Tension!Tension!

PROBLEM SOLVING

HJH. WAHIDAH ZAKARIA

Selesai?Tak selesai?

Problem!!PROBLEM!!

mASaLaH!

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A problem is a situation that an individual wants to resolve arises

but no solution is readily apparent. It is also a situation in which the

individual is confronted by something he/she cannot apply any

model to solve for the unknown. It is the process by which the unfamiliar

situation is resolved.

PROBLEM SOLVING

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Importance of problem solving skills

Enhance self access learning.Relate mathematics with daily life.To develop the concept Integrated use of thinking skillsFor communication.Enrich our life in our recreational pursuits.For mathematics learners about

`word problem’

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Polya’s Problem Solving Model

Four Steps process

UNDERSTANDING THE PROBLEM DEVISING A PLAN CARRYING OUT THE PLAN LOOKING BACK

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THE FLOW CHART ABOUT PS Start

No

NO

Understand the problem

i. Read and understang ii. Get the information giveniii. Clearify the problem

YesTHE END

Devise a PlanSolve

The problem can be solved by using the

Strategy?

Carry out the Plan 

Check the answer.

Correct solution

Yes

Look back and reflect

Divise a plan

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Method used for Problem SolvingSuggessted strategies

Simulation

Draw a diagram

Make a Table

Guessing & Checking

Experimenting

Simplify the problem

Working Backward

Analogy

Identify the Sub-goals

Identify the Pattern

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Simulate the action

Use suitable object

Easy to understand the problem

Simulation

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A man wants to move his sheep, a wolf and a box of cabbage across the river in his boat. The man can bring only one of them on his boat for the journey. Please help the man in the boat to move the sheep,the wolf and the cabbage to other side of theriver.

Notice that: Wolf eats the sheep and the sheep eats the cabbage when the man is not arround.

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Nota:

1. CHOOSE 3 PERSONS TO ACT AS A MAN , WOLF AND A SHEEP

2. Prepare a cabbage.

3. Fix the river bank

4. Act the situation.

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Use the diagram to solve problems

Help pupils to know the solving method.

Draw a diagram

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PROBLEM In a room with 10 people, everyone

shake hands with everybody else exactly once. How many hand shakes are there?

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RM1200

RM400

RM400

RM400

RM100 RM100 RM100 RM100

32

Remaining

Siti Khadijah’s salary is RM1200. She spent of his monthly

salary and kept the remaining in the bank. How much money did

Siti Khadijah banked in every month?

1 3

41 Kept in

bank

14

32

41

32

32

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Looking for Pattern

Pattern appear in many forms such as number pattern,

geometric pattern, word pattern and letter pattern.

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What is the value of x, y and z?

1 6 103 x zy

Solution

See the difference between the numbers.

1 6 103 x zy

2

28

3 4 5

15

6

21

7

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Looking for Pattern Exercise 1. List the next three terms to continue the pattern in each of following: i) 4, 8, 12,__,___,____ ii) 1, 2, 4, 8, ___,___, ___ iii) 1, 4, 9, 16,___,___, ___

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Guessing and Checking(Cuba Jaya )

Guess , Checkthe answer right @ wrong

How

Trial and Error

Systematic Inferens

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In a farm, there are 44 animals consisting of some chickens and rabbitsThe number of legs are 100.How many chickens and how many rabbits are There?

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Solution

First Guess

22

22

44

chickens

rabbits

animals

22 × 2 legs =

22 × 4 legs =

44

88

legs

legs

Jumlah 132 legs

INCORRECT (more legs)Strategy : increase the number of chickens

And decrease the number of rabbits

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Solution

Second guessing

32

12

44

chickens

rabbits

32 × 2 legs =

12 × 4 legs =

64

48

legs

legs

Total 112 legs

Still Inccorrect (More legs)

Strategy :??

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Solution

Third Guessing

40

4

44

Chickens

rabbits

40 × 2 legs =

4 × 4 legs =

80

16

legs

legs

Total 96 legs

ALMOST CORRECT (The no. of legs are still sufficent)

Strategy : Decrease the number of chickens and Increase the number arnab of rabbits

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Solution

Fourth Guessing

38

6

44

Chickens

rabbits

ekor

38 × 2 legs =

6 × 4 legs =

76

24

legs

legs

Total 100 legs

The answer is correct! Congratulation!!

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Making a Table/Chart

Helps pupils to organize and present information in tableSometimes it is easier to solve problem by listing out some or all the possibilitiesConvenient way to organize a list.Used to summarize data or to see a pattern

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You save $3 on Monday. Each day after that you save twice as much as you saved the day before. If this pattern continues, how much would you save on Friday?

Example

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SOLUTION Step 1: Understand the problem

On Monday saved $3.Next day -save twice from the day before.What question do we have to answer?The sum of money that we finally save on Friday.

Step 2: Devise a planList the amount of money you save each day.

Step 3: Carry out the planMaking a table

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CARRY OUT THE PLANDay Amount of Money

SavedMonday $3

Tuesday $6

Wednesday $12

Thursday $24

Friday $48

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MAKING A TABLEExample: Of the 25 soccer games that Chelsea

played, they tied 3 games and won 2 more than they lost. How many games did Chelsea win ?

