Kkp

RM 249

RM 249RM 249

RM 249

RM 249

Question 1:

1. What is the total cost of 5 DVD players if each one cost RM 249?

2. Strategy A: Understand the problem

We first make a drawing or at least visualize the situation. We let T = the cost of 5 DVD players. Repeated addition works well in this case.

Strategy B : devise a plan

We must translet to an equation and make a table or sequence

DVD

DVDDVD

DVD

DVD

3. Elaboration of my strategy A and B :

Strategy A : Understand the problem

Firstly we must understand the problem in the question Read all the problem based on the question Then find important information and take it out To ensure you must ask yourself, what information in the question Do you need to make a Diagram Finally, identify what problem wants to solve and try break problem into parts

Draw a diagram based on the data in the question. Let T is equal the cost of 5 DVD players. Repeated addition is the formula in this problem. Now this problem can be solved.

T = RM249 + RM249 + RM 249 + RM249 + RM249

= RM 1245.00

The total cost of 5 DVD players is RM 1245

Strategy B: devise a plan

make a table or sequence Firstly take out all the data from the question Decide how to solve the problem Solve the problem and continue to use logic Lastly look back and checks

Number of DVD players times cost of each player is total cost

5 X RM 249 = T

The sequence tells what to do. The formula used is multiply and the question can be solved.

RM 249 RM 245 x 5 = T

X 5 1245 = T

RM 1245

Chekcking : We have the answer RM 1245 that is much greater than the cost of any individual DVD player, which is reasonable. We can repeated our calculation. Using estimation method.

RM 249 X 5 = 5 X RM250 = RM 1250 = Rm 1245

The total cost of 5 DVD players is RM 1245

4. The most efficient strategy : Strategy B

Justification :

Multiplication method is easier than using addition method because mistake can be avoided. People always make the mistake, therefore if use multiplication method to solve the question, probability answer is correct is more than used addition method.

5. Similar problem:

What is the total cost of 15 books if each one cost RM 3.50?

Strategy: strategy B (devise a plan)

make a table or sequenceFirstly take out all the data from the questionDecide how to solve the problemSolve the problem and continue to use logicLastly look back and checks

15 Books

Elaboration of the strategy:

Number of Books times cost of each books is total cost

15 X RM 3.50 = T

The sequence and diagram tells what to do. The formula used is multiply and the question can be solved.

RM 3.50 RM 3.50 x 15 = T

X 15 RM 52.50 = T

RM 52.50

Chekcking : We have the answer RM 52.50 that is much greater than the cost of any individual 15 books, which is reasonable. We can repeated our calculation. Using estimation method.

RM 3.50 X 15 = 15 X RM 3.00 = RM 45.00 = RM 52.50

The total cost of 15 books is RM 52.50

Question 2 : aircraft seating

1. MAS corporation builds commercial aircraft. A boeing 767 has a seating configuration with 4 rows of 6 seats across in first class and 35 rows of 7 seats across in economy class. Find the total seating capacity of the plane.


We first make a drawing or at least visualize the situation. We let F = the number of seats in first class. Repeated multiplication works well in this case.


We must translet to an equation by making a table or sequence


Strategy A : Understand the problem

Firstly we must understand the problem in the question Read all the problem based on the question Then find important information and take it out To ensure you must ask yourself, what information in the question Do you need to make a Diagram Finally, identify what problem wants to solve and try break problem into parts

Make a diagram:

Economy class: 35 rows of 7 seats

First class: 4 rows of 6 seats

Draw a diagram based on the data in the question. Let X is equal the total seating capacity of the plane. Repeated addition is the formula in this problem. Now this problem can be solved.

X = economy class + first class

= (35 + 35 + 35 + 35 + 35 + 35 + 35) + (4 + 4 + 4 + 4 + 4 +4)

= 269



Make a table of data based on the question:

Type of seat Economy class First class

Rows 35 4

Seats 7 6

There are three parts to the problem. First find the number of seats in each class. Then add to find the total of seating capacity of the plane.

First class: repeated addition applies here. Thus the following multiplication corresponding to the situation. Let F equal the numbers of seats in first class.

