100 ideas for teaching primary math.pdf

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100 IDEASFOR TEACHING PRIMARY

MATHEMATICS


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CONTINUUM 100 IDEAS FOR THE EARLY YEARS SERIES

100 Ideas for Teaching Communication, Language and Literacy SusanElkin

100 Ideas for Teaching Creative Development Wendy Bowkett andStephen Bowkett

100 Ideas for Teaching Knowledge and Understanding of the World Alan Thwaites

100 Ideas for Teaching Personal, Social and Emotional Development Judith Thwaites

100 Ideas for Teaching Physical Development Simon Brownhill

100 Ideas for Teaching Problem Solving, Reasoning and Numeracy Alan Thwaites

CONTINUUM ONE HUNDREDS SERIES

100+ Ideas for Managing Behaviour Johnnie Young

100+ Ideas for Teaching Creativity Stephen Bowkett

100+ Ideas for Teaching Thinking Skills Stephen Bowkett

100 Ideas for Supply Teachers: Primary School Edition Michael Parry

100 Ideas for Essential Teaching Skills Neal Watkin and JohannesAhrenfelt

100 Ideas for Assemblies: Primary School Edition Fred Sedgwick100 Ideas for Lesson Planning Anthony Haynes


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100 IDEASFOR TEACHING

PRIMARYMATHEMATICS

Alan Thwaites


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Continuum International Publishing GroupThe Tower Building 80 Maiden Lane11 York Road Suite 704London New York, NY 10038SE1 7NX

www.continuumbooks.com

Alan Thwaites 2008

All rights reserved. No part of this publication may be reproducedor transmitted in any form or by any means, electronic or

mechanical, including photocopying, recording, or any informationstorage or retrieval system, without prior permission in writing fromthe publishers.

Alan Thwaites has asserted his right under the Copyright, Designsand Patents Act, 1988, to be identified as Author of this work.

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the BritishLibrary.

ISBN: (paperback) 978 18470 6381 6Library of Congress Cataloging-in-Publication DataA catalog record for this book is available from the Library of Congress.

Designed and typeset by Ben Cracknell Studios |www.benstudios.co.uk

Printed and bound in Great Britain by Cromwell Press,Wiltshire
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ACKNOWLEDGMENTS ix

INTRODUCTION xi

S E C T I O N 1 Short number activities and gamesADD AND TAKE 2

ODD AND EVEN 3

MATCHING PAIRS 4

NOUGHTS AND CROSSES 1: FOUR RULES 5

TABLES 1: SPEED 6

ISLANDS 8

LARGEST AND SMALLEST 9

CIRCLE TIME 10FIRST TO THE FACT 11

ROUND THE WORLD 12

MAKE 50! 13

STEP BY STEP 15

LETS BE POSITIVE . . . OR NEGATIVE 17

TABLES 2: BINGO 18

HIGHER OR LOWER 19

HANGMAN 20

GIVE ME THE FRACTION 21

SEQUENTIAL PATTERNS 22

WHATS MY NUMBER? 23

BUZZ FIZZ 24

MATHS CONSEQUENCES 25

THE DIVIDE SLIDE 27

IN YOUR PRIME 29

C O N T E N T S

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WHATS THE HIGHEST? 30

DOUBLES AND QUADS 32

FRACTION DOMINOES 33

WHATS MY NAME? 34

REMEMBER ME 35

HOW MANY WAYS? 36

SORTED FOR NUMBER 38

GET THE WORD 39

FIRST TO TEN 40

NOUGHTS AND CROSSES 2: COORDINATES 42

HAPPY FAMILIES 43

CRACK THE CODE 44

BUS STOP 45

TIDDLYWINKS 47

WINNING COUNTERS 48

GONE FISHING 49

PATHWAYS 51

DIVIDE AND RULE 52

COMPUTER CALCULATOR 53

GET COORDINATED 54

SPOTS AND NUMBERS 55

THE SIMPLE CARD GAME 56

PE MATHS 57

MYSTERY SUMS 58

KEEP IT ON YOUR HAT 59

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S E C T I O N 2 Investigations and longer activitiesSORTED FOR COLOURS 62

NUMBERS SHAPING UP 63

TEA TIME 64

DOUBLE YOUR MONEY 65

TABLES 3: READY RECKONER 66

TABLES 4: SQUARE PUZZLES 68

MAGIC SQUARES 69

RATIO AND PROPORTION 70

KNOW YOUR ROOTS 72

CROSS-NUMBER PUZZLES 73

HUNT THE NUMBER 75

MAIL ORDER SHOPPING 76

TABLES 5: GRAPHS 77

TRIANGLE, SQUARE, CUBE 79

THE LITTLE BOOK OF NUMBERS 80

TABLES 6: FIND THE PATTERN 82

PROBABILITY: DICE 84

PROBABILITY: CARDS 86

LETTERS AND WORDS: THE MEAN, MODE AND MEDIAN 88

S E C T I O N 3 Measures and timeMORE OR LESS CENTIMETRES 92

WHATS THE TIME, MR WOLF? 93

A NEW ANGLE 94

PLAYGROUND MEASURES 95

TWICE AS SHARP: BISECTING ANGLES 96

CUBES IN A BOX 97

MINUTE WALK 98

PROBLEM MEASURES 99

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TV TIMES 100

WHAT IS A CUPFUL? 101

TIMETABLES 102

PROTRACTED DESIGNS 103

HOW HIGH IS A FOOT? 104

GUESS 250 106

THE THOUSAND TO ONE GAME 107

CALENDAR OF CALENDARS 108

ANALOGUE V DIGITAL 109

S E C T I O N 4 Shape, space and designMR SQUARE AND MRS CIRCLE 112

VENN SHAPES 113

FOLLOW MY SHAPE 114

KIMS SHAPE GAME 115

COMPLETE THE CIRCLE 116

CIRCLES TAKING SHAPES 117

DESIGNER LINE 119

SHAPES ON PARALLEL LINES 121

SHAPE UP! 122THE GREAT QUADRILATERAL INVESTIGATION 123

TETRAHEDRON 124

AREA V PERIMETER 126

LEAFY AREA 127

TRIANGLES FROM COMPASSES 128

STRETCHING AND ENLARGING 130

SIMPLY TESSELLATION 131

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Many thanks to Judith Thwaites for her patience, ideas,

encouragement and proofreading.The ideas in this book have been collected and used

over a number of years, but many have been refreshedand tested further with the enthusiastic help and supportof staff and pupils at Sandown School, Hastings.

ix

A C K N O W L E D G E M E N T S


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The aim of this book is to provide a resource for teachers

and support staff which will supplement and enhance theprimary mathematics syllabus. It is hoped that users willbe able to select activities which will fit alongside theirscheduled syllabus as well as use some of the ideas asongoing consolidation of previously covered areas.

Essentially, all the ideas have been used successfullyin the primary classroom situation. There is an elementof friendly competition in many, most encouragecooperation in pairs or groups and all are intended to beenjoyable. It is hoped that users will find among theseideas, many repeatable favourites of both the childrenand themselves.

MATHS COVERAGE

I have tried to include as wide a range from the commonprimary mathematics syllabus as possible but there is aweighting towards concepts of number. Confidence inthe way numbers are used and work together breedswillingness and enthusiasm to investigate and createfurther. If the idea title does not give a clue to the areacovered then there is a brief reference at the start of eachentry.

DURATION

Almost half the ideas are suited to short sessions of activity, perhaps at the beginning or end of a lesson.However, they could be combined to provide a circus of activities over a longer period of time. Many can beeasily adapted for a longer session, if appropriate, andany short game can be played a number of times.

GROUP SIZE

Recommendations for group sizes are given for each ideabut it will be seen that many suggest, simply, any. Someactivities will lend themselves more to a smaller groupbut this does not mean they cannot be adapted to amuch larger number or even a whole class.Whereas itcould be said that any idea will work better with adult

xi

I N T R O D U C T I O N


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xii

supervision, very many of these activities can be largelyself-sufficient after initial guidance.

DIFFERENTIATION

The great majority of the activities are adaptable withinthe primary age and ability range.Where this is unlikelyto be possible, a recommendation towards a broad agegroup is given. Brief notes on differentiation possibilitiesare included.

RESOURCES

No elaborate resources are required for any of the ideas.

