Textbook
Prathomsuksa 5 © 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
BDRC305031_GoGetMaths TB Prelimpage P5.indd 1
885-87220-0360-9 First Published 2022
24/1/2565 BE 12:02
Contents Chapter 1
Chapter 2
Addition and subtraction of fractions
1
Lesson 1 Lesson 2 Lesson 3 Lesson 4
2 4 10 16
Multiplication of fractions
21
Lesson 1 Lesson 2 Lesson 3 Lesson 4
22 24 29
Lesson 5
Chapter 3
Chapter 4
Chapter 5
Fraction of a set Multiplication of a fraction by a whole number Multiplication of fractions Multiplication of a mixed number by a whole number, and mixed numbers Word problems
34 37
Division of fractions
41
Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5
42 44 47 50 53
Reciprocals Division of a fraction by a whole number Division of a whole number by a fraction Division of fractions Word problems
Mixed operations of fractions
57
Lesson 1 Lesson 2
58 61
Order of operations Word problems
Decimals Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5
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Fractions and division Comparing and ordering fractions Addition and subtraction of fractions Word problems
68 Estimation of decimals Multiplication of decimals Division of decimals Decimals and fractions Word problems
69 73 80 86 88
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Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Percentages
91
Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5
92 94 96 99 103
Percentages Percentages as fractions and decimals Fractions and decimals as percentages Percentage of a quantity Word problems
Units of length and mass
108
Lesson 1 Lesson 2
109 114
Conversion between units Word problems
Volume and capacity
117
Lesson 1 Lesson 2 Lesson 3
Volume and capacity of a cuboid Volume of a liquid Word problems
118 126 129
Perpendicular lines and parallel lines
133
Lesson 1 Lesson 2 Lesson 3
Perpendicular lines Parallel lines Angles
134 138 142
Quadrilaterals and prisms
153
Lesson 1 Lesson 2 Lesson 3 Lesson 4
154 163 169 171
Properties of quadrilaterals Drawing quadrilaterals Angles in quadrilaterals Prisms
Perimeter and area of quadrilaterals
174
Lesson 1 Lesson 2 Lesson 3
175 178 184
Perimeter of a quadrilateral Area of a parallelogram and a rhombus Word problems
Bar graphs and line graphs
187
Lesson 1 Lesson 2
188 198
Bar graphs Line graphs
Computational thinking
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The big idea
Illustrates a scenario through which students can connect to the chapter.
Chapter 8
Volume and capacity
Computational thinking
Special Features
Introduces a new approach for solving complex problems with confidence.
The edge of the cubes is 1 m long. How do we find the volume of each cube? Must we fill it with water to find its volume?
Lesson 1
Volume and capacity of a cuboid
Lesson 2
Volume of a liquid
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
4 _ = ?% 4 _ 5 = ?% 5
Starting point
Can we change a fraction or a decimal into a percentage?
Learning to know
Breaking a complex problem into manageable, smaller problems
Lesson 3 Fractions and decimals as percentages
Learning to know
Algorithms
1.5 = ?% 1.5 = ?%
Developing a set of step-by-step solution
Fractions as percentages
Identifying similarities and differences, and observing similar patterns
Abstraction Focusing on relevant information, and removing irrelevant information
2 Convert 5 into a percentage. Method 1: Convert it into its equivalent fraction with 100 as the denominator.
Introduces new concepts using the CPA approach with engaging illustrations.
Pattern recognition
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. 2 40 5 = 100
Computational thinking | 203
× 20
2 5
= 40%
=
40 100
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× 20
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Method 2: Multiplying the fraction with 100%. 2 2 5 = 5 × 100% 200 = 5 %
Fun with Maths!
= 40%
Thinking corner
Challenges students with unconventional questions to develop higher-order thinking skills.
Which method do you prefer? Why? 96 | Mathematics Prathomsuksa 5
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Allows students to explore mathematical concepts actively either as an individual or in groups.
1. Get into groups of five. 2. Get a few prisms and count the numbers of total faces (bases and lateral faces), vertices and edges of the prisms. Fill in the table. In the table, F stands for the number of total faces, V stands for the number of vertices and E stands for the number of edges. Quadrilaterals
F
V
E
F+V
E+2
Triangular prism Square prism Cuboid Pentagonal prism Hexagonal prism 3. What do you infer from the last two columns? Are they the same? This relationship is known as Euler’s formula. It is applicable for any polyhedrons.
1. Name the parts of this prism.
Try this
2. Name these prisms.
Chapter 10 | 173
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Provides various exercises to immediately evaluate students’ understanding.
