Pupil’s Book 0.2
Maths 5A 3rd Edition
F 2 O% O
F
IST RY O F
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APP R
ON AT I
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us
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•
Dr Fong Ho Kheong • Gan Kee Soon • Chelvi Ramakrishnan
BY
D
D
– e f rom 2017
2
11/7/16 6:33 pm
Preface My Pals Are Here! Maths (3rd Edition) is a comprehensive, task-based and learner-centred programme designed to provide pupils with a solid foundation in mathematics and opportunities to become efficient problem solvers. My Pals Are Here! Maths (3rd Edition) continues to make learning mathematics fun and rewarding through the use of engaging illustrations, photographs, hands-on activities and interactives that help reinforce and consolidate learning for pupils of different abilities. A calculator may be used when
appears.
For the Pupil:
NEW!
Practise new concepts learnt in parallel questions with help from your teacher in TRY!
ber.
TRY 1A
d num 1 ess your answer as a mixe Multiply 2 3 by 3. Expr lator. sing a calcu
Then, check your answer u
Put On Your Thi 1 Anna cycled from
School
TRY 1B
mplest form. s your answer in its si
Multiply. Expres
a 3 6 3 2 5
c
3 1 4 3 8 5
e 2 9 3 16 5
5
d
1
4 2 5
1 8 4 5
ow many marke
rs did Rehna bu
altogether?
f coins. She wro te down the num drink over her p ber of coins she aper. has
but spilled her
20¢
a
ther mixed number and
mber as a product of ano
3 2 umber below.
of Who Chapter 4 Multiplication
le Numbers, Fractions
Workbook A: Practice 3, pages 55–56 and Mixed Numbers
NEW!
Workbook A: Put On Your Thin king Cap! pages 83–84 Review 2, pag es 85–88 Chapter 5 Fract ions: Word Pro
blems
101
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.indd 82
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9
However, she kn ows that 3 of her coins are 50¢ and 10 20¢ coins. Also the rest are , she has more than 50 but few er than 100 coin How many coins s. does she have?
en by Big Idngea le is giv a of a tria a base and the The are of product the height. lf ha onding corresp
Chapter Wrap-Up
Number of Coi ns
50¢
d the missing mixed n
3 2
y
3 Andrea has a box o
er how you found the Share with your partn rs. missing mixed numbe 82
her money on 8 pencils and 2 mar kers. The cost of the cost of eac each
h pencil. She bou ght some more with 5 of her rema markers ining money. H 8
Coin
ethod to fin b Use the same m
5
marker is twice
er as a product.
a Express this mixed nu whole number.
Home
2 Rehna spen 1 t of
Express a mixed numb
1 The model shows 4 2.
2 28 3 5 7 5
9 f 12 3 7 10 5
5
Maths Sharing
3
b 4 3 2 5 5
Post office
is 2 2 km from Ann 5 a’s school. • The mall is 1 1 km from the pos 10 t office. • Anna’s home 3 is 2 km from the 10 mall.
Challenge yourself to solve non-routine questions by applying relevant heuristics and thinking skills in Put On Your Thinking Cap!
1
2 3 3 3 5
Mall
• The post offic e
1
2 3 3 3
nking Cap!
school to home went back to th . She stopped b e m y th Use the followin all to buy lunch. She then head e post office, then g clues to find how ed home from the mall. far Anna’s hom e is from her sch ool.
Consolidate the concepts you have learnt in each chapter in Chapter Wrap-Up!
14/7/16 9:14 am
Area of a Triangle
The area of a triangle is half the area of a rectangle with the same ‘base’ and 1 ‘height’ or 2 3 base 3 height.
Any side of a triangle can be its base. The height is perpendicular to the base.
G
F
Example
Composite Figures
Finding the Area
Base and Height
B
A
A B
E 8 cm
D
height
4 cm Z base
Share your thoughts with your teachers, create your own mathematics questions and become aware of your own mathematical thinking in Maths Sharing!
We can find the area of a composite figure by dividing it into rectangles, squares or triangles.
C
E
2 cm
D
Area of triangle DEF 1 5 2 3 Area of rectangle DEFG 1
5 2 3 EF 3 DE 1 5 3 base 3 height 2 1
523432 2 5 4 cm
3 cm 4 cm
C
Area of figure ABCDE 5 Area of rectangle BCDE 1 Area of triangle ABE Area of rectangle BCDE 5834 2 5 32 cm Area of triangle ABE 1 5 3833 2
5 12 cm
2
Area of the figure 5 32 1 12 2 5 44 cm
ngle Chapter 6 Area of a Tria
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For the Teacher: NEW!
Multiplication of actions , Fr Whole Numbers rs be and Mixed Num
Chapter
4
NEW!