Any equipment needed is likely to be found in theprimary classroom. Some ideas require preparation butthis involves very little time and effort and, onceprepared, the materials can be used repeatedly. Most of the activities require little or no preparation at all.


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1

S E C T I O N

Short number activities andgames

Ideas 148 are ideal for lesson starters or early finishers.They can also be used within a circus of activities for a longer period. All should be used in the context of enjoyment and fun. Many of the games could be

particularly suitable for older children to play with younger ones, rather as paired reading operates.


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I D E A

A D D A N D T A K E

2

Remove the court cards from a pack of playing cardsand shuffle the remaining cards.Divide the pack into two reasonably equal piles, facedown, and explain that as soon as the top two cardsare turned the numbers shown must be added and,also, the difference between them calculated asquickly as possible. Practise a few turns todemonstrate.Answers can be recorded on paper or a whiteboardand solutions then revealed after each one, or after aseries if used as a quiz.This also works well in a group as a friendly knock-

out game where the answers are called as soon as theyare calculated. Once a child has answered, she/hemust not call another answer until everyone else hasachieved one. In the interests of maintaining self-esteem, keep the pressure to a minimum and alwaysinclude a second, third or fourth round whereindividual members can challenge themselves toimprove their own response time.

DIFFERENTIATION

Younger or lower ability children could concentrateon either just adding or just taking away; the highervalue cards should be removed along with the courtcards.Use multiplication and division of the numbersinstead of addition and subtraction, remembering thatsome pairs of numbers will have remainders whendivided.Use all four rules together.Try an add/take variation where the two numbers arefirst added together and then subtracted from 20. Inthis case the only number required to be called orrecorded is the final solution.

K E Y A R E A

Addition andsubtraction

R E S O U R C E S

Pack of playingcardsWhiteboards andpens (optional)

G R O U P S I Z E

Partners, largergroups or wholeclass

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Write a range of numbers some odd, some even on about 30 blank cards and shuffle the cards.Partner A times partner B as she/he sorts the cardsinto separate piles of even and odd numbers.Once the piles are checked, the cards are shuffled andthe partners swap roles.See who wins after two or three turns each.

DIFFERENTIATION

For younger children, spots arranged in groups of twoor three can be used on fewer cards.The numbers can be chosen depending on the ageand ability of the pairs, i.e. single digit to six digitsand decimal numbers. Remember to use tricky

numbers, such as 33,332 or 44.3, and use 0 on theend of some even numbers., e.g. 530, 53.0.

I D E A

O D D A N D E V E N

3

2

K E Y A R E A

Odd and evennumbers

R E S O U R C E S

Blank cardsStopwatch ortimer

G R O U P S I Z E

Pairs


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I D E A

M A T C H I N G P A I R S

4

3 Make a set of about 15 pairs of cards by writing

matching pairs on them, e.g. 16 and 2 8 or 50 and25 + 25. The matching questions and answers willdepend on the ability of the players and the functionto be stressed.Shuffle the cards and lay them out face down inuniform rows. The players then take turns to try toturn over two matching cards.If unsuccessful, the pair of cards is turned back in theoriginal positions, with each player trying tomemorize where previously revealed cards are.If successful, the player keeps the matching pair andhas a further go.When all cards are matched the players count theircards to see who has won.

FURTHER THEMES FOR THE SAME GAME

Fractions make a set of cards with equivalentfractions to match, extending to decimal fractionsand percentages.Vocabulary make a set of matches with the signspaired with the associated words, e.g. + and total.Older children can use the full range of signs to

include: , (n, n), , 2, .Measures use equivalent measurements of varyingunits, e.g. 1 1 2 metres and 1 metre 50cm or 3.4kgand 3kg 400g.Shape matching cards have drawn 2D and/or 3Dshapes paired with their names.

VARIATION

All cards are revealed at the start and players are timedin turn to match them.

DIFFERENTIATION

The chances of turning over a successful pair areincreased if more than one way of matching is used,e.g. 30 and 2 15 as well as 30 and 38 8.

K E Y A R E A

Four rulesR E S O U R C E S

Blank numbercards

G R O U P S I Z E

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I D E A

N O U G H T S A N D C R O S S E S 1 :

F O U R

R U L E S

5

4Set up a 3 3 noughts and crosses grid. Place anumber in each box, choosing from 012 if notincluding multiplication, 036 if multiplying isallowed. Chosen numbers can be repeated if wished.Partners decide who is to be O and who is X andthen take turns to throw the dice. If the spots throwncalculate to a number written on the grid (seeDifferentiation below) the appropriate O or X isentered over it. A row of noughts or crosses wins thegame.Players take turns to start in subsequent games andkeep a record of wins.Discuss the probability of certain numbers comingup, e.g. 0 will result from a subtraction for any double

and, if adding, there are more ways of making 6, 7 or8 with two dice than of making 25 or 912.

DIFFERENTIATION

If dice are to be added only, the numbers in the gridwill have to be between 2 and 12 inclusive.For add and take possibilities, use 012, rememberingthere is only one way to make 11 and 12.

For all four rules use 012 plus 15, 16, 18, 20, 24, 25,30 and 36, remembering again that the highernumbers have fewer chances of turning up.For tables practice, this game can be used withmultiplication only. In this case the numbers possibleto use would be: 16 plus 8, 9, 10, 12, 15, 16, 18, 20,24, 25, 30 and 36.

K E Y A R E A

Fourrules/probability

R E S O U R C E S

Two dice perpairPencils and paper

G R O U P S I Z E

Pairs


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I D E A

T A B L E S 1 :

S P E E D

6

5 Children write, large and clearly on every third line of a sheet of lined file paper, a chosen times table,leaving out the final answer, thus:

0 3 =1 3 =2 3 =to 10 3 = or to 12 3 if the children areaccustomed to that.

Cut small squares of card which will fit comfortablyat the end of each number sentence and the childrenthen write the answers to the table on the cardsquares.

Lay out the prepared card squares randomly, eitherface up or face down depending on the degree of difficulty sought.Set a timer and get the children to place the cardanswer squares in the correct places as quickly aspossible.Subsequent turns can be used for the children to beattheir own times.

EXTENSION

Prepare the tables sheet in a random order, i.e.4 3 =8 3 =6 3 = (and so on)

Practise the inverse of any table by preparing thesheet with the answers and make the cards 110 (or112). It would be advisable in this case to write thenumber sentences in random order to avoid the childsimply placing the numbers in order.

18 3 =12 3 =24 3 = and so on.

K E Y A R E A

Times tablesR E S O U R C E S

A4 lined filepaperCardStopwatch ortimer

G R O U P S I Z E

Any


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7

Try the 15s, 25s, or any others for those who enjoy achallenge.

DIFFERENTIATION

Choose appropriate tables to work with depending onage, ability or class focus.


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I D E A

I S L A N D S

8

6This game is ideally played at the end of a floor work PElesson as part of the clearing away process.

Spread PE mats around the floor with just enoughspace between them for the children to jump fromone to another.Have the children island hop from one mat toanother, no stopping allowed.

Explain that you will call a number (the simplestversion) or a sum and that number or answer must bemade up by the corresponding amount of childrensitting on each island (mat). Any islands with thewrong number either too few or too many are out.Any children who are out can put away the outermats as they go, ensuring that there are enough matsleft for the rest of the players to use.

DIFFERENTIATION

Vary the degree of difficulty with the numbers orquestions called.

The basic game is to call the actual number. Themore advanced version asks the children to calculatesimple sums using all four rules.

For the more able, try division and subtraction usinghigher numbers, 2 squared, 3 squared, square rootsand the first five prime numbers.

K E Y A R E A

NumberR E S O U R C E S

PE matsG R O U P S I Z E

Whole class orlarge group


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I D E A

L A R G E S T A N D S M A L L E S T

9

Shuffle a set of 09 cards and place them face down.Decide how many cards are to be turned two willbe the easiest.The player must place the cards in order to make: thelargest and smallest possible numbers; the largest andsmallest even numbers; and the largest and smallestodd numbers. If played in pairs, the partner helps orchecks.If only two cards are to be used, do not include 0 andeither ensure that there is one odd and one even or,better still, do not call for an odd or even category.If three or more cards are used and all even or all oddcards turn up, swap a card.

DIFFERENTIATION

Adjust the number of cards to suit age and ability. Thisactivity can also be used for decimal numbers. Make oneextra card with a decimal point.

