Welcome!UPPER PRIMARY MATHSTRAINER: MR. MOHAMAD IDRIS ASMURI
WELLINGTON PRIMARY SCHOOL
ACTING HEAD of DEPARTMENT (MATHEMATICS)1
1. Introduction
• What can parents do?
• P5 Topical Distributions
• P6 Topical Distributions
• Cognitive Levels & Supporting Your Child
2. Whole Numbers
• Model Drawing
• Number Pattern
3. Fractions
• Model Drawing
• Branching
4. Quantity vs Value (‘per set’ concept)
5. Percentage2
How parents can help their child prepare for the PSLE Mathematics/Foundation Mathematics Paper?
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Help your child to:1. See the importance and relevance of Mathematics
in everyday life.
2. Know the formula, the multiplication and division tables and common systems of units.
3. Analyse the word problems by asking the following questions so that you can check for understanding. What the word problem is about? What is the quantity/value the problem asking
for? What are the keywords? What are/could be the steps involved?
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How can we present the interpreted information?o Graphso Diagramso Tabular forms (E.g. tables or
diagrams/models to be drawn) What are the steps they can take to solve the
question? o Use of the 4 operations (+, , × , ÷) and
any appropriate heuristics to solve the problem.
o Use of formulae or rule involved. o Use the 4 steps of Polya method.
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4. Show all workings neatly.
5. Make it a habit to:• Check the reasonableness of results (final answers) • Use calculator for Paper 2 questions • Perform estimation for short-answer questions in
Paper 1. 6. Have sufficient daily practice in Mathematics.
7. Set a reasonable time limit for your child to complete work at home.
8. Allow the use of calculator to solve word problems(Paper 2 questions) • Use the time to analyse the word problems instead
of performing long computations
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Remember!
Every child is unique!
Some children may need more practice than others.
Know your child’s strengths and weaknesses in Mathematics. (Obtain information from Math teachers.)
Give a reasonable amount of practice accordingly.
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The examination consists of two written papers comprising three booklets.
For more information on PSLE matters, go the website: http://www.seab.gov.sg
Paper Booklet Item TypeNumber of
Questions
Number
of Marks
per
Question
Weighting Duration
1
AMultiple-
choice
10 1 10%
50 min5 2 10%
BShort-
answer
10 1 10%
5 2 10%
2Structured/L
ong-answer
5 2 10%
1 h 40 min13 3/4/5 50%
Total 48 -- 100% 2 h 30 min
Standard Mathematics
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Paper Booklet Item Type
Number
of
Questions
Number
of Marks
per
Question
Weighting Duration
1 A Multiple-
choice
10 1 10%
1 h10 2 20%
B Short-
answer10 2 20%
2 Structured
/Long-
answer
10 2 20%1 h 15 min
Structured 8 3/4/5 30%
Total 48 -- 100% 2 h 15 min
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Foundation Mathematics
The examination consists of two written papers comprising three booklets.
For more information on PSLE matters, go the website: http://www.seab.gov.sg
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10
Standard Mathematics (SA2)
TopicsProposed
Weightings (%)
Whole Numbers, Fractions, Decimals 45
Ratio 8
Percentage 8
Measurement(Area and Perimeter, and Volume)
18
Geometry (4-sided Figures, Angles and Triangles)
16
Data Analysis (Average and Graphs)
5
Total 100
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11
Foundation Mathematics (SA2)
TopicsProposed
Weightings (%)
Whole Numbers, Fractions, Decimals 55
Measurement(Time, Area and Perimeter, and Volume)
22
Geometry 15
Data Analysis (Average, Tables and Graphs)
8
Total 100
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12
Standard Mathematics (PSLE)
TopicsProposed
Weightings (%)
Whole Numbers, Fractions, Decimals 30
Measurement 25
Geometry 15
Data Analysis 10
Ratio and Percentage 12
Algebra 4
Speed 4
Total 100
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13
Foundation Mathematics (PSLE)
TopicsProposed
Weightings (%)
Whole Numbers, Fractions, Decimals 36
Measurement 28
Data Analysis 14
Geometry 12
Percentage 10
Total 100
1. Multiple-choice Question For each question, four options are provided of which only one is the correct answer. A candidate has to choose one of the options as his correct answer.
2. Short-answer Question For each question, a candidate has to write his answer in the space provided. Any unit required in an answer is provided and a candidate has to give his answer in that unit.
3. Structured / Long-answer Question For each question, a candidate has to show his method of solution (working steps) clearly and write his answer(s) in the space(s) provided.
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Supporting your child in their learning journey!
