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PARENTS
SYMPOSIUM 2019
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PROBLEM SOLVING
STRATEGIESParents Symposium 2019
(Primary 3 and 4)
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Outline
1. Problem solving process
2. Heuristics
• Working backwards
• Make a supposition
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PROBLEM SOLVING
PROCESS
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Mathematics Curriculum
The primary aim of the Mathematics
curriculum is to enable students to develop
their ability in Mathematical PROBLEM
SOLVING.
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Solving Word Problems
• understand the problems well
• use their mathematical knowledge to solve
them
Students sometimes find it difficult to understand a
problem just by reading it and they may need to
highlight key words, draw diagrams or models to
help them visualise the problem.
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Steps to Problem Solving
• Study the problem
• Plan
• Act
• Reasonableness
• Explain
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Study the Problem
CheckingNo
Yes
No
Yes
Explain (Reflection)
• Improving on the
method used.
• Seeking
alternative
solutions.
- Extending the
method to other
problems.
- Can you explain
what you did?
Problem
Solving ProcessPlan (choose a heuristic)
Act – Carry out the plan
Needs modification / a new
plan?
Is the answer
Reasonable?
Explain (Reflection)
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Study the Problem
• What is the question asking for?
• Can you restate the problem in your own words?
• Can you think of a picture or diagram to help you
understand the problem?
• What can you find based on the information
given?
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Plan
• What strategy / strategies should I use?
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Act
• Carry out your plan
• Check each step
• Ensure that the entire solution is written clearly
by checking the following:
• Show all the steps
• Transfer all numbers correctly
• Use correct units
• Neat
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Reasonableness
• Does your answer make sense? Is it reasonable?
• Is there another method to find the solution?
• What worked? What didn’t?
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Explain
• Can you explain what you did earlier?
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HEURISTICS
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Heuristics• Strategies used in problem solving:
give a representation (draw a diagram, make a
list, use equations)
make a calculated guess (guess & check, look
for patterns, make suppositions)
go through the process (act it out, work
backwards)
change the problem (restate the problem,
simplify the problem, solve part of the problem)
(Source: Curriculum Planning & Development Division, MOE, Mathematics
Syllabus Primary 2013)
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Thinking Skills• Skills that can be used in a thinking process:
classifying
comparing
sequencing
generalising
induction
deduction
analysing (from whole to part)
synthesising (from part to whole)
identifying patterns and relationships
spatial visualisation
(Source: Curriculum Planning & Development Division, MOE, Mathematics
Syllabus Primary 2013)
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HEURISTICSWorking Backwords
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1. Mr Tan had some apples. He threw away
24 rotten apples and bought another 14
apples. Then his friend gave him another
13 apples. In the end, he had 87 apples.
How many apples did he have at first?
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1. Mr Tan had some apples. He threw away
24 rotten apples and bought another 14
apples. Then his friend gave him another
13 apples. In the end, he had 87 apples.
How many apples did he have at first?
Result
87A
– 24
B
+ 14 + 13
Start
?
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1. Mr Tan had some apples. He threw away
24 rotten apples and bought another 14
apples. Then his friend gave him another
13 apples. In the end, he had 87 apples.
How many apples did he have at first?
Start
?
Result
87A
– 24
B
+ 14 + 13
– 13– 14+ 24
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Start
?
Result
87A
– 24
B
+ 14 + 13
– 13– 14+ 24
At first = 87 – 13 – 14 + 24
= 84
When do we use
Working
Backwards?
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2. Some passengers boarded the bus at the
interchange. At the first stop, 4 passengers
alighted and 3 passengers boarded the
bus. At the second stop, 7 passengers
alighted and another 10 passengers
boarded the bus. In the end, there were 39
passengers on the bus. How many
passengers boarded the bus at the
interchange?
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2. Some passengers boarded the bus at the
interchange. At the first stop, 4 passengers
alighted and 3 passengers boarded the
bus. At the second stop, 7 passengers
alighted and another 10 passengers
boarded the bus. In the end, there were 39
passengers on the bus. How many
passengers boarded the bus at the
interchange?