Numbers of rows times seats in each row is total number

4 x 6 = 24

Economy class: repeated addition applies here. Thus the following multiplication corresponding to the situation. Let E equal the numbers of seats in economy class.


35 x 7 = 245

Let T = the total number of seats in both classes.

T = F + E

= 24 + 245

= 269

Check: to check repeat our calculations.also check by rounding, multipliying and adding

Answer: there are 269 seats in a MAS boring 767

4. The most efficient strategy : Strategy B

Justification :

Multiplication method is easier than using addition method because mistake can be avoided. People always make the mistake, therefore if use multiplication method to solve the question, probability answer is correct is more than used addition method.

5. Similar problem:

The hall in the school has many chairs. The hall has a seating configuration with 4 rows of 3 seats across in Vip place and 40 rows of 10 seats for the audience. Find the total seating capacity of the hall in the school.

Strategy: strategy B (devise a plan)


Make a diagram:

Audience seats: 40 rows of 10 seats

Vip seats: 4 rows of 3 seats

Type of seat Audience seats Vip seats

Rows 35 4

Seats 7 6

There are three parts to the problem. First find the number of seats in each class. Then add to find the total of seating capacity of the plane.

Vip seats: repeated addition applies here. Thus the following multiplication corresponding to the situation. Let V equal the numbers of seats in Vip seats.


4 x 3 = 12

Audience seats: repeated addition applies here. Thus the following multiplication corresponding to the situation. Let A equal the numbers of seats in audience seats.


40 x 10 = 400

Let T = the total number of seats in both classes.

T = V + A

= 12 + 400

= 412

Check: to check repeat our calculations.also check by rounding, multipliying and adding

Answer: there are 412 seats in the hall of school.

Question 3: pyramid blocks

1. This pyramid blocks is made of cubes. How many cubes would be needed to make the steps 9 steps high?


We first make a drawing or at least visualize the situation. Draw a shape of pyramid blocks so it is easily to solve the problem.


We must translet to an equation and make a table or sequence. Find the best formula to solve the problem


Strategy A: Understand the problem

Firstly we must understand the problem in the questionRead all the problem based on the questionThen find important information and take it outTo ensure you must ask yourself, what information in the questionDo you need to make a Diagram Finally, identify what problem wants to solve and try break problem into parts

List of data : How many cubes would be needed to make the steps 9 steps high

: Pyramid blocks

9(high)

9( lenght)

Solution: number of blocks will decrease by 1 when going up one steps.

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

= 44

Answer: there are 44 blocks of pyramid.



Table of numbers blocks in pyramid

Numbers of blocks

1 2 3 4 5 6 7 8 9

1 Steps

2 Steps

3 Steps

4 Steps

5 Steps

6 Steps

7 Steps

8 Steps

9 Steps

Solution: the table show the sequence and pattern of number blocks in pyramid. To solve the problem, add all the number that has been shaded in the table.

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

= 44

Answer: there are 44 blocks of pyramid.

4. The most efficient strategy : Strategy A

Justification :

Draw a diagram is easier than using table method because mistake can be avoided. People always make the mistake, therefore if use diagram to solve the question, probability answer is correct is more than used table method. Students also like a diagram because it is more attraction than using a table.

5. Similar problem:

This tower is made of blocks. First steps have 20 blocks. How many blocks would be needed to make the steps 9 steps high if the blocks are decrease by 2 if going up one step?



The data : First steps has 20 blocks

: How many blocks would be needed to make the steps 9 steps high if the blocks are decrease by 2 if going up one step.

Table of numbers blocks in towers

Numbers of blocks

2 4 6 8 10 12 14 16 18 20

1 Steps

2 Steps

3 Steps

4 Steps

5 Steps

6 Steps

7 Steps

8 Steps

9 Steps

Solution: the table show the sequence and pattern of number blocks in pyramid. To solve the problem, add all the number that has been shaded in the table.

= 20 + 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4

=108

Answer: there are 108 blocks in the tower.

Question 4:

1. There are 20 people in a room. 10 people are wearing watch and 8 people are wearing hats, 4 people are wearing both. How many people are not wearing watch and hats?


