E-book Code: REAU0001 For Junior Primary

Maths Problem Solving for Juniors Book 1 Problem solving strategies and practice activities for the classroom. Written by Lynne Stephenson. Illustrated by Rod Jefferson. ÂŠ Ready-Ed Publications - 1996. Published by Ready-Ed Publications (1996) P.O. Box 276 Greenwood W.A. 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However, this permission is not transferable and applies only to the purchasing individual or institution. ISBN 1 87526 824 3

Problem Solving Maths Book 1

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Problem Solving Maths Book 1

Book 1 Contents Page ACTIVITIES Section 1 - Developing Logical Thinking

Page 5

Which Dog Belongs To The Smiths? Which Child is Going To The Circus Tomorrow? Help Sam Find Harry’s House Luke’s Caterpillars A Running Race Sports Puzzle Time For Games Playing Cards

6 7 8 9 10 11 12 13

Section 2 - Using Number Concepts To Develop Logical Reasoning

14

An Insect Collection Surrounded By Numbers Shape Count Masked Numbers Matchstick Construction Mystery Number Balloons For Sale Dress Up The Scarecrow Tabby’s Food

15 16 17 18 19 20 21 22 23

Section 3 - Developing Visual Imagery

24

Shapes In Shapes Triangles In Shapes Shape It Trying Triangles Build And Count More To Build And Count Folding Triangles Folding Rectangles

25 26 27 28 29 30 31 32

Section 4 - Pattern Perception

33

Pet Parade A Day At The Beach Block Patterns Grid Patterns - 1 Grid Patterns - 2

34 35 36 37 38

Answers

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39, 40

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Problem Solving Maths Book 1

Teachersâ€™ Notes This Problem Solving Maths set represent a response to current syllabus trends and the considerable emphasis which is placed on the development of problem solving skills in primary school students. Essentially activities are designed to interest and stimulate children in the 6 - 9 years age range. They are presented as Blackline Masters which are able to be photocopied for use in the classroom.

IMPLEMENTING PROBLEM SOLVING MATHS ACTIVITIES A variety of factors will be considered by a teacher when he/she plans a unit of work including, aspects such as the previous problem solving experience of the students, their level of ability and the resources available. The use of an appropriate teaching strategy is often an area of concern when undertaking to implement a different emphasis in a new syllabus. The following considerations may assist: * Time taken to solve the problem prior to presenting it to students often proves to be valuable. It provides the opportunity ... - to be fully aware of the requirements of the problem; - to attempt the solution using a variety of problem solving strategies; - to reduce the problem into stages with appropriate hints for students to use, rather than giving an answer; - to identify possible alternative solutions and their acceptability; - to evaluate the suitability of the activity to the particular class, group or individual. * Initially problem solving activities could be worked through step-by-step with the students. This provides a framework which individuals can use when required to work more independently. Further, it may reduce the frustration at times encountered by mathematically able students or creative thinkers who experience difficulty with reading. During these initial sessions a teacher is able to demonstrate a plan or procedure such as the one below which students can follow, e.g. S Step 1 Read and discuss the problem. S Step 2 Think about it. S Step 3 Ask questions about it. S Step 4 Try and use a strategy. S Step 5 Check the answer. Working through a number of problems in a structured, step-by-step approach allows students to become familiar with a range of problem solving strategies: - estimating - simplifying the problem - organising information into lists, table, etc. - drawing pictures or diagrams - identifying patterns - predicting - thinking logically - evaluating the strategy used, the solution - checking results - working backwards

STRUCTURE OF PROBLEM SOLVING BOOK 1 For convenience the booklet has been divided into four sections. In each section a particular aspect of problem solving is in focus, although it is recognised that a great deal of overlap exists. It is felt that more effective use would be gained by selection of activities from each section rather than working through the package in page number sequence. Generally, within each section a number of similar activities have been provided in order that skills can be introduced and consolidated. Sections are headed by a brief summary of the skill being covered in the pages to follow.

