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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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Ready-Ed
Acknowledgements for Front Cover i.
Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.
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Publications
Title: Brain Benders 1 © 2009 Ready-Ed Publications Printed in Australia Author: Barry Brocas and Brenda Bicknell
Copyright Notice
The purchasing educational institution and its staff have the right to make copies of the whole or part of this book, beyond their rights under the Australian Copyright Act 1968 (the Act), provided that: 1.
The number of copies does not exceed the number reasonably required by the educational institution to satisfy its teaching purposes;
2.
Copies are made only by reprographic means (photocopying), not by electronic/digital means, and not stored or transmitted;
3.
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educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited Level 19, 157 Liverpool Street Sydney NSW 2000 Telephone: (02) 9394 7600 Facsimile: (02) 9394 7601 E-mail: info@copyright.com.au
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The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that that
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Except as otherwise permitted by this blackline master licence or under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address below.
o c . che e r o t r s super Published by: Ready-Ed Publications PO Box 276 Greenwood WA 6024 www.readyed.com.au info@readyed.com.au
ISBN: 978 1 86397 779 1 2
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Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act.
Reproduction and Communication by others
Contents 6 7
Five Stones Answer
32 33
8 9
The Historic Home Answer
34 35
10 11
Piles of Books Answer
36 37
Coloured Pattern Answer
12 13
Going to Town Answer
Guess Who Answer
14 15
Brain Busters
Meeting at the Shop Answer
16 17
Will the Whale Cutting Wood Answers
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Marbles in a Jar Answer
Lining Up Answer
20 21
Children’s Ages Answer
46 47
Coloured Balls Answer
22 23
Animals Legs Answer
24 25
Sisters and Brothers Answer
26 27
Dressed for Work Answer
52 53
28 29
The Stolen Sheep Cows in the Paddock Answers
54 54 55
Name the Pets Answer
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The Picnic Answer
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38 39
40 40 41
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Happy Valley School Answer
Stacking Cups Answer
The Bookworm Answer Making a Quilt Answer
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© ReadyEdPubl i cat i ons Classrooms in a Row 18 Steaks 44 •f orr evi ew uCooking r p o s e s o n l y • Answer 19 p Answer 45
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48 49
50 51
30 31
3
Teachers’ Notes What is this book about? This book contains twenty-six photocopiable mathematical problems. The problems have been written and presented to suit a range of abilities and ways of thinking and learning in junior primary school. Problem solving is an important part of the mathematics curriculum and this book has been designed to help students become familiar with, and put into practice, a range of problem solving techniques. The strategies which this book encourages students to use and develop are: guess and check, looking for patterns, drawing pictures and modelling objects, listing and eliminating possibilities, filling in grids, using timelines and making assumptions and estimates and judging the reasonableness of them. The problems are also designed to highlight the importance of reading mathematical language carefully.
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Why have we written this book? We have both been primary school teachers and are aware of the kind of support materials that busy teachers need. Over the years, we have collected the mathematical problems that appear in this book, and have shared many of them with our peers. It is their promptings that have brought about the publishing of this collection. The problems that appear in this book will add flavour and interest to a mathematics programme. They will create discussion and debate and stimulate mathematical thought. It is our belief that children exposed to such problems as the ones in this book, will develop greater powers to solve problems, investigate information and make decisions inside as well as outside of the classroom. Most of these problems do not have immediately obvious answers. Their solutions might well include group discussion, or time to think them over at school or at home.
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What is different about this book? In spite of the fact that the types of problems that we have published have existed for a long time, are enjoyed by children and are an integral part of the curricula, it seems that not all teachers are using them. We think that one of the reasons for this is that they have not been made available in a ‘ready-to-use’ format. We have published this book in what we believe is a ‘ready-to-use’ format: using large print for creating overhead transparencies, mainly limiting one problem to one page, and providing answers which focus on the step-by-step methods which children are likely to use to solve the problems. We are aware that there are more sophisticated and sometimes shorter explanations of answers to some of the problems, but we have chosen to explain the answers in ways that we think children will best understand them.
