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PARENTS

SYMPOSIUM 2019

PROBLEM SOLVING

STRATEGIESParents Symposium 2019

(Primary 3 and 4)

Outline

1. Problem solving process

2. Heuristics

• Working backwards

• Make a supposition

PROBLEM SOLVING

PROCESS

Mathematics Curriculum

The primary aim of the Mathematics

curriculum is to enable students to develop

their ability in Mathematical PROBLEM

SOLVING.

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.

Steps to Problem Solving

• Study the problem

• Plan

• Act

• Reasonableness

• Explain

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)

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?

Plan

• What strategy / strategies should I use?

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

Reasonableness

• Does your answer make sense? Is it reasonable?

• Is there another method to find the solution?

• What worked? What didn’t?

Explain

• Can you explain what you did earlier?

HEURISTICS

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)

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)

HEURISTICSWorking Backwords

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?

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

?

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

Start

?

Result

87A

– 24

B

+ 14 + 13

– 13– 14+ 24

At first = 87 – 13 – 14 + 24

= 84

When do we use

Working

Backwards?

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?

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

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

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

Question type: Working backwards

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?

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

A

?

C

761B

– 46

+ 35

– 62

+ 98

+ 46

– 35

+ 62

– 98

At B = 761 + 62 – 98

= 725

At A = 725 + 46 – 35

= 736

HEURISTICSMake a Supposition

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?

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

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

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?

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

Question type: Make a supposition

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?

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

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.

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.

Study the problem

Plan

Act

Reasonableness

Explain