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16* In the school context, students may be exposed to problems that are deemedunfamiliar as part of the regular practice. These questions should remain asApplication and Analysis so long as the problem involves a complex situation, eventhough the nature of the problems may have become familiar to the students.
Standard and FoundationLevels Cognitive Level
Knowledge
Knowledge items require students to recall specific mathematical facts, concepts, rules and formulae, and perform straightforward computations.
Comprehension
Comprehension items require students to interpret data and use mathematical concepts, rules and formulae to solve routine or familiarmathematical problems.
Application and Analysis
Application and Analysis items require students to analyse data and/or apply mathematical concepts, rules and formulae in a complex situation, and solve unfamiliar* problems.
• Be involved in your child’s learning in school and at home.
AskPraise Encourage
• Ensure that your child attends all his/her classes punctually.
• Ensure your child revises his/her work
• Ensure that your child completes his/her work.
• Ensure that your child attempts his/her Koobitsportal @problemsums.koobits.com
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Whole Numbers
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Example 1: Model DrawingHarry had $475 more than Anna. He gave $150 to Anna How much more money than Anna had Harry in the end ?
Common mistake:
$475 - $150 = $325
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Harry
Anna
$475
Why do we subtract $150 twice?
Solution:
$475 - $150 = $325
$325 - $150 = $175
$150
$325
Harry
Anna
$475
$150$150
$175
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Study the pattern carefully.
a) How many squares are there in Figure 4?
Figure 1 3
Figure 2 5
Figure 3 7
Figure 4
Figure 1 Figure 2 Figure 3
+ 2
+ 2
7 + 2 = 9Method: Counting on
Example 2: Number Pattern Type 1
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Figure 0 Figure 1 Figure 2 Figure 3
Study the pattern carefully.
b) How many squares are there in Figure 78?
Figure 0 3 – 2 = 1
Figure 1 1 + (1 × 2) = 3
Figure 2 1 + (2 × 2) = 5
Figure 3 1 + (3 × 2) = 7
…
Figure 78 1 + (78 × 2) = 157
Example 2: Number Pattern Type 1
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Figure 1 Figure 2 Figure 3
Method: Working backwards
Example 2: Number Pattern Type 1
Study the pattern carefully.
c) Which figure contains 199 squares?
Number of squares 1 + (Figure Number × 2)
199 – 1 = 198
198 2 = 99
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Figure 1 Figure 2 Figure 3
Let’s practise! (1)
Study the pattern carefully.
a) How many squares are there in Figure 4?
Figure 1 3
Figure 2 6
Figure 3 10
Figure 4
+ 3
+ 4
10 + 5 = 15
Method: Counting on
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(1 + 2) (1 + 2 + 3) (1 + 2 + 3 + 4)
What is the relationship between the last number to add and the figure number?
Let’s practise! (1)
Study the pattern carefully.
b) How many squares are there in Figure 18?
Figure 18 1 + 2 + (3 + 4 + … + 17 + 18 + 19) = ___
Figure 1 Figure 2 Figure 3
Find the sum of
1 + 2 + 3 + … + 16 +17 +18 +19 +20 +21 .
Step 1: Find the number of terms.
No. of terms 𝑙𝑎𝑠𝑡 𝑛𝑜. −𝑓𝑖𝑟𝑠𝑡 𝑛𝑜.
𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒+ 1
21 −1
1+ 1 = 21
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Example 3: Number Pattern Type 2
Find the sum of
1 + 2 + 3 + … +19 + 20 + 21.
Step 2: Find the average of each term.
Average^ of each pair of numbers 𝑙𝑎𝑠𝑡 𝑛𝑜. +𝑓𝑖𝑟𝑠𝑡 𝑛𝑜.
2
21+1
2
= 11 ^Average is a concept taught only in P5 (Term 3).
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22
2222
Example 3: Number Pattern Type 2
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Example 3: Number Pattern Type 2
Find the sum of
1 + 2 + 3 + … + 16 +17 +18 +19 +20 +21 .
Step 3: Find the sum of all the terms.
Multiply the no. of terms (step 1) and the average (step 2)
21 × 11 = 231
Find the sum of
3 + 6 + 9 + ... + 21 + 24 + 27.
Step 1: Find the number of terms.
No. of terms 𝑙𝑎𝑠𝑡 𝑛𝑜. −𝑓𝑖𝑟𝑠𝑡 𝑛𝑜.
𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒+ 1 = _________
Step 2: Find the average of each term.
Average of each pair of numbers
𝑙𝑎𝑠𝑡 𝑛𝑜. +𝑓𝑖𝑟𝑠𝑡 𝑛𝑜.
2= _________
Step 3: Find the sum of all the terms.