Interchange
?2nd stop
39
1st
stop
– 4
+ 3
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At the second stop, 7 passengers alighted
and another 10 passengers boarded the
bus. In the end, there were 39 passengers
on the bus. How many passengers
boarded the bus at the interchange?
Interchange
?2nd stop
39
1st
stop
– 4
+ 3
– 7
+ 10
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Interchange
?2nd stop
39
1st
stop
– 4
+ 3
– 7
+ 10
+ 4
– 3
+ 7
– 10
At 1st stop = 39 + 7 – 10
= 36
At interchange = 36 + 4 – 3
= 37
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Question type: Working backwards
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3. A train has some passengers at Station A.
At Station B, 46 passengers alighted the
train and another 35 passengers boarded
the train. At Station C, 62 passengers
alighted the train and another 98
passengers boarded the train. In the end,
there were 761 passengers on the train.
How many passengers were on the train at
Station A?
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3. A train has some passengers at Station A.
At Station B, 46 passengers alighted the
train and another 35 passengers boarded
the train. At Station C, 62 passengers
alighted the train and another 98
passengers boarded the train. In the end,
there were 761 passengers on the train.
How many passengers were on the train at
Station A?
A
?
C
761B
– 46
+ 35
– 62
+ 98
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A
?
C
761B
– 46
+ 35
– 62
+ 98
+ 46
– 35
+ 62
– 98
At B = 761 + 62 – 98
= 725
At A = 725 + 46 – 35
= 736
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HEURISTICSMake a Supposition
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4. There are 35 cars and bicycles at the car
park. There are 100 wheels in total.
a) How many cars are there?
b) How many bicycles are there?
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Using guess and check
No. of
Bicycles
Wheels
(Bicycles)
No. of
cars
Wheels
(cars)
Total No.
of
Wheels
Check
17 17 × 2 = 34 18 18 × 4 = 72 34 + 72 =
106
20 20 × 2 = 40 15 15 × 4 = 60 40 + 60 =
100
Is this the only way?
Conditions to meet:
1. Total number of bicycles and cars = 35
2. Total number of wheels = 100
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Supposition: 35 bicycles
1 car = 2 extra wheels
Total number of bicycle wheels = 35 × 2
= 70Extra wheels from cars = 100 – 70
= 30
No. of Bicycles = 35 – 15
= 20
No. of Cars = 30 ÷ 2
= 15
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5. A mango cost $2 and a durian cost $5.
Mrs Sim bought a total of 45 mangoes and
durians. She paid $129. How many of each
type of fruit did she buy?
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Supposition : 45 mangoes
1 durian = $3 extra
Total cost = 45 × 2
= 90
Extra cost from durians = 129 – 90
= 39
Mangoes = 45 – 13
= 32
Durians = 39 ÷ 3
= 13
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Question type: Make a supposition
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6. There are 28 fifty-cent and twenty-cent coins.
The total value of coins is $11.60. How many
of each type of coin are there?
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Supposition: 28 20-cent coins
1 50¢ = 30¢ extra
Total value = 28 × 20
= 560
Extra value = 1160 – 560
= 600
20-cent = 28 – 20
= 8
50-cent = 600 ÷ 30
= 20
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Tips for Parents
1. Ensure your child knows the multiplication tables.
2. Have more practices on similar questions.
3. Revise the topics that are currently taught in school. Do not teach ahead or over teach.
4. Teach your child how to check for reasonableness.
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Tips for Parents
Model for your child
• Model the desired problem solving process when you
solve the problems with your child.
• Show your child the whole process, not just the
solutions.
• Guide your child to understand the problem first and
how you make sense of the problem.
• Show your child how you think and select the
heuristic to solve the problem.
• Demonstrate to your child how you check your work.
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Study the problem
Plan
Act
Reasonableness
Explain
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