Scenario Problem Solving Teaching

8/3/2019 Scenario Problem Solving Teaching

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Khoerul Umam, S.Pd (117785002) Mathematics Department Dual Degree Program

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AN INSTRUCTION PERFORMANCE PLANNING

Lesson : MATHEMATICS

Class / Semester : IX / Odd

Total Performances : 1 Performance ( 2 x 40 Minutes )

I. Standard of competence :To understand the properties of cylinder, cone, and sphere and their measurements.

II. Basic ComptenceTo understand the properties of cylinder, cone, and sphere and their measurements.

III. Indicator :Determine the volume of cylinder.

IV. ObjectivityBy doing discussion and guiding with teacher, students are able to determine the formula volume of cylinder such that students are able to apply the

cylinder volume formula for counting volume of sardeni can, milk can, and etc.

V. Learning ApproachProblem Solving


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THE CONVERSATION BETWEEN STUDENTS AND TEACHER IN THE MATHEMEATICS INSTRUCTION PROCESS

Step 1

Present the problem in a general form.

Teacher :I was in the oil station last sunday, I encountered a challanging mathematical problem. I found an empety cylinderical oil drum

stood beside me. I wonder to know the volume of cylinderical oil drum

Note : (Although this problem was not discovered by student, the statement of the situation in which the problem did occur does su ggest one source of

mathematical problems to students)

Step 2

Restate the problem in a solvable form.

Teacher : What is the volume of cylinderical drum oil? (this question denotes students understanding about the problem).

Note :(after the teacher asks this question there are puzzled looks on students faces and a minute of silence )

A Student :I dont understand what you mean..

A Student :Yeah.....yes, I do....I dont understand it either

Teacher :Does anyone understand my question?(Teacher try to investigate and analyze the real problem that student face)

Note :(the class indicates that they do not understand the problem.)

Teacher :Oh...I think I didnt state my question very well. What does make sense?

A Student :What do you mean by cylinderical drum oil?

Teacher : Drum oil formed in cylinder


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A Student :I am still confuse..what do you mean by cylinder ?

Teacher : an other example of cylinder is a milk can (Teacher gives an example of cylinder since they are still confuse)

A Student :Milk can have a lot of shapes and features. Which can of milk do you mean?

Teacher :What could I do to help you?

Same Student : Why dont you draw an example ?

Another Student :No, get a milk can and show us

Teacher :ok, this is a can milk. Can you see what I hold ! Now, would you like to give another example which is similiar to a milk can? .

(Teacher encourage students to give another examples of cylinder in daily life. The purpose of question is investigating theirunderstanding about the cylinder after the teacher give an example)Note (students now appear to understand the meaning of cylinder)

Same Student : Sardines can.....

Another Student : Cornet can

A Student :Oh....I know. Lubricant can ?

Teacher :Are you sure that all the things that you have ment ioned before have the cylinder?

(Teacher ask the question for convincing that they are understand the cylinder)A Student :Yes, Sir.

Teacher :Why?

Same Student : The base of a milk can is circle

Another Student :The top of sardenis can is also circle


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Teacher : Great. Now, lets focus on the given problem. Can anyone tell us the cylinder more clearly ?

A Student : The shape with circular ends and long straight sides !

Teacher :Now, is this problem stated in a way that is understandabe to everyone?

A Student :Yeah ........I understood

Note : the sentence above indicates that students have understood the shape of cylinder

Teacher :Can anyone see an applications of this problem?

Step 3

Formulate hypotheses and procedures for solving the problem.

Teacher : Our goal is to determine the volume cylinder of the drum. Does anyone have an idea?

Note ; (A minute and three passes. Teacher should always provide time for students to think about answers to their questions)

Another Student : We can pour the milk into the drum such that we can measure the volume of it . Then counting the number of milk cans used for it

Teacher : Thats good. However, is that general solution enough?

(Teacher ask the student to think critically about the method which has been suggested)A Student : No, if we buy a lot of milk can. It will spend much money. Why dont we use sand

Another Student : Using sand then pouring it into the drum by using pail such that we can measure the volume. Then counting the number of pail used forit

Teacher : Where can we get sand ?

Another Student : We can get it behind our school but if we were carrying all the sand, it would be very heavy


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Another Student : Why dont we use water !

Another Student : Since it is easily to find and carry, right !

A Student : We can pour the water by using pail, one by one until the volume of cylinder oil drum is full. Then counting the pail used for the volume

Teacher : Thats good idea. Can anyone think of another way ?

(teacher wants to make a strong discussion among the students until they find the best method to solve this problem)

Another Student : Water is quite good. But if we use water, our class is going to be wet. We had just cleaned the class....!

Teacher : Yes I agree with you,because if every cylinder shape volume must be counted by pouring the water. It took a lot of time whilst we are inthe classroom.

Same Student : Then how to count the volume of cylinder?

A Student : We counted the volume of cube by using formula when we studied in the 7 th grade. Why dont we do the same things as well

Another Student : Yeah......I see. What we need is formula !

Teacher : Thats another good idea. We will try it ! Does anyone else have another ideas?

Note ;(No more ideas were offered.)

Teacher : Now, lets summarize our methods and list the strenghs and weaknesses of each method

Note : the class lists the 2 methods and list the strengths and weaknesses of each method)

Teacher : Lets try to find a formula. What have we known about this problem ?