Answer the question using “making a table” method.

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SOLUTIONWin Lost Tied Total

8 6 3 17 X

10 8 3 21 X

12 10 3 25 /

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Sesuatu masalah yang rumit perlu dipermudahkan faktanya terlebih dahulu.

Kaedah yang mudah itu digunakan untuk menyelesaikan masalah asal.

Simplify The Problem

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Cari jumlah luas tapak bangunan ini ?10 m

10 m

6 m

6 m4 m

4 m

6 m

6 m

8 m

Penyelesaian

A

B

CLuas tapak A = 10 m x 4 m = 40 m2

Luas tapak B = 20 m x 6 m = 120 m2

Luas tapak C = 6 m x 8 m = 48m²

Luas tapak ABC 208 m²

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Logical Reasoning

Menaakul mengikut syarat-syarat yang diberi

Menggunakan fikiran yang logik

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The product of four numbers (i.e 1,2,3,4,56,7,8,9 and 10) in sequence is 3024. Use your logical reasoning to find the numbers?

1 543

29

8

7

6

10

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Solution

a. The product does not have 0 digit in place value ones, therefore 10 is not included in these numbers.b. Number 5 is also not one of the four numbers because

the answer does not end with number 5 or 0c. The four sequence numbers may be 1,2,3,4 or

6,7,8,9.d. 1 x 2 x 3 x 4 ≠ 3024e. 6 x 7 x 8 x 9 = 3024f. So the answers are 6 , 7 , 8 and 9

1 5432 9876 10

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Work backward

The last information is given.

Determine what had happen before that .

Use the strategy to solve the question .

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Datuk Hassan said ”If you multiply my ageby 3, add the product with 17 and then divided by 2, the answer is 100”.How old is Datuk Hassan?

NomborAsal 100

× 3 + 17 ÷ 2

× 2- 17÷ 3

Example

20018361

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Mengguna Algebra

Kenal pasti masalah

Membentuk satu persamaan

Jawapan diperolehi melalui penyelesaian masalah

TAHAP YANG AGAK TINGGI

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Seekor kera bertanya mengenai umur seekor kucing yang dijumpainya. Kucing itu berkata, ”Semasa saya berumur 8 bulan,bapa saya berumur 34 bulan. Sekarang umur bapa saya tiga kali umur saya”. Kera itu pun menggarukan kepalanya. Bolehkah anda menolongnya mencari umur kucing itu?

Membentuk persamaan

Penyelesaian

Anggaplah umur kucing itu sebagai x Dari maklumat yang diberi ;

3x - x = 34 - 82x = 26 x = 13

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Analogy

Is use to solve mathematics problem which contains solution step similar to other previous mathematics problem.

While solving such new mathematics problem, the teacher can draw the pupil’s attention based on their prevoius experience.

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A. In a room with 5 people, everyone shake hands with everybody else exactly once. How many hand shakes are there?

Compare problem A and problem B.

B. There are 5 points at the circumference. Every point is joined by straight line.

How many straight line are there?.

Solution for problem A help to Solve problem B.The same method can be used to Find the total number of matches in a football games.

Examples

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Contoh-contoh Masalah Tambahan(Selesaikan dengan pelbagai strategi) Bagaimana kamu hendak menyusun lapan angka 8 supaya hasil tambahnya bersamaan 1000?

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JAWAPAN

8 8 8 8 8 8 8 + 8 1 0 0 0

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Kepala seekor lembu sedang menghala ke utara. Ia memusing separuh bulatan ke belakang, kemudian satu pusingan lengkap (360o) lagi ke kanannya. Sekarang ekornya menghala ke mana?

T

U

B

S

Contoh-contoh Masalah Tambahan(Selesaikan dengan pelbagai strategi)

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Bahagikan gambarajah di bawah kepada empat bahagian yang kongruen.Anda tidak dibenarkan membahagi dengan garis lengkok.

Contoh-contoh Masalah Tambahan(Selesaikan dengan pelbagai strategi)

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Jawapan

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Contoh-contoh Masalah Tambahan(Selesaikan dengan pelbagai strategi)

Cari nombor-nombor yang diwakili oleh abjad di bawah.

F I V ET W O

O N E +

E I G H T

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9 0 7 1 8 2 6 + 6 4 1 1 0 5 3 8

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Tuliskan angka 1,2,3,4,5,6,7,8 dan 9 sekali sahaja ke dalam kotak di bawah supaya apabila nombor-nombor yang terbentuk itu ditambah hasilnya ialah 999.

9 9 9 1 +

Contoh-contoh Masalah Tambahan(Selesaikan dengan pelbagai strategi)

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Jawapan + 4

56

93 7

8

21

9 9 9

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SARANAN KEPADA GURU

Membimbing pelajar merancang strategi untuk penyelesaian masalahMewujudkan keinginan mencuba di kalangan pelajarMemberi ruang dan peluang kepada pelajar untuk berbincangMenggalakkan penggunaaan lakaran, membina carta atau peta mindaMemberi penekanan kepada pemikiran kretif dan kritisMenyarankan strategi-strategi lain sekiranya mengalami kebuntuanMenimbulkan suasana sukses

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, Jumpa Lagi Di Lain Masa

InsyaallahTERIMA KASIH