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Preface
Maths (2nd Edition) is a comprehensive, activity-based
programme designed to provide pupils with a firm foundation in Maths and to
develop creative and critical thinking skills resulting in efficient problem solvers.
Maths (2nd Edition) continues to make learning Maths fun
and rewarding through the use of engaging illustrations and games that help to
reinforce and consolidate learning.
For the Teacher:
Use the engaging and highly scaffolded
Let’s Learn! to introduce concepts.
Parallel questions allow for immediate
assessment and consolidation of concepts learnt.
Pie Charts
Let’s Learn!
Understanding Pie Charts
1
About 70% of the Earth’s surface is water. The remaining 30% of the Earth’s
surface is land. We can show this fact in a table.
Earth’s Surface
NEW
100%
Let’s Explore!
Carry out investigative activities
in Let’s Explore! These allow
pupils to apply concepts learnt.
Work in pairs:
1
Draw the rectangle and square on a
piece of paper and cut them out.
3 cm
7 cm
3 cm
2 cm
2
Put On Your Thinking Caps!
In the figure below, the area of the shaded part is 30% of the area of Circle P. It is
also 20% of the area of Circle Q. What percentage of the figure is shaded? Express your
answer correct to 2 decimal places. (Hint : Find the ratio of the area of the shaded part
to the unshaded part.)
Challenge pupils to solve non-routine
questions by applying relevant heuristics and
thinking skills in Put On Your Thinking Caps!
Q
P
NEW
With the rectangle and the square form these three types of composite figures
Indicates that appropriate use of calculators is allowed for the activities and
practices to enhance the teaching and learning processes.
National Education
provides opportunities for teacher-pupil interaction on Singapore.
For the Parent/Guardian:
Make Maths come alive by using the tips found
Home
in Maths to apply mathematical concepts
to common scenarios in and around the home.
MPH(M) CB_6A_Prefaces.indd iv
NEW
Home
Maths
Get your child to help you make konnyaku jelly by mixing konnyaku jelly powder, sugar and water.
Show your child the recipe and ask him/her to find the ratio of the amount of konnyaku jelly powder
to that of sugar. Ask your child to find the amount of sugar needed to make twice the amount of
konnyaku jelly.
To make 24 jellies
Ingredients: 10 g konnyaku jelly powder
210 g sugar
950 ml water
Recipe: 1) Mix the konnyaku jelly powder and sugar together. Mix well.
2) Pour the mixture of konnyaku jelly powder and sugar into water gradually and stir till
boiling.
3) Turn off the flame and continue stirring for 5 minutes, until the bubbles dissipate and the
konnyaku jelly solution turns clear.
4) Pour the solution into moulds and chill to set.
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For the Pupil:
5
Carry out this activity.
Trace out the nets shown in 4 and identify the two coloured faces of each solid
by shading these faces on the nets. Cut out the nets and fold them to form the
solids. Did you shade the correct faces?
y IT
Tr
6
!
Choose a solid from the ones you have learnt about previously. Use the
drawing tool in your computer to draw a net of the solid you have chosen.
Print out the net, cut it out and form the solid. Does the net you have
drawn form the solid you wanted?
Mat hs Jo u r n al
Enjoy
Maths (2nd Edition)
Carry out this activity
with your friends.
will lead you to discover games and activities
that involve the use of Maths.
Noraini was shown the two solids below.
NEW
Share with your teachers what you have
learnt, create your own Maths questions,
and become aware of your own mathematical
thinking in
Use computers to carry
IT!
out fun-filled activities in Try
.
Area And Perimeter
Let’s Learn!
Recall skills taught in earlier
Area And Perimeter Of Composite Figures
levels and link them to new concepts
in the current chapter.
Below are the nets of four solids. Name the solid formed by each net.
a
A side of the square is 6 cm.
6 cm
Perimeter of closed figure with
straight sides = Sum of its sides
Let’s Practise! comprises diagnostic
and practice questions that provide
opportunities for further practice.
Let’s Practise! 3b
1
Let us revise area and perimeter of the following figures: square, rectangle,
triangle and circle.
1
b
Let’s Wrap It Up!
Let’s Wrap It Up! summarises the concepts you
have learnt in the current chapter, while Let’s
revise! provides a worked example that covers
the key concepts for ease of revision.
NEW
You have learnt to:
•
•
•
•
•
calculate speed, distance and time given the other 2 quantities
use the formula:
• Speed ! Distance " Time
• Distance ! Speed # Time
• Time ! Distance " Speed
find the average speed given a word problem scenario
read, interpret and write speed in different units: km/h, m/min, m/s and cm/s
draw models to solve word problems in speed
Let’s revise!
1
Jane took 1 2 h to travel from Town A to Town B at an average speed of
Think It Through
Use graded worked examples and questions
to understand problem-solving strategies for
heuristics-based higher order problems.
Whole Number
1
Tim’s age now is a multiple of 5. In one year’s time, his age will be a multiple of
7 and in two years’ time, it will be a multiple of 11. If he is less than 60 years old,
how old is Tim now?
NEW
Solve the problem step by step.
a
Step
Review C
Tim’s possible age
List the multiples of 5 which are
less than 60
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
1
Write 2150 in words.
