Welcome! UPPER PRIMARY MATHS - MOE€¦ · (Obtain information from Math teachers.) Give a...

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?

3

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?

4

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.

5

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

6

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.

7

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

8

http://www.seab.gov.sg/


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

9

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



17

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

17

11

Foundation Mathematics (SA2)

TopicsProposed

Weightings (%)


Measurement(Time, Area and Perimeter, and Volume)

22

Geometry 15

Data Analysis (Average, Tables and Graphs)

8

Total 100

17

12

Standard Mathematics (PSLE)

TopicsProposed

Weightings (%)


Measurement 25

Geometry 15

Data Analysis 10

Ratio and Percentage 12

Algebra 4

Speed 4

Total 100

17

13

Foundation Mathematics (PSLE)

TopicsProposed

Weightings (%)


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.

14

Supporting your child in their learning journey!

15

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

17

Whole Numbers

18

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

19

Harry

Anna

$475

Why do we subtract $150 twice?

Solution:

$475 - $150 = $325

$325 - $150 = $175

$150

$325

Harry

Anna

$475

$150$150

$175

20

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

21

Figure 0 Figure 1 Figure 2 Figure 3


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


22


Method: Working backwards



c) Which figure contains 199 squares?

Number of squares 1 + (Figure Number × 2)

199 – 1 = 198

198 2 = 99

23


Let’s practise! (1)


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

24

(1 + 2) (1 + 2 + 3) (1 + 2 + 3 + 4)

What is the relationship between the last number to add and the figure number?



b) How many squares are there in Figure 18?

Figure 18 1 + 2 + (3 + 4 + … + 17 + 18 + 19) = ___


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

25


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).

26

22

2222


27


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


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.

29


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

31

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.

32


3of String A and

4

5of



If your child doesn’t understand, you can use the following example:

33

Tips!

𝟏

𝟒of 8 is 2.

𝟏

𝟒of 16 is 4.

Both fractions are 1

4of each set.

However, the values are different.

34

Step 1: Understand the problem.Step 2: Devise a plan.Step 3: Carry out the plan.Step 4: Look back.

(Are the results reasonable?)

35


3of String A and

4

5of



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) ?

36

A

B


3of String A and

4

5of



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


3of String A and

4

5of



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


Step 1: Understand the question. (Key words)

39

blouse

scarf ?



3


was left?


Step 2: Devise a plan.

1 –1

3= 2

3

1

4×

2

3= 𝟏

𝟔40

blouse

scarf ?



3


was left?




41

1 –1

3=

2

3

1

3Blouse

Remaining

3

4

Money left

scarfR

R

Fraction of the whole

1

4

Money



3


was left?

Example 5: Branch Method


1 –3

4=

1

4

42

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



3


was left?

Example 5: Branch Method



1 –1

3=

2

3

1

3Blouse

Remaining

3

4

Money left

scarfR

R1

4

Money

43

Quantity versus Value (‘per set’ concept)

44

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?


Step 1: Understand the question. (Keywords)

45



10 ¢

50 ¢

Number of coins Value of coins10 ¢

50 ¢

10 ¢10 10 10 10

Draw a model.


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



10 ¢

50 ¢


50 ¢

10 ¢10 10 10 10



47

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?



48


10 ¢

50 ¢


50 ¢

10 ¢10 10 10 10

Draw a model.



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



10 ¢

50 ¢


50 ¢

10 ¢10 10 10 10




50

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?


51


10 ¢

50 ¢


50 ¢

10 ¢10 10 10 10

Draw a model.


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



10 ¢

50 ¢


50 ¢

10 ¢10 10 10 10



53

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)

54

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



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?

57

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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