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How might you use this book? Teachers can use these problems in a variety of ways. Some teachers have found it effective to give their students a problem at the end of a mathematics lesson as a starter discussion for the following day. Students are often sufficiently interested in the problems to discuss them at home. The most important thing for teachers to realise, is that if the problems are at the right level for their students, then they will not be solved immediately but will require some thought and possibly some discussion and debate. At the back of the book we have created a Brain Buster section which includes more difficult mathematical problems. You may use the problems which appear in this section as you wish. They could, for example, be used to extend more able students or to occupy fast finishers. We hope that you and your students enjoy solving these problems. Barry Brocas and Brenda Bicknell 4
Curriculum Links NSW Working Mathematically (stage 2) Number (stage 2) Patterns and Algebra (stage 2) Measurement (stage 2) Space and Geometry (stage 2)
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WA Appreciating Mathematics (1) Working Mathematically (3) (4) (5) Number (6) (7) (8) Measurement (9) (10) (11) Space (15) (16) Algebra (19) QLD Essential Learnings Year 3 Number Algebra Measurement Space
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NT Spatial Sense (band 1) Movement and Data Sense (band 1) Number Sense (band 1)
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SA Essential Learnings Measurement (standard 2) Number (standard 2) Pattern and Algebraic Reasoning (standard 2) Spatial Sense and Geometric Reasoning (standard 2)
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VIC Victorian Essential Learning Statements Number (level 3) Space (level 3) Measure (level 3) Structure (level 3) Working Mathematically (level 3)
5
Brain Bender 1
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Marbles in a Jar On Monday, Troy put one marble in a jar. Each day after that, he doubled the number of marbles in the jar. After six days, the jar was full of marbles.
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Monday
Tuesday
Wednesday
Thursday
Friday
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How many days did it take before the jar was half-full of marbles?
Saturday
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Brain Bender 1
Answer
Marbles in a Jar
r o e t s Bo r e p ok u S So the answer is five days.
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If the jar was full after six days, then it must have been half-full the previous day, because each day Troy doubled the number of marbles that he placed in the jar.
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Brain Bender 2
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Name the Pets Four pets are kept in cages in a back yard as shown below. There is a rabbit, a hen, a guinea pig and a rooster. Their names are Chip, Tommy, Dale and Mickey.
Teac he r Clue 2
Dale is opposite the guinea pig.
Clue 3
The hen is called Chip.
Clue 4
Mickey is opposite the hen.
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r o e t s B r e Use the clues belowp to match the names to theo pets. ok u Clue 1 The Sguinea pig is next to the hen and the rooster.
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Hen Guinea Pig Rooster
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Brain Bender 2
Answer
Name the Pets
r o e t s B r e obeoopposite The first clue tells us that the rabbit must p u k the guinea pig, so the rabbit’s name is Dale (the Sclue). second
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The clues lead to the following deductions:
The hen and the rooster must be opposite each other (the first clue), so the rooster’s name is Mickey. We can tell this from the fourth clue. We are told that the hen’s name is Chip (the third clue), so the guinea pig’s name must be Tommy.
© ReadyEdPubl i cat i ons So the answer is:w p Rabbit •f o rr evi e u r posesDale onl y•
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Chip Tommy Mickey
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Hen Guinea Pig Rooster
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Brain Bender 3
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
The Picnic Amy, Bianca and Carla went on a picnic together. One of the girls took sandwiches in an esky, another girl, who went in her mother’s van, took chips and the third girl, who biked to the picnic, took a soft drink.
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r o e t s Bo r Use the clues belowp to e work out who took what too the picnic. u k Clue 1 Amy’s mother drives a new car. S Clue 2
Carla doesn’t have a bike because it is too hilly to ride a bike where she lives.
Clue 3
Bianca’s mother borrowed a esky for her for the day.
Amy
Bianca
Carla
Sandwiches © Read yEdPubl i cat i ons Chips •f orr evi ew pur posesonl y•
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Soft drink
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Hint: Put ticks and crosses in the boxes of the grid to help you solve the problem. 10
Brain Bender 3
Answer
r o e t s Bo r e p o3k Chips x x u SSoft drink 3 x x Sandwiches
Amy x
Bianca 3
Carla x
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The Picnic
The first clue tells us that Amy did not take the chips, so an X should be placed in that box. The second clue tells us that Carla did not take the soft drink. An X should be placed in that box.
© ReadyEdPubl i cat i ons The third clue tells us that Bianca took the •f orr ev i e w ur p o sesonl y• sandwiches. So the boxp should be ticked.
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Each row and column of the grid must have only one tick. So the above grid shows the only possible arrangement.