Use scenarios pupils can relate to in the chapter openers to capture their interest, provide an engaging introduction to the topics and jump-start learning.
s 1. How can This recipe serve of each I find the amount servings? ingredient for 3
Introduce concepts through context-based tasks in Before you learn. At the end of each task, a question is posed to develop pupils’ creative and critical thinking skills.
Lesson
Less
ons
1 2 3
a
Order of operations
Before you learn ... Ally and Joe worked out the value o Ally’s answer was 5. Joe’s answe f the expression 8 1 20 4 4 2 2. r was 11. Whose answer is correct? Explain.
EAR
L
Ide
_04.indd 70
Solve word proble
ms.
Work in groups. Station 1
1 Read the word pro
blem. Draw a mod
el for the problem
. example A retailer sold 5 vacuu m cleaners. 2 of th and the others co e vacuum cleaners st $478 each. How cost $659 each much money did t the sale of the 5 va he retailer make fr cuum cleaners? om $659
10 2 4 1 5 5 ? Ally’s solution: 10 2 4 5 6 6 1 5 5 11 Nellie had 11 stickers in the en d.
Use
to check the answer.
given away
bought
10 2 4 1 5 5 6 1 5 5 11 Nellie had 11 stickers in the end.
Lesson 3 Order of Operatio ns
35
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Chapter 7 Review 1
2 Estimate the a nswer.
NEW!
olve the problem.
4 Compare the answ
ers in 2 and 3 to check for reaso
5 Switch roles. Repe at 1 to 4 with these problems.
nableness.
Assess understanding when pupils apply concepts learnt in Review.
a M ary bought 24 boxe s of beads. Each b There were 2184 re ox contained 245 beads. d beads and the r est were blue beads all the blue beads . She used to make 42 brace lets. How many blu used for each brac e beads were elet? b Farah baked 72 cu pcakes and 55 mu ffins. She sold 22 c She then packed upcakes. the remaining cup cakes equally into She gave away 2 b 5 boxes. oxes of cupcakes. How many cupcak have left? es did she
of black caps
s to the number
umber of red cap
The ratio of the n
:
.
is
The ratio of the n
is
r of red caps
aps to the numbe
umber of black c
:
. bers.
num 2 Find the missing a
b
A
B
A : B 5
a 9 : 6 5
A : B 5
:
.
its simplest form
Chapter 2 Opera tions of Wh
A
B
o in 3 Express each rati
44
Joe’s solution: 4 1 5 5 9 10 2 9 5 1 Nellie had 1 sticker in the end .
?
3 Use the model to s
Carry out Hands-On Activity to promote active and collaborative learning. Where possible, pupils will complete station-based activities in rotating groups to best utilise class time.
$478
a N ellie had 10 stickers. She ga ve awa How many stickers did Nellie have y 4 and bought 5 more. in the end?
07_(M)MPaHTB5A
hands-On activity
olved them differently.
Who is correct?
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LearN
1 For the following problems, Ally and Joe s
Whole numbers, d fractions and mixe numbers can be multiplied in any combination.
n and Product of a Fractio a Whole Number tions Frac f Two uct o Prod Number Product of a Mixed er and a Whole Numb
Order of Operations
N
Big
3
Teach concepts in concise steps using real-life contexts, manipulatives and meaningful visuals in LEARN.
:
b 8 : 20 : 16 5
bers.
num 4 Find the missing
ole Numbers
a 7 : 8 5 21 :
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142
b 42 : 49 5 : c 4 : 3 : 7 5 20 5 d 40 : 55 : 15
: 7 : :
: 3
Chapter 7 Ratio 11/7/16 6:29 pm
d 142 PaHTB5A_07.ind
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02_(M)MPaHTB5A_Preface.indd 3
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CONTENTS
1 Whole Numbers
Lesson 1 Numbers to 10 Million
6
7
2 Operations of Whole Numbers
16
3 Fractions and Mixed Numbers
53
4 Multiplication of Whole Numbers, Fractions and Mixed Numbers
70
Lesson Lesson Lesson Lesson
1 Multiplying by 10, 100, 1000 and Their Multiples 2 Dividing by 10, 100, 1000 and Their Multiples 3 Order of Operations 4 Solving Word Problems
Lesson 1 Fractions and Division Lesson 2 Addition of Mixed Numbers Lesson 3 Subtraction of Mixed Numbers
Lesson 1 Product of a Fraction and a Whole Number Lesson 2 Product of Two Fractions Lesson 3 Product of a Mixed Number and a Whole Number
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17 27 35 41
54 60 63
71 74 81
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5 Fractions: Word Problems 6
Lesson 1 Solving Word Problems Area of a Triangle Lesson 1 Area of a Triangle Lesson 2 Composite Figures
86
87
102 103 110
7 Ratio
118
8 Volume of Cubes and Cuboids
146
Lesson Lesson Lesson Lesson
Lesson Lesson Lesson Lesson
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1 Finding Ratios 2 Equivalent Ratios 3 Comparing Three Quantities 4 Solving Word Problems
1 Volume of a Solid 2 Drawing Cubes and Cuboids 3 Volume of a Cube and a Cuboid 4 Volume of a Liquid
119 124 128 131
147 151 159 164
19/7/16 7:44 am
Chapter
1
Whole Numbers
In the 1980s, your grandfather bought a 3-bedroom condominium for $450 000. How much does a 3-bedroom condominium cost now?