Multiply the no. of terms (Step 1) and the average (Step 2)
_____________________ = ___________ 28
Let’s practise! (2)
1. Add all the numbers from 32 to 60.
2. Add all the even numbers from 368 to 400.
3. Find 250 + 255 + 260 + … + 345 + 350 + 355.
4. *Find 300 – 290 + 280 – 270 + …– 230 + 220 – 210.
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Let’s practise! (3)
Pre
par
ed b
y M
r Id
ris
Asm
uri
20
15
30
Fractions
String A is 21 cm shorter than String B. 2
3of String A and
4
5of
String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first.
Misconception:
String A (left) 1 -2
3= 1
3
String B (left) 1 -4
5= 1
5
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1
3is a bigger
fraction than 1
5.
Why is the remaining String B more than String A?
Example 4: Model Drawing
Q: How to help my child make meaning of the fractions?
A: Provide scaffolding for your child. Allow your child some time to think before answering.
• Are we talking about 2
3of String A or B? (String A)
So, 2
3of String A represents a VALUE.
• Are we talking about 4
5of String A or B? (String B)
So, 4
5of String B represents another VALUE.
• We’re not comparing fractions here, but the values.
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String A is 21 cm shorter than String B. 2
3of String A and
4
5of
String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first.
Example 4: Model Drawing
If your child doesn’t understand, you can use the following example:
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Tips!
𝟏
𝟒of 8 is 2.
𝟏
𝟒of 16 is 4.
Both fractions are 1
4of each set.
However, the values are different.
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Step 1: Understand the problem.Step 2: Devise a plan.Step 3: Carry out the plan.Step 4: Look back.
(Are the results reasonable?)
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String A is 21 cm shorter than String B. 2
3of String A and
4
5of
String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first.
Example 4: Model Drawing
Step 1: Understand the question.
String A (at first) 21 cm shorter than String B
String A (used)2
3
String B (used)4
5
String A (left) 2 unitsString B (left) 1 units
String B (at first) ?
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A
B
String A is 21 cm shorter than String B. 2
3of String A and
4
5of
String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first.
Example 4: Model Drawing
Step 2: Devise a plan. (Work backwards)Visualise the end model.
7 units 21 cm
1 unit 3 cm
10 units 10 × 3 cm
= 30 cm37
A
B
used
used
21 cm shorter
String A is 21 cm shorter than String B. 2
3of String A and
4
5of
String B were used. In the end, there was twice as much String B as String A left. Find the length of String B at first.
Example 4: Model Drawing
Step 3: Carry out the plan. (Solve it.)
Step 4: Look back. (Are the results reasonable?)
Sally had some money. She spent 1
3of her money on a blouse and
3
4of the remaining money on a scarf. What fraction of her money
was left?
Blouse1
3
Remainder ?
Remainder 1 –1
3= 2
3
Scarf3
4of the remainder
3
4×
2
3= 𝟏
𝟐38
Example 5: Model Drawing
Step 1: Understand the question. (Key words)
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blouse
scarf ?
Sally had some money. She spent 1
3of her money on a blouse and
3
4of the remaining money on a scarf. What fraction of her money
was left?
Example 5: Model Drawing
Step 2: Devise a plan.
1 –1
3= 2
3
1
4×
2
3= 𝟏
𝟔40
blouse
scarf ?
Sally had some money. She spent 1
3of her money on a blouse and
3
4of the remaining money on a scarf. What fraction of her money
was left?
Example 5: Model Drawing
Step 3: Carry out the plan. (Solve it.)
Step 4: Look back. (Are the results reasonable?)
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1 –1
3=
2
3
1
3Blouse
Remaining
3
4
Money left
scarfR
R
Fraction of the whole
1
4
Money
Sally had some money. She spent 1
3of her money on a blouse and
3
4of the remaining money on a scarf. What fraction of her money
was left?
Example 5: Branch Method
Step 2: Devise a plan.
1 –3
4=
1
4
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Fraction of the whole
1
3= 2
6
3
4×
2
3= 1
2=
3
6
1
4×
2
3= 𝟏
𝟔
Checking:2
6+
3
6+
1
6= 1
Sally had some money. She spent 1
3of her money on a blouse and
3
4of the remaining money on a scarf. What fraction of her money
was left?
Example 5: Branch Method
Step 3: Carry out the plan. (Solve it.)
Step 4: Look back. (Are the results reasonable?)
1 –1
3=
2
3
1
3Blouse
Remaining
3
4
Money left
scarfR
R1
4
Money
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Quantity versus Value (‘per set’ concept)
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There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all?
Example 6: Model Drawing
Step 1: Understand the question. (Keywords)
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Example 6: Model Drawing
Step 2: Devise a plan.
