Making your teaching life easier is a major aim of this series. ... You'll find easy-to-follow instructions with clear-
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EXPLORING
Fractions Bev Dunbar
positional only
Activities, blackline masters & assessment pages that are fun and easy to use
N U M B E R
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P R I M A R Y
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Introduction Exploring Fractions is part of the Exploring Mathematics series of teacher resources for 5 - 7 year olds. Although common fractions no longer have the same emphasis as they did prior to metrics, they are still used in daily conversation. They have an important role to play in the development of your students’ understanding of numbers and our numeration system. In this book, your students will explore the many ways we can divide a set of objects or a whole object into equal or unequal parts. By playing games with fractions, by talking about them with a partner, by actively cutting, tearing, drawing or sharing fractional parts, your students will see how easy fractions are to construct, compare and order. Making your teaching life easier is a major aim of this series. The book is divided into five sequenced units. Each unit is packed with enough activities for small groups, or a whole class, to explore for at least a week. You’ll find easy-to-follow instructions with clearly stated outcomes. There are plenty of photocopiable playing cards, activity cards and worksheets. Each unit also includes a sample Check-up worksheet to assist with your assessment strategies. Each activity is designed to maximise the way in which your students build up their understanding of fractions. The activities are open-ended and encourage your students to think and work mathematically.The emphasis is on mental recall as well as the practical manipulation of objects. Look forward to exploring the joys of fractions with your students.
Copyright © Bev Dunbar Maths Matters 2000 Exploring Fractions ISBN 186509 227 4 Published by Blake Education Locked Bag 2022 Glebe NSW 2037 Series editor: Garda Turner Illustration and design by Janice Bowles Printed by Printing Creations - Reprinted 2003 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 Equal Parts
3
Exploring Halves
15
Exploring Quarters
31
Exploring Tenths
47
Exploring Other Fractions
63
Fraction Biscuit Recipe
89
Fraction Jokes
90
Outcome Indicators Record
92
Sample Yearly Programs
93
Sample Weekly Program
94
How to use this Book 30 Teaching Ideas More than 30 exciting teaching ideas have been placed into 5 units to assist your lesson planning. Each activity has clearly coded learning outcomes and easy-to-follow instructions. Activities are open-ended and encourage your students to think for themselves. Each unit also includes a sample ‘Check-up’ worksheet for written assessment.
50 Blackline Masters There are four types provided for you here.
Cake pieces
Reusable Resources These support your free exploration as well as structured activities. Laminate them for reuse in small group activities. Sets of 10 Playing Cards Cut these out, shuffle and use over and over again for small group games. Photocopy each set in different colours. Activity Cards Each set of 8 cards can be used by parent helpers or fluent readers to stimulate group work. The language is simple and easy-to-follow. Encourage your students to develop cards too.
Colour the te nths 52
s Exploring Fraction
Multi-use Worksheets Recopy and use again with the same group, varying your instructions.
Outcomes Indicator Record The complete list of learning outcomes is available on page 92. Use this to record individual student progress.
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Exploring Fraction s
Sample Yearly Programs You’ll never be stuck for programming ideas again. See page 93 for examples of how to organise a 40 week term for Mathematics in your classroom.
Sample Weekly Program On page 94 you’ll find one example of how to organise a selection of activities from ‘Exploring Quarters’ as a 5 day unit.
And there’s even more! You’ll find a sample recipe (see p.89) and some Fraction Jokes (see p.90) to add to your class collection. There are even some Poems (see p.91) to practise for school assembly.
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Exploring Fractions
Is it fair? What are you trying to do?
★ Recognise equal/unequal groups (EF1). ★ Use the terms ‘fair share’ and ‘unfair share’ (EF2).
How many can play? ★ A small group
What do you need?
★ 10 koalas (10 x BLM p.5 - coloured, laminated) ★ 20 gum leaves (If you can’t find real ones use 2 x BLM p.6 - coloured, laminated, cut into separate leaves) ★ (optional) 10 sorting cards (BLM p.7 photocopied onto coloured paper)
How do you play?
