Brain Benders Series: Book 3 - Ages 10-13 by Teacher Superstore

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Ready-Ed

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Publications

Acknowledgements for Front Cover

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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 781 4 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 r o e t s Bo r e p ok u S

Upside Down Triangle Answer

8 9

Matching Ages Answer

10 11

A Line of Stones Answer

12 13

The Broken Vase Answer

14 15

River Crossing Answer

20 21

The Prisoners' Hats Answer

22 23

Brain Busters

Ding Dong Bells Answer

32 33

Counters on an Array Answer

34 35

Room for Honesty Answer Dishonest Shopkeeper? Answer

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Playing Cards Answer

6 7

36 37 38 39

The Bike Ride 40 © R e a d y E d P u b l i c a t i o n s Answer 41 Twelve Counters 16 Answer Path? •f orr evi ew17 puWhich r p o sesonl y•4342 Answer

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Brain Teasers Just a Symbol What is it? Adding Weight Cakes

44 45

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The Broken Window Answer

Ellie and Edgar Answer

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Friends, Houses, Pets and Drinks Answer

26 27

Going Out or Staying Home Answer

28 29

47 47 47 47

Bottle and Cork The Indians My Pets A Weighty Problem

48 48 48 48

Cigarette Poison Square Numbers Gold What Day is it?

49 49 49 49

Pesky Possums My Medicine Tim's Truck Coloured Socks

50 50 50 50

Answers

51 3

Teachers’ Notes What is this book about? This book contains thirty-four photocopiable mathematical problems. The problems have been written and presented to suit a range of abilities and ways of thinking and learning in upper 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, there is a Brain Teaser section which consists of sixteen short mathematical problems, which can be solved quickly and used as warm ups to any lesson. In the middle 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

SA Essential Learnings Measurement (standard 4) Number (standard 4) Pattern and Algebraic Reasoning (standard 4) Spatial Sense and Geometric Reasoning (standard 4)

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NT Spatial Sense (band 3) Movement and Data Sense (bands 3) Number Sense (bands 3&4) Space and Measurement (band 4) Chance and Data (band 4) WA Appreciating Mathematics (1) Working Mathematically (3) (4) (5) Number (6) (7) (8) Measurement (9) (10) (11) Space (15) (16) Algebra (19)

VIC Victorian Essential Learning Statements Number (level 5) Space (level 5) Measure (level 5) Structure (level 5) Working Mathematically (level 5)

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NSW Working Mathematically (stage 4) Number (stage 4) Patterns and Algebra (stage 4) Measurement (stage 4) Space and Geometry (stage 4)

TAS Working Mathematically (standards 3&4) Number (standards 3&4) Algebra, Function and Pattern (standards 3&4) Space (standards 3&4)

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ACT The student understands and applies number (16.EA) The student chooses and uses measures (17.EA) The student recognises and represents patterns and relationships (18.EA)

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QLD Essential Learnings Year 7 Number Algerbra Measurement Space

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Brain Bender 1

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Upside Down Triangle

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The triangle below is made up of ten counters. Move only three counters to create a triangle that is the same as this triangle, but turned upside down. Colour the counters that you will move and draw a line to indicate where you will move them to.

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Hint: Use counters on a table to help you work this out. 6

Brain Bender 1

Answer

Upside Down Triangle

Students can examine use counters all the possibilities. to solve this problem.

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Students should move the three black counters( ) to the new positions as shown below ( )to obtain the new arrangement.

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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!

Playing Cards Three playing cards are placed in a row. There is a three on the right of, and next to, a two. There is a three on the left of, and next to, a three. There is a spade on the right of, and next to, a heart and a heart on the right of, and next to, a heart.

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Name the three playing cards.

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Brain Bender 2

Answer

Playing Cards

Students should eliminate possibilities.

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If students follow the instructions carefully, it will lead them to the following solution:

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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!

Matching Ages Amy said, “Chris is three times as old as me and he is also twice as old as Brad.” Brad said, “Two years ago, I was twice as old as Amy was then.”

r o e t s Bo r e Years p Ages Now Ages Two o u Ago k S

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How old are Amy, Brad and Chris?

