Mathematics

Helping your child in

non-routine questions

Mdm Nur Hazreen LH2 / Math Mr Yeo Kian Ho ST/ Math

Today’s session..

OVERVIEW

Thinking Skills

Heuristics

4 Steps in Problem Solving

Hands-on session

Conclusion

Non-routine problems

Complex math problem that involve the use of a combination of thinking skills and appropriate

heuristic strategy.

Mathematics Framework

Cheng ME/ 8 Nov 2014

Mathematics Framework

Cheng ME/ 8 Nov 2014

Mathematics Framework

Cheng ME/ 8 Nov 2014

Thinking Skills

• Classifying

• Comparing

• Sequencing

• Analysing parts and wholes

• Identifying patterns and relationships

• Induction

• Deduction

• Spatial Visualisation

Heuristics

Make a calculated guess

Draw a diagram

Make a list

Use equations

Give a Representation

Guess and check

Look for patterns

Make suppositions

Go through the process

Act it out

Work backwards

Before-after

Change the problem

Restate the problem

Simplify the problem

Solve part of the problem

4 Steps in Problem Solving

1 •UNDERSTAND the problem

2 •PLAN what to do / Devise a plan

3 •DO it / Carry out the Plan

4 •CHECK the solution / Review

Problem-solving

Thinking Skills

4-step process

Heuristics

4 Steps in Problem Solving

Example

A B

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?

Understand

Read sentence by sentence and understand the information given in each sentence.

Study the diagram to extract relevant information.

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.

Plan - Group the sides of each triangle as a set :

- Find the number of sets.

A B

- Perimeter can be divided by the number of sets to find the total length of each set.

1 short, 1 medium and 1 long

4 Steps in Problem Solving

A B

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?

Do

Length AB is equivalent to the total length of 1 set.

Number of sets = 4

Length AB ---------- 112 ÷ 4 = 28

Ans : 28 cm

4 Steps in Problem Solving

A B

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?

Check

Mathematics

Hands-On Session by

Mr Yeo Kian Ho

ST Math

4 Steps in Problem Solving

1 •UNDERSTAND the problem

2 •PLAN what to do / Devise a plan

3 •DO it / Carry out the Plan

4 •CHECK the solution / Review

Question 1

Question 1

• Understand the Problem

The colours follow a pattern

Each segment – 1 cm

Total length of the repeated pattern is 60 cm

3 colours – white, grey and black

Question 1

• Plan

- Think of possible patterns

- Write or draw the different patterns to

check if they are correct

Question 1

• Plan Examples

- White, Black, Grey, White, Grey……….

- Grey, White, Black, Grey, White ……….

- White, Grey, White, Black, Grey ……….

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

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

Question 2

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?

Question 2a

Units that are black squares ----> (4 + 1) = 5

Total units in Figure 1 -------------> 9

Fraction of Figure 1 that are black squares = 5

9

5

9 of the square tile in figure 1 is made up of

black squares.

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

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

Question 2b

• Plan

- Simplifying the problem

Figure A Figure B Figure C

𝟓

𝟗 of each figure above is shaded, therefore

𝟓

𝟗 of Figure 2 is covered by black squares

𝟓

𝟗 is shaded

𝟏𝟎

𝟏𝟖 =

𝟓

𝟗 is shaded

𝟏𝟓

𝟐𝟕 =

𝟓

𝟗 is shaded

Question 2b

• Do

Area of floor -----------> 18 m x 18 m

= 324 m2

5

9 of area of floor ------>

5

9 x 324 m2

= 180 m2

Total area of floor covered by black squares is 180 m2

Question 3

Question 3

• Understand

- Side of square paper: 23 cm

- Area of small square: 49 cm2

- 8 identical right-angled triangles

- Figure 2, Triangle PQR is one such triangle

Question 3

• Do

Area of square paper-----> 23 cm x 23 cm

= 529 cm2

Area of 8 triangles---------> 529 cm2 – 49 cm2 = 480 cm2

Area of 1 triangle ----------> 480 ÷ 8 = 60 cm2

Area of 4 triangles ---------> 60 x 4 = 240 cm2

Question 3

• Do

Area of 4 triangles --------> 60 x 4 = 240 cm2

P

Q

O

N

• Check

Area of square NOPQ----> 529 – 240 = 289 cm2 Since 17 x 17 = 289

PQ-----> 17 cm

Question 4

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

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

Question 4

• Do

Since MN = QN = QM

MNQ is a equilateral

MQN = 60o

MQP =NQP = 60o ÷ 2

= 30o

60o

60o

30o

30o

Question 4

• Do

Since MQ = PQ

MPQ is an isosceles

75o

30o

75o

30o

75o 75o

• Check

MPQ = (180 – 30) ÷ 2 = 150o ÷ 2 = 75o

MPQ =QPN = 75o MPN = 75o + 75o = 150o

Supporting our children

• Ask your child to explain how he solved the problem

Not Helpful

• Providing the answers immediately

Helpful

Learning mathematics is more than finding the correct answer. It is a process of solving problems and applying mathematical

knowledge to new problems.

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.

Thank you!

Mdm Nur Hazreen LH2 / Math Mr Yeo Kian Ho Senior Teacher / Math