★ One player is the leader. He/she takes a handful of leaves and 2 or more koalas. The other players close their eyes, while the leader sorts the leaves between the koalas. ★ The other players open their eyes and look at the groups of leaves. What questions can you ask each other? e.g. “How many koalas?” “How many leaves for each koala?” “Does each koala have the same number of leaves?” “Is it a fair share?” ★ Check by counting. ★ Return all the pieces to the middle. Select a new leader.
Variations
★ Select one player to be the guesser, while the other players secretly sort up to 20 leaves between some koalas. ★ Find the card which matches the sorting for each round.
e.g.
3 fair shares
★ Shuffle the cards. Turn over the top card and sort the koalas/leaves to match.
e.g.
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Exploring Fractions
5 unequal shares
Exploring Fractions
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6
Exploring Fractions
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fair shares
unfair shares
3
fair shares
3
unfair shares
4
fair shares
4
unfair shares
5
fair shares
5
unfair shares
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10
fair shares
2
unfair shares
Pattern parts What are you trying to do?
★ Divide an object into 2 equal parts (H2). ★ Use the term ‘1 of 2 equal parts’ (H4). ★ Use the term ‘half’ (H5).
How many can play?
★ A small group, up to the whole class
What do you need?
★ Pattern blocks, mosaic tiles ★ Scrap paper, pencils ★ Pattern parts worksheet (BLM p. 19 - cut into 4 strips)
How do you play?
★ Discuss how the blocks can be used to make patterns. Explore different ways the pieces fit together.
★ Find 2 blocks which are exactly the same shape and size. Discover a new shape made by joining these 2 blocks together.
e.g.
Each piece is one of 2 equal pieces. It’s called a half.
★ How many new shapes can you make from these 2 halves?
★ Record your discoveries by tracing your 2 halves onto paper.
Variations
★ Use the Pattern parts worksheet. Draw in the line to show half of each block. Decorate to make a colourful halves pattern. Reuse later to show quarters. ★ Hold up 1 block. Ask your partner to quickly find a matching half. Together make a new shape.
★ Can you discover 1 larger block which can be covered by 2 smaller blocks?
e.g. Discover more blocks which can be broken into 2 halves.
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Exploring Fractions
Pattern parts
Pattern parts
Pattern parts
Pattern parts
Find a fourth What are you trying to do?
★ Divide a set of objects into 4 equal parts (Q1). ★ Use the term ‘1 of 4 equal parts’ (Q4). ★ Use the term ‘one fourth’ (Q5).
How many can play? ★ A small group
What do you need? ★ ★ ★ ★
A large pile of counters, buttons or dried corn 4 chickens (BLM p.33 - decorated, laminated, cut out) 10 number cards (BLM p.34) Find a fourth workstrip for each player (BLM p.35 - cut into 4 strips)
How do you play?
★ Shuffle the number cards and place them face down in the centre. Turn over the top card and count out the matching pieces of ‘corn’. ★ Guess how many pieces of corn each chicken will receive if you divide these between 4 chickens.
★ Find one fourth. How close was your guess? Each chicken now has one of 4 equal parts. ★ Record your actions on the workstrip.
Variations
★ Use any number of counters. Find a fourth. What will you do with the leftovers? ★ Share birthday candles onto 4 plasticine cakes, in place of the chickens and corn. ★ Share bottle tops onto 4 margarine lids.
★ Share small counters into 4 matchboxes.
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Exploring Fractions
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Find a fourth
Find a fourth
Find a fourth
Find a fourth
one tenth
two tenths
three tenths
four tenths
five tenths
six tenths
seven tenths eight tenths nine tenths
ten tenths
Where are the tenths? What are you trying to do?
★ Divide a set into 10 equal parts (T1). ★ Use the term ‘one tenth’ (T5).
How many can play?
★ Pairs, up to the whole class
What do you need? ★ ★ ★ ★
Up to 100 counters Scrap paper, pencils 10 cards (BLM p.55) Where are the tenths? worksheet (BLM p.60)
How do you play?
★ Take a large handful of counters. Guess how many counters in one group if you share them into 10 equal groups. ★ Check by sharing. Are there any leftovers? What will you do with these?