Amy Chris Brad

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Chris ____

Hint: To help you solve the problem, make an assumption about how old Amy is now, then use the information to check it. Use the grid to help you. 10

Brain Bender 3

Matching Ages

Answer

Ages Now Ages Two Years r o e t s B r e ooAgo p u k Amy 12 10 S Chris

Brad

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Students should use a guess and check approach and fill in the grid provided to solve Students examine all the possibilities. this problem.

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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!

A Line of Stones One hundred stones are placed in a line with a one metre gap between each stone. There is a basket at the end of the line that is one metre away from the first stone. Emily starts at the basket and aims to pick up each stone, one at a time, and place each one in the basket.

___________ metres r o e t s Bo r e p okmetres u ___________ S

1. What distance does she travel to pick up and place one stone in the basket?

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2. What distance does she travel to pick up and place two stones in the basket? 3. What distance does she travel to pick up and place three stones in the basket?

___________ metres

4. What distance does she travel to pick up and place four stones in the basket?

___________ metres

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5. Can you see a pattern emerging? Can you use the pattern to work out the distance that Emily will have to travel to pick up all of the one hundred stones and place them in the basket?

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Hint: drawing a time-line may help you work out the answers to the first four questions. 12

Brain Bender 4

Answer

A Line of Stones

Students should examine look all for the patterns possibilities. to solve this problem.

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1. The distance to the first stone and back to the basket is two metres. 2. The distance to the second stone and back to the basket is four metres. 3. The distance to the third stone and back to the basket is six metres.

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4. The distance to the fourth stone and back to the basket is eight metres 5. The distance increases by two metres each time an extra stone is picked up and placed in the basket. So the answer is 200 metres.

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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!

The Broken Vase Four girls were having a pillow fight in the lounge when one of the girls broke a vase. Aunty Clare was a witness to the accident. Derryn’s mother walked in and questioned the four girls. This is what they said:

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Alana said,

“Derryn did it.”

Alinsleigh said,

“I didn’t do it.”

Derryn said,

“Miriam did it.”

“Derryn lied when she said I did it.”

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Miriam said,

Derryn’s mother asked Aunty Clare to say who had broken the vase. Aunty Clare always tells the truth but wouldn’t say who had broken the vase. Aunty Clare replied, “Only one of the four girls is lying.” Who broke the vase?

Derryn

Miriam

Alana

Ainsleigh

Derryn

Alana

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Ainsleigh

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ASSUMPTION: Alana is lying

ASSUMPTION: Derryn is lying

Broke the vase

Derryn Alana

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Broke the vase

Derryn Alana

Ainsleigh

Miriam

Hint: Make four assumptions and check to see which assumption matches the information given. For example, first assume that Alana is lying, then Ainsleigh is lying, and so on. Use the grids to help you check your assumptions. 14

Brain Bender 5

Answer

The Broken Vase

Students should examine make all the assumptions possibilities. and check their reasonableness to solve this problem.

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When students assume that Derryn is lying, they should arrive at the answer that Derryn broke the vase.

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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!

Twelve Counters

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You need 12 counters. Place two counters on the corners of the grid as shown below. These two counters are fixed. Now place the other ten counters on the grid so that there is no more than one counter on each square and no more than two counters on any horizontal, vertical or diagonal line. A diagonal line refers to any line that is a diagonal of the square or is parallel to the diagonals of the square.

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Hint: Draw a 6 x 6 grid and draw in the two fixed counters. Take a pencil and cross out all of the non-available squares. For example, start by crossing out all of the squares on the diagonal containing the fixed counters. Each time you place a counter that gives two counters in a row or column or on a line parallel to a diagonal of the square, cross out the remaining squares in that row or column or diagonal line. 16

Brain Bender 6

Twelve Counters

Answer

Students use counters on a grid or a guess and check approach to solve this problem. Some students may notice that the solutions have a half-turn symmetry about the centre.

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Two possible solutions are:

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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!

Going to the Movies Kirk, Cherie, Suzanne and Carolyn are all teenagers who belong to the same family. They are thinking about going to the movies. Read the clues below to work out who went to the movies and who stayed home.

r o e t s Bo r e p ok u S Clue 1 Cherie and Suzanne will not both go.

Clue 2 If Suzanne stays at home then Kirk will go.

