exploring - Blake Education

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Volume Mass E X P LO R I N G

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Bev Dunbar

Activities, blackline masters & assessment pages that are fun and easy to use M e a s u r e m e n T

L O W E R

P R I M A R Y

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Exploring Volume and Mass with Lower Primary

Bev Dunbar

Introduction Exploring 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 the Exploring Maths series. Volume is a measure of the amount of space occupied by a 3-dimensional object. Capacity relates to containers. It is a measure of the amount of another substance that a container can hold inside it. For example, a brick has a fixed volume but no capacity. Mass is a measure of the amount of substance in a 3-dimensional object. It remains the same wherever it is measured. Weight relates to the effect of gravity on a mass. Weight varies depending on where it is measured. For example, in space you are ‘weightless’ yet your mass is still the same. Most people generally ignore this distinction and talk only about ‘weight’. In this book, the more correct word, ‘mass’, is emphasised. These particular substrands can easily be neglected in schools because they’re seen as messy, wet or requiring extra equipment. To help inspire you, here are over 30 action-packed ideas for developing skills in exploring, comparing and using 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 divided into sequenced units, each packed with enough photocopiable discussion and activity cards for small groups or a whole class to explore, for up to a week at a time. You’ll find easy-to-follow instructions, with assessment help in the form of clearly stated outcomes linked to a checklist (see p.91). Each activity is designed to maximise the way in which your students construct their own understandings about volume and mass. The activities are generally open-ended and encourage each student to think and work mathematically, with an emphasis on practical manipulation of materials and the development of language and recording skills. Look forward now, to exploring these concepts with your students.

Copyright © Bev Dunbar Maths Matters 2001 Reprinted 2004 Exploring Volume and Mass ISBN 186509 224 X 224 9 978 1 86509 Published by Blake Education Locked Bag 2022 Glebe NSW 2037 Series editor: Garda Turner Illustration 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.

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

© Blake Education 978 1 86509 224 9

Exploring Maths - Measurement - Exploring Volume and Mass

How to use this Book Over 30 Teaching Ideas More than 30 exciting teaching ideas have been placed into 7 sections to assist your lesson planning for the whole class or small groups. Each activity has clearly coded learning outcomes and easy-to-follow instructions. Activities are open-ended and encourage your students to think for themselves.

Over 50 Blackline Masters There are 3 types of blackline masters. Label cards e.g. p.19 Which is larger? These support free exploration as well as structured activities. Laminate them for reuse with small groups.

takes up much more space than

takes up a little more space than

takes up about the same space as

Discussion Cards e.g. p.58 Is it heavier? Cut these out, shuffle and use over and over again for small group games. Photocopy each set in different colours.

takes up a little less space than

takes up much less space than

19

Exploring Volume and Mass

Activity Cards e.g. p.42 Blocks Use these as an additional stimulus for small group work. The language is simple and easy-to-follow. Encourage your students to invent their own activity cards too. You can laminate them so that they last for years.

a brick a kitten a bottle

of drink

a kang

aroo

an appl

e a bunc

h of ce

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

lery

a spac

e alien a bicycl

e

58

Exploring

Volume

and Mass

Outcomes Indicator Record The 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 Programs On 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 Units for a whole class.



giraffe

a bed

Essential Resources Lists

2

a baby


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.) Exploring Volume and Mass



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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 you think 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. What can you see that is about as large as this balloon? Is it hollow also? Does the size depend on whether it is hollow or not? ★ Blindfold a student. Ask them to feel a variety of objects. Can they identify whether each object feels large or small or even the same size as another object? 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 elephant might 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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5

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) ★ Use volume and capacity language (V1-4)

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 you know if your cup is full or not? Demonstrate by filling a cup with water. Is it full to the brim or does it have a small gap left? ★ Discuss what happens when you open a carton of milk. Where does the milk come up to inside? Why? e.g. When you are packing liquids you usually want a gap at the 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 box with marbles, then predict what will happen if you add more. ★ Walk around your environment, inside and outside, looking for examples of containers. Predict whether they are empty, half full or full before you check the contents 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 different packing 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 to show where the milk is in the carton if it is half full.

