© 2009 Mathematics Department Hougang Primary School 25 April 2009
Feb 02, 2016
© 2009 Mathematics Department
Hougang Primary School
25 April 2009
© 2009 Mathematics Department
Hougang Primary School
* Help parents have a better understanding of how a Mathematical
problem is solved.
* To show parents how pupils should present their solutions.
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
© 2009 Mathematics Department
Hougang Primary School
?
Answer
What is next?
?Answer
What about this?
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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 :
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
Some oval beads are arranged as follows:
Pattern 1 Pattern 2 Pattern 4Pattern 3
© 2009 Mathematics Department
Hougang Primary School
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 ?
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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 ……. ?
© 2009 Mathematics Department
Hougang Primary School
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?
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
© 2009 Mathematics Department
Hougang Primary School
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.
© 2009 Mathematics Department
Hougang Primary School
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?
© 2009 Mathematics Department
Hougang Primary School
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.
© 2009 Mathematics Department
Hougang Primary School
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.
© 2009 Mathematics Department
Hougang Primary School
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.
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
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.
© 2009 Mathematics Department
Hougang Primary School
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
© 2009 Mathematics Department
Hougang Primary School
$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.
© 2009 Mathematics Department
Hougang Primary School
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