Possibility 1:

Clue 4 Suzanne and Carolyn will both go or will both stay at home.

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Clue 3 At least one of Kirk and Cherie will go.

Clue 5 If Cherie does not go then Kirk will not go.

Stay

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Possibility 2:

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Cherie

o c . che e r o stay at home stay at home t r s s r u e p Suzanne go to the movies go to the movies stay at home go to the movies

Carolyn

stay at home go to the movies

Hint: Make two lists under the headings Go and Stay. The fourth clue lends itself to two possibilities. Check which possibility matches the clues. 18

Brain Bender 7

Answer

Going to the Movies

Students should eliminate possibilities to solve this problem.

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Students should test the possibilities created by the clues and they will arrive at the following answer:

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Kirk and Cherie go to the movies, Suzanne and Carolyn stay at home.

Kirk

stay at home go to the movies

Suzanne

stay at home go to the movies

Cherie

stay at home go to the movies

Carolyn

stay at home go to the movies

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How do you rate this Brain Bender?

Brain Bender 8

Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

River Crossing Three cannibals and three missionaries are travelling together and arrive at a river crossing. There is a boat there, but it holds only two people. At no time, on either bank, even as the boat moors, can the cannibals outnumber the missionaries. If this happens, the cannibals might start to eat the missionaries.

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start

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Left Bank

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cannibal

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M missionary C

Show how the cannibals and missionaries can cross from the left bank to the right bank safely.

Key

Brain Bender 8

Answer

River Crossing

There are a number of possible solutions.

3x 1x

3x 2x

3x 1x

arrive on bank

left behind

TRIP 2

on bank

TRIP 3

left behind

TRIP 4

on bank

left behind

2x 2x

TRIP 5

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behind

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TRIP 1

on bank

left behind

TRIP 6

TRIP 7

left behind

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on bank

left behind

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3x 1x

M TRIP 8

on bank

left behind

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3x 2x

TRIP 10

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on bank

M C

on bank left behind

on bank

TRIP 11

no-one left behind

C 3x

Brain Bender 9

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

The Prisoners' Hats Two prisoners, Andy and Mandy are offered a special deal by their captors. They are seated in such a way that Andy cannot see Mandy but Mandy is looking at the back of Andy’s head. They are blindfolded while a hat is put on each of their heads.

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When the blindfolds are removed, their captors tell them that there are two white hats and one black hat. If either of them can say what colour hat they are wearing, they can both go free. If however they are wrong, they will both be executed immediately.

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There is silence for a long time, then one of them speaks.

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Who speaks and what colour hat is that person wearing?

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Hint: Think about why there is silence for some time. 22

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Brain Bender 9

Answer

The Prisoners’ Hats

Students must read the mathematical problem carefully.

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If Andy was wearing a black hat then Mandy would see this and would have instantly said that she was wearing a white hat. But she has said nothing after quite some time, so Andy knows that he must be wearing a white hat.

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So it is Andy who speaks and says that his hat is white.

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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!

The Broken Window Hayden, Jacob and Seth are playing catch with a ball in their grandfather's back garden. One of the boys throws the ball too far and smashes a window in the house. Their grandfather rushes out and asks which of the boys has broken the window. One of the boys never tells the truth, another never tells lies, and the third sometimes tells the truth and sometimes lies.

r o e t s Bo r e p ok u S Hayden said, “I didn’t do it. Jacob didn’t do it.” Jacob said, Seth said,

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On this occasion, one boy tells two lies, one boy makes two true statements, and the third boy makes one statement that is false and one that is true. This is what they said:

“Hayden didn’t do it. Seth did it.” “I didn’t do it. Hayden did it.”

Who broke the window?

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Jacob

Seth

Hint: This problem is solved by making assumptions and checking their accuracy. For example, assume that Seth broke the window. If he did it, do the boys' statements meet the criteria? 24

Brain Bender 10

Answer

The Broken Window

Students will solve this problem by making assumptions and checking their Students examine all the possibilities. accuracy.

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If students assume, for example, that Seth broke the window then Hayden and Jacob have both made two true statements, so our assumption that Seth broke the window is wrong. I didn’t do it (T). Jacob didn’t do it (T). Hayden didn’t do it (T). Seth did it (T).