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Problem Solving Maths Book 1

Section 1 Developing Logical Thinking The activities in this section encourage the ability to think clearly and to reason logically. A number of activities require students to organise their information in table format, i.e. matrix logic problems.

Procedure for Matrix Logic Problems 1. Names are listed down the left side of the table. 2. Across the top of the grid the features are listed, e.g. position, colour, sport, etc. 3. The information is tabled by ticking the appropriate box. Once a box is ticked all other boxes across from, and above or below, the feature are crossed. e.g. A Running Race Position 1st

2nd

3rd

4th

5th

Names Joe

Patrick

N.B. Further information is entered as clues are used to solve the problem.

Table Logic Problems In Table Logic Problems diagrams must show the correct seating around a table. Students need to know that: * Partners always sit opposite each other. * People sit facing the table. (This is important when working out who sits to the left or right of a person.) * A person's first (given) name is written on the top line, surname on the bottom. * Answers may appear to be different from your solution. Make sure that each person has the correct partner and the correct person to the left and right. e.g. Ross Miles John Smith

David Long David Long

Pam Thomas

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Can be Ross Miles shown as ...

Pam Thomas John Smith

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Name: ................................

Which Dog Belongs To The Smiths?

Problem Solving Maths Book 1 Understanding and applying mathematics.

R Use the clues below to help you decide.

R The Smith’s dog has long ears. R It does not have a collar. R It has short hair. Colour the Smith’s dog brown and white. Colour the other dogs in your favourite ‘dog colours’.

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Problem Solving Maths Book 1

Name: ................................

Understanding and applying mathematics.

Which Child Is Going To The Circus Tomorrow? Use the clues below to help you decide. R The child has dark shoes. R The child is standing on only one box. R The child is not wearing a dress.

Betty

Susan

Tommy

Barry

Write your answer here _______________________ Colour: The children who wonâ€™t go to the circus in red and blue. The child who will go to the circus in brown and green. Ready-Ed Publications

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Problem Solving Maths Book 1

Name: ................................

Shape and space: Properties of 2D shapes.

Help Sam Find Harry's House

R Harryâ€™s house is not a half-circle shape. R It is not a cube shape. R It does have square windows.

Tick the

which shows Harryâ€™s house.

On another piece of paper draw a house that you would like. Make sure it has some square parts and some round parts. Page 8

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Name: ................................

Problem Solving Maths Book 1

Lukeâ€™s Caterpillars

Understanding and applying mathematics.

Luke has collected some different caterpillars from around his garden.

1. Which caterpillar did Luke find on the plant? Use the clues. R It was not thin. R It was hairy. R It had no feelers. Colour it brown. 2. Which caterpillar did Luke find on the wall? Use the clues. R It was not hairy. R It was thin. R It had feelers. Colour it green. Put Luke's caterpillars in an aquarium. Make it a home that caterpillars like. Ready-Ed Publications

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Name: ................................

A Running Race

Problem Solving Maths Book 1 Understanding and applying mathematics. Data handling.

R It was Sports Day. Five children ran in a 50 metre race. Joe was the first to cross the line. Patrick came last. If Sally was behind Sue and Ed was behind Sally, whocame second in the race? R Use the clues above.

Names

Joe

5th (last)

1st (first)

Complete the table (matrix) below to help you. (Some information has been entered as a guide.)

x

Patrick

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Problem Solving Maths Book 1

Name: ................................

Sportsâ€™ Puzzle

Understanding and applying mathematics. Data handling.

Sally, Ricky, Erin, Toni and Paul each have a favourite sport. No two children have the same favourite. Which sport is the favourite of each child? R Match each child to the sporting gear for his or her favourite sport.

R Clues 1. Sallyâ€™s favourite is not basketball. 2. Ricky does not like to play basketball or tennis. 3. One person really loves to play baseball. 4. Erin enjoys playing cricket. 5. Toni is not able to play rugby. 6. Paul really enjoys playing the sport that Toni is not able to play. Complete the table (matrix).