6




Pack it in 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?

Fill it up 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?




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Pour it in You need cups, funnels, plastic tubes, 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 easier to pour?

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

8




How full is it?




9

Will they fit? What are you trying to do? ★ Observe, discuss the space occupied by objects (V1-1) ★ Pack a variety of objects into defined spaces (V1-3) ★ Use volume and capacity language (V1-4)



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 perfect fit. Identify some things that you know are a good fit, e.g. a hand and a glove, a dress on your big sister. Tell me some things you know are not a good fit. e.g. Our garage 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 you guess will fit inside? Is there any space left over? e.g. I guess you need 6 oranges to fill that bag. ★ Shuffle the sets of cards into two separate piles. Turn and read out the top card in each pile. Imagine the situation and discuss it together. Estimate the size of the items 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 and a 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 container with an exact fit for each set of objects.

10




your feet

2 cats

3 cars

4 whales

8 grandmas

10 students

15 cans

20 fish

50 beetles

100 people

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


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12

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







13

Find, or design and make, a container for 6 toys. Guess first what size you will need, then check. Try to find more than one way to do it.

Find, or design and make, a container for 5 apples. Guess first what size you will need, then check. Try to find more than one way to do it.

Find, or design and make, a container for 3 bananas. Guess first what size you will need, then check. Try to find more than one way to do it.

Find, or design and make, a container for 4 lunch boxes. Guess first what size you will need, then check. Try to find more than one way to do it.

Tip it out What 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) ★ Pack a variety of objects into defined spaces (V1-3) ★ Use volume and capacity language (V1-4)

How many can play? ★ Small groups


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 in a 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 was when it was inside. List objects that you know like this, e.g. a toy car, a cake of soap, some cans of pet food. ★ Discuss what happens to water in a container. e.g. If you spill a glass of water, 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 you tipped them out from a container. e.g. A bag of marbles would spill out onto the floor but a box of books would stay the same shape if you removed the cardboard 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. Try dry sand, damp sand then really wet sand. What do you notice when you tip out the shapes each time? 14




Sand 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 can make? ... the smallest? Make one huge sand shape together.

Jelly 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.




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Plaster Explore different ways to make shapes from plaster. Leave them 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 plaster shape together.

Cake Explore different ways to make shapes from cake mix. Put them in an oven to cook. 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 cake shape together.

16




Comparing Volumes


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)




17

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 to judge size? How do you know just by looking? Discuss ideas together. ★ Discuss the 5 label cards. Demonstrate how to place objects on either side of each 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 is larger? Compare pairs of objects which are quite different in size, as well as objects 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? Consider different possibilities, e.g. a cricket ball is only small but a beach ball can be very large. ★ Invent 10 more discussion cards for another team to try. 18




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

takes up much less space than Exploring Volume and Mass © Blake Education 978 1 86509 224 9


19

a wombat

a television set

a pumpkin

a carton of milk

a puppy

a ball

a rooster

a rock

a koala

a baby



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


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 one place to another. ★ What can you put in a container? e.g. I pack all my clothes in a large suitcase when 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 one full container to another to see whether it overflows. ★ Take 2 containers, e.g. 2 cans. Demonstrate how to check which one holds more marbles. Discuss the 5 label cards. Demonstrate how to use them for recording 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. Decide which one holds more. Justify why you think this. Try to put three or more in order 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 more than

holds a little more than

holds about the same as

holds a little less than

holds much less than

22




a garbage truck

a storeroom

a school bag

a bookshelf

a paper bag

a shopping trolley

a pelican’s beak

a wheelbarrow

a refrigerator

a bicycle carry basket



Bottles You need 2 bottles. Which one holds more water? Guess first, then check. Find another container you think holds 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.

Sponges You need 2 sponges. Which one holds more water? Guess first, then check. Find another sponge you think holds 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.

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Buckets You need 2 buckets. Which one holds more balls? Guess first, then check. Find another container you think holds 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.

Boxes You need 2 boxes. Which one holds more blocks? Guess first, then check. Find another box you think holds even 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.