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K E Y A R E A


09 numbercards

G R O U P S I Z E

Individually orin pairs withingroups or wholeclass


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I D E A

C I R C L E T I M E

10

8 The object of this game is to score points by being thefirst to complete a circuit of the group circle.Have the groups sitting in large, equal-sized circles.Allocate a number to each child in the group. Thenumbers should correspond to answers to sums

which will be called out.They do not have to beconsecutive but this is advisable until everyonebecomes accustomed to the game.

Jot down the numbers allocated so that you can keeptrack of the calls, giving everyone a turn.Let us say, for example, you have allocated thenumbers 110. Call How many 3s in 15? Childnumber 5 from each group should immediately jumpup and run right round the outside of the circle andsit back down in their original place.The first child to sit back down scores a point for thatgroup.Continue calling sums for the rest of the numbers.When all the numbers have had a turn, tot up thepoints to find the overall winning group.

DIFFERENTIATION

There is no limit to the possibilities for complexquestioning. If you make a list of questions, say, on thetables you are learning, or equal/decimal fractions,simply allocate the answers at random around the group.

With very small children, use a large foam dice in thecentre of a group of six. Children count the spots to cue

their circle run. In this case, decide the number of dicethrows to determine the end of the game as somenumbers will, of course, arise more than once.

K E Y A R E A


NoneG R O U P S I Z E

Any number of children ingroups of about812


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I D E A

F I R S T T O T H

E F A C T

11

This is aimed at upper KS2 children. Reduce thenumber range for younger or less able children.

Distribute blank number cards to the children in thegroup or class, giving smaller groups three or fourcards each, a whole class about two per child. These

cards can be handmade or the wipe-clean variety.They can, of course, be reused any number of timesfor this or any other activity.Have the children write large, clear numbers between2 and 50 on the cards.Try to obtain numbersthroughout the range, but it does not matter if someare repeated.The cards are placed face down on the table with noone knowing where any particular number is.Make a card for each of the four function signs.Choose a child to turn over a card, lets say it was 14,and another child to turn a second, say 26.Somebody else picks out one of the function signs,again at random. If it is the sign then the sumformed is 14 26.The first person to provide the correct answer is thewinner.You can make any rules to determine winners, suchas a running total to produce an overall winner after agiven number of sums or amount of time.Clearly, some of the sums produced can be very easyand some quite difficult. It is worth having acalculator handy to double check answers before they

are produced by the first child.

DIFFERENTIATION

You can make the calculations easier or harder byvarying the numbers written on the cards or removingthe multiplication and/or division signs. Include decimalnumbers for a further challenge.

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K E Y A R E A


Blank numbercardsScrap paper forjottings

G R O U P S I Z E

Small groups orwhole class


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I D E A

R O U N D T H E W O R L D

12

10This game is an old favourite. It can be used to reinforce

any aspect being covered at the time, from times tablesto decimals, fractions and percentages. The object of thegame is to be the first of a pair to call out the correctanswer to a question. For this example tables are used asthe theme.

Choose a child to start who stands behind a seatedchallenger.

Ask a question of the pair, say, 5

4 .The rest of the group or class must remain silent butthe first of the chosen pair to call out the correctanswer wins. If a wrong answer is given, second triesshould not be allowed and the other child of the pairhas an opportunity to calculate with less pressure. If both give a wrong answer, none at all or both call atthe same time then a new question should be givenuntil a clear winner results.The winner moves to the next seated child (orcountry) and a new challenge begins. If the winneris the seated child then the seat is taken by the loseras the journey continues around the group or class.The overall winner is the child who has movedsuccessfully around most countries.To give everytraveller a fair chance, once everyone in the group orclass has had a challenge, keep going until the lasttraveller loses a question.

DIFFERENTIATION

Vary the questions asked to suit age and ability.

K E Y A R E A



Any


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14

When a zero calculation is used, i.e. when a double isused as a subtraction, the throw must still be countedtowards the final number of throws.Most 50s are reached in about 1012 throws but anagreement could be made for a player to pass the diceover to a partner if the 50 has not been reached bythe twentieth throw (or another agreed number).If the second player exceeds the first players numberof throws, she/he should be allowed to continue andmake the target.Play the best of three games if time permits.

DIFFERENTIATION

To simplify the game, thry any combination of: a) useonly adding and subtracting; b) remove the 6 rule; c)reduce the 50 target number; d) count the number of throws to pass the target number rather than reach itexactly.To make the game much harder, use three dice with atarget of 100 or 150.This gives more complexpossibilities for using mixed operations in any onethrow.


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I D E A

S T E P B Y S T E P

15

This develops the concept of multi-step operations.

Use about 20 blank cards per group, and write anumber on each within a chosen range to suit theability of the players.On each of another 20 cards write the function

symbol: +, ,

, . Have six cards of each symbol butonly two cards for .Shuffle the number cards and place them in a pileface down. Do the same with the symbol cards.Children can take turns to work through a sum orcooperate on the calculations.They must record thesum in all its stages as they go. The number of stepsshould be decided at the outset.Turn the top number card, lets say it is 23, then asymbol card, say +, and a second number, perhaps 9.The calculation is then made, i.e. 23 + 9 = 32.This answer is then used as the first part of the nextstep, made by drawing another symbol card followedby another number. For this example: the 32 with and 15.This would produce 480. The 480 would thenbe used for a further step if desired.If the division symbol is revealed and the numberspicked are not divisible, another function is chosen.The division is calculated as soon as two numbersappear which are divisible.The calculator can be used either for simplecalculator practice or to check paper-and-pencilcalculations.

When the final calculation is made, set the challengeto undo the whole process by inverse operations andreturn to the first card chosen.

DIFFERENTIATION

Simplify the calculations by any combination of: a)restrict the range of numbers on the cards; b) restrict

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K E Y A R E A

Multi-stepquestions andinverseoperations

R E S O U R C E S

Blank numbercardsPencils and paperCalculators

G R O U P S I Z E

Pairs or smallgroups


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the functions to simply adding or adding andsubtracting; c) limit the number of steps to two.If anyone enjoys a challenge, include some decimalnumbers or include extra division symbol cards toresult in decimal answers to be carried forward.

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I D E A

L E T S B E P O S I T I V E

. . .

O R N E G A T I V E

17

This game is for upper KS2 or those familiar with theconcept of positive and negative numbers. Make two setsof number cards. Set one is numbered 1 to 9, each of the nine to be written twice, giving 18 cards in all. Settwo has nine cards numbered 1 to 9 and another ninecards numbered 1 to 9, giving nine positive and ninenegative numbers.These will be necessary to allow thepossibility of adding either a positive or a negativenumber to a negative number.

Shuffle both sets of cards and place them face downin separate piles.Turn the top card of Set one, lets say it is 2.Explain that the top card of Set two must be added tothis number and turn that card lets say that it is 5.The children write the answer on their whiteboards,in this case 7.Repeat the card-turning at whatever speed isappropriate for the group and include any competitiveelement you wish.

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K E Y A R E A

Positive andnegativenumbers

R E S O U R C E S

Blank numbercardsWhiteboards andpens

G R O U P S I Z E

Best in smallgroups but it canwork with thefull class


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I D E A

T A B L E S 2 :

B I N G O

18

14 Choose one of the tables, say the fours.The children draw a 3 3 grid and in each box writetheir own choices of a mixture of any of the multiples,i.e. in this example 0, 4, 8, 12, and so on, and thetimes number, i.e. any from 010 or 12.When everyone has a completed grid, call randomquestions in the four times table both forwards andinverse giving an appropriate time for calculationand remembering to keep a record of the questionscalled.The players use counters to cover squares whichcorrespond to the answers or, alternatively, scorethrough with a single line so as not to obscure thenumber entered.

In true Bingo style, the player who first fills her/hiscard calls out, and the numbers are checked to ensureagainst mistakes.

VARIATION

With slightly larger squares on the 3 3 grid, the playerswrite the questions in the boxes, e.g. 3 4, 8 4, 40 4,and so on.The caller calls random multiples and

dividends.NB Whichever way the game is played there will be

some numbers which can be used either as a multiple ora dividend; in this example, 0, 4, 8 and 12. This is onlysignificant in the lower order tables and can beovercome, if thought necessary, by ruling that only oneor two of such numbers are permissible.

DIFFERENTIATIONVary the times table chosen.

