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River Valley Primary School – Strive for the Best
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 Q n A
Programme
River Valley Primary School – Strive for the Best
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.
Objectives
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
•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
Problem Solving Heuristics
River Valley Primary School – Strive for the Best
Working BackwardsSharon 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
End
1 unit
1 unit
Extra
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
Melissa
1 u
2 u
-$36
+$36
1 u $36 + $36 = $72
Amt. of money each received at first $72 +$36 = $108
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)
River Valley Primary School – Strive for the Best
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 60
Girls 1u 12 Left
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
1 unit 60 – 12 = 48
48 + 60 = 108
60
12
P4-page 30
River Valley Primary School – Strive for the Best
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)
Ray
Rauf
224 – 30 = 194
194 – 12 = 182
182 ÷ 2 = 91
12
30
224
P4-page 34
River Valley Primary School – Strive for the Best
Equal Stage
There was an equal number of boys and girls at an exhibition. After 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)
5
3
River Valley Primary School – Strive for the Best
Equal Stage - Fraction (Type 1)
Boys
Girls
3u 42 – 12 = 30
1u 30 ÷ 3 = 10
10u 10 x 10 = 100
12
42
P4-pge 96
River Valley Primary School – Strive for the Best
Equal Stage
There is a total of 620 apples and oranges at a stall.
of the oranges is equal to of the apples. How many apples are there at the stall ? (P4 – pg 105)
8
3
5
2
River Valley Primary School – Strive for the Best
Equal Stage - Fraction (Type 3)
Oranges Apples
Oranges 16uApples 15uTotal 31u 6201u 620 ÷ 31 = 2015u 20 x 15 = 300
P4- Page 105
River Valley Primary School – Strive for the Best
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 of the boys and of the girls
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)
8
5
5
3
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 = 450P4- Page 106
River Valley Primary School – Strive for the Best
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 12
3B 1u
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
Jane
Esther 40
86 - 40 = 46
46 2 =23
She gives 23 stickers
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)
David Serene
4u 32 + 32 = 641u 64 ÷ 4 = 16Serene: 16David: 16 x 5 = 80
32
32
5u
4u
P4- Page 38
River Valley Primary School – Strive for the Best
Linear FormationTrees 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 FormationTrees 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)
A
B
257
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 Fig 3 4 dots 7 dots 10 dots
Fig 1 – 4 dotsFig 2 – 4 + 3Fig 3 – 4 + 3 + 3Fig 5 – 4 + 3 + 3 + 3 + 3 = 16Fig 20 – 4 + 19 x 3 = 61 109 dots -- 109 – 4 = 105 105 3 = 35 35 + 1 = 36 figure (P3 – pg 37)
River Valley Primary School – Strive for the Best
Equal Distribution without RemainderMrs 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
333
33 needed
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.
54 extra
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
2u 15 + 45 = 60
1u 60 ÷ 2 = 30
3u 30 x 3 = 90
45
15
2u
P4 – Page 21
River Valley Primary School – Strive for the Best
More than / Less than (External Unchanged)There were thrice as many swimmers as non- swimmers 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)
Swim
Non-swim
2u 40 x 3 = 120
1u 120 ÷ 2 = 60
5u 60 x 5 = 300
5u
40
40 40 40
1u
1u1u1u
P4 – Page 24
River Valley Primary School – Strive for the Best
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)
Ryan
Aaron 40
40 40
1563u = 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)
Mrs Tan
Mrs Lim
At first
12
4 : from equal amount, decrease by 4 (gave away)
bought
12 + 4 = 16 ---- forms 1 unit
Each of them had ---16 + 4 = 20 pies at first.
River Valley Primary School – Strive for the Best
External Unchanged
There were as many men as women at a concert. Halfway during the concert, some of the men left the concert and the number of men became 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)
12
7
3
1
Men
women
5u = 80
1u = 16
3u = 48
48 men left the concert
left
River Valley Primary School – Strive for the Best
External Unchanged
During a class gathering were boys and the rest were girls. Halfway, 22 more girls joined in the gathering and there were as many boys as girls. Find the number of students at the class gathering in the end. (P4 – pg 113)
7
4
5
3
Boys Girls
+ 22
3u 3u 3u 3u 3u 3u 3u
4u 4u 4u 4u 4u 4u 4u 4u
20u – 9u = 11u
11u = 22
1u = 2
32u = 64
There are 64 students in the end.
River Valley Primary School – Strive for the Best
External Unchanged
Johnson had as many red marbles as blue marbles. If he bought another 12 red marbles, he would be left with as many red marbles as blue marbles. How many marbles did he have altogether ? (P4 – pg 114)
3
1
5
2
Red
Blue
+ 125u 5u 5u
3u 3u 3u 3u 3u
6u
5u1u = 12
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)
4u = 2500 – 1500 = 1000
1 u = 250
3 u = 750 OR 7u = 1750
1500 – 750 = 750 (g) 2500 – 1750 = 750 (g)
2 500
1500
River Valley Primary School – Strive for the Best
Repeated Identity
Serene had as many chocolates as Melvin. Melvin had 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)
7
4
5
4
Serene
Melvin
Esther
4u 4u 4u 4u 4u 4u 4u
4u 4u 4u 4u
7u 7u 7u 7u
35u
35 – 16 = 19
19u = 38
1u = 2
79u = 158There 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)
Red
Blue
Green 15
4u = 141 – (3 x 15 )
= 96
1u = 24
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
Aaron156
3 units 156
1 unit 156 ÷3 = 52
No. of bottle caps Ryan had at first 52 x 2 + 40 = 144
40
?
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)
A
B
Green blue
180
320
Red
2u = 320 -140
= 140
1u = 70
180 – 70 = 110
110 x 2 = 220There were 220 green balls.
River Valley Primary School – Strive for the Best
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)
At a swimming event, of the students were boys. Given that of the girls and 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)
4
1
5
25
3
5u 5u 5u 5u
Boys girls
2u 3u 6u 9u
11 u = 54
1u = 14
20u = 280
River Valley Primary School – Strive for the Best
Parents’ Help with Child At Home •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
Math in real life
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