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Hayden: Jacob:

Suppose their next assumption is that Jacob broke the window. If Jacob broke the window then Hayden and Jacob have both made one true and one false statement, so their assumption that Jacob broke the window is wrong. Hayden: Jacob:

I didn’t do it (T). Jacob didn’t do it (F). Hayden didn’t do it (T). Seth did it (F).

© ReadyEdPubl i cat i ons If students assume that Hayden broke the window, they will realise that this assumption fits the criteria. •f orr evi ew pur posesonl y• I didn’t do it (F). Jacob didn’t do it (T). Hayden didn’t do it (F). Seth did it (F). I didn’t do it (T). Hayden did it (T).

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So the answer is: Hayden broke the window.

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Hayden: Jacob: Seth:

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Jacob

Seth

How do you rate this Brain Bender?

Brain Bender 11

Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Friends, Houses, Pets and Drinks Three friends, Jonah, Kiri and Chris, live in three different types of houses. These houses are next to each other on one side of a street. The friends have three different pets and drink three different drinks.

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Clue 2

Water is drunk in the house to the left of where Chris lives.

Clue 3

Jonah lives in the house on the left.

Clue 4

Kiri has a puppy.

Clue 5

The cat lives in the house next door to Kiri.

Clue 6

The puppy lives in the house on the right.

Clue 7

Juice is drunk in the wooden house.

Clue 8

The brick house is immediately to the left of the stucco house.

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Milk is drunk in the middle house.

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Clue 1

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2. What type of house does Chris live in?

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3. What does Jonah drink?

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4. What kind of pet does the owner of the brick house have?

Hint: Create a table … 26

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1. Who owns the horse?

Brain Bender 11

Answer

Friends, Houses, Pets and Drinks

Students should eliminate possibilities to solve this problem.

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If students write inside the three houses provided as they read the information, they should conclude that: Jonah owns the horse, Chris lives in the stucco house, Jonah drinks water and the owner of the brick house has the horse.

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How do you rate this Brain Bender?

Brain Bender 12

Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Going Out or Staying Home Anna, Brent, Carlos, Dana and Emma are discussing going out together for the evening. The following six statements are all true. Statement 1:

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Anna and Brent don’t like each other and have decided that whatever one does the other will do the opposite.

Statement 2:

Carlos and Emma cannot both go out.

If Dana goes out, then Emma will stay home.

Statement 4:

Dana and Brent decide that at least one of them will go out.

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Statement 3:

Statement 5:

If Anna stays at home, then Carlos will go out.

Statement 6:

It is not possible to have Carlos going out and Emma staying at home.

Who went out and who stayed home?

Carlos

stay at home went out

Emma

stay at home went out

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Hint: Look at the different possibilities by making assumptions. 28

Brain Bender 12

Answer

Going Out or Staying Home

Students will solve this problem by making assumptions and checking their accuracy.

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Students need to make assumptions and check whether their assumptions match the rest of the information provided.

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The first statement lends itself to two possibilities. If the students assume that Anna will go out and Brent will stay at home, this matches the rest of the statements.

So the answer is: Anna will go out Brent will stay at home Carlos will stay at home Dana will go out Emma will stay at home

Anna

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The second statement lends itself to two possibilities. If the students assume that Carlos and Emma will both stay at home, then this will match the rest of the information given.

stay at home went out

stay at home © ReadyEdP ubl i ca t i o ns Brent went out •f orr evi ew pur posesonl y• stay at home went out

Dana

stay at home went out

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Carlos

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stay at home went out

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r o e t s Bo r e p Bustersok u Brain S

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Brain Bender 13

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Ding Dong Bells A bell-ringer rings a sequence of chimes from two bells. One of the bells makes a ding sound and the other a dong sound. In the sequence, the bell-ringer is not allowed a ding if only one bell has rung since a ding. Also, the bell-ringer is not allowed a dong if exactly two bells have rung since a dong.

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So the following sequences are not allowed: Ding or Dong

Dong

Ding or Dong

Ding

Ding or Dong

Dong

What is the longest sequence that the bell-ringer can ring?

