helping your child in non-routine questions
TRANSCRIPT
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