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Chapter 1
Addition and subtraction of fractions
How do you divide the two pizzas equally among the three of them?
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Lesson 1
Fractions and division
Lesson 2
Comparing and ordering fractions
Lesson 3
Addition and subtraction of fractions
Lesson 4
Word problems
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Lesson 1
Fractions and division
Starting point
There are two children. There is a pizza. How do we divide the pizza equally among the children? What fraction of a pizza will each child get?
Learning to know
Fractions as division
When 2 pizzas are divided equally between 2 children, each child gets 1 pizza. 2 2÷2= 2 =1
When 2 pizzas are divided equally among 3 children, each child gets 2 pizza. 3
2 2÷3= 3 2 1444442444443
We can use a bar model to represent it.
2 3
2 3
2 3
2 | Mathematics Prathomsuksa 5
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3 When 3 pizzas are divided equally among 4 children, each child gets 4 pizza.
3 14444444244444443
3 3÷4= 4
3 4
3 4
3 4
3 4
What fraction of a pizza does a child get when 3 similar pizzas are shared equally between 2 children? 3 3÷2= 2
3 144424443 3 2
3 2
1 = 12
or
1 2 3 – 2 1
3 1 Each child gets 2 or 1 2 of a pizza.
Express each as a fraction or a mixed number in its simplest form. 1. 3 ÷ 5 =
2. 9 ÷ 12 =
3. 16 ÷ 10 =
Chapter 1 | 3
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Lesson 2 Comparing and ordering fractions Starting point
1 3
Analyze the 3 fractions.
4 9
Which is the greatest? Which is the smallest? How do you find out?
7 18
Comparing fractions
Learning to know
Which is greater, 1 or 3 ? 3 5 We cannot compare them directly because they have different denominators. We need to change them to fractions with the same denominator first.
×5
1 3
= ×5
×3
5 15
3 5
9 15
= ×3
Now, compare 5 and 9 . 15 15
5 15
9 15
9 is greater than 5 . 15 15 So, 3 is greater than 1 . 5 3 4 | Mathematics Prathomsuksa 5
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3 1 Which is smaller, 5 or 2 ? ×2
3 5
×5
6 10
=
1 2
×2
5 10
= ×5
6 10
5 10
5 is smaller than 6 . 10 10 So, 1 is smaller than 3 . 2 5 2 1 Which is greater, 1 3 or 1 2 ? Since the whole numbers of both mixed numbers are the same, we need to compare only the fractional parts. ×2
2 3
=
×3
4 6
1 2
=
×2
×3
4 6
3 6
3 6
4 is greater than 3 . 6 6 So, 1 2 is greater than 1 1 . 3 2 Chapter 1 | 5
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1 5 Which is smaller, 3 4 or 1 7 ?
When comparing mixed numbers, compare the whole numbers first.
1 is smaller than 3. 5 1 So, 1 7 is smaller than 3 4 .
5 Which is greater, 2 6 or 14 ? 5 Method 1: Convert the mixed number into an improper fraction. ×6
×5
5 17 26 = 6
85 30
=
14 5
84 30
= ×6
×5
85 is greater than 84 . 30 30 5 So, 2 6 is greater than 14 . 5
Method 2: Convert the improper fraction into a mixed number. ×5
5 26
=
×6
25 2 30
14 4 5 =25
×5
=
24 2 30
×6
2 25 is greater than 2 24 . 30 30 5 So, 2 6 is greater than 14 . 5
Which method is easier for you? Why?
6 | Mathematics Prathomsuksa 5
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Which is smaller, 45 or 5 2 ? 8 3 Method 1: Convert the mixed number into an improper fraction. ×3
45 8
×8
2 17 53 = 3
135 24
=
=
×3
136 24
×8
135 is smaller than 136 . 24 24 So, 45 is smaller than 5 2 . 8 3 Method 2: Convert the improper fraction into a mixed number. ×3
45 5 = 5 8 8
×8
2 53
15 5 24
=
=
×3
16 5 24
×8
5 15 is smaller than 5 16 . 24 24 So, 45 is smaller than 5 2 . 8 3 Compare 11 and 15 . 8 11 × 11
11 8
=
×8
121 88
15 11
× 11
121 120 88 is greater than 88 . So, 11 is greater than 15 . 8 11
=
120 88
×8
or
120 121 88 is smaller than 88 . So, 15 is smaller than 11 . 11 8 Chapter 1 | 7
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