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Ding

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Hint: You may want to draw a tree diagram. 32

Brain Bender 13

Answer

Ding Dong Bells

Students may find that drawing a tree diagram is useful to solve this problem.

r o e t s Bo r e p ok u S ding

dong

ding

dong

ding

dong

ding

dong

ding

ew i ev Pr

Teac he r

ding

dong

ding

If the bell-ringer starts with a ding, the longest sequence possible is: ding, ding, dong, dong, dong, ding, ding. ding ding

dong ÂŠ R e a d yEdPubl i cat i ons dong ding ding â&#x20AC;˘f ordong r evi ew p ur posesonl yâ&#x20AC;˘ dong

ding

So the longest possible sequence is:

. te

ding, ding, dong, dong, dong, ding, ding.

m . u

w ww

If the bell-ringer starts with a dong, the longest sequence possible is: dong, dong, dong, ding, ding.

o c . che e r o t r s super

Brain Bender 14

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Counters on an Array Twelve counters are placed on a six by six array as shown below.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

Show how to divide the whole array so that there are four identically shaped regions with three counters in each region. Use a highlighter to mark the regions.

w ww

. te

m . u

o c . che e r o t r s super

Hint: There is more than one possible solution. 34

Brain Bender 14

Answer

Counters on an Array

Students could cut out possible shapes and fit them onto the grid.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

One solution is:

w ww

. te

m . u

Another solution is:

o c . che e r o t r s super

Brain Bender 15

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Room for Honesty There are four people from Logicland in a room. Among them are truth-tellers and liars. Read the four statements below to work out how many honest people were in the room.

r o e t s Bo r e p ok u S “There are no honest people in this room”.

The second person (P2) says,

“There is not more than one honest person in this room”.

The third person (P3) says,

“There are no more than two honest people in this room”.

The fourth person (P4) says,

“There are not more than three honest people in this room”.

How many honest people were in the room?

ew i ev Pr

Teac he r

The first person (P1) says,

w ww

. te

m . u

o c . che e r o t r s super

_____________ honest people in the room

Hint: Adopt a guess and check approach. Make an assumption, e.g. P2 is lying and see if this matches the rest of the information. 36

Brain Bender 15

Answer

Room for Honesty

Students should adopt a guess and check approach to solve this problem.

r o e t s Bo r e p ok u S P1 L

P2 ?

P3 ?

P4 ?

ew i ev Pr

Teac he r

P1 says that there are no honest people in the room – that is, everyone is a liar. So if P1 was telling the truth P1 would also have to be a liar. This would be a contradiction, since a liar would not tell the truth. So P1 is a liar.

So P4 must be telling the truth, because if P4 wasn’t, there would have to be four or more truth-tellers and that is not possible if P1 is a liar. P1 L

P2 ?

P3 ?

P4 T

© ad E Publ i cat i ons But P2R sayse there arey not, so P2d is lying. P1 P2 P3 s P4 •f orr e v i e w p u r p o e s onl y• L L ? T If P2 were a truth-teller, there would be two honest people in the room.

. te

P1 L

P2 L

P3 T

P4 T

m . u

w ww

P3 says there are no more than two honest people in the room. If this were false there would have to be at least three honest people. This cannot be, since we already know that P1 and P2 are liars. So P3 is a truth-teller.

o c . che e r o t r s super

P1 and P2 are liars, P3 and P4 are truth-tellers.

So the answer is: there are two honest people in the room.

How do you rate this Brain Bender?

Brain Bender 16

Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Dishonest Shopkeeper? Three children bought $25 worth of collector cards between them. They each gave the shopkeeper $10. He was unable to split the $5 change evenly between them, so they each took $1 change and told him to keep $2. As they walked home, they started thinking about what had happened. Each of the three children had paid $9 and the shopkeeper had $2. That adds up to $29.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

What had happened to the other dollar? Had the shopkeeper stolen it?

w ww

. te

o c . che e r o t r s super

Hint: Think about whether the children are working things out correctly 38

m . u

Brain Bender 16

Answer

Dishonest Shopkeeper?