K E Y A R E A


Paper and pencilsCounters(optional)

G R O U P S I Z E

Any


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I D E A

H

I G H E R O R L O W E R

19

Shuffle the cards.

The players take turns to hold the cards and revealone at a time.Player A turns the top card and player B decideswhether the next will be higher or lower, given that 7is in the middle, the ace is low and jack, queen, kingascend in that order.If player B is correct she/he keeps the two cards. If theguess is incorrect, the cards go to the dealer, playerA. If the cards are the same value they are notcounted by either player.The game continues in this way until all the cards areused.Both players count and record the number of cardsthey win.The cards are then shuffled and the players swap

roles.The overall winner is the player with the highestcombined total over the two games.

VARIATION

Include the possibility of guessing that the pair of cardsdrawn will be the same. If this is the rule then the dealerkeeps any such pair if a guess of simply higher or lower

is given. If a player guesses correctly that any two cardsare the same, however, she/he keeps them and, inaddition, captures four further cards from her/hisopponent.

DIFFERENTIATION

Remove the court cards and the tens for an easierversion.

15

K E Y A R E A

ProbabilityR E S O U R C E S

Pack of cardsG R O U P S I Z E

Pairs


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I D E A

H A N G M A N

20

16 This is just the same as the spelling game but withnumbers.A child calculates a secret number sentence anddraws boxes in place of digits, leaving gaps wherever afunction sign should be.The equals sign is put in at

the start as that would be an obvious call for theguessers.Thus 23 + 94 = 117 would be written:

=Everyone else guesses numbers or signs which mightbe in the equation.Wrong guesses are recorded asreminders, and a part of the traditional gallows isdrawn. Correct guesses are written into the equation

wherever they occur.The object is, of course, to encourage logical thoughtrather than random guesses.The first to guess the whole equation correctly setsthe next puzzle.

DIFFERENTIATION

Adjust the possibilities to the age and ability of the

group. Naturally, the simplest would be to use single-digit numbers and only addition.There is no limit at the upper ability level, especiallyif calculators are used. Decimal points can beincluded (in a box). Use more than one function,possibly on both sides of the equation andincorporate the use of BODMAS (the order of calculation, being Brackets Off Division Multiplication Addition Subtraction).

K E Y A R E A


Pencils and paperor whiteboards,Calculators(optional)

G R O U P S I Z E

Any


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I D E A

G I V E M E T H E F R A C T I O N

21

Make appropriate fraction cards for the number of Multilink cubes used, say 12. In this example, thefraction cards would be: any number of twelfths,sixths, quarters, thirds, halves. Any means of makingone whole, e.g. 6 6, can also be included.Place the [12] cubes in a fixed line.Shuffle the fraction cards and place them face down.Players take turns to turn a card and take the correctnumber of cubes for that fraction, e.g. the 3 4 cardshould render nine cubes separated.

DIFFERENTIATION

The simplest way to play is using varying numbers of bricks and the child finds just half or quarter.

Use the single numerator for intermediate difficulty.For the ultimate challenge, include decimal fractionsand percentages with larger multiples of cubes.

17

K E Y A R E A

FractionsR E S O U R C E S

Multilink cubesor similarFraction cards

G R O U P S I Z E

Any


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I D E A

S E Q U E N T I A L P A T T E R N S

22

This is an early sequencing activity for KS1.

Draw a line of 12 blank squares, either adjoining in astraight line or curved like a snake.The squaresshould match the size of cubes to be used. Photocopyfor current and future use.Explain the nature of sequential, repeating patterns.The children make a row of 12 coloured cubes in asequential pattern using a specified number of different colours, say, three.The pattern produced must then be recorded exactlyonto the photocopied sheet.Keep the resources available for use in a range of choosing activities.

DIFFERENTIATION

Vary the number of colours used, keeping to factorsof 12.Extend the line to 18 squares.

K E Y A R E A

SequencesR E S O U R C E S

Assortedcoloured cubesPhotocopiedgrids (seepreparationbelow)Colouringpencils

G R O U P S I Z E

Any

18


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I D E A

W H A T S M Y N U

M B E R ?

23

The object of this game is to identify a secret number

within ten questions.A chosen person thinks of a number.This can berestricted to a two-digit number or have norestrictions placed on it at all. Decimal numbers,however, can be somewhat frustrating unless there arelimits placed on the overall number of digits.Guessers ask questions to which the only answers can

be either Yes or No.Wild guesses should bediscouraged in favour of questions which seek logicalinformation and continually narrow down thepossibilities.Typical questions would be: Is it odd or even?, Is ita three-digit number?, Is it divisible by 5?, Is itbelow 50?

DIFFERENTIATION

Vary the size of the numbers used.

19

K E Y A R E A



Any


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I D E A

B U Z Z F I Z Z

24

20The object of this game is simply to count consecutivelyfrom one to however many you would like to reach.Thedifference is using words instead of certain numbers, so:

If the number is divisible by 2 then buzz should besaid.If the number is divisible by 3 then fizz should becalled.

If the number is divisible by both 2 and 3 then buzzfizz is the response.

The first 12 numbers would therefore sound, one, buzz,fizz, buzz, five, buzz fizz, seven, buzz, fizz, buzz, eleven,buzz fizz.

Each member of the group gives the next number, oralternative expression, either in regular turn orrandomly around the room or group. If an incorrectresponse is given, the next person must attempt itrather than have it corrected. A class of 30 childrennew to this game, therefore, may only reach about 18(buzz fizz) by the time they have all had a go, butregular playing improves their ability very quickly .A decision can be made, depending on the characterand experience of the group, whether or not toimpose penalties for incorrect responses. A typical setof penalties is to stand after a first fault, hold an earon the second, hold the nose on the third, and so on.These forfeits are removed by subsequent correctresponses.

DIFFERENTIATION

Begin with just buzz for even numbers.Insert fizz for the threes when the three times tableis more familiar.Introduce plop for fives once the game is familiar.For a real challenge use an additional hooray forsquare numbers and eek for prime numbers.

K E Y A R E A



56 to wholeclass


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I D E A

M A T H S C O N S E Q U E N C E S

25

This is based on the crazy sentence game.

Explain that things will be written at the top of thestrip of paper in a particular order and passed onround the group. Each time something is written thepaper has to be folded back so that it is not seen bythe next person. The folds always have to be just once

backwards and the new number or symbol must bewritten against the fold, at the top.Each member of the group has a strip of paper andsecretly writes a two-digit number at the top.She/he folds the paper to the back, concealing onlythe number and passes it to the group member toher/his left.Each group member then draws a function sign, +, , , or , at the top of the new strip of paper where ithas been folded.This is then folded over again andpassed to the left.The third person writes a single-digit number at thetop, folds it in the same way and passes it on.If there are five people in the group, the fourth playeradds a function sign and the fifth a two-digit number.For a group of seven, the sixth player adds a sign andthe seventh a single-digit number.When everyone in the group has written somethingon every piece of paper then it is time to begin thecalculations. Whatever strip each member ends upwith, that is the one she/he must work out.Decide whether the rules of BODMAS (see Idea 16)should be followed or calculations made in the order

of writing or perhaps both. Also make a decision onthe use of calculators.Allow individuals to help each other work out theproblems.

21

K E Y A R E A


Paper and pencilsCalculators(optional)

G R O U P S I Z E

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26

DIFFERENTIATION

Beginners work in groups of three and use onlyaddition and subtraction.To avoid possible negative number results allow theminus sign only as the first function, i.e. the initialtwo-digit number minus the single digit.To avoid decimals or fractions do not includedivision.To ensure decimals or fractions insist on division.Include the possibility of decimal numbers but onlyto one decimal place.


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I D E A

T H E D I V I D E S L I D E

27

This is an easy-to-make aid for multiplication anddivision by 10, 100 and 1,000.

Each child will require up to ten strips of 2cmsquared paper, each about 20cm long by 2cm wideand put aside.Cut one strip the same length but 6cm wide.

