12 August 2011
River Valley Primary School – Strive for the Best
Programme
5.45 – 6.00 – Registration
6.15 – 6.30 – Overview of our Primary
Mathematics Curriculum
6.30 – 7.00
Heuristic 1
7.00 – 7.30
Dinner
7.30 - 9.15
Heuristic 2
9.15 – 9.30
QnA
River Valley Primary School – Strive for the Best
Objectives
To familiarise parents with the more challenging
heuristics from “Conquer Math”.
To partner with parents so that they can help their
children with the approaches the school uses to
each problem solving.
River Valley Primary School – Strive for the Best
Mathematics Curriculum
1. Concepts
Basic mathematical knowledge needed for
solving mathematical problems.
- Numerical concepts
- Geometrical concepts
- Algebraic concepts
- Statistical concepts
River Valley Primary School – Strive for the Best
Mathematics Curriculum
2. Skills
Topic-related manipulative skills that pupils are
expected to perform when solving problems.
- Estimation & approximation
- Mental calculation
- communication
- use of mathematical tools
- arithmetic & algebraic manipulation
- handling data
- use of calculator
River Valley Primary School – Strive for the Best
Mathematics Curriculum
2. Processes
The knowledge skills ( process skills) involved
in the process of acquiring and applying
mathematical knowledge :
- reasoning
- communication and connection
- thinking skills and heuristics
- application and modelling
River Valley Primary School – Strive for the Best
Problem Solving Heuristics
•To give a representation
- draw a diagram (eg. model) , make a list,
use equation
• To make a calculated guess
- guess and check, look for patterns, make
supposition
• To go through the process
- act it out , work backwards, before-after
• To change the problem
- restate the problem, simplify the problem,
solve part of the problem
River Valley Primary School – Strive for the Best
Working Backwards
Sharon had some sweets at first. After she gave away
5 sweets to her sister and ate another 3 sweets, she
went to buy another 48 sweets. In the end she had
thrice as many sweets as before. How many sweets
did she have at first ?
(P3 - pg 20)
?
At First
Extra
1 unit
1 unit
End
Extra
48 – 3 – 5 = 40
2 units
40
1 unit
40 ÷2 = 20 (She had 20 sweets at first.)
River Valley Primary School – Strive for the Best
Equal Concept Model (Internal Transfer)
Dinesh and Melissa shared a sum of money equally.
After Dinesh gave $36 to Melissa, Melissa had twice
as much money as Dinesh. How much money did
each of them receive at first ?
(P3 – pg 15)
1u
Dinesh
-$36
Melissa
+$36
2u
1u
$36 + $36 = $72
Amt. of money each received at first
$108
River Valley Primary School – Strive for the Best
$72 +$36 =
Equal Stage
There was an equal number of boys and girls at a
gathering at first. After 60 boys and 12 girls had left
the gathering, there were twice as many girls as
boys that remained behind. Find the number of
boys at first ?
(P4 – pg 30)
Boys
1u
Girls
1u
left
60
12
Left
1u = 60 – 12 = 48
48 + 60 = 108
There were 108 boys
River Valley Primary School – Strive for the Best
Equal Stage Type 1
(Beginning)
Boys
Girls
60
12
1 unit  60 – 12 = 48
48 + 60 = 108
River Valley Primary School – Strive for the Best
P4-page 30
Equal Stage
Raymond and Rauf had a total of 224 marbles at
first. After Raymond had bought another 12
marbles and Rauf had given away 30 of his
marbles, both had the same number of marbles
left. How many marbles did Raymond have at first ?
(P4 – pg 34)
River Valley Primary School – Strive for the Best
Equal Stage Type 2 (End)
224
12
Ray
Rauf
30
224 – 30 = 194
194 – 12 = 182
182 ÷ 2 = 91
River Valley Primary School – Strive for the Best
P4-page 34
Equal Stage
There was an equal number of boys and girls at an
exhibition. After 53 of the boys and 42 girls had left
the exhibition, there were 12 more boys than girls at
the exhibition. How many students were there at the
exhibition at first ?
(P4 – pg 96)
River Valley Primary School – Strive for the Best
Equal Stage - Fraction
(Type 1)
Boys
Girls
12
42
3u  42 – 12 = 30
1u  30 ÷ 3 = 10
10u  10 x 10 = 100
River Valley Primary School – Strive for the Best
P4-pge 96
Equal Stage
There is a total of 620 apples and oranges at a stall.
