Go Get Maths Textbook P6 samplebook

Textbook

Prathomsuksa 6 © Pelangi Publishing (Thailand) Co., Ltd. 2022 All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means without permission of Pelangi Publishing (Thailand) Co., Ltd. 2022

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885-87220-0361-6 First Published 2022

29/1/2565 BE 13:38

Contents Chapter 1

Chapter 2

Factors and multiples

1

Lesson 1 Lesson 2 Lesson 3 Lesson 4

2 8 11 15

Fractions Lesson 1 Lesson 2 Lesson 3 Lesson 4

Chapter 3

Chapter 6

21 26 30 32

39 Decimals and fractions Division of decimals by decimals Word problems

40 45 47

54 Ratios Equivalent ratios Word problems

55 59 63

Percentages

68

Lesson 1 Lesson 2 Lesson 3 Lesson 4

69 71 76 84

Percentage of a quantity Percentage increase and decrease Profit and loss Word problems

Patterns Lesson 1 Lesson 2

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Comparing and ordering fractions Addition and subtraction of fractions Mixed operations of fractions Word problems

Ratios Lesson 1 Lesson 2 Lesson 3

Chapter 5

20

Decimals Lesson 1 Lesson 2 Lesson 3

Chapter 4

Factors Highest common factor (HCF) Lowest common multiple (LCM) Word problems

92 Geometric and number patterns Word problems

93 100

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Chapter 7

Triangles Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5

Chapter 8

Chapter 11

Angles in polygons Perimeter of a polygon Area of a polygon Word problems

153 Parts of a circle Drawing circles Circumference of a circle Area of a circle Word problems

154 158 161 165 168

172

Lesson 1 Lesson 2 Lesson 3

173 180 184

Volume and capacity of cuboids and cubes Volume and capacity of solids Word problems

Solids

188 Cones, cylinders, spheres and pyramids Nets of solids

189 192

Pie charts

199

Lesson 1 Lesson 2

200 205

Reading a pie chart Word problems

Computational thinking

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131 140 143 148

Volume and capacity

Lesson 1 Lesson 2

Chapter 12

105 113 117 120 127

130

Circles Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5

Chapter 10

Triangles Drawing triangles Perimeter of a triangle Area of a triangle Word problems

Polygons Lesson 1 Lesson 2 Lesson 3 Lesson 4

Chapter 9

104

210

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The big idea

Illustrates a scenario through which students can connect to the chapter.

Chapter 4

Ratios

Computational thinking

Special Features

Introduces a new approach for solving complex problems with confidence.

The ratio of the number of fish to the number of turtles to the number of crabs is 5 : 2 : 3.

Lesson 1

Ratios

Lesson 2

Equivalent ratios

Lesson 3

Word problems

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Starting point

Provides questions to initiate thinking and jump-start learning.

Computational thinking is not about programming a computer or thinking like a computer. It is rather a set of systematic approaches to solving problems. Then, we can present the solutions in a way a computer or a human or both can understand.

There are four skills or elements in computational thinking.

Decomposition Breaking a complex problem into manageable, smaller problems

Angles in polygons

Lesson 1 Starting point

The 2 angles in the trapezium are 90º each.

The third angle is 72º. What is the size of the fourth angle? How do we find it?

Developing a set of step-by-step solution

72°

Exterior angle

Exterior angle

Interior angle

With this new approach, we will be able to tackle unfamiliar and complex problems with confidence.

It trains us to analyze information and deal with problems across disciplines. It will help us see a relationship between the school and the outside world.

Interior angle

The sum of the interior angles of a triangle is 180º.

25°

75°

50°

36°

55°

75º + 50º + 55º = 180º

Identifying similarities and differences, and observing similar patterns

Focusing on relevant information, and removing irrelevant information

Interior angle is the angle in the shape.

Exterior angle is the angle outside the shape.

Introduces new concepts using the CPA approach with engaging illustrations.

Pattern recognition

Abstraction

Interior angles of polygons

Learning to know

Learning to know

Algorithms

y

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119°

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36º + 25º + 119º = 180º Measure the angles with a protractor.

Thinking corner

Challenges students with unconventional questions to develop higher-order thinking skills.

Fun with Maths!

The sum of the interior angles of a quadrilateral is 360º. A quadrilateral is made up of 2 triangles. A pentagon is made up of 3 triangles. Is the sum of thek interior angles of a pentagon 540º?

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Allows students to explore mathematical concepts actively either as an individual or in groups.

1. Make groups of 4.

2. Each group is given 20 pieces of cards numbered 1 to 20.

15

3. Each student takes 2 cards and makes a fraction with the number on the first card as the numerator and the number on the second card as the denominator.

2

4. Compare the fractions.

5. The person who can tell the greatest fraction from the 4 fractions correctly wins a point.

6. Return the cards and shuffle them. Repeat the game for 5 times.

7. The person with the most points wins.

1. Fill in the blanks with > or <.

23 (a) 1 5 12 14

(b) 11 12

7 8

(c) 23 15

31 20

(d) 7 4

17 10

(e) 2 9 14

2 13 21

(f) 5 7 9

35 6

7 10

Try this

Provides various exercises to immediately evaluate students’ understanding.

2. Arrange these fractions. (a) In ascending order: 2 5

3 10

3 8

7 16

3 4

5 8

15 18

19 12

5 16

(b) In descending order: 5 9

7 12

2 3

(c) In ascending order: 18 15

17 10

2 15

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Chapter 1

Factors and multiples

The red lights flash every 5 seconds. The blue lights flash every 3 seconds. Now they are flashing. After how many seconds later will they flash again?