Fold the 6cm-wide strip in half, lengthwise. Thisshould produce a crease through the middle row of squares.Find the middle square of the folded row.Carefully cut two slits, a little less than 1cm apart,from the folded edge into the middle square, cuttingto the printed horizontal lines.This will give a bar justunder 1cm wide and 2cm long in the middle of thestrip.Open out the 6cm strip and mark a decimal pointclearly on the bar.For demonstration purposes, have the children write anumber, say 360,000, on one of the 2cm strips.Theymust begin the number in the first square at the leftand ensure that each digit is written centrally in itsown square, allowing at least 1cm between digits.Thread this strip through the slits under the bar sothat it can be slid to and fro giving different valuesdepending on where the number is divided by thedecimal point.Give a few examples, such as, Make the number read360, pointing out that any number of zeros can beincluded on the end after the decimal point. Divide

this by 10, which means move the digits one place tothe right. If the children do this correctly they will seeclearly that they end up with 36 or 36.0000. Multiplythis 36 by 100, which means moving the digits twoplaces to the left.The children should see that theanswer is 3,600.00.

22

K E Y A R E A

DecimalsR E S O U R C E S

2cm squaredpaperScissors

G R O U P S I Z E

Any


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When the children are confident with the process, setquestions which they can check by using the blankstrip.

T I P

Pre-write strings of digits for multiplication and divisionexercises and photocopy. Cut these into strips asnecessary.

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I D E A

I N Y O U R

P R I M E

29

This is a game for older and more able children who arefamiliar with at least the lower range of prime numbers.Tell the children that any throw of three dice can resultin a prime number, when any of the four rules areapplied. Give a few examples to show how this works, i.e.a throw of 2, 4 and 5 could be simply 2 + 4 + 5 = 11. Athrow of 1, 4 and 5, however, is more tricky but it can bedone either with 5 (4 1) = 2 or (5 4) + 1 = 2.

There are a number of ways to play the game:

Option 1Players take turns to throw the dice and calculatetheir own throw.A minute timer is set as soon as the dice are thrown.Each player scores points equal to the prime numbercorrectly calculated. The higher value prime numbersare less easily achieved.If an answer is not reached within the time limit or isincorrect then no points are scored.

Option 2Players take turns to throw the dice but all then,individually, calculate a prime number.The timing

and scoring is the same as option 1.Option 3 (Better played simply for the satisfaction of obtaining correct answers rather than in competition)

Play as a class with nominated child/ren throwing thedice.Time the calculations as before, with the childrencompleting them on whiteboards.

VARIATION

Try the same game but find square or cube numbers.

23

K E Y A R E A

Prime numbersR E S O U R C E S

Three diceOne timer pergroup

G R O U P S I Z E

Any


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I D E A

W H A T S T H E H I G H E S T ?

30

24 Demonstrate how a throw of three dice can be multipliedand/or added to produce the highest possible number,e.g. a throw of 2, 4 and 5 could be multiplied together inany order to make 40. It becomes much moreinteresting, however, when a 1 is included in the throw. If the numbers are simply multiplied together then it willnot produce the highest possible score. Using theexample of a 1, 4, 5 throw, these are the possibilities:

1 4 5 = 20(1 + 5) 4 = 24(1 + 4) 5 = 25

The trick is adding the 1 to the smaller of the other twoand multiplying by the larger.

There are a number of ways to play the game:

Option 1Players take turns to throw the dice and calculatetheir own throw.A minute timer is set as soon as the dice are thrown.Each player scores points equal to the numbercorrectly calculated.If an answer is not reached within the time limit or isincorrect then no points are scored.

Option 2Players take turns to throw the dice but all then,individually, calculate the highest possible number.The timing and scoring is the same as option 1.

Option 3 (Better played simply for the satisfaction of obtaining correct answers rather than in competition)

Play as a class with nominated child/ren throwing thedice.Time the calculations as before, with childrencompleting them on whiteboards.

K E Y A R E A


Three diceOne timer pergroup

G R O U P S I Z E

Any


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31

VARIATION

Play the same game but the object is to find the smallestpossible number, using any of the four rules. It can beused to reinforce negative numbers, e.g. 1 4 5 = 8but it is perhaps more challenging to make the object toachieve 0 or to get as near as possible to it. In thisexample 0 can be reached with 5 4 1. Using theexample of a 6, 3, 2 throw and the range of four rules,this could be: 6 (3 2) = 0 or 6 3 2 = 0.Thewinners, if scores are kept, would be those with thelowest number of points.

DIFFERENTIATION

For easier versions:

use just two diceplay using simple addition and subtraction.


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I D E A

D O U

B L E S A N D Q U A D S

32

25Try these quick-fire, real-life questions for consolidatingdoubling and times 4 (double and double again).Youmay wish to prepare a set of questions but it is quite easyto be spontaneous.

Remind the children that a short-cut to multiplicationby 4 is double and double again. Ask a number of questions requiring doubling or quadrupling to find theanswer, e.g. How many arms on 12 people?, Howmany legs on nine cows?

Suggestions for doubles:

Wings on penguins (or other birds), aeroplanesEyes on people, snakes, birds, horsesEars on rabbits, giantsHands/feet on people

Handles on doorsGoalposts on football pitches.

Suggestions for quadruples:

Legs on elephants (or other four-legged animals),chairs, tablesWheels on carsProngs on forks

Corners/sides on squares/rectangles/parallelograms.There are a number of ways to operate this activity, suchas:

Using whiteboards showing answers on the givensignalAs a mental arithmetic testAs a warm-up lesson starterTo decide an order of leaving, i.e. form a line forleaving at the end of a session in the order of whoanswers correctly.

DIFFERENTIATION

Vary the numbers to be doubled and quadrupledaccording to ability.

K E Y A R E A

MultiplicationR E S O U R C E S

Whiteboards(optional)

G R O U P S I Z E

Any


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I D E A

W

H A T S M Y N A M E ?

34

27The object of this game is to say the name of a numberfrom a given number of digits.

Use two sets of 09 number cards.Shuffle the cards and place them in a pile face down.Agree a number of cards to be turned, say, five. Thiscan change during the game if appropriate.The cards are turned, say, 7, 3, 0, 2, 7 and the player

names the number, seventy-three thousand andtwenty-seven. Discard a zero if it turns up first, ormake it the second digit.Success can be purely for personal satisfaction or ascoring system can be easily devised if players are inpairs and are well matched.

DIFFERENTIATION

Adjust to age and ability the number of cards turnedin any go.For an added element of difficulty, include a numberof decimal point cards, treating them as an extrawhen they turn up in the example above of a five-digit number, six cards would be turned if one was adecimal point. Discard any further decimal pointcards if one is already turned.

K E Y A R E A


09 numbercards

G R O U P S I Z E

Any


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I D E A

H O W

M A N Y

W A Y S ?

36

29Try this team quiz for KS2.

Set up the teams with one member nominated towrite down the answers.Explain that they should confer but without allowingother teams to overhear.The same question goes to all teams each time andwill take the form of a number.Once given the number, say 2, the team must write

down as many two words or two associations asthey can in a given amount of time. The length of time will vary depending on how many words arelikely to be derived from any given number.Examples of what a team might have for 2 are:double, twice, duet, duo, bicycle, biplane, binoculars,bicentenary, pair, scissors, trousers, shoes, spectacles,fortnight, weekend. Accept any reasonably logical linkwith the given number.Team points are scored for each acceptable answer.Other numbers particularly suitable for this game,with examples of responses are:

1 solo, single, first, monorail, unicycle, annual3 trio, third, treble, triple, triangle, triplets4 quads, any four-sided 2D shape, tetrahedron,

quadruped (or any four-legged animal)5 pentagon,The Pentagon, fingers of hand, toes

of foot, fifth, pentathlon, Guy Fawkes6 sixth, hexagon, half-a-dozen, honeycomb, dice,

cube7 seventh, 20p piece, 50p piece, heptagon, week,

September8 eighth, octagon, octogenarian, October,

Hanukkah, spider10 decimal, tenth, December, decagon, two

hands, two feet, decade, decathlon12 twelfth, dodecagon,Twelfth Night, dozen,

yearBonus points could be awarded for the first team tocome up with the number associated with a word

K E Y A R E A


Paper and pencilsG R O U P S I Z E

Teams of 25


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called, e.g. score (20); century (100); gross (144);weeks in a year/cards in a pack (52); football team(11), cats lives (9), dalmatians (101), millennium(1,000).

DIFFERENTIATION

Ensure that teams are evenly balanced for ability.

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S O R T E D F O R N U M B E R

38

30 Make a set of number cards appropriate to the age andability of the group and the area of number on whichyou want to focus. This example uses even numbers andmultiples of 5.

Make number cards as follows: four multiples of 5, ending in 5

two multiples of 5 ending in 0 three even numbers not ending in 0 two odd numbers not ending in 5.