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Find a pair

What 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


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 the same 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 longer and 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 same amount 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 shapes you discover or make. Look at the size of each one in your pair. What do you notice?

26






Find or make 2 containers that hold the same amount of marbles but are different shapes. Next find a container that holds exactly 5 marbles.

Find or make 2 containers that hold the same amount of blocks but are different shapes. Next find a container that holds exactly 10 blocks.

Find or make 2 containers that hold the same amount of rice but are different shapes. Next find a container that holds exactly 1 cup of rice.

Find or make 2 containers that hold the same amount of water but are different shapes. Next find a container that holds exactly half a cup of water.

Race away What are you trying to do?

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



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 all the 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 for starters. Collect the equipment you need. Discuss the rules behind each race.

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

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



29

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

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

30




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) Exploring Volume and Mass



31

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 comparing 2 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 many smaller containers you need to fill each of the containers. Demonstrate by filling one of the containers with cups of water. How will you keep count? e.g. Make tally marks on paper. How many cups do you need to fill the second container? Estimate then check. 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 you need. Estimate how many of each unit you will use. Discuss with your partners at least two 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 your results with friends back at school.

32




How many cups of water in a saucepan?

How many marbles in a bag?

How many blocks in a box?

How many books in a school bag?

How many cups of water in a teapot?

How many cans of water in a bucket?

How many lunch boxes in a basket?

How many spoons of rice in a cup?

How many pencils in a pencil case?

How many matches in a matchbox?



33

Groceries 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, pairs


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 only have one can? e.g. Estimate the space one can takes up and keep mentally adding spaces until you’ve ‘filled’ the whole bag. ★ Explore stacking and packing in groups. Investigate how many of each item you’d need to fill a crate, a bag or a box. Are some items easier to pack than others? What about how heavy they feel? Can you still carry them safely even though 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. Demonstrate with your hands. Discuss different possibilities. Justify why you selected this size and 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

10 packets of biscuits

3 boxes of soap powder

20 cans of soup

2 bags of chips

8 bottles of drink

5 packets of cheese

18 yoghurt containers

4 apple pies

13 loaves of bread



35

Oranges What are you trying to do? ★ Use informal units to estimate, measure volume, capacity (V3-1) ★ Record volume, capacity measurements using tallying (V3-2) ★ Order 3 or more volumes, capacities using informal units (V3-5)



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? Estimate first, 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 activities you 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. How many apples do you need to make a cup of juice?

36




Oranges How 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?

Oranges How 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?



37

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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Orange Fruit Shake What do you need?

1 mixing bowl 1 wooden spoon cups

1 ripe banana 1 cup of plain yoghurt 1 cup of orange juice 1 tablespoon of honey

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.

Orange Fruit Balls What do you need? 3/4 cup butter 1/2 cup honey 1/2 cup milk 1/2 cup coconut 1/2 cup chopped raisins 1/2 cup wheatgerm 1/2 cup lecithin meal 1 teaspoon grated orange rind

1 wooden spoon 1 saucepan 1 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. Exploring Volume and Mass



39

Orange Triangles What do you need? 1 cup of self-raising flour a pinch of salt 1 dessertspoon of butter 1 teaspoon grated orange rind 1 tablespoon of orange juice 4 tablespoons of milk

mixing bowl wooden spoon greased tray dessertspoon plastic knife paintbrush

What do you do? o

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 Faces What do you need?

1 cup of butter 1 cup of sugar 2 eggs 1 teaspoon grated orange rind a few drops of vanilla 2 cups self-raising flour

1 large bowl wooden spoon rolling pin plastic knife greased tray

1 cup cream cheese 1 tablespoon honey orange food colouring Smarties

What do you do? o

Preheat oven to 180 C. Beat butter and sugar in bowl until creamy. Beat in eggs one 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 colouring to make icing. Cover top of each biscuit with icing. Create face with Smarties for eyes and nose. 40




Blocks What 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 could look 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 much space 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 you build a model with 8 blocks? ★ Race your friends to build a model from blocks in a given time, e.g. 1 minute. Who has built 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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42




Exploring Displacement


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 in What 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 when you get in completely? e.g. It goes up. What happens to the water level when you 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 put in 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 Adding ice cubes to a drink, adding potatoes to a pot of water. ★ Form small groups with an activity card for each group. Find the equipment you need. Explore different ways to solve your problem. Think of extra activities on the same topic. ★ Discuss problems. e.g. How many different ways can you place an object into the water? ... with a piece of string tied around it ... just by pressing down with your 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 largest object spills the most water.