So the answer is: Amy took the soft drink, Bianca took the sandwiches and Carla took the chips.
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Brain Bender 4
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Coloured Pattern Take sixteen counters. Four must be red, another four green, four white and another four blue.
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Arrange the sixteen counters on the squares below so that only one of each of the colours is in each row and only one of each colour is in each column.
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Hint: Use sixteen coloured counters and move them around on the grid provided until you find the solution. Tip: There is more than one solution to this problem. 12
Brain Bender 4
Coloured Pattern
Answer
There are many possible solutions. Solutions will be found by adopting a guess and check approach.
r o e t s Bo r e p ok u SRed Blue White Green Green
Red
Blue
White
White
Green
Red
Blue
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One solution is:
© Re adyWhite EdP ubl i c at i ons Blue Green Red •f orr evi ew pur posesonl y•
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Blue
White
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Another solution is:
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White
Green
Red
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Brain Bender 5
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Guess Who After reading the clues, match the names to the children drawn below.
r o e t s Bon.o r Clue 1 Ben and Erena have shoes e p o Clue 2 uBen and Clare are wearing hats. k S Daniel is eating an ice cream. Clue 3
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The names of the children are Amy, Ben, Clare, Daniel and Erena.
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Brain Bender 5
Guess Who
Answer
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A solution is found by eliminating possibilities.
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Clare
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Brain Bender 6
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Meeting at the Shop Mr. Seth and Mrs. Paris both shop at the same grocery store between half past five and six o’clock.
r o e t s Bo r e p ok u The last time that they met at the shop was on a Thursday. Mr. Seth S shops every four days and Mrs. Paris shops every five days.
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The shop is open seven days a week.
On what day of the week will they next meet at the grocery shop?
Sun Mon Tues Wed Thurs
Fri
Sat
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Brain Bender 6
Meeting at the Shop
Answer
There are a few ways that students might solve this problem. Method 1 – Fill out the calendar as shown below.
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P
S
P
S
S
P S/P
They next meet on a Wednesday.
S
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© ReadyEdPubl i cat i ons Method 2 –v The number before meet •f orr e i e w pofudays r po sethey so nl y•
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again, will be a multiple of four (for Mr. Seth) and a multiple of five (for Mrs. Paris).
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So it will be the least common multiple of four and five. So they will meet in twenty days time. That is one day less than three weeks, so it will be a Wednesday.
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Brain Bender 7
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Classrooms in a Row Five classrooms are positioned next to each other in a row.
r o e t s Bo r e pand match the teachers too Look at the clues below their u k classrooms. S
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The five classroom teachers are Mrs. Jones, Mr. Smith, Miss Hall, Miss Good and Mr. Dean.
Clue 1
Mrs. Jones’ room is at one end of the block.
Clue 2
Miss Hall’s room is between Mr. Smith’s and Miss Good’s rooms.
Clue 3
Mr. Smith’s room is next to Mrs. Jones’ room.
Clue 4
Mr. Dean’s room is not Room 1.
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Room 2
Room 3
Room 4
Room 5
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Brain Bender 7
Answer
Classrooms in a Row
Miss Mr. Dean r o e t s B r Good e oo p u k S Note: The first clue gives two possible scenarios, one Room 1
Room 3
Room 4
Room 5
Mr. Smith Miss Hall
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Mrs. Jones
Room 2
of them is eliminated by the fourth clue. Students will solve this problem using the process of elimination.
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Brain Bender 8
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Lining Up Seven children are lined up in order of their height.
r o e t s Bo r e p David is in the middle of the line. o u k S Paul is taller than Sarah.
Put the children in order, starting from the shortest and ending with the tallest by following the clues below. Clue 1 Clue 3
Cath is the shortest.
Clue 4
Mark stands between Anne and Jane.
Clue 4
Anne is not the tallest.
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Clue 2
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Brain Bender 8
Lining Up
Answer
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Cath
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The first clue labels David in the middle of the line and the third clue labels Cath as the shortest.
David
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From the fourth clue, we know that Mark, Anne and Jane are stood together so they must be in the three tallest positions. Also from the fourth clue, we know that Mark is between Anne and Jane, so Mark must be in the second tallest place. From the fifth clue, we know that Anne is not the tallest, so Jane must be the tallest. Paul and Sarah are the only two people left to join the line. We are told that Paul is taller than Sarah. So the answer is:
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Jane
Anne
Paul David
Mark
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Brain Bender 9
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Coloured Balls Jenny bought some coloured balls. They were green, blue, white and yellow. Use the clues below to find out how many balls she bought altogether.
