1. © 2009 Mathematics Department Hougang Primary School 25 April 2009

2. © 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.

3. © 2009 Mathematics Department Hougang Primary School WHY ARE THEY NOT ABLE TO DO THE PROBELMS? Too difficult Do not understand Question too long Not able to pick out the gist of the question Simply give up Language

4. © 2009 Mathematics Department Hougang Primary School Understand Plan/Devise Do/Carry Out Check 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=75673http://www.hougangpri.moe.edu.sg/cos/o.x?c=/wbn/pagetree&func=view&rid=75673

5. © 2009 Mathematics Department Hougang Primary School

6. © 2009 Mathematics Department Hougang Primary School ? Answer What is next? ? Answer What about this?

7. © 2009 Mathematics Department Hougang Primary School Complete the number pattern shown below : 8, 9, 10, 12, 13, 14, 16,17, ____, ____ +1 +2+1 +2+1 +2 1820 800, 850, 950, 1 100, 1 300, 1 550, ______ +50+100+150 +200 +250+300 1 850

8. © 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 :

9. © 2009 Mathematics Department Hougang Primary School Fig.No. of rows No. of bricks Pattern Observed 1111 2231 + 2 3361 + 2 + 3 44 8 (a) There are 36 bricks in Fig. 8. 10 1 + 2 + 3 + 4 1 + 2 + 3 + 4 + … + 8 8 36 10 1 + 2 + 3 + 4 + … + 9 + 10 55 (b) There are 55 bricks in Fig. 10. 10

10. © 2009 Mathematics Department Hougang Primary School Some oval beads are arranged as follows: Pattern 1 Pattern 2 Pattern 4 Pattern 3

11. © 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. PatternNo. of beads 11 24 39 416 b) What pattern is formed by 484 beads ?

12. © 2009 Mathematics Department Hougang Primary School Pattern 12 – 12² = 12 x 12 = 144 There are 144 beads in Pattern 12. a) PatternNo. of beadsPattern Observed 11 24 39 416 1 = 1 x 1 = 1 2 4 = 2 x 2 = 2 2 9 = 3 x 3 = 3 2 16 = 4 x 4 = 4 2

13. © 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 beadsPattern No. 1 1 4 = 2 x 2 2 9 = 3 x 3 3 16 = 4 x 4 4 Pattern observed

14. © 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) 1234…….7 Total number of blocks needed 151430…….?

15. © 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?

16. © 2009 Mathematics Department Hougang Primary School What pattern do you observe? No. of Level(s) Total no. of blocks Pattern 11Nil 251 + 4 = 1 + (2 x 2) 314 1 + 4 + 9 = 1 + (2x2) + (3x3) 430 1 + 4 + 9 + 16 =1 + 2 2 =1 + 2 2 + 3 2 =1 + 2 2 +3 2 + 4 2 7 1 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 140 a) 7 levels require 140 blocks. b) No. of blocks required – 21 x 21 = 221

17. © 2009 Mathematics Department Hougang Primary School

18. © 2009 Mathematics Department Hougang Primary School 4 chickens and rabbits have 10 legs altogether. How many chickens and how many rabbits are there? 224 Chickens Rabbits Total No. Legs No. Legs No. Legs 4812 3146410 There are 3 chickens and 1 rabbit.

19. © 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?

20. © 2009 Mathematics Department Hougang Primary School 336 Spiders Dragonfly Total No. Legs No. Legs No. Legs 241842 246162440 There are 2 spiders and 4 dragonflies.

21. © 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 30 $5 $10 Total No. Amount No. Amount No. Amount $75$150$225 161430$80$140$220 Cindy has 14 $10 notes.

22. © 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.

23. © 2009 Mathematics Department Hougang Primary School 15 30 $2 $5 Total No. Amount No. Amount No. Amount $30$75$105 141630$28$80$108 Samantha has 10 $2 notes and 20 $5 notes. 121830$24$90$114 102030$20$100$120

24. © 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

25. © 2009 Mathematics Department Hougang Primary School 40 $240 40$8080$160 Files Notebooks No.No. Amount Amount Difference ($120) Total no. (80) 30 $180 50$10080$80 35 $210 45$9080$120 Denny bought 35 files and 45 notebooks.

26. © 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

27. © 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.

28. © 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