3
2
of the oranges is equal to 5 of the apples. How
8
many apples are there at the stall ?
River Valley Primary School – Strive for the Best
(P4 – pg 105)
Equal Stage - Fraction
(Type 3)
Oranges
Apples
Oranges  16u
Apples  15u
Total  31u  620
1u  620 ÷ 31 = 20
15u  20 x 15 = 300
River Valley Primary School – Strive for the Best
P4- Page 105
Equal Stage – Fractions
(Type 3)
Unitary Method:
3
2
8
5
6
6
16 15
Oranges  16u
Apples  15u
Total  31u  620
1u  620 ÷ 31 = 20
15u  20 x 15 = 300
River Valley Primary School – Strive for the Best
Equal Stage
At the graduation ceremony, there were 30 less boys
than girls. After 3 of the boys and 5 of the girls
5
8
had left the hall for recess, there was an equal number
of boy and girls that remained behind. Find the
number of boys who were present at the graduation
ceremony
(P4 – pg 106)
River Valley Primary School – Strive for the Best
Equal Stage – Fractions
(Type 3)
Unitary Method:
2
3
5
8
6
6
15
16
Boys  15u
Girls  16u
Difference  16u – 15u = 1u
1u  30
15u  30 x 15 = 450
River Valley Primary School – Strive for the Best
P4- Page 106
Internal Transfer
Two classes ,3A and 3B , had an equal number
of pupils. After 12 pupils left class 3A to join
class 3B, there were twice as many pupils in
class 3B as in class 3A. Find the number of
pupils in each class at first ?
(P3 – pg 23)
3A
1u
3B
1u
12
1u = 24
24 + 12 = 36
There were 36 pupils in each class
River Valley Primary School – Strive for the Best
Internal Transfer
Esther has 86 more stickers than Jane. How
many stickers must Esther give to Jane so that
Esther will have 40 more stickers than Jane ?
(P3 – pg 26)
Esther
86
86 - 40 = 46

46 2 =23
Jane
She gives 23 stickers
Esther
40
River Valley Primary School – Strive for the Best
Equal Stage (Internal Transfer)
David had 5 times as many marbles as Serene.
After David had given 32 of his marbles to Serene,
they had an equal number of marbles in the end.
Find the number of marbles each of them had at
first .
(P4 – pg 38)
River Valley Primary School – Strive for the Best
Equal Stage Type 3 (Internal
Transfer)
5u
David
Serene
32
32
4u
4u  32 + 32 = 64
1u  64 ÷ 4 = 16
Serene: 16
David: 16 x 5 = 80
River Valley Primary School – Strive for the Best
P4- Page 38
Linear Formation
Trees were planted along each side of a
square garden so that an equal number of
trees are formed along each side of the garden.
If there were 60 trees planted, how many trees
were there along each side of the garden ?
60 ÷ 4 = 15 (because of 4 sides)..Nope..
Let’s pick a smaller number - 12.
So 12 ÷ 4 = 3 trees per side. Right?
WRONG!
As you can see, when sets of 3 were put along
the sides, some trees be part of ANOTHER side.
It is 3 + 1 = 4 trees on each side of the garden.
So, it is 15 + 1 = 16 trees on
each side of the garden.
River Valley Primary School – Strive for the Best
Linear Formation
Trees were planted along each side of a
square garden so that an equal number of
trees are formed along each side of the garden.
If there were 60 trees planted, how many trees
were there along each side of the garden ?
Since the 4 corners are
repeated, we take
60 – 4 = 56
Then 56 divided equally
by 4 sides = 14 per side
14 + 2 ( 2 corners ) and
we get 16 trees per
side.
River Valley Primary School – Strive for the Best
Internal Transfer
There are 25 more passengers on Bus A than
Bus B. If 7 passengers transferred from Bus A
to Bus B, how many more passengers will
there be in Bus A than in Bus B ? (P3 – pg 25)
25
7
A
B
7
25 – 7 – 7 = 11
There will be 11 more passengers in Bus A
River Valley Primary School – Strive for the Best
Regular Gaps
Fig 1
Fig 2
4 dots
7 dots
Fig 1 – 4 dots
Fig 2 – 4 + 3
Fig 3 – 4 + 3 + 3
Fig 5 – 4 + 3 + 3 + 3 + 3 = 16
Fig 20 – 4 + 19 x 3 = 61
109 dots -- 109 – 4 = 105
105  3 = 35
35 + 1 = 36 figure

Fig 3
10 dots
River Valley Primary School – Strive for the Best
(P3 – pg 37)
Equal Distribution without Remainder
Mrs Singh has a certain number of sweets to
distribute to her class. If she gives each of
them 5 sweets, she will have 54 extra sweets.