Names

tennis

base ball

Sports

Sally Ricky Erin

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Name: ................................

Problem Solving Maths Book 1 Understanding and applying mathematics.

Time For Games Some children have finished their work. Four of them decide to play a card game. Where does each sit?

R Use these clues. 1. 2. 3. 4.

John, Tammy, Anna and Ross are playing a card game. John is the dealer and deals the first card to his right. Anna gets the first card. Ross, who is sitting across from Anna, wins.

Remember to use the rules for table logic activities. R Write the childrenâ€™s names around the table. Page 12

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Name: ................................

Playing Cards

Problem Solving Maths Book 1 Understanding and applying mathematics.

Cameron and Ross are new children to the class. They are the only twins in the room. Two girls ask the boys to play cards. The boys are keen to join in and make new friends. R Find out where each person sits during the card game.

R Use these clues. 1. Cameron and Ross are twins. 2. Rebecca and Jane often play together so they decide to be partners. 3. Ross peeks at Miss Tan's cards, so Jane playfully slaps Ross across the shoulder with her left hand, without turning her chair. 4. Cameron Yates keeps score because he has neat handwriting. 5. Ms Jones sits to the right of Ross. Ready-Ed Publications

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Problem Solving Maths Book 1

Section 2 Using Number Concepts To Develop Logical Reasoning This section places emphasis on the application of number and measurement skills in logical thinking activities. Appearing on the top right corner of many of the worksheets is a calculator symbol indicating that a calculator is a useful aid in completing the activities on the page. Students require a basic level of understanding and skills in the use of a calculator.

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Problem Solving Maths Book 1

Name: ................................

Making sense of number problems. Data handling.

An Insect Collection

R Count The Insects 1. There are _____ insects in the circle but not in the rectangle or the hexagon. 2. There are _____ insects in the rectangle but not in the circle or hexagon. 3. There are _____ insects in the hexagon but not in the circle or the rectangle. 4. There are _____ insects in the rectangle and circle but not the hexagon. (Hint for 4 & 5: In the area where the circle and the rectangle overlap.) 5. There are _____ insects in the rectangle and hexagon but not the circle. 6. Altogether there are______

insects. Write the number

sentence here. _________________________________ Ready-Ed Publications

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Problem Solving Maths Book 1

Name: ................................

Surrounded By Numbers

Making sense of number problems. Reasoning about nos.

R WRITE THE NUMBER SENTENCES 1. Add the number above the car to the number under the truck. __________ + __________ = __________ 2. Add the number behind the truck to the number under the car. __________ + __________ = __________ 3. From the number in front of the helicopter take the number in front of the car. __________ + __________ = __________ 4. Take the number in front of the car from the number above the truck. __________

+

__________

=

__________

5. In the boxes write the total of the numbers around each picture. 6. Colour the picture with the highest total around it. Page 16

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Problem Solving Maths Book 1

Name: ................................

Shape Count

Making sense of number problems. Solving no. puzzles.

R Calculate the values of the shapes below. Use ...

each straight line is worth 1. each circle is worth 2. each black circle is worth 5.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

R Use coin(s) and a ruler. Draw a different shape picture worth:

8.

9.

10.

Make up some of your own.

Give them to a partner to work out. Ready-Ed Publications

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Problem Solving Maths Book 1

Name: ................................

Masked Numbers

Making sense of number problems. Solving no. puzzles.

Calculate the â€˜number valuesâ€™ of the masks below. Use ...

each straight line is worth 1. each white circle is worth 5. each black circle is worth 10.

R In the box draw a clown mask. Make it worth more than 50.

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Problem Solving Maths Book 1

Name: ................................

Making sense of number problems. Solving no. puzzles.