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green balls.
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r o e t s B r e oblue balls Clue 1 p She bought the same number ofo u k as green balls. S Clue 2 She bought twice as many white balls as Clue 3
She bought twice as many yellow balls as the blue and green ones combined.
Clue 4
Jenny bought four white balls.
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_________ Balls Hint: Begin with the fourth clue, then the second clue. 22
Brain Bender 9
Answer
Coloured Balls
r o e t s Bo r e p ok u The S second clue tells us that she bought twice as many white balls than green balls, so she bought two green balls.
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Teac he r
This problem is best solved using the information given in the fourth clue first. The fourth clue tells us that Jenny bought four white balls.
Therefore she bought two blue balls. (First clue)
There are twice as many yellow balls than green and blue balls together. So there are eight yellow balls.
© ReadyEdPubl i cat i ons Four white balls •f or r eballs vi ew pur posesonl y• Two green
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Total: sixteen balls
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Two blue balls Eight yellow balls
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Brain Bender 10
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Happy Valley School Lauren, Amber and Marcelle all have different ways of getting to Happy Valley School. One of the girls rides a bike, one of them walks and the other one goes in a car.
Teac he r
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r o e t s Bo r e p Use the clues below to find out how each girl getso to k school. u S Clue 1 It is raining today so Lauren will get very wet going to school. Clue 2 At Happy Valley School, children must be at least nine years old to bike to school. Amber is eight years old. Clue 3 Lauren is nine years old but her parents won’t let her bike to school.
Lauren Amber Marcelle © Rea dyEdPubl i cat i ons Bike •f orr evi ew pur posesonl y•
Walk
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Car
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Hint: Pzzut a tick (3) for ‘yes’ or a cross (x) for ‘no’ in the boxes on the grid as you read the clues. 24
Brain Bender 10
Answer
Happy Valley School Lauren
Marcelle
x 3 r o e t s B r e oxo x Walkp 3 u k SCar x x 3 Bike
x
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Amber
Lauren gets very wet going to school so she doesn’t go in the car. An X should be placed in the bottom left box. Amber is eight so she doesn’t ride a bike. An X should be placed in the middle of the top row. Lauren isn’t allowed to bike to school. An X should be placed in the top left square.
© ReadyEdPubl i cat i ons Marcelle must ride the bike. A 3 should be placed in the • f o rr ev ewbepplaced ur pino sesquares son l y• top right and Xsi should both below that.
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So Amber must go by car. A 3 should be placed in the middle of the bottom row, and an X should be placed above it.
. t eanswer is Lauren walks, Amber goes byc o So the car and . che Marcelle bikes. e r o r st super So, Lauren must walk. A 3 should be placed in the remaining space.
Lauren
Amber
Marcelle 25
Brain Bender 11
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Stacking Cups A child places seven stacking cups on top of each other. Each cup is a different colour. The cups are: blue, brown, green, orange, red, white and yellow.
Teac he r Clue 2
The blue cup is on top of the green cup.
Clue 3
The white cup is on the bottom.
Clue 4
The orange cup is directly below the yellow cup.
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r o e t s B r e othe Use the following clues to help you discover how cups are p o u stacked. k S Clue 1 The yellow cup is in the middle.
cup isE ond theP top. ©TheRbrown ead yubl i cat i ons •f orr evi ew pur posesonl y•
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Clue 5
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Hint: Use coloured counters to model the cups. 26
Brain Bender 11
Stacking Cups
r o e t s Bo r e p ok Brown u S Blue Green
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Teac he r
Answer
© ReadyEd Publ i cat i ons Yellow •f orr evi ew pur posesonl y•
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Brain Bender 12
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
The Bookworm Three books are standing in a bookcase as shown in the picture below. A worm eats its way from the front cover of the first book to the back cover of the third book. Each book is two centimetres thick.
