Download - Problem Solving -Mula
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