Lesson 1

Factors

Lesson 2

Highest common factor (HCF)

Lesson 3

Lowest common multiple (LCM)

Lesson 4

Word problems

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Lesson 1

Factors

Starting point

Every whole number is a factor of itself.

1 is a factor of every whole number.

What is a factor?

Learning to know

Factors The factors of a whole number are the numbers that can divide the whole number exactly, that is without any remainders.

12 ÷ 3 = 4 Factor

No remainder

We can divide 12 by 3 exactly. So, 3 is a factor of 12.

12 ÷ 2 = 6 Factor

No remainder

We can divide 12 by 2 exactly. So, 2 is also a factor of 12.

A whole number has 2 or more factors.

Are there any more factors of 12? Is 1 a factor of 12 too?

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12 ÷ 1 = 12 12 ÷ 2 = 6 12 ÷ 3 = 4

12 ÷ 4 = 3 12 ÷ 6 = 2 12 ÷ 12 = 1

The factors of 12 are 1, 2, 3, 4, 6 and 12.

We can also use multiplication to find the factors of a whole number.

20 = 1 × 20

20 = 4 × 5

20 = 2 × 10

Factors

Factors

Factors

The factors of 20 are 1, 2, 4, 5, 10 and 20.

List the factors of 40.

40 = 1 × 40 40 = 4 × 10

40 = 2 × 20 40 = 5 × 8

The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

Is 6 a factor of 140?

23 6 140 – 12 20– 18 2

Every whole number has at least 2 factors, which are 1 and the number itself.

140 cannot be divided by 6 exactly.

So, 6 is not a factor of 140.

Chapter 1 | 3

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Learning to know

Prime numbers A prime number can be divided by 1 and the number itself only. It has only 2 factors, 1 and itself.

7÷1=7

7÷7=1

7 cannot be divided by any other numbers exactly except 1 and 7.

So, 7 is a prime number.

0 and 1 are not prime numbers.

The only even prime number is 2. All other even numbers can be divided by 2. All even numbers except 2 are not prime numbers.

If the sum of all the digits in the number is divisible by 3, the number is divisible by 3. Then, the number is not a prime number except 3.

Whole numbers with 5 in the ones place are not prime numbers except 5. They can be divided by 5.

So, to prove if a number is a prime number, go through the criteria above. Then, try to divide it by other prime numbers such as 7, 11 and 13.

Is 105 a prime number?

105 has 5 in the ones place.

105 ÷ 5 = 21 So, 105 is not a prime number.

Is 78 a prime number?

78 is an even number.

78 ÷ 2 = 39 So, 78 is not a prime number.

Is 159 a prime number?

1 + 5 + 9 = 15 15 is divisible by 3.

159 ÷ 3 = 53 So, 159 is not a prime number.

Is 17 a prime number?

17 is not divisible by 2, 3, 5, 7, 11 and 13.

So, 17 is a prime number.

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Prime factors

Learning to know

Prime factors are factors of a whole number which are prime numbers themselves.

36 = 1 × 36 36 = 2 × 18

36 = 3 × 12 36 = 4 × 9

36 = 6 × 6

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Among the factors, 2 and 3 are prime numbers.

So, the prime factors of 36 are 2 and 3.

List all the prime factors of 42.

42 = 1 × 42 42 = 3 × 14

42 = 2 × 21 42 = 6 × 7

The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

The prime factors of 42 are 2, 3 and 7.

1. Get into groups of 5.

2. The teacher will show a whole number on the board.

3. 2 persons in each group will list the factors of the whole number on a piece of paper. 2 other persons will identify the prime numbers from the list of factors.

The last person will raise his/her hand to tell the prime factors of the whole number.

4. The fastest group with the correct answer will get a point.

5. This goes on for 10 rounds with each team member changes his/her role in each round.

6. The group with the most points wins the game.

Chapter 1 | 5

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Learning to know

Prime factorization

A whole number can be expressed as a product of its prime factors. The method to find this is known as prime factorization.

Express 60 in the form of prime factorization.

Method 1: Repeated short division Divide by the smallest prime number. Keep dividing until the quotient is 1.

2 60 30 123

2 30 3 15 5 5 1 60 = 2 × 2 × 3 × 5

60 ÷ 2 = 30

Continue dividing with the smallest prime number.

Divide until the quotient is 1.

Multiply all the divisors.

Method 2: Factor tree 60 60 = 6 × 10

6=2×3

6

10

5 2144424443 3 2

10 = 2 × 5

Keep factorizing them until all are prime factors.

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We can write 60 = 2 × 2 × 3 × 5 as 60 = 22 × 3 × 5.

We read 22 as 2 to the power of 2 which means 2 × 2.

43

75

We read 43 as 4 to the power of 3 which means 4 × 4 × 4.

We read 75 as 7 to the power of 5 which means 7 × 7 × 7 × 7 × 7.

This method of expressing the repeated multiplication is known as index notation.

Express 120 in the form of prime factorization.

Method 1: Repeated short division

Method 2: Factor tree 120

2 1 20 2 60 2 30 15 3 5 5 1

6 2

20 3

4 2

120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5

1. List the factors of (a) 24

5 2

120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5

(b) 56

(c) 102

2. List the first 10 prime numbers.

3. State if these numbers are prime numbers. (a) 59 (b) 85

(c) 91

4. List the prime factors of (a) 42 (b) 81

(c) 124

5. Express these numbers in the form of prime factorization. Write them in index notation. (a) 165 (b) 88 (c) 216 Chapter 1 | 7

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