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Draw a model.
There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all?
In 1 set:
No. of coins four 10 ¢ coins and one 50 ¢ coin 5 coins
Value of coins 4 × 10 ¢ + 50 ¢ = 90 ¢
No. of sets Total value ÷ value = $9 ÷$0.90 = 10
No. of coins 9 sets of 5 coins 10 × 5 = 5046
Example 6: Model Drawing
Step 3: Carry out the plan. (Solve it.)
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Step 4: Look back. (Are the results reasonable?)
There are 4 times as many 10-cent coins as 50-cent coins. The total value of the 10-cent coins and 50-cent coins is $9. How many coins are there in all?
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There are 4 times as many 10-cent coins as 50-cent coins. The difference in value between the 10-cent coins and 50-cent coins is $1. How many coins are there in all?
Example 7: Model Drawing
Step 1: Understand the question. (Keywords)
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Step 2: Devise a plan.
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Draw a model.
There are 4 times as many 10-cent coins as 50-cent coins. The difference in value between the 10-cent coins and 50-cent coins is $1. How many coins are there in all?
Example 7: Model Drawing
In 1 set:
No. of coins 4 × 10-¢ coins and 1 × 50-¢ coin 5 coins
Difference in value 50¢ - (4 × 10 ¢) = 10¢
No. of sets Total difference ÷ difference per set
= $1 ÷$0.10 = 10
No. of coins 10 sets of 5 coins 10 × 5 = 5049
Step 3: Carry out the plan. (Solve it.)
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Step 4: Look back. (Are the results reasonable?)
There are 4 times as many 10-cent coins as 50-cent coins. The difference in value between the 10-cent coins and 50-cent coins is $1. How many coins are there in all?
Example 7: Model Drawing
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Let’s practise! (4)The ratio of the number of 10-cent coins to the number of 50-cent coinsis 4:1. The difference in value between the 10-cent coins and the 50-cent coins is $1. How many coins are there in all?
Step 1: Understand the question. (Keywords)
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Step 2: Devise a plan.
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Draw a model.
Let’s practise! (4)The ratio of the number of 10-cent coins to the number of 50-cent coinsis 4:1. The difference in value between the 10-cent coins and the 50-cent coins is $1. How many coins are there in all?
In 1 set:
No. of coins four 10 ¢ coins and one 50 ¢ coin 5 coins
Value of coins 4 × 10 ¢ + 50 ¢ = 90 ¢
No. of sets Total value ÷ value = $9 ÷$0.90 = 10
No. of coins 9 sets of 5 coins 10 × 5 = 5052
Step 3: Carry out the plan. (Solve it.)
10 ¢
50 ¢
Number of coins Value of coins10 ¢
50 ¢
10 ¢10 10 10 10
Step 4: Look back. (Are the results reasonable?)
Let’s practise! (4)The ratio of the number of 10-cent coins to the number of 50-cent coinsis 4:1. The difference in value between the 10-cent coins and the 50-cent coins is $1. How many coins are there in all?
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Let’s practise! (5)There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet?Step 1: Understand the question. (Keywords)
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Step 2: Devise a plan. Draw a model.
Let’s practise! (5)There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet?
$5 $5 $5 $5
$2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2$14
In unknown sets:
No. of notes one $2 note and one $5 note 2 notes
Difference $14 + $16 = $30
Difference per set $5 $2 = $3
No. of sets Difference ÷ difference per set
= $30 ÷$3 = 1055
Step 3: Carry out the plan. (Solve it.)
Step 4: Look back. (Are the results reasonable?)
Let’s practise! (5)There are 8 more $2 notes than $5 notes in my wallet. The difference between the $2 notes and $5 notes is $14. How many $5 notes are there in my wallet?
Draw a model.
$5 $5 $5 $5
$2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2 $2$14
Percentage
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• % Out of 100
• i.e. 70% 70 out of 100
Q: How to help your child make meaning of percentage?
A: Help them relate to everyday context.
1. If a television is selling at a discount of 20%, what is the amount I have to pay for it?
2. A movie ticket was sold at 10% discount. If I bought 3 such tickets, do I get 30% off the total price?
3. A dinner meal cost $120 before GST and service charge. How did I pay in all, after GST and service charge?
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ALWAYS RELATE PERCENTAGE TO A VALUE.
What does percent mean?
1) 368
2) 12672
3) 6655
4) Find 300 – 290 + 280 – 270 + …– 230 + 220 – 210.
How many tens do we have to add? 5
5 × 10 = 50
10 $5notes 58
10 10 10
Let’s practise! (3)Answer Key
Let’s practise! (5)Answer Key
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