Type
Floor Area (m2)
Price ($)
2-bedroom
70
1 170 000
3-bedroom
93
1 209 000
4-bedroom
123
1 599 000
5-bedroom
150
2 080 000
How do I read $1 209 000?
dea I g i B
n Lesso
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1
Numbers to 10 Million
The next two place values after ten thousands are hundred thousands and millions.
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Lesson
1
Numbers to 10 Million
Reading and writing 6-digit numbers Before you learn ... There are 147 853 people in a queue. Use
1 000 000
100 000
10 000
1000
100
10
1
to count aloud
and show the number of people in the queue. Recall Count in thousands. 1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
10 000
10 000, 20 000, 30 000, 40 000, 50 000, 60 000, 70 000, 80 000, 90 000, 100 000
10 thousands 5 1 ten thousand L
N
EAR 1A
Count in ten thousands.
10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000
10 ten thousands 5 1 hundred thousand
1 ten thousand 5 10 thousands 10 ten thousands 5 100 thousands So, 1 hundred thousand 5 100 thousands.
L
N
EAR 1B
100 000
Count in hundred thousands. 100 000
100 000
100 000
100 000
100 000
100 000
100 000
100 000
100 000
100 000
10 hundred thousands 5 1 million
1 hundred thousand 5 100 thousands 10 hundred thousands 5 1000 thousands So, 1000 thousands 5 1 million.
1 000 000
100 000, 200 000, 300 000, 400 000, 500 000, 600 000, 700 000, 800 000, 900 000, 1 000 000
Lesson 1 Numbers to 10 Million
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L
N
EAR 1C
Count using
1 000 000
100 000
10 000
1000
100
10
1
.
100 000
10 000
1000
100
100
10
1
100 000
10 000
1000
100
100
10
1
100 000
10 000
1000
100
100
1
1000
100
100
1
100 000
1
100
100 000
Hundred Ten Thousands Hundreds Thousands Thousands 5
3
4
five hundred and thirty-four thousand
8
9
Tens
Ones
2
6
stands for stands for stands for stands for stands for stands for 4 thousands 9 hundreds 2 tens 5 hundred 3 ten 6 ones thousands thousands 4000 900 20 6 500 000 30 000
1
534 926
nine hundred and twenty-six
five hundred and thirty-four thousand, nine hundred and twenty-six
Chapter 1 Whole Numbers
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TRY
1A Write in numerals and in words. 100 000
10 000 10 000
1000
100
100
10
100 000
10 000 10 000
1000
100
100
10
100 000
10 000
1000
100
100
100 000
10 000
100
100
100 000
10 000
100
1
Numerals:
Words: TRY
1B Write in figures. a
six hundred and seventy-three thousand, nine hundred and eleven
b
five hundred and eighteen thousand and four
c
two hundred thousand, one hundred and six
TRY
1C Write in words.
a
320 176
b
438 830
c
906 095
TRY
1D Find the missing numbers.
a
234 156 5 234 000 1
b
318 205 5
1 205
c
482 000 1
5 482 670
d
1 780 5 600 780 Lesson 1 Numbers to 10 Million
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Reading and writing 7-digit numbers Before you learn ... Mr Krishnan donated $10 000 000 to a charity. Use
1 000 000
100 000
10 000
1000
100
10
1
to count
aloud and show the amount of money he donated. L
N
EAR 1A
Count in millions. 1 000 000
1 000 000
1 000 000
1 000 000
1 000 000
1 000 000
1 000 000
1 000 000
1 000 000
10 000 000 ten millions
1 000 000
1 000 000, 2 000 000, 3 000 000, 4 000 000, 5 000 000, 6 000 000, 7 000 000, 8 000 000, 9 000 000, 10 000 000 L
N
EAR 1B
Count using
100 000
10 000
1000
100
10
1
.