Matchstick Construction Chris and James enjoy making shapes using coloured matchsticks. For extra fun they give the different colours a number * * * *

pink matchsticks are worth 1, yellow matchsticks are worth 2, blue matchsticks are worth 3, plain (not dyed) matchsticks are worth 4.

R With your matchsticks (you will need about 8 of each colour) make the shapes described below. Draw your shape in the box. Colour it.

A square worth 4

A square worth 8

A rectangle worth 6.

A square worth

A rectangle worth 18.

With some matchsticks and some Blue-Tac or play dough build a colourful cube. Draw it.

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This cube is worth

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Problem Solving Maths Book 1

Name: ................................

Mystery Number

Making sense of number problems. Solving no. puzzles.

R Connie and Peter often play Mystery Number.

Is your mystery number greater than ...?

In this game one person writes down a mystery number. His or her partner tries to guess the mystery number. The idea is to guess the mystery number with as few questions as possible.

Hints: * In the beginning play the game with Mystery Numbers less than 10 or less than 20. * Ask questions like: Is it greater than 5? Is it an odd number? ... rather than guessing a specific number.

R Connie has played Mystery Number many times. She has worked out the sort of questions which will give her the Mystery Number after asking only a few questions. Try it! What is the least number of questions Connie could ask Peter ... ...if the Mystery Number is 6? ________________ ...if the Mystery Number is 10? _______________ ...if the Mystery Number is 20? _______________ Page 20

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Name: ................................

Balloons For Sale

Problem Solving Maths Book 1 Making sense of number problems. Solving no. puzzles.

R

Bobo the clown is selling balloons. The round balloons he is holding are worth 70c altogether. (Each round balloon costs the same amount.)

R

Draw a heart shaped balloon on the eighth string. Now the balloons Bobo is holding are worth $1.00.

R

Bobo sells only blue, pink, yellow or green balloons.

Use the clues above to solve these problems. On Sunday Bobo sold out of balloons after two hours. If he sold a heart shaped balloon every ten minutes and four different colour round balloons every thirty minutes: * How many heart shaped balloons did he sell? _________________ * How much did he sell them for altogether? ____________________ * How many round balloons did he sell? _______________________ * How much money did he make from round balloons? ____________ Ready-Ed Publications

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Name: ................................

Problem Solving Maths Book 1 Making sense of number problems. Problems in 'real life'.

Dress Up The Scarecrow

Hat 50c

Trousers $1.00

R

T-shirt 50c

Jacket $1.00

Boots $1.00

Farmer Jones spent $2.00 buying clothes to dress the scarecrow.

There are six different outfits he could have bought for $2.00. Show them on the scarecrow in each box.

1. e.g. jacket, boots

2. ____________

3. ____________

4. ____________

5. ____________

6. ____________

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Problem Solving Maths Book 1

Name: ................................

Making sense of number problems. Solving no. puzzles.

Tabby’s Food R

Rosie kept a record of the cost of Tabby’s food each day.

$1.00

Bowl of biscuits - 20c

Saucer of milk - 5c

1.

On Monday Tabby’s food cost 25c. What food was Tabby given?

2.

On Tuesday Tabby’s food cost $1.05. What food did Rosie give Tabby?

3.

On Wednesday Tabby was unwell. Her food cost only 10c. What was Tabby given?

4.

On Thursday Tabby’s food cost $1.30. Rosie gave Tabby

5.

On Friday, Saturday and Sunday Tabby was given the same food as on Thursday. This week Rosie needed to buy ____ cans of food for Tabby.

6.

Rosie had 40c of her pocket money left after buying Tabby’s food. How much pocket money did she have to start with?

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Problem Solving Maths Book 1

Section 3 Developing Visual Imagery This section of the book includes activities which develop skills of copying, distinguishing features, and changing or reconstructing diagrams or models. Concrete activity is a vital component and should be encouraged as part of the problem solving process.

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Problem Solving Maths Book 1

Name: ................................

