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
BDRC306031_GoGetMaths TB Prelimpage P6.indd 1
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
210 | Mathematics Prathomsuksa 6
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? Chapter 8 | 131
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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
Chapter 2 | 25
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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? 2 | Mathematics Prathomsuksa 6
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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.
4 | Mathematics Prathomsuksa 6
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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.
60 = 2 × 2 × 3 × 5 6 | Mathematics Prathomsuksa 6
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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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