2
1 $ 3 $ 5 $ 7 $ … $ 97 $ 99
When the odd numbers from 1 to 99 are added up, what is the digit in the ones
place?
3
a
Round off the following to the nearest ten.
i
512
ii
2786
Cumulative reviews provide more practice
to help you consolidate the concepts
learnt in the previous topics; with higherorder questions marked with *.
Have fun learning Maths with Googol and his pals!
MPH(M) CB_6A_Prefaces.indd v
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Contents
Algebra
Using Letters As Numbers
Simplifying Algebraic Expressions
Word Problems
2
13
19
Review A
24
Angles In Geometric Figures
Finding Unknown Angles
30
Review B
43
Nets
MPH(M) CB_6A_contents.indd 2
Solids
Nets Of Solids
48
53
Review C
63
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Fractions
Four Operations With Fractions
Dividing By A Proper Fraction
Word Problems
70
72
87
Review D
95
Ratio
Ratio And Fraction
Word Problems (I)
Comparing Ratios
Word Problems (2)
101
109
117
125
Review E
134
Percentage
MPH(M) CB_6A_contents.indd 3
Finding Percentages
Word Problems (1)
Word Problems (2)
141
148
155
Review F
168
Review G
174
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Algebra
Let’s Learn!
Using Letters As Numbers
1
Rani is now 12 years old.
a
How old will Rani be in 1 year’s time?
12 ! 1 " 13
Rani will be 13 years old in 1 year’s time.
b
How old will Rani be in 2 years’ time?
12 ! 2 " 14
Rani will be 14 years old in 2 years’ time.
c
How old was Rani 1 year ago?
12 # 1 " 11
Rani was 11 years old 1 year ago.
d
How old was Rani 2 years ago?
12 # 2 " 10
Rani was 10 years old 2 years ago.
2
01 MPH!(M) P6 CB.indd 2
Chapter 1: Algebra
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2
Mr Tan is the form teacher of Primary 6C.
The class does not know how old he is.
Let Mr Tan be x years old.
In algebra, we use a
letter to represent an
unknown number.
a
If Mr Tan is 47 years old,
then x represents 47.
If Mr Tan is 38 years old,
then x represents 38.
How old will Mr Tan be in 1 year’s time?
x!1
Mr Tan will be (x ! 1) years old in 1 year’s time.
b
How old will Mr Tan be in 2 years’ time?
x!2
Mr Tan will be (x ! 2) years old in 2 years’ time.
x ! 1 and x ! 2 are examples of algebraic expressions in terms of x.
3
Refer to the table below. What is Mr Tan’s age in terms of x?
Mr Tan’s age (years)
Now
In 3 years’ time
x+3
In 4 years’ time
x+4
In 7 years’ time
x+7
In 10 years’ time
x + 10
In 15 years’ time
x + 15
Chapter 1: Algebra
01 MPH!(M) P6 CB.indd 3
x
3
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4
Madam Fauziah is the principal of Angsana Primary School.
The pupils do not know her age.
Let Madam Fauziah be y years old.
a
How old was Madam Fauziah 1 year ago?
y!1
Any letter can be
used to denote an
unknown number.
Madam Fauziah was (y ! 1) years old 1 year ago.
How old was Madam Fauziah 2 years ago?
b
y!2
Madam Fauziah was (y ! 2) years old 2 years ago.
y ! 1 and y ! 2 are examples of algebraic expressions in terms of y.
5
Refer to the table below. What is Madam Fauziah’s age in terms of y?
Madam Fauziah’s age (years)
Now
6
y
3 years ago
y–3
5 years ago
y–5
8 years ago
y–8
12 years ago
y – 12
20 years ago
y – 20
a
i
Add 2 to 6.
ii
6"2#8
b
i
Subtract 3 from 4.
4!3#1
4
01 MPH!(M) P6 CB.indd 4
Add x to 6.
6"x
ii
Subtract 3 from y.
y!3
Chapter 1: Algebra
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c
i
What is 4 more than 8?
ii
8 ! 4 " 12
d
i
What is 5 less than 9?
8!x
ii
9#5"4
7
8
What is x more than 8?
What is 5 less than y?
y#5
State the algebraic expression for each of the following.
a
Add 5 to z z + 5
b
Add z to 8 8 + z
c
Subtract 7 from z z – 7
d
Subtract z from 10 10 – z
e
9 more than z z + 9
f
z more than 9 9 + z
g
11 less than z z – 11
h
z less than 11 11 – z
Algebraic expressions can be evaluated for given values of the letter.
a
Find the value of x ! 5 when x " 9.
When x " 9,
x!5 "9!5
" 14
b
Substitute the letter
with the given number.
Find the value of 5 ! x when x " 23.
When x " 23,
5 ! x " 5 ! 23
" 28
c
Find the value of y # 7 when y " 15.
When y " 15,
y # 7 " 15 # 7
"8
d
Find the value of 30 # y when y " 7.
When y " 7,
30 # y " 30 # 7
" 23
Chapter 1: Algebra
01 MPH!(M) P6 CB.indd 5
5
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