Shape and space: properties of 2D shapes.

Shapes In Shapes

Look carefully at the shapes below. Use different coloured pencils to outline each shape as you find it. How many squares? 1.

_________________

2.

______________

(n.b. The answer is not 9.)

3. How many triangles?

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4. How many rectangles?

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Problem Solving Maths Book 1

Name: ................................

Triangles in Shapes

Shape and space: properties of 2D shapes.

Trace this triangle onto a piece of paper. Cut it out. Use it to show how many triangles like this were used to make the shapes below.

This diamond is made

This hexagon is made

up of ________ triangles.

up of ________ triangles.

This parallelogram is made up of ________ triangles. This larger triangle is made up of ________ triangles. R Make up a shape of your own which is made up of ten of the triangles.

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Problem Solving Maths Book 1

Name: ................................

Shape and space: properties of 2D shapes.

Shape It

Copy these shapes onto the grid below. 1.

2.

3.

4.

If this rectangle is worth 4 write the value of the shapes below.

1.

2.

3.

4.

5.

R Make up some more of your own.

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Problem Solving Maths Book 1

Name: ................................

Trying Triangles

Shape and space: properties of 2D shapes.

Copy the shapes onto the grid below. 1. 2. 3.

4.

Solve these problems. If is worth 2 ... 1.

2.

3.

is worth

is worth

4.

is worth

is worth

R Make a shape worth 20. Page 28

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Problem Solving Maths Book 1

Name: ................................

Build And Count

Shape and space: properties of 3D shapes.

R Look carefully at the cube â€˜buildingsâ€™ below. Estimate how many cubes were used to build each. Use a coloured pencil to record them. Make each building using cubes. Count the cubes you needed. Record the number on your page. 1.

2.

3.

estimated ______

estimated ______

estimated ______

counted _______

counted________

counted _______

4.

5.

6.

estimated ______

estimated ______

estimated ______

counted _______

counted________

counted _______

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Problem Solving Maths Book 1

Name: ................................

Shape and space: properties of 3D shapes.

More To Build And Count

R Look carefully at the cube â€˜buildingsâ€™ below. Estimate how many cubes were used to build each. Use a coloured pencil to record your estimations. Make each building using cubes. Count the cubes you needed. Record the number on your page. 1.

2.

3.

estimated ______

estimated ______

estimated ______

counted _______

counted________

counted _______

4.

5.

6.

estimated ______

estimated ______

estimated ______

counted _______

counted________

counted

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Problem Solving Maths Book 1

Name: ................................

Shape and space: properties of 2D shapes.

Folding Triangles

Sally has been busily folding paper triangles. She has made some very interesting shapes.

R Match the triangles to the shapes they make when folded. 1.

A.

2.

B.

3.

C.

4.

D.

5.

E.

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Problem Solving Maths Book 1

Name: ................................

Folding Rectangles

Shape and space: properties of 2D shapes.

R Phillip is interested in origami (paper folding). He has found that lots of different shapes can be made by folding a rectangle in different ways. Match the rectangles showing the fold lines Phillip made to the new shapes they formed. You may like to fold some rectangles to check. 1.

A.

2.

B.

3.

C.

4.

D.

5.

E.

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Problem Solving Maths Book 1

Section 4 Pattern Perception This section acknowledges that recognising patterns is a significant strategy in problem solving. More complex problems require that a patterning strategy is used, e.g. Pet Parade - 3 cats are indicated as A B C. The use of a definite patterning strategy helps to organise different arrangements 1. ABC 2. ACB 3. BAC 4. BCA 5. CAB 6. CBA

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Problem Solving Maths Book 1

Name: ................................

Understanding and applying mathematics.

Pet Parade

R Here are pictures of my three cats. In how many different ways can I paste them in my photograph album? Show three different ways the catsâ€™ photos could be pasted into the album. Write the letter that matches the cat in each box. A.

B.

C.