Spread the prepared number cards randomly.Overlap two small PE hoops, one labelled evennumbers and the other labelled multiples of 5.Set the task to sort the number cards into the correcthoops, remembering that some of the cards (thoseending in 0) will need to go into the overlapped areaand some (the odd numbers not ending in 5) willneed to be placed outside the hoops.

DIFFERENTIATION

Vary the complexity of the categories.

K E Y A R E A

Venn diagramsR E S O U R C E S

Blank numbercardsSmall PE hoops

G R O U P S I Z E

24


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G E T T H E

W O R D

39

This game introduces a mildly competitive element intofour rules vocabulary.

Make a set of word cards for the vocabulary of thefour rules, i.e. plus, total, add, minus, difference between,take away, subtract, times, multiply, product,greater/more than, smaller/less than, how many . . . in . .., share, divide.

The vocabulary cards are shuffled and placed in apile, face down.Turn two number cards at random.When all group members are ready, the top card of the vocabulary pile is turned.The first player to calculate the resulting questioncorrectly wins and that player turns the nextvocabulary card.Keep going, using the same two numbers, until all thevocabulary cards have been turned.

For randomly selected numbers which do not divideexactly, decide if the winner is: the first to say cant orthe first to give a correct dividend, including a remainderin an acceptable form.

DIFFERENTIATION

Group similar ability children together and include onlythe appropriate vocabulary cards for the respectivegroups.

31

K E Y A R E A


09 cardsBlank cards

G R O U P S I Z E

24 of similarability


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I D E A

F I R S T T O T E N

40

32 This is a dice game which is enjoyed on many levels.Thesimple object is to achieve a count of 110 in consecutiveorder.Game 1 for the youngest players in a group withsupport for recording

At the start, make a list of the numbers 110 (or 16

if not using a second dice later).Use a single dice, preferably a large foam one.Players take turns to throw and the number cast isdeleted from the list when it appears for the firsttime. Repeated numbers are ignored.When the numbers 16 have been achieved,introduce a second dice, if appropriate, in order tocount the spots for 710. Either discard throws of 11and 12 or add them to the list at the start.

Game 2 intermediateAt the start, make a list of the numbers 110.Using two dice, players take turns to throw.Each throw of the dice can be added, subtracted,multiplied or divided in order to make one of thenumbers 110.

Numbers achieved must be deleted, reducing thepossibilities as the game progresses.Alternatively, it could be ruled that the numbers 110must be obtained in consecutive order, which takeslonger.To make the game competitive, play in pairs or teamsof two to find the quickest to reach all ten numbers.You will have to decide if quickest refers to thefewest throws or the quickest player or teamirrespective of the number of throws.

K E Y A R E A


DicePaper and pencilsor whiteboards

G R O U P S I Z E

Any


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41

Game 3 advancedSame basic rules as game 2 but with a menu of modifications from which to choose:

Use three dice, allowing a second function in thecalculations.Extend the required count from 110 to 120.The two functions cannot be the same in any giventhrow.

DIFFERENTIATION

Use the appropriate game, adapting as necessary.


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I D E A

N O U G H T S A N

D C R O S S E S 2 :

C O O R D I N A T E S

42

Draw a 3 3 noughts and crosses grid on thewhiteboard or flipchart.Starting from the origin 0, label the rows andcolumns 1, 2, 3.Choose two children as challengers one is O andthe other X.The challengers stand side by side in front of thegrid, unable to see it and facing the rest of the group.Decide which player goes first, say, X.X gives a pair of coordinates and the cross is placedin that square.The players then take turns to give a pair of coordinates for their respective symbol.They have tovisualize the grid as it fills up in order to make a line

and to prevent their opponent doing so.If a player chooses a square already filled then she/hemisses that turn.

DIFFERENTIATION

To make the game easier, label the x axis A, B, C and they axis 1, 2, 3. Accept only coordinates with letter first.

K E Y A R E A

CoordinatesR E S O U R C E S

Clearly visiblewhiteboard orflipchart

G R O U P S I Z E

Any

33


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This knock-out game for a lot of people is ideal as aparty game and also a good way to end a PE lesson. Itcan be played in a cleared area of the classroom but ahall is better.

Make up to eight bus stop signs giving simply the busnumber. Choose both odd and even numbers andnumbers which are multiples of tables selected for

practice.The example here will be answers to the fiveand four times tables, using the bus numbers: 16, 25,28, 32, 35, 36, 40, 55.Place the bus stops around the sides of the availablespace, preferably at eye level.Make a set of postcards which refer to the busnumbers you have used. For this example thepostcards could read: odd numbers; even numbers;even multiples of five; odd multiples of five;multiples of four.The group moves around in the available space untilthe signal is called, All aboard! or similar,whereupon everyone must stand still and listen to theinstructions. A card is chosen at random and readout. On picking out, say, odd numbers, the callerdecides whether to say odd numbers only arerunning or no odd numbers running today.Immediately, the players must go to an appropriatestop. Any player not at a bus stop after a given time isout. If odd numbers only are running is called in thisexample, then buses 25, 35 and 55 should be the onlynumbers with a queue. Anyone waiting at the othernumbers would be out.

A limit is placed on the number at the bus stopdepending on how many players are left in the gameat the time and how many different correct choicescan be made.As the number of players dwindles, remove busesfrom service until only one or two winners are left.Prizes are optional.

I D E A

B U

S S T O P

45

36

K E Y A R E A


Card signsBlank postcards

G R O U P S I Z E

Large


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DIFFERENTIATION

Choose appropriate numbers and options from thesimplest level of just odd or even numbers to quitecomplicated three-digit requirements.

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I D E A

T I D D L Y

W I N K S

47

A numerical interpretation of the traditional game, this isbest played on the floor.

Put down a small PE hoop or similar a marked areaapproximately 40cm across is required.Shuffle two or three sets of 09 cards and put themface down in the hoop/space, ensuring that they donot overlap and the spaces between them are verysmall.Players choose which colour they are to be and taketwo to five counters of that colour.The more thecounters the more difficult the mathematics.The first player uses one counter to flip the othersinto the hoop, one at a time, aiming to land each on acard. Misses cannot be retaken.Any card with a counter fully on it is revealed, andthe numbers tallied to give total points for that go.Numbers can be added or multiplied depending onthe ability of the players.The score is recorded and the second and subsequentplayers have their turns.The winner is the player with the highest score.

DIFFERENTIATION

Younger children could use a limited range of numbers, say, 14.For a more advanced game make cards with highernumbers, decimal numbers or calculations.

37

K E Y A R E A

Addition and/ormultiplication

R E S O U R C E S

Counters09 numbercardsSmall PE hoopsPaper and pencilsor whiteboardsand pensCalculators(optional)

G R O U P S I Z E

24


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This is a game to spice up mental maths. The object is tomake a path from either top to bottom or side to side of a 5 5 grid. The pathway cannot be diagonal.

Draw a 5 5 grid on squared paper.

Two players choose a colour each and decide whogoes first.The third member of the group poses questions frompublished mental maths practice materials.Players are asked questions in turn. If the answer iscorrect the player colours in any free square on thegrid. If incorrect, no square is coloured.The firstanswer only can be taken.Paths can be blocked which is, of course, part of thestrategy. Players can go round a block using adjacentsquares.

Note:This game can be played successfully in groups of five, i.e. two teams of two and a questionmaster.

DIFFERENTIATION

Select questions at the appropriate level.

I D E A

P A T H W A Y S

51

K E Y A R E A


Squared paperColouringpencilsMental mathsquestions

G R O U P S I Z E

Threes (rotatingwith twocompeting andthe third askingquestions) 40


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I D E A

D I V I D E A N D R U L E

52

41This game is for reluctant dividers in KS2.

Shuffle the cards and place them in a pile, face down.

The top two cards are turned to make a two-digitnumber. It can be a free choice of which cardrepresents tens and which the units but, oncedecided, the order cannot be changed.A dice is thrown and players must divide the two-digit number by the number shown as quickly aspossible, including any remainders (see below).The first correct answer scores a point.Play continues until all the cards have been used.

This game works well with showing answers onwhiteboards and entrusting players with their ownscoring.

DIFFERENTIATION

An easier version is to ignore the cards, throw a diceand if it is, say, a 3, call a multiple of 3 for thedivision sum to be written on a whiteboard.Decide how remainders are to be expressed. This isuseful for consolidating rounding if calculators areallowed.More confident players can be challenged with three-digit numbers.