If she gives each of them 8 sweets, she would
need another 33 more. How many pupils does
she have in her class?
(P3 – pg 45)
5 5 5 5
54 extra
5 5 5 5
54 extra
33 needed
3 3 3
Sets of 5 is the same
(number of students fixed)
54 + 33 = 87 sweets needed to form
extra sets of 3s.
Hence, 87 ÷ 3 = 29 pupils in her class.
River Valley Primary School – Strive for the Best
More than / Less than (External Unchanged)
Joshua had 45 more stickers than Melvin at
first. After Melvin had used up 15 of his
stickers, Joshua had thrice as many stickers as
Melvin in the end. Find the number of stickers
Joshua had at first.
(P4 – pg 21)
River Valley Primary School – Strive for the Best
More / Less than (External
Unchanged)
Joshua
Melvin
45
15
2u
2u  15 + 45 = 60
1u  60 ÷ 2 = 30
3u  30 x 3 = 90
River Valley Primary School – Strive for the Best
P4 – Page 21
More than / Less than (External Unchanged)
There were thrice as many swimmers as nonswimmers at a swimming carnival. After 40
non-swimmers had left the carnival ,there were
5 times as many swimmers as non-swimmers
at the carnival. How many swimmers were
there at the carnival ?
(P4 – pg 24)
River Valley Primary School – Strive for the Best
More/ Less than (External
Unchanged)
5u
1u 40
Swim 1u
Non-swim
1u 40 1u
40
40
2u  40 x 3 = 120
1u  120 ÷ 2 = 60
5u  60 x 5 = 300
River Valley Primary School – Strive for the Best
P4 – Page 24
Internal Transfer
Ryan and Aaron had 156 bottle caps. After
Ryan gave 40 bottle caps to Aaron, Ryan had
twice as many bottle caps as Aaron. How many
bottle caps did Ryan at first ?
(P3 – pg 69)
40
40
Ryan
Aaron
156
40
3u = 156 – 120
= 36
1u = 12
24 + 120 = 144
River Valley Primary School – Strive for the Best
External Change Concept
Mrs Tan and Mrs Lim had an equal number of
pies at first. After Mrs Tan bought another 12
pies and Mrs Lim gave away 4 pies, Mrs Tan
had twice as many pies as Mrs Lim. How many
pies did each of them have at first ? (P3 – pg
77)
At first
Mrs Tan
Mrs Lim
12
bought
4 : from equal amount, decrease by 4 (gave away)
12 + 4 = 16 ---- forms 1 unit
Each ofRiver
them
hadPrimary
---16 +School
4 = 20
pies for
at first.
Valley
– Strive
the Best
External Unchanged
7
There were 12 as many men as women at a
concert. Halfway during the concert, some of
the men left
the concert and the number of men
1
became 3 of the number of women. Given
that there were 80 more women than men at
first, find the number of men who left the
concert halfway ?
(P4 – pg 110)
left
Men
5u = 80
women
1u = 16
3u = 48
48 men left the concert
River Valley Primary School – Strive for the Best
External Unchanged
4
During a class gathering were boys and the
7
rest were girls. Halfway, 22 more
girls joined in
3
the gathering and there were 5 as many boys
as girls. Find the number of students at the
class gathering in the end. (P4 – pg 113)
+ 22
Boys
Girls
3u 3u 3u 3u
4u
4u
4u
3u 3u 3u
20u – 9u = 11u
11u = 22
1u = 2
32u = 64
4u 4u 4u 4u 4u
There are 64 students in the end.
River Valley Primary School – Strive for the Best
External Unchanged
1
Johnson had as many red marbles as blue
3
marbles. If he bought another 12 red marbles,
he would be left with 2 as many red marbles
5
as blue marbles. How many marbles did he
have altogether ?
(P4 – pg 114)
6u
Red
Blue
5u
5u
1u = 12
+ 12
5u
5u
3u 3u 3u 3u 3u
20u = 240
He had 240 marbles.