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r o e t s Bo r e pgo? ok How far does theu worm S
Book 3
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Book 1
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Hint: Make sure that you work out exactly where the front and the back covers of the books are. Don’t rush this one! 28
Brain Bender 12
Answer
The Bookworm
r o e t s Bo r e p ok u S
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Teac he r
Initially it might seem that the worm has eaten its way through all three books, so the answer would be six centimetres. However if we think about where the front cover of Book 1 is compared to the position of the back cover of Book 3, we see that the two covers are only two centimetres apart. So the answer is two centimetres.
Book 3
Book 3
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29
Brain Bender 13
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Making a Quilt Mary is sewing blocks of her quilt together.
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1 block
2 blocks
Answer these questions
1. How long will it take her to join six blocks in a row?
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Teac he r
It takes Mary one minute to sew two blocks of her quilt together.
______ minutes
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2. How long will it take Mary to sew fifteen blocks together?
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______ minutes 3. How long will it take Mary to sew twenty blocks together?
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______ minutes
blocks in a row how many minutes would it take her?
______ minutes Hint: can you see a pattern in your answers to questions 1-3? This may help you to work out question 4 quickly. 30
Brain Bender 13
Answer
Making a Quilt
1. Five minutes.
r o e t s B r e oo 3. Nineteen minutes p u k 4. Ninety-nine minutes S
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2. Fourteen minutes
When working out the first three questions, students should be able to recognise that a pattern has emerged: the number of joins is one less than the number of blocks. This should help them to work out the answer to question four quickly without the need to draw a hundred blocks of quilts.
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Brain Bender 14
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Five Stones Five stones are placed on the ground in a line one metre apart from each other. The first stone is one metre from a basket that is at the start of the line.
Teac he r
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r o e t s Bobasket and r How far does a person e travel who starts from the p ok brings the stonesu to the basket one at a time? S
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Brain Bender 14
Answer
Five Stones
r o e t s Bo r e pto the second stone and backo The distance to the u k basket is four metres. S The distance to the third stone and back to the basket is six metres.
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Teac he r
The distance to the first stone and back to the basket is two metres.
The distance to the fourth stone and back to the basket is eight metres.
Š Read E d Pu bback l i ca i o ns The distance to y the fifth stone and tot the basket is ten metres. •f orr evi ew pur posesonl y•
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(2 + 4 + 6 + 8 + 10 = 30)
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So the total distance that the person travels to bring the stones to the basket is thirty metres.
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33
Brain Bender 15
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
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The Historic Home
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Front Door
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Teac he r
Back Door
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Mr. Trotter was asked to save an historic home which consisted of sixteen rooms as shown above.
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The only way that he could save it was to invite tourists to visit the home. He wanted to create a path through the house from the front door to the back door. The path would have to go through each room once and only once.
. te o Is such a path possible if one room isn’t visited? c . che e r o t r s super Is such a path possible?
34
Brain Bender 15
Answer
The Historic Home
It cannot be done for the original sixteen room arrangement. However if we remove one room from the path it can be done. This can be any room other than the rooms with the front or back doors.
Teac he r
Back Door
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r o e t s Bo r e p ok u OneS possible path is shown below.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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Another possible path is:
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Back Door
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Front Door
o c . che e r o t r s super Front Door
35
Brain Bender 16
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
Super Dooper Brain Bending!
Piles of Books A teacher has two piles of books on her desk. There are three books in each pile. There is one book on each of the following subjects: Science, Mathematics, English, History, Health, and Art.
Teac he r
Clue 2 Clue 3 Clue 4
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r o e t s Bo r e pbelow to put the books in order. ok Use the clues u Clue 1S The Mathematics book is directly under
the English book. The Art book is in the second pile but is not on top of the pile. The History book is on top of the English book. The Health book is between the Science book and the Art book.
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Brain Bender 16
r o e t s Bo r e p ok u S Pile 1
Mathematics English History
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Answer
Pile 2
Art Health Science
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37
Brain Bender 17
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
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Going to Town Richard lives in the country and once a week he walks to town. He always goes to town on the same day of the week.
r o e t s Bo r e p oknot work u On every second trip, he has a haircut. The hairdresser does Smarket is open on Mondays, Wednesdays and on Mondays. The Saturdays. The bank is closed on Saturdays and Sundays. On what day does Richard go to town?
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Teac he r
On each visit, he goes to the bank for money and to the market for his vegetables.