K E Y A R E A

DivisionR E S O U R C E S

Two or three setsof 09 numbercardsConventionaldice

Jotting paper orwhiteboards

G R O U P S I Z E

Any, but thisworks well withteams of 2


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Familiarize the children with calculators on computers.Introduce the path on your computer for setting upits calculator.Allow time to experiment with it and gain familiarity,e.g. provide a range of questions on the computer tocalculate or allow the children to devise their own.Show some of the general functions of calculators,

such as repeat click on = to obtain a continuousfunction result.Visit websites which present work suitable forcalculator-assisted solutions.

I D E A

C O M P U

T E R C A L C U

L A T O R

53

K E Y A R E A


ComputerG R O U P S I Z E

Individual orpairs

42


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I D E A

G E T C O O R D I N A T E D

54

This is a fun way to consolidate coordinates in KS2.Theobject of this game is for players to simultaneously andcovertly draw the same shape from coordinates providedindependently.

Players draw x and y axes on squared paper andnumber them on the lines , 110 from the origin.

Players then take turns to give a pair of coordinateswhich every player must plot without the othersseeing.Plotted points should be joined each time a new pairis given. Players should give coordinates which do notinvolve this path crossing itself but nothing should besaid if anyone believes this to be the case.When every player has given a pair of coordinates, thelast pair is joined to the first to complete the shape.For small groups, each player could provide two pairsof coordinates.Players then reveal their completed shapes which are,hopefully, identical.

VARIATION

Players take turns secretly to draw a shape and then giveall of the coordinates for the other players to match.

DIFFERENTIATION

Confident players can try plotting shapes using all fourquadrants.

K E Y A R E A

CoordinatesR E S O U R C E S

Squared paperRulersPencils

G R O U P S I Z E

46

43


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Try this number recognition game with KS1 children.

Each player has the numbers 16 in front of her/him.Players take turns to throw the dice.The first player to hold up the card with the correctnumber corresponding to the dots on the dice throw

is the winner.

VARIATION

Roll using varying numbers of plastic cubes to becounted as quickly as possible.

DIFFERENTIATION

Ensure that every child has an opportunity to win.

Use two dice with the numbers 112.

I D E A

S P O T S A N D N U

M B E R S

55

K E Y A R E A


Large foam diceCards numbered16 or plasticnumbers 16

G R O U P S I Z E

24

44


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This is a PE warm-up activity for KS1. During the

warm-up, call numbers to elicit the following responses:1 gentle nods of the head2 wave arms high above the head3 hold arms up and stand on one leg4 lie down on the back and wave arms and legs inthe air5 wiggle the fingers on one hand

6 wiggle the fingers on one hand and gently nod thehead7 wiggle seven fingers8 wiggle eight fingers9 wiggle nine fingers10 wiggle fingers on both hands (or fingers on onehand and toes on one foot).

When the children are accustomed to the responses, putthe numbers into a general warm-up activity, callingthem at random, e.g. as children are moving around thespace, call a number and they have to stop immediatelyand perform the action before continuing on a signal.

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M Y S T E R Y S U M S

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Make a bank of questions to consolidate current orprevious work which are easily administered by thechildren themselves.

Write questions on blank cards referring to unknownnumbers in columns A and B, e.g. Double A B, A +

B, 50% of A + B, (A

2) + (B

4). Preserve these asa bank from which the children can choose freely orchoose an unseen card at random. Alternatively, theymay have to take the top card or they may have a cardselected for them.The children make two columns, A and B. Eachcolumn contains the numbers 09 in random order,thus creating the basis for ten sums.They then choose or receive a question card underthe prevailing rules and calculate the resulting sums,i.e. ten sums from the one card.A calculator may be used to check answers if necessary and they can self-mark, or pairs of childrencan mark each others.

Example

A child writes 09 in columns A and B as below andchooses the card: (A 2) + (B 4)

A B answer

3 6 6 + 24 = 307 0 14 + 0 = 146 5 12 + 20 = 329 2 18 + 8 = 262 4 4 + 16 = 200 9 0 + 36 = 364 3 8 + 12 = 201 1 2 + 4 = 68 7 16 + 28 = 445 8 10 + 32 = 42

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Blank cardsPaper and pencilsCalculators(optional)

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This is a game of deduction.Children sit in a circle and take turns to wear the hat.Write a function and number, such as + 4, on a post-it note and fix it to the hat without the wearer seeingwhat is on it.Give a number, say 6, which the rest of the groupmust combine with the hat message and give an

answer. For this example the answer would be 10.From the answer, the hat-wearer must guess what iswritten on the hat. Numbers will often work in morethan one way, e.g. if 5 is given to the group and 6 ison the hat the answer is 30 but the hat-wearer couldsay, correctly, plus 25. In such cases, either acceptany correct answer or press further for the actual oneon the hat.The hat is passed on to the next player with a newpost-it note, and so on around the group.

DIFFERENTIATION

Vary the post-it notes from simple addition orsubtraction to higher number multiplication anddivision.

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K E E P I T O N Y O U R H A T

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K E Y A R E A

Inverseoperations

R E S O U R C E S

HatPost-it notes

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S E C T I O N

2Investigations andlonger activities

Most of the ideas in this section are number based but other areas of mathematics are included.


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This involves number and shape recognition for KS1children.

The children write or trace a large number, say 5, ona sheet of paper.They then draw groups of [five] shapes, e.g. [five]

circles, [five] triangles, using card or plastic shapes astemplates.Ask, Can we make a set of [five] different shapes?either drawn or chosen from the card/plastic ones.

DIFFERENTIATION

Vary the number used.When complete, ask the child to colour the third,fourth or last shape in each set.

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N U M B E R S S H A P I N G U P

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K E Y A R E A

Number/shapeR E S O U R C E S

Plastic or cardshapesPaper andpencils

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T E A T I M E

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Here are some real number problems for KS1.

Arrange a tea party with three or four friends.Thechildren may like to write invitations to one another.

Involve individuals in the group in laying a table withthe correct number of plates, cups and cutlery.Assist the children with making a sandwich foreveryone in the group, using a half or whole slice of healthy bread per person.Divide the fruit into several pieces sliced banana,segmented orange or apple and ask the children towork out how many pieces of each fruit they shouldhave for an equal share. A small box of raisins is aparticularly useful inclusion with this as it gives more,individual items.Finally, involve the children in trying to estimate howmuch water is needed in a jug to give everyone acupful.When everyone has their ingredients, enjoy the meal.Engage everyone in the cleaning-up operationafterwards.

SAFETY NOTE

Beware of nut and other food allergies. Keep sharpobjects out of reach.

K E Y A R E A

Numberproblems

R E S O U R C E S

Plastic tablewareFruitBreadDrinking waterHealthy spread(optional)

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It is, of course, possible to purchase a tables square butmaking their own enables children to see patterns in thenumbers and how they are interconnected. This design isfor tables 212 so you will need to reduce the grid sizeaccordingly if you want only 210. Actually, the 15 table is a useful one to include due to its association withminutes in an hour.

Draw a 12 12 grid on 1cm squared paper.Place an in the top left corner square.Write the numbers 212 consecutively from left toright in the squares across the remainder of the topline and from top to bottom in the remainder of thesquares in the left-hand column.Colour this column and line in a pastel shade so thatthe numbers show clearly; these are the key lines.Elicit the easiest table, say the tens, and enter in thevalues horizontally from the 10 key on the left andvertically from the 10 key at the top, i.e. 20, 30, 40,50 . . . .Do the same with the next easiest tables in turn, saythe twos, fives, elevens, nines and threes.Gradually it can be pointed out that there are not somany gaps in their tables knowledge/expertise as thechildren may think.These gaps can be filled by

careful counting on.Trim the finished squares and mount onto card about15cm square. Some may like to personalize theirsquare further at this point by giving it a name on thereverse, such as Maths Muncher or Tables Teller.If the finished squares are laminated it will enableconstant future use without wear and tear.

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Times TablesR E S O U R C E S

Squared paper(cm)CardColouringpencilsGlue stickLaminator(optional)

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Use the ready reckoners frequently both as an aid inmathematics lessons and for regular short oralactivities. Most children understand readily how thisaids multiplication but are unsure of how it can beused for division.

