Problem Solving (Guna)

7/29/2019 Problem Solving (Guna)

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Learning to solve

problems is the

principle reason forstudying mathematics


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WHAT IS

THE PROBLEM?

STUDENTS

LANGUAGE

MONEY

$$$$$$

FAMILY

PROGRAMME

60 : 40


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PROBLEMS

???????????

A statement or daily

life situation that

requires solutions.


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Kinds of Problems

Routine

Problem

NonRoutine

Problem

Application @

Modelling problem ExploringProblem


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Routine Problems

Normally confront.

Involve one mathematical operation.

Basic skills and sequencial steps.

Need understanding, gather information,

choose operation and algorithms.

Solve through story telling and relate it to

real situation.


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Non-routine Problems

Complex problem.

Require complex solving process.

Use different strategies

Use various methods.

Use critical and creative thinking

skills.


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A SYSTEMATIC PROCESSTHAT REQUIRES THINKING

SKILLS TO ACHIEVE THE

REQUIRED AIM IN A

CERTAIN PROBLEM USING

VARIOUS STRATEGIES,KNOWLEDGE AND

EXPERIENCE.

PROBLEM SOLVING


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8

WHY PROBLEMSOLVING ?

MATHS

SKILLS

PLANNING

CONCEPT

COMMUNICATION

THINKING

SKILLS

SELF-ACCESS

LEARNING

VALUESELF-ESTEEM

DECISION

MAKING


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9

If you give a man a loaf of bread, you feedhim for a day;

but if you teach the man to bake, you feed him

for a lifetime.

If you give a boy a fish, he will have fish for

a meal;but if you teach him how to fish, he will have

fish for a lifetime.

A Strategy Can Be Mastered By Practise


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4STEP PLAN TO SOLVE PROBLEMS

Based on Polya model

Explore.

Plan.

Solve.

Examine.


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PROBLEM SOLVING STRATEGIES

Suggested strategies for primary schools are:

Representation of Objects

Guess, check and improve

Look for a pattern

Draw a diagram

Make a table

Try a simpler case

Make an analogy

Acta situation

Work backwards


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1. Representation of objects

Representing numbers with objects.


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There are 5 marbles in a box.

Mum add in 2 more.

How many marbles are there in the box?
http://localhost/var/www/apps/conversion/tmp/scratch_8/sheepgame.exe


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2. Guess, check and improve

Make a guess

Check the answers Work out systematically

Guess the answers according to certain sequence
http://localhost/var/www/apps/conversion/tmp/scratch_8/GUESS%20AND%20CHECK.ppt


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Complete the given circles with numbers 1

to 6 so that the sums of all the sides of the

triangle is 12.

4

1

23

5 6


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The sum of 3 successive numbers is 243. Make an

estimation and work out the numbers.

+ + = 243

3 = 81243

Make an estimation

Make a guess

a) 81 + 82 + 83 = 246

b) 79 + 80 + 81 = 240

c) 80 + 81 + 82 = 243

80 81 82


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3. Look for a pattern

Introduces the idea that many sequences can be constructed

Studies specific pattern

Making generalisation for a solution

Carry out the generalisation


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1 3 6 10, , , , 15


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4. Draw a diagram

Use to clarify a problem

Guide the students to solve the problems


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The membership fee of a clubfor men and women is in the

ratio of 4:3. A group of 2 men

and 5 women paid RM4600as the total membership fee.

How much is the membership feefor a men?


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TRY TO SOLVE IT..


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Yati earns RM1 200 monthly. She spends of it and keeps

of the remainder as monthly savings. How much is her monthly

savings?

RM1200

RM400

RM400

RM400

RM100 RM100 RM100 RM100

3

2

3

1

3

2

4

1

Spent

left

4

1Savings


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5. Make a table

List out the possibilities systematically

Overcomes the disability to interpret problems


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Item Quantity Price per unit Total

Total

Rosnah decided to hold a party. She bought 2 kg of chicken at RM5.50

per kg and 800 g of lettuce costing RM2 a kg. How much did she spend?

Chicken 2 kg RM5.50 RM11.00

Lettuce 800 g RM2.00 RM 1.60

RM12.60

1 kg RM2.00

RM2 x 800 g 1600800 g

1000=

1000

= RM 1.60


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6. Try a simpler case

Some complicated problems

can be solve by trying out asimpler case which has a or

some similarities.


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+ 3 = 7

34

56

7

1

1

1

1

4

+ 3 = 74

362


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362

462

562

662

762

100

100

100

400

72

82

92

9394

100

4331010

95

30

1

1

1

3

10


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+ 362 = 795433


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7. Make an analogy

Problem A compared with problem B.

Procedures to solution already known.

A problem similar to B problem

and continue using it.

If only part of problem B is the same,do some minor changes.


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Find the total surface of a pyramid.

Feel the surface of a cube

Relate it to the surface of a pyramid


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8. Act a situation Acting activity is being carried out

Suitable objects can be used

Clearer and easier to understand the problems


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Puan Siti has RM100. She bought two blouses

at RM18 each. How much money left?

RM18

RM18

RM100 RM18 RM18 = RM64_ _


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9. Working Backwards

The end information is given.

Figure out what happened before.

Use this strategy to solve the problem.


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A bus from Taiping reached Kuala Lumpur at 4.30

p.m. It stopped at Tapah for 30 minutes. If the journey

took 4 hours and 30 minutes, what times does the

bus leave from Taiping ?

Determine the informations:

a) Arrived KL at 4.30 p.m

b) Break for 30 minutesc) Duration time 4 hours 30 minutes


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11.30 12.30 1.30 2.30 3.30 4.3012.00Break

Arrivals

1 hr 1 hr 1 hr 1 hr30 mins30 mins

Departure time at

11.30 a.m


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CONCLUSIONFor effective T&L

use non routine questions with routine questions

use questions which have one answer/more answers use a diverge question and more challenging

use creative and critical thinking (KBKK)

use different solving strategies

carry out problem solving in T&L and assessment

Problem Solving (Guna)

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