River Valley Primary School – Strive for the Best
Repeated Identity
The mass of a container with 7 glasses is 2 500 g
The same container with 3 glasses is 1 500g.
What is the mass of the container ?
(P3 – pg 101)
(Container+7 glasses) – (Container+3 glasses) = (No container + 4 glasses)
2 500 – 1 500 = 1 000
1 000 ÷ 4 = 250  1 glass
250 x 3 = 750  3 glasses
1 500 – 750 = 750  container
River Valley Primary School – Strive for the Best
Repeated Identity
The mass of a container with 7 glasses is 2 500 g
The same container with 3 glasses is 1 500g.
What is the mass of the container ?
(P3 – pg 101)
1500
2 500
4u = 2500 – 1500 = 1000
1 u = 250
3 u = 750
OR 7u = 1750
1500 – 750 = 750 (g)
2500 – 1750 = 750 (g)
River Valley Primary School – Strive for the Best
Repeated Identity
4
had
4 7
Serene
as many chocolates as Melvin.
Melvin had 5 as many chocolates as Esther. If
Esther had 38 more chocolates than Serene, find
the total number of chocolates that was shared
among these 3 children at first.
(P4 – pg 117)
Serene 4u
4u
4u
4u
Melvin
4u
4u
4u
4u
7u
Esther
7u
35 – 16 = 19
4u
7u
4u
4u
7u
35u
19u = 38
1u = 2
79u = 158
There are 158 chocolates.
River Valley Primary School – Strive for the Best
Repeated Identity
Inside a bag, there were twice as many red
balloons as blue balloons and 15 more blue
balloons than green balloons. If there was a total
of 141 balloons of these colours, how many green
balloons were there in the bag at first ?
(P4 – pg 56)
4u = 141 – (3 x 15 )
Red
= 96
Blue
1u = 24
Green
15
There were 24 green balloons.
River Valley Primary School – Strive for the Best
Internal Transfer (No change in total)
Ryan and Aaron had 156 bottle caps. After
Ryan gave 40 bottle caps to Aaron, Ryan had
twice as many bottle caps as Aaron. How many
bottle caps did Ryan at first ? (P3 – pg 69)
?
Ryan
40
156
Aaron
3 units
156
1 unit
156 ÷3 = 52
No. of bottle caps Ryan had at first
52 x 2 + 40 = 144
River Valley Primary School – Strive for the Best
Repeated Identity
There are 180 blue and green balls in bag A.
There are 320 green and red balls in bag B.
Given that there are thrice as many red balls as
blue balls, and the number of green balls in both
bags is the same, find the total number of green
balls in both bags ?
(P4 – pg 59)
Green
blue
A
180
B
320
2u = 320 -140
= 140
1u = 70
Red
There were 220 green balls.
River Valley Primary School – Strive for the Best
180 – 70 = 110
110 x 2 = 220
Repeated Identity
Serene and Tommy have a total of 130 sweets.
Tommy and Clara have a total of 141 sweets.
Serene and Clara have a total of 99 sweets. How
many sweets does Serene have ?
(P4 – pg 60)
S + T = 130
T + C = 141
S
+ C = 99
S + T + C = (130 + 141 + 99) = 185
2
185 – 141 = 44
River Valley Primary School – Strive for the Best
Fraction (Part-Whole Relationship)
1
At a swimming event, 4 of the students were
3
2
boys. Given that 5 of the girls and 5 of the
boys did not know how to swim, how many
students were there altogether if there were
154 swimmers at the event ?
(P4 – pg 88)
Boys
girls
5u
2u 3u
5u
5u
6u
5u
9u
11 u = 54
1u = 14
20u = 280
River Valley Primary School – Strive for the Best
Parents’ Help with Child At Home
Math in real life
•Talk to your children about mathematics and
help them to see the usefulness of math in our
daily life.
•Be observant to improve their visualisation.
•Real life application of measurements
River Valley Primary School – Strive for the Best
Reference
Conquer Problem Sums (Primary 3 and Primary 4 )
-Published by onSponge Pte Ltd
-Mathematics Syllabus Primary 2007
River Valley Primary School – Strive for the Best
Kathleen_lee_mui_hwa@moe.edu.sg
River Valley Primary School – Strive for the Best
River Valley Primary School – Strive for the Best