We first make a drawing or at least visualize the situation. Draw a shape of people wearing watch, hats and not wearing both so it is easily to solve the problem.


We must translet to an equation and make a table or sequence.Find the best formula to solve the problem. Get the tricks to solve the problem.

10 people are wearing watch




List of data: 20 people in a room


8 people are wearing hats

4 people are wearing both



6

6 4

Solution:

The diagram shows the real number of people wearing hats and watch. The total of people is 20. So the balance of people in the diagram is the answer of this problem.

= 6 + 4 + 4 (wearing watch + wearing hats + wearing both)

= 20 – 14

Answer = 6



List of data: 20 people in a room




People Number

Wearing watch 10

Wearing hats 8

Wearing both 4

Not wearing hats and watch ?Total of people 20

The table shows the real number of people wearing hats and watch. The total of people is 20. The operation used to solve the problem is combined operation. The number of people wearing hats and watch is minus number of people wearing both. Then answer minus by 20.

= 10 + 8 – 4

= 20 – 14

Answer = 6

Appreciation

Assalamualaikum. First of all, may I wish a very thank you to my God, Allah the

Almighty because of Him I could do my task successfully without any trouble and

problem. I hope my work that I had done on time will be accept by my lecturer. Kkp of

basic Mathematics is quiet hard to do because we must used polya strategies to solve

the problem.

Second, I would like to thank my lecturer, En Hamzah Bin Nun. He had taught

and shows me how to complete this task correctly. En Hamzah also likes to help his

student when he saw his student like blur and confuse. I learned many things when

doing this task such as learned how to search books from library, from internet and from

text books.

Next, I also want to thank my lovely parent. Because of them, I can buy my item

and equipments to finish this task with creatively. They also help me and give me moral

support to done this task without any problem and tension. My mother always contacts

me and give supported. I have tried very hard to finish my problem solving in basic

mathematics.

Not to be forgetting is my friends who have helped me to give their ideas and

information that I don’t know. Especially Faiz and Munir always help me to complete my

work in problem solving. They all give me support too when I cannot find this task

solution how to done it. I learned many things when we discuss this task in my room.

We find the material of problem solving in the internet and books. We also ask the

senior about problem solving and how to used Polya strategies.

I hope anyone who read my task will always be happy and understand what I

want to carried out in this task. Finally, I hope this task reader will enjoy reading it.

Thank you.

Contents

Inside Page

Appreciation

Polya strategies

Non-routine problem

Two type of strategies

Elaboration of non-routine problem

The best strategies

Similar problem

Reflection

Bibliography

Bibliography

Mamn L. bittinjer, basic Mathematics 9th edition. Indiana University Purdue

University Inetianapolis

Billstein, liberkind, lott. A problem solving approach to Mathematics. University of

Oxford, Australia

http//: www.mathematicsisfun.com

http//: www.kidnumbers.com

http//: www.mathstories.com

http//: www.conval.edu/sup.carner/curriculum/math

http//: www.efn.org/~kinne/math

http://www.efn.org/~kinne/math

http://www.conval.edu/sup.carner/curriculum/math

http://www.mathstories.com/

http://www.kidnumbers.com/

http://www.mathematicsisfun.com/

Reflection

In my work to done this task, I had reaches many trouble. I can’t find the material

of problem solving. So I try to find another way. I try to find the material of problem

solving in internet and books from library.

I also cannot find the polya strategies in the books from library because it not

state polya strategies when solve the problem solving. So I decide to go to asked En

Hamzah about the polya strategies and where I can find the material of problem solving.

After that I learned the polya strategies that I found in the internet. I tried to use polya

strategies to solve my problem solving. It is quite hard to solve but I tried my best.

Beside that, I also stuck when I do this task because of the task’s question. I

cannot understand what is the task exactly wanted. So I decide to see my lecturer, En

Hamzah Bin Nun to ask him kindness to show me what are this task really want. It is not

easy to meet with En Hamzah because he always not is around the Institute.

Sometimes he has meeting and Bina Insan Guru, so I cannot see him if I have a

problem in my task.

Because of him, now I have understand what to do and then I do it on my own

and completely done before the date of submission. I really thankful to all of who had

helped me to did my work.