MON TUE WED THUR FRI SAT ©SUN Rea dyEdP ubl i cat i ons •f orr evi ew pur posesonl y•
Hairdresser
Bank
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Market
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Richard goes to town on a ______________ Hint: Fill in the days Richard can NOT visit each place. 38
Brain Bender 17
Answer
Going to Town
r o e t s Bo r e p ok u S
Completing a grid is the best way to solve this problem. Students should use the information provided to eliminate the unsuitable days.
Teac he r
TUE No market
WED
THUR No market
FRI SAT No No bank market
So the answer is: Richard goes to town on a Wednesday.
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SUN MON No No bank or hairdresser market
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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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39
Brain Bender 18
How do you rate this Brain Bender? Brain boring!
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Will the Whale The length of Will the Whale is twelve metres, plus half of his own length.
r o e t s Bo r e p ok u S
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Teac he r
How long is Will the Whale?
_______ metres
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Brain Bender 19
How do you rate this Brain Bender? Brain boring!
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It takes James ten minutes to cut through a log of wood.
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Cutting Wood How long will it take James to cut the log into ten equal pieces if he continues to cut at the same speed?
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_______ minutes Hint: draw the cuts on the log of wood. Don’t rush this one! 40
Brain Bender 18
Answer
Will the Whale
Twenty-four metres long.
r o e t s Bo r e p ok u S
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Teac he r
Twelve metres must also be a half of the whale’s length, because when added to the other half it makes up the whole whale.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Answer
Cutting Wood
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Brain Bender 19
. tit will take ninety minutes. o Soe c . che e r o t r s super It takes only nine cuts to cut the log into ten pieces.
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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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r o e t s Bo r e p ok u SBrain Busters
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43
Brain Bender 20
How do you rate this Brain Bender? Brain Boring!
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Cooking Steaks There are three pieces of steak and each piece needs to be cooked for fourteen minutes on the barbecue; seven minutes each side.
r o e t s Bo r e p ok u S
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Teac he r
If the barbecue plate is big enough for only two steaks at a time, what is the least amount of time needed to cook three steaks?
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© ReadyEd Putime___________ bl i cat i ons Total •f orr evi ew pur posesonl y•
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Hint: Remember you want to cook 3 three steaks in the LEAST amount of time. 44
Brain Bender 20
Answer
Cooking Steaks
r o e t s Bo r e p ok u This S time can be shortened by cooking the steaks in the following way: First Seven Minutes:
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Teac he r
If you cook two steaks on the barbecue first and then cook the final steak, it will take you twenty-eight minutes.
Steak 1
Steak 2
Steak 1
Steak 3
Second Seven Minutes:
© eaMinutes: dyEdPubl i cat i ons ThirdR Seven Steak 2 Steak 3 •f orr evi ew pur p oseso nl y•
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Total time: Twenty-one minutes
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45
Brain Bender 21
How do you rate this Brain Bender? Brain Boring!
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Children’s Ages Three children A, B and C are discussing their ages.
r o e t s Bo r e p o u k How old are the three children? S
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Teac he r
A says, “C is twice as old as me and four years older than B.” B says, “I am two years older than A.”
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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Child A ______
o c Childe B. ______ che r o t r s super Child C ______
Hint: Try a guess and check approach. Choose different numbers, e.g. if child A was 2,3,4… then child B would be … 46
Brain Bender 21
Answer
Children’s Ages
r o e t s Bo r e ocheck Method 1:p Students may adopt a guess and u k approach. S If a student guesses that A is six years old,
Teac he r
There are a number of ways that a student might work this problem out.
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they should arrive at the answer using the rest of the information given in the conversation. Method 2: Students might draw a time-line starting at zero to solve the problem.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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So the answer is: A is six years old, B is eight years old and C is twelve years old.
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47
Brain Bender 22
How do you rate this Brain Bender? Brain Boring!
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Animals’ Legs There are seventeen animals in a yard. Some are chickens and some are pigs. There is a total of forty-eight legs.
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_________ Chickens
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Teac he r
How many chickens and how many pigs are there in the yard?
_________ Pigs
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Hint: Use a guess and check approach. 48
Brain Bender 22
Answer
Animals’ Legs
r o e t s Bo r e pable students may be able to understand ok Some more u S below if taught. the method
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Teac he r
This type of problem lends itself to several different approaches. Children could adopt a guess and check approach.
If all seventeen animals had two legs we would have thirty-four legs.
But we have fourteen more legs than that. So there must be seven pigs to create the fourteen extra legs.