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

44




Drop it in 1 Find 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 2 Find 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.




45

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

Drop it in 4 Make 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.

46




Take it out What are you trying to do?

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



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 you open 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 goes down 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 many people 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. Find the equipment you need. Remember to select objects that can get wet without any damage. Explore different ways to solve your problem. Think of extra activities on the same 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 that amount? 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. Exploring Volume and Mass



47

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

Take it out 2 You need 3 large objects, a box and some foam 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 the object out. How can you use this to measure size? Place your objects in order of size using the results. Do your estimates get more accurate? Try this again with completely different objects.

48




Take it out 3 You need a full container of rice and a cup. Guess how many cups of rice there are altogether. Predict the new level when you pour out one cup of rice each time. Do it again. Do your estimates get more accurate? Try this again with different shaped containers.

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




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6 cups

4 bowls

3 ice-cream tubs

2 jugs

5 saucepans

1 small bottle

8 margarine tubs

15 matchboxes

10 spoons

6 bags

50




Exploring Mass Language


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 heavy What 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)



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 might be 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 if you were correct. e.g. Tie a rope around very heavy objects and then try to pull them. 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 the largest 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.

is hard to push

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

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is easy to push

is easy to pull

is easy to carry

is hard to push

is hard to pull

is hard to carry Exploring Volume and Mass © Blake Education 978 1 86509 224 9


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


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 into order by heaviness. ★ How can you check your guesses? e.g. Place an object in each hand and say which feels 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 differences are 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 feeling how 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.




55

Is it heavier? 1 Tell 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? 2 Find 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.

56




Is it heavier? 3 Select 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? 4 Point 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?



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58

a brick

a kitten

a bottle of drink

a baby giraffe

a bed

a kangaroo

an apple

a bunch of celery

a space alien

a bicycle




Mystery parcels What are you trying to do? ★ 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)


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, they are 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 the same 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 each card. Name 3 things a lot heavier than... a bit lighter than ... much lighter than each object. Discuss suggestions together.




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60




same mass.

from lightest

another parcel.

feel as heavy as

which together

Find 2 parcels

parcels.

the lightest

heaviest and

Find the

parcels with the

parcels in order

to heaviest.

Find pairs of

Put any 4

Does large mean heavy? What are you trying to do? ★ Heft to compare 2 or more masses (M1-3) ★ Understand that size is not always related to mass (M1-4)


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 heaviest now? 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 largest object? 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 smallest object? 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 to the book as a new item that fits the criteria is discovered. Collect examples from around the home too.




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62




heavy as a large

than a book?

box?

empty

can discover that feels as

can discover that feels heavier

heavy as a calculator?

lighter than a shoe?

What’s the smallest object you

can discover that feels as

you can discover that feels

What’s the smallest object you

What’s the largest object you

What’s the largest object

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 balance 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) ★ 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 do they do? ★ Discuss the pan, bucket and rocker balances. What can you do with one of these? 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 one pan 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 in either 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



65

Coat hanger balance

Yoghurt tub balance

66







67

object is heavier. Check by hefting. What do you notice?

happen to each side

when you place them

on a balance. What

What do you notice?

Check with a balance.

the same mass.

which you think have

Heft objects to find 2

What do you notice?

to check.

Heft first, then use a balance

order by heaviness.

Put 3 or more objects into

balance. Say which

then check, what will

do you notice?