Question 5:

1. Kim, Raelene, Jim and Rick finished first, second, third and fourth in a motor bike

race. If their numbers were 5, 17, 1 and 7, use the following clues to find out who

had what number and what order they finished in.

17 said she would have placed higher if her bike had not stalled at the start

Rick finished before 7 but after Raelene

1’s father, said he was very proud of his daughter’s finish

Kim finished after 5

Jim wasn’t third


We first make a drawing or at least visualize the situation. List all the information that found in the question. Based on it make a try and error to fing the answer.


We must translet to an equation by making a table or sequence. Find the best formula to solve the problem. Get the tricks to solve the problem. We also must complete the table, so it is easily to get the answer for the clue.

3.Elaboration of my strategy A and B :



The information:





Jim wasn’t third

First =?

Second =?

Third =?

Fourth =?

Kim Raelene Jim Rick

The solution: Try to solve each of the clue used polya steps, try and error strategies.


=17 must be in fourth


= the sequence is Raelene, Rick, 7


= shows that 1 is the winner of the race


= the sequence is 5, kim

Jim wasn’t third

= so Jim must be fourth and last

The visualization:

First ( 1 )

Second ( 5 )

Third ( 7 )

Fourth ( 17 )

Raelene

Rick

?

?

The clue said that jim is the fourth and kim below 5, so the place is third.

Final Answer:

First ( 1 )

Second ( 5 )

Third ( 7 )

Fourth ( 17 )

Rick

Kim

Jim

Raelene



List of data:





Jim wasn’t third

Make a table:

Place/ clue first second third fourth

5 Possible answer Possible answer

17 17 said she

would have

placed higher if

her bike had not

stalled at the

start

1 1’s father, said

he was very

proud of his

daughter’s finish

7 Possible answer Possible answer

The solution: now the table can shows the place of the people. Complete the clue of

second and third place, the question can be solved.


=17 must be in fourth


= the sequence is Raelene, Rick, 7


= shows that 1 is the winner of the race


= the sequence is 5, kim

Jim wasn’t third

= so Jim must be fourth and last

Place/ clue first second third fourth

5 Rick

17 Jim

1 Realene

7 Kim

The answer: Realene, Rick, Kim and Jim

4. The most efficient strategy : Strategy A

Justification :

Draw a diagram is easier than using table method because mistake can be avoided. People always make the mistake, therefore if use diagram to solve the question, probability answer is correct is more than used table method. Students also like a diagram because it is more attraction than using a table.

5. Similar problem:

Ahmad, Mutu, Amal and Amir finished first, second, third and fourth in a Drift race. If

their numbers were X, Y, Z and Q, use the following clues to find out who had what

number and what order they finished in and who is the Campion of the Drift race.

Y said she would champion of the drift race if her Mitsubishi car had not

blower engine at the start

Rick finished before Q but lost with some mistake drift style to Raelene

Z’s girlfriend’s, said she was very proud of his boyfriend’s finish

Kim finished with excellent drift style after X

Jim wasn’t finished in number 3



The clue:

Y said she would champion of the drift race if her Mitsubishi car had not

blower engine at the start

Amir finished before Q but lost with some mistake drift style to Mutu


Ahmad finished with excellent drift style after X

Amal wasn’t finished in number 3

First =?

Second =?

Third =?

Fourth =?

The solution: Try to solve each of the clue used polya steps, try and error strategies.

Y said she would champion of the drift race if her Mitsubishi car had not blower

engine at the start

=Y must be in fourth

Amir finished before Q but lost with some mistake drift style to Mutu

= the sequence is Mutu, Amir, Q


= shows that Z is the winner of the race

Ahmad finished with excellent drift style after X

= the sequence is X, Ahmad

Amal wasn’t finished in number 3

= so Amal must be fourth and last

The visualization:

first(Z)mutu Third not state

Second(X) Amir fourth not state

Now the answer for first and second place is state in the clue but third and fourth place not stated. But the last clue said that Amal is the fourth and Ahmad below X, so the place is third.

Final Answer:

First (Z) mutu

Second(X) Amir

Third (Q) Ahmad

Fourth(Y) Amal

Date post:	27-Jun-2015
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