© 2009 mathematics department hougang primary school 25 april 2009

© 2009 Mathematics Department

Hougang Primary School

25 April 2009



* Help parents have a better understanding of how a Mathematical

problem is solved.

* To show parents how pupils should present their solutions.



WHY ARE THEY NOT ABLE TO DO THE PROBELMS?

Too difficultDo not understand

Question too long

Not able to pick out the gist

of the question

Simply give up

Language



UnderstandUnderstand

Plan/DevisePlan/Devise

Do/Carry OutDo/Carry Out

CheckCheck

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



?

Answer

What is next?

?Answer

What about this?



Complete the number pattern shown below :

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

+1

+1

+2

+1

+1

+2

+1

+1

+2

18 20

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

+50 +100 +150 +200 +250 +300

1 850



Some bricks are arranged as follows:

(a)How many bricks are there in Fig. 8?(b)How many bricks are there in Fig. 10?

Fig. 1 Fig. 2 Fig. 3

Now try this :



Fig. No. of rows

No. of bricks

Pattern Observed

1 1 1 1

2 2 3 1 + 2

3 3 6 1 + 2 + 3

4 4

8

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

10 1 + 2 + 3 + 41 + 2 + 3 + 4 + … + 88 36

10 1 + 2 + 3 + 4 + … + 9 + 1055

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

10



Some oval beads are arranged as follows:

Pattern 1 Pattern 2 Pattern 4Pattern 3



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

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

Pattern No. of beads

1 12 43 94 16

b) What pattern is formed by 484 beads ?



Pattern 12 – 12² = 12 x 12 = 144

There are 144 beads in Pattern 12.

a) Pattern No. of beads Pattern Observed

1 1

2 4 3 9

4 16

1 = 1 x 1= 12

4 = 2 x 2= 22

9 = 3 x 3= 32

16 = 4 x 4= 42



b)

Pattern Number = √No. of beads

Therefore, Pattern Number = = 22

Pattern 22 is formed by 484 beads.

No. of beads PatternNo.

1 1

4 = 2 x 2 2

9 = 3 x 3 3

16 = 4 x 4 4

Pattern observed

4916

1

484



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

The pattern observed are recorded in the table below.

No. of Level(s)

1 2 3 4 ……. 7Total

number of blocks needed

1 5 14 30 ……. ?



a) Find the number of blocks needed to make up 7 levels.

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?No. of

Level(s)Total no. of

blocksPattern

1 1 Nil

2 5 1 + 4 = 1 + (2 x 2)

3 141 + 4 + 9 = 1 + (2x2) + (3x3)

4 301 + 4 + 9 + 16

=1 + 22

=1 + 22 + 32

=1 + 22+32 + 42

7 1 + 22 + 32 + 42 + 52 + 62 + 72140

a) 7 levels require 140 blocks.b) No. of blocks required – 21 x 21 = 221



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

2 2 4

Chickens Rabbits Total

No. Legs No. Legs No. Legs

4 8 12

3 1 46 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?



3 3 6

Spiders Dragonfly Total

No. Legs No. Legs No. Legs

24 18 42

2 4 616 24 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?

15 15 30

$5 $10 Total

No. Amount No. Amount No. Amount

$75 $150 $225

16 14 30$80 $140 $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.



15 15 30

$2 $5 Total

No. Amount No. Amount No. Amount

$30 $75 $105

14 16 30$28 $80 $108

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

12 18 30$24 $90 $114

10 20 30$20 $100 $120



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

80



40 $240 40 $80 80 $160

Files Notebooks No. No.Amount Amount

Difference ($120)

Total no. (80)

30 $180 50 $100 80 $80

35 $210 45 $90 80 $120

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



$2

No. Amount

$5

No. Amount

Total

No. Amount

24 $48 24 $120 48 $168

26 22 48$52 $110 $162

28 20 48

30 18 48

32 16 48

$56 $100 $156

$60 $90 $150

$64 $80 $144

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



Some books that you can use with your child :

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

© 2009 mathematics department hougang primary school 25 april 2009

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