Students useStudents mental computation examine all the to solve possibilities. the problem.

r o e t s Bo r e p ok u S

Teac he r

ew i ev Pr

The problem arises because the children are trying to balance the wrong things. The money can be balanced in two ways: Cost of cards: $25.00 Total change given: $ 3.00 Gift to shopkeeper: $ 2.00 Total: $30.00 Or: $9.00 cost to each child $27.00 $1.00 change given to each child $ 3.00 Total: $30.00

The children are trying to balance the $27 total payment with the $2 gift to the shopkeeper. So there is no extra dollar for the shopkeeper to take. So the answer is: no, the shopkeeper has not stolen a dollar from the children.

w ww

. te

m . u

o c . che e r o t r s super

Brain Bender 17

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

The Bike Ride A cyclist took three minutes to ride one kilometre from his home to his friend’s home, riding with wind assistance. He took six minutes to complete the return journey, cycling into the wind. The cyclist applies the same force to the pedals at all times.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

How long would it take him to ride one kilometre, if there was no wind?

w ww

. te

m . u

o c . che e r o t r s super

_____ minutes Hint: Work out how far the cyclist would go when biking with the wind for the same length of time biking against the wind. 40

Brain Bender 17

Answer

The Bike Ride

Students need to work out how far the cyclist would go in the same amount of time when biking with wind assistance and when biking with wind resistance.

To compare the effect of wind assistance and wind resistance, students need to have the rider experience biking in both conditions for the same length of time, such as six minutes.

r o e t s Bo r e p ok u S

In six minutes, with the wind, the rider would travel two kilometres.

ew i ev Pr

Teac he r

In six minutes against the wind, the rider would travel one kilometre. That is a total of three kilometres in 12 minutes (half of that time is with wind assistance and half of the time is with wind resistance). That is a rate of one kilometre in four minutes. So the answer is: it would take him four minutes to ride one kilometre if there was no wind.

w ww

. te

m . u

ÂŠ ReadyEdPubl i cat i ons â&#x20AC;˘f orr evi ew pur posesonl yâ&#x20AC;˘

o c . che e r o t r s super

Brain Bender 18

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Which Path? A traveller arrives on an island inhabited by two tribes. All members of one tribe always tell the truth and all members of the other tribe always lie. The traveller comes to the junction of two paths where he meets one of the islanders. One path leads to the village and the other path leads to the jungle. He wants to know which path he should take to reach the village.

r o e t s Bo r e p ok u S

The traveller has no way of knowing whether the islander is a truth-teller or a liar. The traveller thinks for a while and then asks only one question. From the islander’s answer to his question, he knows which path to take to get to the village.

ew i ev Pr

Teac he r

What question could the traveller have asked?

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m . u

o c . che e r o t r s super

Question: Hint: There is more than one question that the traveller could have asked. 42

Brain Bender 18

Answer

Which Path?

Students to test out different possibilities. Students examine all the possibilities. There is more than one possible solution to this problem.

r o e t s Bo r e p ok u S

One possible solution is:

“If you were a member of the other tribe, which way would you tell me to go to get to the village?”

ew i ev Pr

Teac he r

Consider the responses:

the V illag

ngl

Truth teller

w ww

. te

m . u

The truth-teller always tells the truth and he knows that a member of the other tribe will lie and point to the jungle, so he points to the jungle.

o c . che e r o t r s super To

the V illag

ngl

o T

Ju the

Liar

The liar knows that the truth-teller will point to the village, so he lies and points to the jungle. Solution: Ask the questions above and take the opposite path.

Brain Bender 19

How do you rate this Brain Bender? Brain Boring!

Easy on the Brain!

Brain Bending!

Super Dooper Brain Bending!

Ellie and Edgar Two tribes live on an island. Members of one tribe always tell the truth and members of the other tribe always lie. You meet two islanders named Ellie and Edgar. Ellie says, “We are from different tribes.” Edgar says, “Ellie is from the tribe of liars.”

r o e t s Bo r e p ok u S

Which tribe is Ellie from?

ew i ev Pr

Teac he r

Which tribe is Edgar from?