R Now you may like to draw and colour the cats in the boxes. Page 34

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Name: ................................

A Day At The Beach

Problem Solving Maths Book 1 Understanding and applying mathematics.

Tanya canâ€™t decide what to take to the beach. She has a green towel and a blue towel, a red bathing costume and a black bathing costume. R Use your colouring pencils to show the four different outfits Tanya could wear.

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Name: ................................

Block Patterns

Problem Solving Maths Book 1 Understanding and applying mathematics.

R Make these patterns using unifix cubes. Complete them on the spaces or over the page. 1.

2.

3.

4.

R Make up a pattern of your own. Draw it on another piece of paper. R Colour the cubes to show the patterns. Page 36

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Problem Solving Maths Book 1

Name: ................................

Shape and space: position, direction, movement and angle.

Grid Patterns - 1 R Complete the patterns. Copy the pattern underneath. Colour or illustrate each.

Start *

Start *

Start *

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Problem Solving Maths Book 1

Name: ................................

Grid Patterns - 2

Shape and space: position, direction, movement and angle.

R Complete each line of patterns. Copy the pattern underneath. Colour the patterns. . .

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R Try these patterns. They are called networks. You draw the pattern without taking your pencil off the paper and without going over any line twice.

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Problem Solving Maths Book 1

Answers P6

dog top right

P7

Barry

P8

bottom left

P9

on plant - bottom line left; on wall - mddle line left.

P10

Sue came second.

P11

Sally - tennis; Ricky - baseball; Erin cricket; Toni - basketball; Paul - rugby. Ross

P12

John

Tammy Anna

P13

Rebecca Tan Ross Yates

Cameron Yates Jane Jones

P15

1. 6

P16

1. 7 + 1 = 8, 2. 4 + 5 = 9, 3. 9 - 3 = 6, 4. 8 - 3 = 5 5. car 15 truck 13

helicopter 18

P17

1. 4 5. 3 9. 9

3. 6 7. 5 11. 3

P18

P20

Dog 27 bird 25 elephant 44 cat 58 pink square, yellow square, pink rectangle, blue rectangle or rectangle with blue short ends and yellow and plain longer ends. 6-3 10 - 4 20 - 5

P21

12, $3.60,

P19

2. 4

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3. 5

4. 2 5. 0

2. 9 6. 5 10. 7

6. 21

4. 9 8. 6 12. 8

16, $1.60

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Problem Solving Maths Book 1 P22

jacket, trousers jacket, t-shirt, hat trousers, t-shirt, hat trousers, boots boots, t-shirt, hat

P23 1. biscuits, saucer of milk or 5 saucers of milk. 2. can of food, saucer of milk or 5 bowls of biscuits & saucer of milk or 25 saucers of milk. 3. 2 saucers of milk or half a bowl of biscuits 4. can, biscuits, 2 saucers of milk or can, 1 1/2 bowls biscuits or 1 can, 6 saucers of milk or 6 bowls biscuits, 2 saucers of milk 5. The most common answer is 5. Other answers may be acceptable if alternative combinations of food are used. Check for adding accuracy. 6. $7.00 P25 1. 14 2. 18 3. 13 4. 29 P26 diamond-2 hexagon-6 parallelogram-3 triangle-9 P27 1. 2 2. 6 3. 8 4. 12 5. 10 P28 1. 1 2. 4 3. 4 4. 12 P29 1. 8 2. 6 3. 6 4. 10 5. 5 6. 10 P30 1. 12 2. 10 3.16 4. 17 5. 19 6. 27 P31 1. c 2. d 3. e 4. b 5. a P32 1. e 2. c 3. a 4. b 5. d P34 There are 6 different ways they could be ordered ACB CAB BCA CBA BAC ABC P35 1. Green towel and red bathing costume. 2. Green towel and black bathing costume. 3. Blue towel and red bathing costume. 4. Blue towel and black bathing costume.

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