Helping your child in non-routine questions

Transcription

1 Mathematics Helping your child in non-routine questions Mdm Nur Hazreen LH2 / Math Mr Yeo Kian Ho ST/ Math

2 Today s session.. OVERVIEW Thinking Skills Heuristics 4 Steps in Problem Solving Hands-on session Conclusion

3 Non-routine problems Complex math problem that involve the use of a combination of thinking skills and appropriate heuristic strategy.

4 Mathematics Framework Cheng ME/ 8 Nov 2014

5 Mathematics Framework Cheng ME/ 8 Nov 2014

6 Mathematics Framework Cheng ME/ 8 Nov 2014

7 Thinking Skills Classifying Comparing Sequencing Analysing parts and wholes Identifying patterns and relationships Induction Deduction Spatial Visualisation

8 Heuristics Make a calculated guess Give a Representation Go through the process Change the problem Draw a diagram Guess and check Act it out Restate the problem Make a list Look for patterns Work backwards Simplify the problem Use equations Make suppositions Before-after Solve part of the problem

9 4 Steps in Problem Solving 1 UNDERSTAND the problem PLAN what to do / Devise a plan 2 DO it / Carry out the Plan 3 CHECK the solution / Review 4

10 Thinking Skills Heuristics Problem-solving 4-step process

11 4 Steps in Problem Solving Example The figure below is made up of 6 equilateral triangles. Given that the perimeter of the figure is 112 cm, what is the length of AB? A B Understand Read sentence by sentence and understand the information given in each sentence. Study the diagram to extract relevant information.

12 Understand - 6 equilateral triangles [2 small, 2 medium and 2 large] - Perimeter of figure is 112 cm A B - The sides of two similar sized triangles are of equal length.

13 Plan - Group the sides of each triangle as a set : - Find the number of sets. 1 short, 1 medium and 1 long A B - Perimeter can be divided by the number of sets to find the total length of each set.

14 4 Steps in Problem Solving Do The figure below is made up of 6 equilateral triangles. Given that the perimeter of the figure is 112 cm, what is the length of AB? A B Length AB is equivalent to the total length of 1 set. Number of sets = 4 Length AB = 28 Ans : 28 cm

15 4 Steps in Problem Solving Check The figure below is made up of 6 equilateral triangles. Given that the perimeter of the figure is 112 cm, what is the length of AB? A B

16 Mathematics Hands-On Session by Mr Yeo Kian Ho ST Math

17 4 Steps in Problem Solving 1 UNDERSTAND the problem PLAN what to do / Devise a plan 2 DO it / Carry out the Plan 3 CHECK the solution / Review 4

18 Question 1

19 Question 1 Understand the Problem 3 colours white, grey and black The colours follow a pattern Each segment 1 cm Total length of the repeated pattern is 60 cm

20 Question 1 Plan - Think of possible patterns - Write or draw the different patterns to check if they are correct

21 Question 1 Plan Examples - White, Black, Grey, White, Grey. - Grey, White, Black, Grey, White. - White, Grey, White, Black, Grey.

22 Question 1 Plan - Find the number of grey segments in each pattern - Find the number of sets of the same pattern in 60 cm of ribbon - Find the number of grey segments in 60 cm

23 Question 1 Do Pattern > White, Grey, White, Black and Grey Length of pattern ----> 5 cm Number of grey segment in pattern > 2 Number of sets of 5 cm > 60 5 = 12 Total number of grey segments ---> 2 x 12 =24 Check

24 Question 2

25 Question 2a Figure 1 shows a square tile made up of 2 black squares, P and Q, and 2 identical white rectangles R. The length of 1 side of square Q is twice the length of 1 side of square P. a) What fraction of the square tile in figure 1 is made up of black squares?

26 Question 2a Units that are black squares ----> (4 + 1) = 5 Total units in Figure > 9 Fraction of Figure 1 that are black squares = of the square tile in figure 1 is made up of black squares.

27 Question 2b b) Figure 2 shows a floor laid with the square tiles. The floor is 18 m by 18 m and is completely covered with the square tiles. Find the total area covered by the black tiles

28 Question 2b Understand - Area of figure 2 ---> 18 m x 18 m - Figure 2 is completely covered by tiles - Each tile is 5 9 covered with black squares

29 Question 2b Plan - Simplifying the problem Figure A Figure B Figure C 5 9 is shaded = 5 9 is shaded = 5 9 is shaded 5 9 of each figure above is shaded, therefore 5 9 of Figure 2 is covered by black squares

30 Question 2b Do Area of floor > 18 m x 18 m 5 = 324 m 2 of area of floor > 5 x 324 m2 9 9 = 180 m 2 Total area of floor covered by black squares is 180 m 2

31 Question 3

32 Question 3 Understand - Side of square paper: 23 cm - Area of small square: 49 cm 2-8 identical right-angled triangles - Figure 2, Triangle PQR is one such triangle

33 Question 3 Do Area of square paper-----> 23 cm x 23 cm = 529 cm 2 Area of 8 triangles > 529 cm 2 49 cm 2 = 480 cm 2 Area of 1 triangle > = 60 cm 2 Area of 4 triangles > 60 x 4 = 240 cm 2

34 Question 3 Do Area of 4 triangles > 60 x 4 = 240 cm 2 Area of square NOPQ----> = 289 cm 2 Since 17 x 17 = 289 PQ-----> 17 cm P Q Check O N

35 Question 4

36 Question 4 Understand - the whole figure ABCD is a square, therefore AB = BC = CD = DA - QM = QP = QN and QM = QN = MN - MN is PQ, therefore MQP = NQP

37 Question 4 Plan - Solve part of the problem a) Finding MQP and NQP using equilateral MNQ b) Finding QPN and QPM using isosceles NPQ and isosceles MPQ

38 Question 4 Do Since MN = QN = QM MNQ is a equilateral MQN = 60 o MQP = NQP = 60 o 2 60 o 60 o 30 o 30 o = 30 o

39 Question 4 Do Since MQ = PQ MPQ is an isosceles MPQ = (180 30) 2 = 150 o 2 = 75 o MPQ = QPN = 75 o MPN = 75 o + 75 o = 150 o Check 75 o 75 o 30 o 75 o 75 o 30 o

40 Supporting our children Helpful Ask your child to explain how he solved the problem Not Helpful Providing the answers immediately Learning mathematics is more than finding the correct answer. It is a process of solving problems and applying mathematical knowledge to new problems.

41 Conclusion Know the current ability of your child Build his/her confidence Help your child grow Thinking and heuristics skills are cultivated while the child is working on problems, getting them wrong, struggling through them till he gets them right.

42 Thank you! Mdm Nur Hazreen LH2 / Math Mr Yeo Kian Ho Senior Teacher / Math