

DM

easu

rem

ent

SU

BST

RA

ND

Mas

s -

Usi

ng In

form

al U

nits

GR

AD

E2

TE

RM

2

W

EEK

6

OU

TCO

MES

• U

ses

info

rmal

uni

ts t

o es

timat

e, m

easu

re m

ass

(M3-

1)

• S

elec

ts a

n ap

pro

pria

te u

nit

to m

easu

re m

ass

(M3-

2)•

Rec

ords

mas

s m

easu

rem

ents

usi

ng t

ally

ing

(M3-

3)•

Ord

ers

3 or

mor

e m

asse

s us

ing

info

rmal

uni

ts (

M3-

4)

MO

ND

AY

TUES

DAY

WED

NES

DAY

TH

UR

SDAY

F

RID

AY

• W

hole

cla

ss:

D

iscu

ss h

ow y

ou k

now

so

met

hing

is a

s he

avy

as

anot

her

thin

g.

• Re

vise

how

to

chec

k a

bala

nce

for

accu

racy

.

• Pa

ir ac

tivity

:

Find

pai

rs o

f ob

ject

s w

hich

bal

ance

ea

ch o

ther

.

• Pa

ir ga

me:

Bala

nce

it.

• W

hole

cla

ss:

H

ow m

any

...?

D

iscu

ss u

sing

info

rmal

un

its t

o ba

lanc

e an

d co

mp

are

obje

cts.

• D

iscu

ss li

ght,

med

ium

and

heav

y un

its.

Whe

n w

ould

eac

h be

ap

pro

pria

te?

• G

roup

act

iviti

es:

A

: he

avy

obje

cts

B:

ligh

t ob

ject

s

C:

med

ium

mas

s ob

ject

sD

: cu

ps

of w

ater

, ric

e.

• R

otat

e gr

oup

s on

ce.

•

Who

le c

lass

:

How

man

y ...

?

Dis

cuss

ion

card

s.

e.g.

Est

imat

e ho

w m

any

tiles

to

bala

nce

a ba

nana

.

•

Gro

up a

ctiv

ities

:

A:

med

ium

mas

s ob

ject

sB:

cup

s of

wat

er,

rice

C

: he

avy

obje

cts

D

: lig

ht o

bjec

ts.

• Ro

tate

gro

ups

once

.

• Re

cord

bes

t di

scov

erie

sin

wor

kboo

ks.

•

Who

le c

lass

:

How

man

y ...

?

Dis

cuss

ion

card

s.

e.g.

Est

imat

e nu

mbe

r of

pap

ercl

ips

to b

alan

ce a

sh

oe.

Is t

his

a su

itabl

eun

it? W

hy?

•

Gro

up a

ctiv

ities

:

Find

2 o

bjec

ts t

hat

bala

nce

the

sam

e nu

mbe

rof

uni

ts

A

: ve

geta

bles

B:

fru

it

C:

vege

tabl

es

D:

frui

t.

•

Rota

te g

roup

s on

ce.

•

Reco

rd b

est

disc

over

ies

in w

orkb

ooks

.

LAN

GU

AG

E•

thi

s is

hea

vier

, lig

hter

tha

n ...

•

thi

s is

as

heav

y as

, as

ligh

t as

...

• t

his

is t

he li

ghte

st,

the

heav

iest

•

thi

s ha

s th

e sa

me

mas

s as

• t

his

mas

s is

bal

ance

d by

...

9224X_0704R1_p91-94 10/18/04 12:11 PM Page 94



NUMBER Exploring 1-5Exploring 6-10Games and Activities for 0-10Exploring 0-50 NumerationExploring 0-50 Operations

Numbers to 50 Picture PackExploring 0-100 NumerationExploring 0-100 OperationsExploring Calculators Exploring FractionsExploring Money

MEASUREMENTExploring Length/AreaExploring Volume/MassExploring Temperature/Time

EXPLORING VOLUME AND MASS MEASUREMENT LOWER PRIMARY

About the authorOriginally a primary school teacher, Bev Dunbar is now actively involved in teacher education as a Mathematics Consultant and University Lecturer in Mathematics Education.

Bev is a passionate believer in fun, practical resources which help teachers make maths lessons a highlight of the day.

• Seven carefully sequenced units whichdevelop skills in practical measurement

• Over 25 activity-based, easy-to-useteaching ideas

• A sample yearly maths overview • Two sample weekly programs • Useful activity cards for independent

small group work

• An outcome indicators record forassessing individual progress

• Over 50 blackline masters

In fact, almost everything you need to explore volume and mass in your classroom.

Titles in the Exploring Maths series

The Exploring Maths series is designed to provide busy teacherswith practical resources that are mathematically up-to-date, fun andeasy to use. Each book contains a wealth of activities, blackline mastersand assessment tasks for a whole life-time of teaching. These activitiesencourage your children to think mathematically by exploring, experimenting, being creative and taking risks. By asking questions andactive discovery, children learn to enjoy using mathematics as part oftheir everyday lives.

Exploring Volume and Mass includes:


Activities,blackline masters & assessment pages that are fun and

easy to use

BevDunbar

EXPLORINGEXPLORING

VolumeMass

ISBN 1-86509-224-X

9

781865 092249

and

M e a s u r e m e n T L O W E R P R I M A R Y 2

COVER, Volume/Mass 9/30/04 9:08 AM Page 2

Documents

EXPLORING MAT HS Vol EXPLORINGume - Blake Education€¦ · These activities encourage your children to think mathematically by exploring, experimenting, being creative and taking