Same Student : We should find the radius of circle in base, and the height of cylinder

Teacher : Would these dimensions be easy to find?

Same Student : Sure, we could use a centimeters


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Step 4

Test hypotesises and carry out strategies to solve the problem.

Teacher : Suppose we let trepresent the height of the cylinder, r is the radius circle in base. Does anyone have a suggestion to find the formula?

(Three minutes of silince occurs)

Teacher : Have you ever found the volume of any figures before?

Same Student : Yes, we have studied the volume before

Teacher : Would you like to tell me, whats kind volume of figures have you studied?

Another Student : We studied about volume of prism, cube, and etc, in the last year. When we were in the 7th grade

Teacher : That is great........Do you still remember what is the volume formula for prism?

( Teacher try to remind the students with the previous knowledge)Note : (Let the students think for a while to remember.............)

A Student : If I am not mistaken......the area of the base times the height of prism...........!

Another Student : Yes. I do agree with you....! his answer is right, sir !

Teacher : Ok..good. Can you compare those shapes?

Another Student : I dont understand what you mean ?

A Student : Why dont you try to draw these figures ! so that we can see the different


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Teacher : Is there anyone who wants to help me to draw the cylinder and an example of prism on the white board !

Cylinder Upright rectangular Prism

Same Student : Ok....I can do it, sir

Teacher : Thank you very much for your pleasure to draw on the white board. Look at the drawing ! Are those right ?

Students : Eh.......I think. Those are right

Teacher : Well .......so can you see the difference between those things?

Note : (Students discuss each other to find the difference between upright rectangular prism and cylinder. After waiting for a minute, teacher ask again)

Teacher : Is there any differences between the height of cylinder and upright rectangular prism ?

Another Student : No, the height of both are the same

Teacher : So, can you see the differences between cylinder and upright rectangular prism ?

Another Student : I guess the base of them are different.

A Student : I guess the top of them are also different .


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Another Student : So....the bottom and the top of both cylinder and upright rectangular prism are different

Same Student : Oh.....I see....you are right. The base and top of both cylinder and upright rectangular prism are different

Teacher :What are the different of those shapes?

(Teacher check students understanding about the comparasion in two shapes)Another Student : The top and base of cylinder are circle whilst the base and top of upright rectangular prism are rectangular

Teacher :Can anyone help me to remind us about the formula of volume prism ?

A Student : If I am not mistaken......the area of the base times the height of prism...........!

Teacher : Great....Whats our next step to find the formula of cylinder ?

A Student : Using the formula of volume prism which is the area of the base times the height of prism........!

Same Student : Just change the area of base of prism into the area of base of cylinder.

Teacher : Wonderful, it is awesome. What is the base of cylinder ?

Another Student : The base of cylinder is circle.

Teacher : Would you like to show us, what is the area of circle?

Same Student : The area of circle is

Teacher : Anyone can help me to answer the problem. What is the volume ofcylinder ?

Same Student : Then the volume of cylinder is

Note : it is clear to do this step since the students have known the formula of cylinder

Step 5

Verify the solution and analyze the solution strategies


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Teacher : Now, how do we know that is correct?

(Teacher wants to know how students prove the formula)Same Student : Try it out

Teacher : OK...lets try the formula. Whats kind ofmedia we want to try?

Student : Yes, we can use the milk can? We find its height, and radius of base cylinder

Another Student : So.....afterward, we have to find the area base of milk can then times it with the height of milk can

Note : (Teacher is waiting students to find the volume of milk can for 10 minutes)

A Student : Yes, we get it

Teacher : Are the volume of cylinder by using formula the same as the volume of information given in the milk can ?

Same Student : Yes, they are not the same exactly but they are very close

Teacher : Now, lets try use this formula by using other kinds of material ?

Students : We can use sardine can as well

Same Student : Lets do it

Another Student : We have to find the area base of sardine canthen times it with the height of sardine can

Note : (Teacher is waiting students to find the volume of sardine can for 10 minutes)

A Student : Yes, we get it

Teacher : Did you get the same answer by using formula as you did by using the information given in the sardine can ?

Same Student : Yes, they are almost the same

Teacher : How could we prove the formula is true ?


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Note :After a brief discussion the class concludes that the formula is true because we have try the formula with two different kind of

examples. Those answers are similar to the information given on those cans.

Teacher : What general strategies did you see in solving this problem ?

(Teacher asks students to restate the steps of general strategy in the learing process based on their experiences)Same Student : We have to understand the real shape of cylinder first

A Student : Afterwards, we try to find the other shape which is similar to cylinder

Another Student : Then, we compare those two shapes and find the comparison and the same things between two shapes

Teacher : Is there any additional ?

A Student : Using the formula of volume shape which is similar to solve our problem

Same Student : Then we change the formula after analyzing the comparison and the equality of them

Same Student : Then we tried out the formula

Teacher : Is there anything else ?

Same Student : After applying the formula for several kinds of material. We check whether the formula is right or wrong

Same Student : Afer checking the formula, we conclude that it is true...

Same Student : You give a lot of question to us......... it took a lot of time to think and remember our previous lesson

Teacher : You have stated some of general step to solve this problem, by doing discussion, using our previous lesson, and comparing two shapes.You can solve the problem easily.

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Scenario Problem Solving Teaching