Look at 2 objects on a

Heft 2 objects. Predict,

Grocery detective What are you trying to do? ★ Predict, interpret actions of an equal arm balance (M2-2) ★ Order 3 or more masses by hefting, check using a balance (M2-3)



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? Which one 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 place 3 groceries in order from lightest to heaviest just by hefting. ★ Remove your blindfold. Check what happens when you use the balance to compare 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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69

Vegetable detective What are you trying to do? ★ Predict, interpret actions of an equal arm balance (M2-2) ★ Order 3 or more masses by hefting, check using a balance (M2-3)



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 one feels the lightest? Do any items feel as heavy as each other? ★ Are you a successful vegetable detective? In turn, put on the blindfold and place 3 vegetables in order from lightest to heaviest just by hefting. ★ Remove your blindfold. Predict then check what happens when you use the balance 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 these into order in a workbook. ★ Repeat the above activities using objects from around your classroom. Use the cut-out pictures, or draw your own, to record some of your discoveries.

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71

72




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 each side 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, then check what happens to each side when you use a balance. ★ What lighter objects balance one of these objects? e.g. How many bolts balance the toy? How many shells? Guess first then check. ★ What if you have 4 pine cones in one side? What will balance these? Guess first then check, e.g. 14 pencils. ★ Form small groups with an activity card for each group. Check your balances for accuracy. ★ 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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74




Find different things to balance one thing, e.g. one stapler balanced by 40 blocks or a small book. How many can you find within the time limit?

Find two objects that balance each other. How many pairs can you find within the time limit?

Balance sets of heavy objects. If there are three on one side how many on the other? If there are four on one side how many on the other?

Place a heavy object on one side. How many lighter objects balance the heavy one? How many sets can you find within the time limit?

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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What balances it? 2 cups of rice 1 tub of pasta 3 eggcups of water 5 lidfuls of water 10 spoons of beans

What balances it? 1 rock 4 small books 7 pencils 11 buttons 15 paperclips

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Using Informal Mass Units


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)




77

Balance it 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)

How many can play? ★ Pairs


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 of scissors. How heavy is a handful of counters? Estimate how many counters you’ll need 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 matching number 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 to the 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 the mass 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 object using 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 C may use medium objects. Group D may explore continuous materials like cups of 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

marbles

different size rocks

cotton reels

bathroom tiles

shells (different sizes, shapes)

bottle tops

pine cones

paperclips

building blocks

80




apple

shoe

school cap

orange

banana

toy

brick

garbage bin

pencil

book



81

Unit detectives What 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)



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, bolts are quite heavy. ★ Check your balances for accuracy. ★ In your group, work with a partner. Select 4 different items to measure. How heavy does each object feel? ★ Select one item and a unit to measure it with, e.g. an apple and pegs. Estimate how many of this unit you’ll need to balance your object then check using the selected 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 group to reveal their records. Select one of the units used, e.g. bottle tops. Try to work out the order of heaviness of the objects measured with bottle tops, just by looking at the 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 with light, 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



83

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 animals could you collect there? ★ You’ve decided to find the mass of each animal using a special unit called 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 to collect. Spin the spinner and keep a tally of how many kangas you have altogether. 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 with the 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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echidna

wombat

koala

5 kangas

30 kangas

5 and a half kangas

platypus

snake

tasmanian devil

1 kanga

10 kangas

8 kangas

bandicoot

kangaroo

possum

1 and a half kangas

40 kangas

1 and a half kangas Exploring Volume and Mass



85

g a s 5

10 s ga kan

2 kangas

half a kanga 3 kan ga

1 a g kan

10 s ga kan

as

ka 5 n g

s

Copy onto cardboard, cut out, place match through centre.

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3 kan ga

2 kangas

half a kanga Copy onto cardboard, cut out, place match through centre.

k a n

Kangas Spinners

1 s

a g n

ka




Fat cats What 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 how heavy 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 the problem 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.




87

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?

88




Essential Volume Resources Boxes/cartons About 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.

Containers About 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 equipment In a large, clearly labelled, plastic container, e.g. funnels, plastic tubing, sponges, sieves, cups, spoons (teaspoons, tablespoons), scoops.

Packing resources, informal volume units In 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 resources e.g. balloons, plasticine, playdough, washing-up bowls, buckets.