© ReadyEdPubl i cat i ons •f o r e vi ew pu r pos eseven sonl y• Sor the solution is: ten chickens and pigs.
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To check the answer: (10x2) + (7x4) = 48
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49
Brain Bender 23
How do you rate this Brain Bender? Brain Boring!
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Sisters and Brothers
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?
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Teac he r
How many girls and how many boys are there in a family in which each girl has as many brothers as sisters but each boy has twice as many sisters as brothers?
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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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_________ Girls
_________ Boys
Hint: Try a guess and check approach. Choose different numbers, e.g. if child A was 2,3,4… then child B would be … 50
Brain Bender 23
Answer
Sisters and Brothers
r o e t s Bo r e p okas Firstly, note that each girl has as many brothers u sisters. So the number of girls in the family must be S one more than the number of boys.
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Teac he r
A guess and check approach can be used to solve this problem.
So a first guess could be GGB. This does not match the statement that each boy has twice as many sisters as brothers.
Try GGGBB. This does not match the information given either, because each boy has three sisters and one brother.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
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So the answer is: four girls and three boys.
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Try GGGGBBB. This matches all of the information given, because now each boy has two brothers and four sisters.
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51
Brain Bender 24
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
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Dressed for Work
r o e t s Bo r e p ok u S
What is the colour of Mr. White’s shirt? What is the colour of Mr. Grey’s tie? Use the grid below to help you solve this problem.
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Teac he r
Mr. Blue, Mr. White and Mr. Grey are all wearing shirts and ties. Each man is wearing both a shirt and a tie. Clue 1 They are all wearing different coloured ties. Clue 2 They are all wearing different coloured shirts. Clue 3 The shirts and ties are coloured blue, white or grey. Clue 4 No man’s clothing is the same colour as his name. Clue 5 Mr. Blue’s tie is the same colour as Mr. Grey’s shirt.
Mr. Blue Mr. White Mr. Grey © Read y Ed P ubl i ca t i ons Blue •f or r evi ew pur posesonl y• Shirt
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Grey Shirt
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o c . Blue c e r Tie h er o t s s r u e p White Mr. Blue Mr. White Mr. Grey
Tie Grey Tie Hint: There can be only one tick in each row and column. 52
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White Shirt
Brain Bender 24
Answer
Dressed for Work Mr. Blue Mr. White Mr. Grey
xt x 3 r o e s B r e o p o White u x x 3k Shirt S Grey Shirt
3
x
x
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Blue Shirt
Mr. Blue Mr. White Mr. Grey Blue Tie
x
x
3
Grey Tie
x
3
x
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© RWhite eadyEdPubl i cat i ons x x 3 Tie •f orr evi ew pur posesonl y•
No man’s clothing is the same colour as his name. So Xs should be placed in the appropriate boxes.
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Mr. Blue’s tie cannot be blue and Mr. Grey’s shirt cannot be grey, so they must both be white, because they have to be the same colour. 3s should be placed in the appropriate boxes and Xs should be placed to complete the rows and columns with 3s. There can only be one tick in each column or row because they are all wearing different coloured shirts and are all wearing different coloured ties. So the answer is: Mr. White’s shirt is blue and Mr. Grey’s tie is blue. 53
Brain Bender 25
How do you rate this Brain Bender? Brain Boring!
Easy on the Brain!
Brain Bending!
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The Stolen Sheep Some sheep stealers made off with half of a farmer’s flock. The following day they stole half of what they had left the day before. This left the farmer with only sixteen sheep.
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Teac he r
r o e t s Bo r e pthe farmer have to start with?ok How many sheepu did S
_______ sheep
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• How do you rate this Brain Bender? Brain boring!
Easy on the Brain!
Brain bending!
Super Dooper Brain Bending!
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Cows in the Paddock
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Brain Bender 26
If a six-hectare paddock provides enough grass for twelve cows for a month, for how long would a three-hectare paddock provide six cows with grass?
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_______________ 54
Brain Bender 25
Answer
The Stolen Sheep
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Teac he r
The farmer was left with sixteen sheep. The day before he would have had thirty-two sheep. So the farmer started with sixty-four sheep.
© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•
Brain Bender 26
Cows in the Paddock
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Answer
A three-hectare paddock is half the size of a sixhectare paddock, so it would provide enough grass for six cows for one month.
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