★ How many counters in one tenth? Two tenths? Three tenths? Count how many in ten groups. What do you notice? Is there a pattern?
★ Shuffle the cards. Turn over the top card. Using just your head can you work out how many counters there must be ?
Variations
★ Draw a random number of dots. With your partner, guess how many dots in 1 tenth of these dots. How can you check?
e.g.
Take a matching number of counters. Divide these into 10 equal groups. Remove any extras.
★ Look at the worksheet. Find a way to divide each set into tenths. Ask your partner questions about 1 to 10 tenths.
e.g.
How many fish in 4 tenths of these fish?
Exploring Fractions
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Where are the tenths?
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Exploring Fractions
Brilliant things to do with pizza cards What are you trying to do?
★ Divide an object into any number of equal parts (OF2). ★ Use fraction names (e.g. 3 out of 4 parts) (OF3). ★ Order 3 or more fractions by size (OF4).
How many can play? ★ Pairs, small groups
What do you need? ★ ★ ★ ★ ★
10 pizza cards (BLM p.72) Pizza activity cards (BLMs p.73 - 76) Tokens, counters for winners A timer (for ‘Fast Sort’) Paper, pencils (for ‘Draw my Pizza’)
How do you play?
★ Imagine the cards show the amount of pizza left on a plate after a party. ★ Select any pizza card. What part of the original pizza is left? How do you know what name to give this piece?
e.g.
. .
★ What part has been eaten? Explain how you worked it out.
e.g. The part left and the part eaten together make a whole pizza. There was 1 out of 3 parts left so 2 parts must have been eaten.
★ Briefly explain the different group activities. Any questions? ★ Rotate activities amongst the pairs or groups.
Variation
★ Design a different set of fraction cards. Make up your own games using these new cards.
Exploring Fractions
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More or less Take a card each.
What part of the original pizza is left?
Who has the larger piece?
Win a token if your piece of pizza is larger.
Find the match Shuffle the cards.
Place them face down in rows.
Play ‘Memory’.
Which 2 cards go together to make one whole pizza? Try to collect the most matching pairs.
Exploring Fractions
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Guess my fraction Secretly take a pizza card.
Ask your partner to guess your fraction
by asking questions.
You can only answer “Yes” or “No”.
Can they guess your fraction in fewer than
5 questions?
Name my pizza Ask a partner to show you a
pizza card for a short time, then hide it.
Can you correctly name the fraction?
Check, then swap roles.
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Exploring Fractions
Fast sort Shuffle the pizza cards.
In turn, sort the 10 cards into order from the smallest to the largest piece.
Win a counter if your time is the shortest.
Try sorting from the largest to the smallest piece too!
Draw my pizza Shuffle the pizza cards.
Ask your partner to show you one card for a short time,
then hide it.
Can you draw a matching pizza piece? Check by looking at the pizza card.
Exploring Fractions
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What’s missing? Shuffle the pizza cards.
Ask your partner to show you the top card for a short time, then hide it.
Can you name the pizza piece that has been eaten? Check by working out the name together.
In the middle Shuffle the pizza cards. Turn over two cards.
Which piece is smaller? Which piece is larger? Can you draw another piece that would fit in
between these two sizes?
Can you name it?
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Exploring Fractions
EXPLORING FRACTIONS
NUMBER
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.
positional only
Exploring Fractions includes: • An outcome indicators record to help you record individual progress.
• Five carefully sequenced units to develop fraction skills with 5, 6 and 7 year olds • Over 30 activity-based, easy-to-use teaching ideas • Over 50 blackline masters • Useful activity cards for independent small group work
In fact, almost everything you need to explore halves, quarters, tenths and more, 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 working in both the State and Catholic Education systems. 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
Exploring 0 - 50 Numeration Exploring 0 - 50 Operations
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Numbers to 50 Picture Pack Exploring 0 - 100 Numeration Exploring 0 - 100 Operations Exploring Calculators Exploring Fractions Exploring Money
NUMBER Exploring 1 - 5 Exploring 6 - 10 Games and Activities for 0 - 10
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