We are from different tribes

m . u

w ww

. te

Ellie is from the tribe of liars

o c . che e r o t r s super

Ellie is from the tribe who_____________

Edgar is from the tribe who_____________

Hint: Use a guess and check approach to solve this problem. Assume that Ellie is lying, then check your assumption, if it does not make sense, make another assumption to check. 44

Brain Bender 19

Answer

Ellie and Edgar

Students should make assumptions and check their accuracy.

r o e t s Bo r e p ok u S

The four possibilities are:

Teac he r • • • • •

Edgar T F T F

ew i ev Pr

Possibility 1 Possibility 2 Possibility 3 Possibility 4

Ellie T T F F

The first is not possible because Ellie would be lying. The second is possible because Ellie would be telling the truth. The third is not possible because Ellie would be telling the truth. The fourth is possible because Ellie would be lying. Either way, Edgar is a liar.

So Edgar will be lying when he says that Ellie is a liar. So Ellie is a truth teller. So the answer is: Ellie is from the tribe who tell the truth and Edgar is from the tribe who lie.

w ww

. te

m . u

o c . che e r o t r s super Ellie is from the tribe who tells the truth

Edgar is from the tribe who lies

Teac he r

ew i ev Pr

r o e t s Bo r e p Teasers ok u Brain S

w ww

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m . u

o c . che e r o t r s super

Brain Teaser 1

Brain Teaser 2

Just a Symbol

Adding Weight What can you put in a box that weighs nine kilograms to make it weigh eight kilograms?

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

What arithmetic symbol can be placed between two and three to make a number greater than two but less than three?

w ww

A half is a third of it. What is it?

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Cakes

m . u

What is it?

A girl had seven cakes and ate all but three. How many were left?

o c . che e r o t r s super

Brain Teaser 5

Brain Teaser 6

Bottle and Cork

My Pets How many pets do I have if all of them are cats except two, all are dogs except two, and all are budgies except two?

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

A bottle and its cork together cost 11 cents. The bottle costs ten cents more than the cork. How much does the bottle cost?

w ww

A big Indian and a little Indian are sitting on a fence. The little Indian is the son of the big Indian, but the big Indian is not the father of the little Indian. How are the Indians related?

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A Weighty Problem

m . u

The Indians

o c . che e Which is lighter – a tonne of r o t r sor a tonne of feathers? supebricks r

Brain Teaser 9

Brain Teaser 10

Cigarette Poison

Gold

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

If there are 500 identifiable poisons in one cigarette, how many are there in two such cigarettes?

Today we have $10 notes and $20 notes, but in the past, we had $10 and $20 solid gold coins. A $20 gold piece, contained twice as much gold as a $10 gold piece and both were pure gold. Which would be worth more: half a kilogram of gold $20 pieces or one kilogram of $10 gold pieces?

w ww

If a number is increased or decreased by ten, we will have a square number. What is the number?

. te

What Day is it?

m . u

Square Numbers

The day after the day after tomorrow, will be the day before the day before Sunday. What day is it today?

o c . che e r o t r s super

Brain Teaser 14

Pesky Possums

Tim's Truck

Anna was sure that possums had been eating her peaches. One night she fired a shot and half of the possums ran away, but one returned. Anna took aim again and once more, half of the possums ran away and one returned. When she counted them there were as many possums left as there were to start with. How many possums were there to start with?

Tim drives a truck. He stops at a tunnel with a sign that says, “Clearance Four Metres”. Tim knows that his truck is just over four metres high. What can he do to get through the tunnel?

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

Brain Teaser 13

w ww

My doctor gave me five pills to be taken at halfhourly intervals. If I follow her instructions, over what period of time will I take the pills?

. te

Coloured Socks

m . u

My Medicine

In my drawer, I have four red socks and four black socks. If it was dark and I couldn’t see the colours, what would be the least number of socks that I would need to take out to make sure that I had a pair of the same colour?

o c . che e r o t r s super

Answers to Brain Teasers

r o e t s Bo r e p ok 2. A hole u S3. One and a half 4. Three 5. Ten and a half cents 6. Three

ew i ev Pr

Teac he r

1. A decimal point

7. The big Indian is the little Indian’s mother

w ww

11.

12.

Tuesday

13.

Two

14.

Lower the tyre pressures

m . u

15. Two hours . te 16. Three o c . che e r o t r s super

Teac he r

ew i ev Pr

r o e t s Bo r e p ok u S

w ww

. te

m . u

o c . che e r o t r s super