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T A B L E S 4 :

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Once made, these puzzles can be kept carefully in setsfor repeated use.

Make photocopies, one per child, of a tables square.Trim off the key horizontal line and vertical column

and mount the remainder of the grid onto a square of card exactly the same size.Each child cuts the grid carefully along the squares,in irregular shapes, comprising 47 squares, varyingthe shapes as much as possible. Great care shouldalso be taken so that the children do not mix theirown pieces with those of others.Players then swap their set with another childs setand piece the tables square together using clues fromthe numbers in the lines and columns.

DIFFERENTIATION

Make larger pieces to make the puzzle easier.

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Copies of tablessquaresCardGlueScissors

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This is an easy way for KS2 children to make magicnumber squares.

Explain what makes a magic square, i.e. it is a grid of squares filled with numbers in such a way that eachhorizontal, vertical and diagonal line adds to the sametotal.

Children draw a 3

3 grid.They choose any number divisible by 3, say 21.For this example of 21, 7 (21 3) is written in eachof the diagonal squares either direction is OK butonly one direction should be used.Children then choose two different numbers whichtotal 14 (the difference between 7 and 21), say 9 and5.These are written in the remaining squares in the topline in either order.The remaining four squares of the grid are thencompleted with either 9 or 5 so that each vertical andhorizontal line and the remaining diagonal total the21. There are possible variations with the actualpositioning of the numbers, as this example shows:

7 5 9 7 9 5 9 5 7 5 9 79 7 5 5 7 9 5 7 9 9 7 55 9 7 9 5 7 7 9 5 7 5 9

This works with any multiple of 3 except 3 itself.

DIFFERENTIATION

A similar process works with multiples of 4 on a 4 4

grid but it is trickier to fit the remaining threenumbers in appropriate squares and the seconddiagonal will not add to the common number.It is not necessary to confine this to single-digitnumbers on the grid.It also works with decimal numbers.

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M A G I C S Q

U A R E S

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AdditionR E S O U R C E S

Paper and pencilsCalculators

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R A T I O A N D P R O P O R T I O N

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This is a practical way to help with these tricky conceptsin upper KS2.

RATIO

Children choose a quantity of counters or bricks of

just two colours, say, 20 red and 20 green.Separate out one [red] and three [green], explainingthat this is in the ratio 1:3.Ask, If we wanted two [red] in the same ratio, howmany [green] would be needed?Hopefully, the answer six would result and this can beshown with the counters or bricks, presenting them inclear, separate columns.Now suggest the groupings continue in thatpresentation until, say, 15 [greens] are coupled withfive [red].A pattern might be evident to the children withencouragement and, if appropriate, it can be directlyrelated to the rules of equivalent fractions.Try other ratios, such as 2:5, to consolidate.

PROPORTION

(It is not recommended to cover both ratio andproportion in the same session.)

Children take a total of ten counters/bricks, five eachof two colours.Show that there are five out of ten [red] and five outof ten [green] and relate it to half are [red] and half are [green], bringing out, if appropriate, theconnection with equivalent fractions and, possibly,percentages.Now ask the children to take a total of tencounters/bricks in a random mix of the two colours.Ask, How many out of the ten are [red]? Lets saythe answer is six.Then the proportion of [red]

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Ratio andproportion

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Colouredcounters orcolouredinterlockingbricks

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counters/bricks is six out of ten. It follows, in thiscase, that the proportion of [green] counters/bricks isfour out of ten.More able children at this point may be happy withdiscussion on the difference between ratio andproportion.Ask the children to take random amounts of bothcolours and work out the respective proportions.

DIFFERENTIATION

For a further challenge with either ratio or proportion or

both, add a third or fourth colour.


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One for the more confident children in upper KS2, thisactivity shows how square numbers plotted on a graphcan help with calculations or close estimates of square roots and the squares of decimal numbers.

With a sheet of graph paper in portrait position,children draw x and y axes (arrowed at the ends toindicate that the scales could continue).The x axis is numbered on the cm lines from theorigin 0 to 15 or as far as it will go and labelledNumber (square root).The y axis is numbered on the cm lines from theorigin 0 in tens to 200 or as far as it will go andlabelled Square number.Explain that the graph will begin at the origin as 0 2 is0.Ask the children to plot the squares of all wholenumbers and join them to make as smooth a curve aspossible.Show how, say, 6.8 2, can be calculated by following6.8 on the x axis up to the drawn line and reading off the answer on the y axis. An accurately drawn andread graph would produce an answer between 45 and47.In reverse, square roots can be shown.Taking 90 asan example, follow the 90 line on the y axis to thedrawn line and read down to the x axis. In this case, a

reasonably accurate answer would be about 9.5.Ask children to use the graph to calculate moresquares and square roots, checking accuracy oncalculators.

K E Y A R E A

Square numbersand square roots

R E S O U R C E S

A4 1, 5 and10mm graphpaperRulersPencilsCalculators

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These are like a crossword but with numbers and arefar easier to make than the wordy relative. It isrecommended that a standard grid is produced andcopied to make enough for two copies per child. Insteadof numbering the clued squares, letters can be used toavoid confusion with the number solutions. If thechildren make their own it is time consuming and theytend to become confused over the designations of the

squares, losing interest by the time the real mathematicsbegins. A selection of grids would be useful, some larger,allowing for a few four- and five-digit numbers and somesmaller, restricting the solutions to two- or three-digitnumbers. No solutions should be single-digit numbers.

This is the process once the grids have beenproduced:

The solutions are written on one copy of the grid.The children may have a reason for placing some of the numbers, with particular clues in mind. Othersmay be numbers placed simply in order to fit. Careshould be taken that no solutions begin with a zero.No clues are needed on this grid.The second grid remains blank for another child tocomplete.The compiler writes clues for the numbers

she/he has already placed. Encouragement is neededto provide as many novel and interesting clues aspossible but some will inevitably be morestraightforward. For example, a solution of 25 couldbe clued either as A quarter of a century or 5 5.When two people of similar abilities have completedtheir clues, they swap, each solving the others puzzle.

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Twophotocopiedgrids per child(optional)Rulers if childrenmake their owngridsPaper and pencilsCalculators

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VARIATION

Try a 3 3 grid without blanked squares. Children makethem in the same way, producing just three across clues,A, D and E and three down clues, A, B and C, eachsolution being a three-digit number. Those who enjoy achallenge could make this type of puzzle on a 4 4 grid.

DIFFERENTIATION

Vary the size of the grids, and therefore the size of thenumbers in the solution.

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Search for numbers in the immediate environment

and outside. These could be overt as on charts, signs,drain covers and telephone numbers or they could bederived from, say, the number of window panes in adoor or the number of fence posts on a given borderof the playground.The more obscure the position of the number the greater the value for the searcher.Formulate questions for such numbers in one of twoways:

a (particularly useful if the numbers are outside)Designate with letters the positions, on a mapor simple diagram, where the solutions are to befound.Whether or not solutions need to befound in alphabetical order will need to bedecided. A typical example for an entry in thisquiz might be, Go to point A.What date is

engraved on the foundation stone?b Direct the players to specific numbers eitherto calculate them or simply to find them andthen use those numbers to solve a furtherproblem, such as, What is the number of wordson the healthy eating poster minus the numberof posters in the classroom?

Alternatively, this could be an investigation of how

numbers are used in and around the school with anincentive to find the most or the most unusual.This activity is far-reaching and can take a while tocomplete, especially if the children are devising theirown questions ready to be presented to anothergroup. An award ceremony could be held at the endto congratulate as many participants as possible for,say, the most correct answers, best thinkers, mostsensible searchers, first-to-spot [individual question],most tenacious.

SAFETY NOTE

Assess the level of supervision necessary when thechildren are working over a wide area inside or outsidethe building.

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Paper and pencilsG R O U P S I Z E

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60 This is an imaginary way to spend for KS2 childrenwhich raises awareness of the cost of items as well asproviding practice with calculations.

Decide on a theme for spending, depending on theparticular catalogues available sports goods, toys

and games, clothing, jewellery. This could varybetween groups.Allocate an amount to spend for each group.This willdepend to some extent on the cost of items in thegiven catalogue, e.g. 200 to be spent on sportinggoods.The children work collaboratively to make a shoppinglist of desired items, ensuring that they are within thebudget and calculating what change, if any, therewould be.The final outcome could be presented on a char

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