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* Help parents have a better

understanding of how a Mathematical

problem is solved.

* To show parents how pupils should

present their solutions.

DO THE PROBELMS?

Too difficult

Do not understand

Question too long

Not able to pick out the gist

of the question

Language

Simply give up

Problem Solving

Understand

Plan/Devise

Check

Do/Carry Out

For more detailed explanation, please refer to the Mathematics Department webpage

at http://www.hougangpri.moe.edu.sg/cos/o.x?c=/wbn/pagetree&func=view&rid=75673

Complete the number pattern shown below :

18

20

8 , 9 , 10 , 12 , 13 , 14 , 16 ,17 , ____, ____

+1

+1

+2

+1

+1

+2

+1

+1

+2

1 850

800, 850, 950, 1 100, 1 300, 1 550, ______

+200

+50

+100

+150

+250

+300

Some bricks are arranged as follows:

Fig. 1 Fig. 2 Fig. 3

- How many bricks are there in Fig. 8?
- How many bricks are there in Fig. 10?

10

8

36

1 + 2 + 3 + 4 + … + 8

10

10

55

1 + 2 + 3 + 4 + … + 9 + 10

(a) There are 36 bricks in Fig. 8.

(b) There are 55 bricks in Fig. 10.

The pattern observed for the four patterns are recorded in the table below.

a) How many oval beads are there in Pattern 12 ?

b) What pattern is formed by 484 beads ?

a) the table below.

1 = 1 x 1

= 12

4 = 2 x 2

= 22

9 = 3 x 3

= 32

16 = 4 x 4

= 42

Pattern 12 –

12² = 12 x 12

= 144

There are 144 beads in Pattern 12.

b) the table below.

Pattern Number = √No. of beads

Pattern observed

Therefore, Pattern Number =

= 22

Pattern 22is formed by 484 beads.

The figure is made up of 4 levels of blocks stacked against a corner.

The pattern observed are recorded in the table below.

b) How many more blocks must be added to a 20-level high figure to form a 21-level high figure?

What pattern do you observe? a corner.

=1 + 22

=1 + 22 + 32

=1 + 22+32 + 42

140

1 + 22 + 32 + 42 + 52 + 62 + 72

7

a) 7 levels require 140 blocks.

b) No. of blocks required – 21 x 21

= 221

Guess & Check a corner.

Systematic Listing

4 chickens and rabbits have 10 legs altogether. How many chickens and how many rabbits are there?

Rabbits

Chickens

Total

No.

No.

No.

Legs

Legs

Legs

2

4

2

8

4

12

3

6

1

4

4

10

There are 3 chickens and 1 rabbit.

A spider has 8 legs. A dragonfly has 6 legs. 6 spiders and dragonflies have 40 legs altogether. How many spiders and how many dragonflies are there?

Dragonfly dragonfly has 6 legs. 6 spiders and dragonflies have 40 legs altogether. How many spiders and how many dragonflies are there?

Spiders

Total

No.

No.

No.

Legs

Legs

Legs

3

24

3

18

6

42

2

16

4

24

6

40

There are 2 spiders and 4 dragonflies.

Cindy has 30 pieces of $5 and $10 notes. Her total savings is $220. How many pieces of $10 notes does Cindy have?

$10

$5

Total

No.

No.

No.

Amount

Amount

Amount

15

$75

15

$150

30

$225

16

$80

14

$140

30

$220

Cindy has 14 $10 notes.

Samantha has 30 pieces of $2 and $5 notes altogether. The total value of the money she has is $120. Find the number of pieces of $2 notes and the number of pieces of $5 notes that Samantha has.

$5 total value of the money she has is $120. Find the number of pieces of $2 notes and the number of pieces of $5 notes that Samantha has.

$2

Total

No.

No.

No.

Amount

Amount

Amount

15

$30

15

$75

30

$105

14

$28

16

$80

30

$108

12

$24

18

$90

30

$114

10

$20

20

$100

30

$120

Samantha has 10 $2 notes and 20 $5 notes.

80 total value of the money she has is $120. Find the number of pieces of $2 notes and the number of pieces of $5 notes that Samantha has.

Denny bought a total of 80 files and notebooks. Each file cost $6 and each notebook cost $2. If the total cost of the files is $120 more than the total cost of the notebooks, how many files and how many notebooks did Denny buy?

$120 more

Files total value of the money she has is $120. Find the number of pieces of $2 notes and the number of pieces of $5 notes that Samantha has.

Notebooks

Total no. (80)

Difference ($120)

No.

No.

Amount

Amount

40

40

$80

80

$160

$240

30

50

$100

80

$80

$180

35

45

$90

80

$120

$210

Denny bought 35 files and 45 notebooks.

Darren has a total of 48 $2 and $5 notes. If he has $144 altogether, how many $2-notes and how many $5 notes does he have?

48 $2 and $5 notes

$144

$5 altogether, how many $2-notes and how many $5 notes does he have?

Total

$2

Amount

No.

Amount

Amount

No.

No.

$48

$168

24

48

$120

24

26

48

$52

$162

22

$110

28

48

$56

$156

20

$100

30

48

$60

$150

18

$90

32

48

16

$64

$144

$80

Darren has 32 $2-notes and 16 $5-notes.

Some books that you can use with your child : altogether, how many $2-notes and how many $5 notes does he have?

MathQuest Approach To Learning PSLE MATH Vol. 1

- Chok Sitt Fan & Karen Tsang, Butterfly Publications

Solving Challenging Mathematical Problems – The Heuristics Approach for Primary School

Fong Ho Kheong, Kingsfield Educational Services

Sharpen Your Skills For Problem-Solving

Anne Joshua, Longman

Thinking Maths

Tan Ger Imm & Lee Pey Ren, EduPro Station, Singapore

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