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Essential Mass Resources Informal mass units

(in clear plastic containers with lids) e.g. Light paddle-pop sticks bottle tops tiny shells metal washers

buttons dried beans beads

cotton balls pasta paperclips

Medium small shells pebbles

pegs cotton reels

marbles plastic cubes bear counters farm animals

Heavy

blocks rocks

large shells large tiles ball bearings

bolts pine cones

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

Mystery parcels To 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 and securely 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 objects e.g. bricks wooden offcuts

Commercial balances rocker balances pan balances bucket balances

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NAME

Outcome Indicators Record Sheet EXPLORING VOLUME

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, capacitymay mayhave haveaadifferent differentshape shape capacity

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 into smaller smaller parts parts broken

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


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Sample Yearly Mathematics Topics Mathematics Topics for 5 year olds Week 1 2 3 4 5 6 7 8 9 10

Term 1 Prenumber Prenumber Space: 3D Exploring 1 Space: 3D Exploring 2 Space: 2D Exploring 3 Space: 2D Exploring 4

Term 2 Exploring 5 Length Exploring 6 Time Exploring 7 Mass Temperature Exploring 8 Money Revision

Term 3 Chance/Data Exploring 9 Space: Position Exploring 0 Space: 3D Space: 2D Time Exploring 10 Volume Revision

Term 4 Chance/Data Early Fractions Length Early +/Area Time Mass/Volume Space: Position Number Revision Measurement Revision

Mathematics Topics for 6 year olds Week 1 2 3 4 5 6 7 8 9 10

Term 1 Revisiting 0-9 3D Space Length Exploring +/2D Space Volume Exploring 10-90 Mass Time Revision

Term 2 Exploring 11-19 3D Space Length Exploring +/Money Volume Exploring x Mass Fractions Revision

Term 3 Revision 0-20 2D Space Area Exploring +/Position Time Exploring x Temperature Fractions Revision

Term 4 Exploring 0-50 3D Space Chance/Data Exploring +/2D Space Position Exploring ÷ Measurement Revision Number Revision Space Revision

Mathematics Topics for 7 year olds Week 1 2 3 4 5 6 7 8 9 10 92

Term 1 Revisiting 0-20 3D Space Exploring +/Length 2D Space Volume Revisiting 10-90 Time Exploring x Revision

Term 2 Exploring 0-99 3D Space Exploring +/Area Fractions Mass Exploring x Money Position Revision

Term 3 Exploring 0-99 2D Space Exploring +/Length Exploring x Temperature Exploring ÷ Chance/Data Fractions Revision

Term 4 Exploring 100 Time Exploring +/2D Space Exploring x Volume Exploring ÷ Measurement Revision Number Revision Space Revision







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TUESDAY

• Whole class: Which holds more? Discuss containers and how much they can hold.

• Pair activity: Label objects around room, e.g. holds about as much as.

• Record in workbooks.

• Whole class: Discussion cards (e.g. school bag/paper bag).

• Whole class: Which is larger? Discuss size and how much space an object occupies.

• Pair activity: Label objects around room e.g. takes up much less space than.

• Record in workbooks.

• Whole class: Discussion cards (e.g. wombat/rooster).

Various containers, water Volume measuring equipment Packing resources BLMs pp.22,23

MONDAY

Classroom objects BLMs pp.19,20 Workbooks

RESOURCES

this this this this this this

WEDNESDAY

• Whole class: Discussion cards (e.g. storeroom/truck).

• Rotating group activities: Which holds more? A: Bottles B: Sponges C: Buckets D: Boxes

• Whole class: Discussion cards.

• Rotating group activities: Find a pair. A: Rice B: Marbles C: Water D: Blocks

• Whole class: Find a pair. Discuss containers which look different but hold the same amount.

THURSDAY

Containers Water, rice, marbles, blocks Plasticine BLM p.27

takes up a little more space than ... takes up much less space than ... holds as much as ... is larger than ... is smaller than ... is the largest, smallest

Buckets, bottles, boxes, sponges Water, balls, blocks Volume measuring equipment BLMs pp.24,25

• • • • • •

LANGUAGE

SUBSTRAND Volume - Comparing volumes TERM 1 WEEK 6

• Whole class: Which holds more? Discuss ways to place 3 containers in order.