1 000 000
100 000
10 000 10 000
1000
100
100
10
1 000 000
100 000
10 000
1000
100
100
10
1 000 000
100 000
10 000
100
10
100 000
10 000
100
10
10 000
100
10
Millions 3
1 000 000
Hundred Ten Thousands Hundreds Thousands Thousands 4
6
2
7
1
Tens
Ones
5
1
stands for stands for stands for stands for stands for stands stands 3 millions 4 hundred 6 ten 2 thousands 7 hundreds for for 3 000 000 thousands thousands 2000 700 5 tens 1 one 400 000 60 000 50 1
3 462 751
three million seven hundred and fifty-one four hundred and sixty-two thousand
10
three million, four hundred and sixty-two thousand, seven hundred and fifty-one
Chapter 1 Whole Numbers
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R LEA N
Read and write large numbers.
Hands-On Activity
Work in groups.
1 Use
1 000 000
100 000
10 000
1000
100
10
to show 458 712.
1
2 Write in words.
Example
3 Switch roles. Repeat a
543 201
1 and 2 with these numbers.
b
c 1 645 027
359 490
d
2 000 546
TRY
1A Write in figures and in words. 10 000 10 000
100
10
1
100 000
10 000 10 000
100
10
1
100 000
10 000 10 000
100
1
100 000
10 000 10 000
100
1
100 000
10 000
1 000 000
100 000
1 000 000
1 000 000
100 000
1
Figures:
Words:
Lesson 1 Numbers to 10 Million
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TRY
1B Write in figures.
a
three million, five hundred and sixty-seven thousand and forty-five
b
four million, six hundred and five thousand, three hundred and seventy-nine
c
six million, three hundred and twenty-one thousand, five hundred and four
TRY
1C Write in words.
a
1 234 567
b
8 090 909
c
2 653 870
TRY
1D Find the missing numbers.
a
2 300 598 5 2 000 000 1
b
4 216 350 5
1 216 000 1 350
c
5 000 000 1
1 946 5 5 081 946
d
9 000 000 1
1 20 5 9 106 020
Maths Sharing
12
1 598
Find examples of numbers in the millions from the Internet and develop a sense of the size of 1 million.
1 Search the Internet for the seating capacity of the Singapore Indoor Stadium. Imagine that a new indoor stadium with a seating capacity of 1 000 000 will be built. How many times as large as the Singapore Indoor Stadium will the new indoor stadium be? Discuss.
Chapter 1 Whole Numbers
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2 Look up the Internet for three different examples of numbers in millions up to 10 million.
Example The population of Singapore was 5 076 700 in 2010.
Discuss. Workbook A: Practice 1, pages 5–6
Chapter 1 Review 1 Write in numerals.
a
three hundred and seventy-six thousand, two hundred and fourteen
b
seven million, four hundred and fifty thousand, nine hundred and eighty-six
2 Write in words.
a
872 649
b
5 380 170
3 Find the missing numbers.
a
578 312 5 578 000 1
b
4 623 180 5
c
d
1 623 000 1 180
1 608 5 210 608 9 000 000 1 408 000 1
5 9 408 326 Workbook A: Chapter 1 Review, page 7 Maths Journal, page 8
Chapter 1 Whole Numbers
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Big Idealues after
Chapter Wrap-Up
o place va usands The next tw undred tho h re a s d n ten thousa s. and million
Whole Numbers Reading and Writing 6-digit Numbers Reading Hundred Ten Thousands Hundreds Thousands Thousands 6
3
4
0
six hundred and thirty-four thousand
Tens
Ones
5
8
fifty-eight
six hundred and thirty-four thousand and fifty-eight Writing In numerals or figures: 634 058 In words: six hundred and thirty-four thousand and fifty-eight Reading and Writing 7-digit Numbers Reading Millions 4 four million
Hundred Ten Thousands Hundreds Tens Thousands Thousands 1
5 one hundred and fifty-two thousand
2
0
8
Ones 0
eighty
four million, one hundred and fifty-two thousand and eighty Writing In numerals or figures: 4 152 080 In words: four million, one hundred and fifty-two thousand and eighty
14
Chapter 1 Whole Numbers
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Put On Your Thinking Cap!
1 Carina wants to solve a 7-digit secret code to a safe. Use the clues to help Carina solve the secret code.
• All seven digits are different. • The digit in the ten thousands place is 5. • The digit in the thousands place is twice the digit in the hundred thousands place. • The digit in the ones place is 2 more than the digit in the millions place. • The digit in the millions place is 8 less than the digit in the hundreds place. • The digit in the millions place is 1 less than the digit in the tens place.
What is the secret code?
2 a Without adding the 99s together, find the value of each of the following.
i
99 + 99
ii
99 + 99 + 99 + 99 + 99 + 99
What is the value of the digit in the ones place in each case?
b
F ind the smallest number of 99s that must be added to get a 1 in the ones place.
c
ithout multiplying 99 by 45, explain how you can find the sum of W 45 ninety-nines.
Workbook A: Put On Your Thinking Cap! pages 9–10
Chapter 1 Whole Numbers
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