• Compares, describes 2 or more volumes, capacities (V2-1) • Identifies objects with the same volume, capacity (V2-2) • Understands objects with the same volume may have a different shape (V2-3) • Orders 3 or more volumes, capacities (V2-4)

OUTCOMES

STRAND Measurement GRADE 1

Sample Weekly Program

• Whole class: Discuss results. Ideas for alternate games.

• Whole class outdoor team game: Race away 2.

• Whole class outdoor team game: Race away 1.

• Discuss the fastest way to fill a container with water.

• Revise week’s activities.

FRIDAY

Water, cup, funnel, A large container

For each team:

94




• Pair game: Balance it.

• Pair activity: Find pairs of objects which balance each other.

• Rotate groups once.

• Group activities: A: heavy objects B: light objects C: medium mass objects D: cups of water, rice.

• Discuss light, medium and heavy units. When would each be appropriate?

• Whole class: How many ...? Discuss using informal units to balance and compare objects.

• Whole class: Discuss how you know something is as heavy as another thing.

• Revise how to check a balance for accuracy.

TUESDAY

MONDAY

Various balances Dice, informal units, objects Workbooks

Various balances Informal mass units Small, medium, large objects

Uses informal units to estimate, measure mass (M3-1) Selects an appropriate unit to measure mass (M3-2) Records mass measurements using tallying (M3-3) Orders 3 or more masses using informal units (M3-4)

RESOURCES

• • • •

OUTCOMES

STRAND Measurement GRADE 2 this this this this this

• Record best discoveries in workbooks.


• Group activities: A: medium mass objects B: cups of water, rice C: heavy objects D: light objects.

• Whole class: How many ...? Discussion cards. e.g. Estimate how many tiles to balance a banana.

WEDNESDAY

• Record best discoveries in workbooks.


• Group activities: Find 2 objects that balance the same number of units A: vegetables B: fruit C: vegetables D: fruit.

• Whole class: How many ...? Discussion cards. e.g. Estimate number of paperclips to balance a shoe. Is this a suitable unit? Why?

THURSDAY

Various balances Informal mass units Fruit, vegetables

is heavier, lighter than ... is as heavy as, as light as ... is the lightest, the heaviest has the same mass as mass is balanced by ...

Various balances Informal mass units Small, medium, large objects BLMs pp.80,81

• • • • •

LANGUAGE

SUBSTRAND Mass - Using Informal Units TERM 2 WEEK 6

Sample Weekly Program

• Class challenge: Who is the best estimator using informal units? - light, medium, heavy.

• Record on worksheet.

• Estimate, measure, compare mass of objects using informal units.

• Revise week’s activities. • Check balances for accuracy. • Group activity: Unit detectives.

FRIDAY

Various balances Informal mass units Fruit, vegetables BLM p.83

EXPLORING VOLUME AND MASS

MEASUREMENT

LOWER PRIMARY

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

Exploring Volume and Mass includes: • Seven carefully sequenced units which develop skills in practical measurement • Over 25 activity-based, easy-to-use teaching ideas • A sample yearly maths overview • Two sample weekly programs • Useful activity cards for independent small group work

• An outcome indicators record for assessing individual progress • Over 50 blackline masters In fact, almost everything you need to explore volume and mass in your classroom.

About the author Originally 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.

Titles in the Exploring Maths series NUMBER Exploring 1-5 Exploring 6-10 Games and Activities for 0-10 Exploring 0-50 Numeration Exploring 0-50 Operations

E

X

P

L

Numbers to 50 Picture Pack Exploring 0-100 Numeration Exploring 0-100 Operations Exploring Calculators Exploring Fractions Exploring Money

O

R

I

N

MEASUREMENT Exploring Length/Area Exploring Volume/Mass Exploring Temperature/Time

ISBN 1-86509-224-X

9 781865 092249

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