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Elicit

Explore

Engage

Lesson 5

 Solving Routine and Non-Routine Problems Involving

Circumference of a Circle

 

Find the

Can you also solve this problem you posed?

 Pause & Answer 

How well do I know how to solve problems involving circumference of a circle?

Am I prepared to move further to this lesson?

Create then solve one routine and another one non-routine problem using the following

key words:

! "# meters $! %ogging &! Circular road

Can you do it with ease?

 Pause & Answer 

'hat do I want to know to create then solve routine and non-routine problems

involving circumference of a circle?

'hat do I want to learn about this?

(tudy how the problem on circumference of a circle can be constructed and

solved using the facts below!

Facts to )se!

! $# cm

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$! *lastic binder 

&! +lectric fan

A repair shop is trying to improvise a plastic binder that could hold together the two

circular steel body of an electric fan whose diameter is $# cm! How long should the plastic binder be that could bind together the entire edge of the body of the electric fan?

What information are needed when

constructing and then solving routine

problems involving circumference of a

circle?

Where is this information in the

problem?

 How to construct the problem?

1. (tate the situation that gives either the

radius or the diameter of any circular

ob,ect or thing in reality!

A repair shop is trying to improvise a plastic

 binder that could hold together the two

circular steel body of an electric fan whose

diameter is $# cm!

$! *ose a uestion that reuires getting

the circumference of the circle!

How long should the plastic binder be that

could bind together the entire edge of the body

of the electric fan?

 How to answer the problem?

3. (how the solution to the problem!

.emember that this problem has a

defined or one clearly correct answer!

C / $ 0 r or 01C / &!23 4 $# cm5

C / 3$!6&$ cm

4. (tate the answer to the problem! 7he plastic binder should be 3$!6&$ cm

long!

"! Check the reasonableness of the given

answer to the problem!

Check the reasonableness of the answer

 by dividing 3$!6&$ by &!23 and what

one should get is $#cm8 which is the

diameter of the circle!!

 9ow try to eamine what you did under +;ICI7! 1oes the problem satisfy the conditions

set in constructing then solving routine problems involving circumference of a circle? If not8 then

try to reconstruct it or construct another one!

(tudy this time how to construct and solve a non-routine problem using the same facts for 

the circumference of the circle!

Facts to )se!

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! $# cm

$! *lastic binder 

&! +lectric fan

What information is needed when

constructing and solving non-routineproblems involving circumference of a

circle?

Where is this information in theproblem?

 How to construct the problem?

1. (tate the situation reuiring use of

circumference of a circle!

A repair shop is trying to improvise a plastic

 binder that could hold together the two

circular steel body of an electric fan whose

diameter is $# cm! 7he plastic binder that

could bind together the entire edge of the body

of the electric fan should be $"!332 cm!

2. *ose a problem that invites many

 possible answers!

Could the given length of the plastic binder 

eactly surround the circumference of thecircular steel body of the electric fan?

 How to answer the problem?

3. (how at least two solutions or answers

to the problem! .emember that this

 problem has many possible answers!

Hidden Problem : 9eed to know the

compute the circumference of the circle!

7his was already computed earlier using

the formula C / 01 and that is 3$!6&$ cm!

Possible Answer 1:

<es8 but there is an ecess of 3$!6&$ cm!

Possible Answer 2:

 9o8 the length given is too long for the

circumference of the circle8 which is ,ust

3$!6&$ cm!

4. (tate the answer to the problem! 7here are many possible answers but two

are shown as eamples:

! <es8 but there is an ecess of

3$!6&$ cm!

$! 9o8 the length given is too long for 

the circumference of the circle8

which is ,ust 3$!6&$ cm!

"! Check the reasonableness of the given 7o check if the answer is correct8 then we

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8/9/2019 p516 521 Unit 9 L5 Meas Unay

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Explain

Elaborate

answer to the problem! need to go back to the problem and see if

it was answered correctly! 7he problem

really reuires ,udging whether the given

circumference of the circle is right or

wrong and it was answered with either yes

or no with eplanation!

 

 9ow eamine again the problems you constructed under +;ICI7! Is there any

 problem that is non-routine? If none8 then construct your own non-routine problem

involving circumference of a circle!

=elow are the ideas you should have learned about this lesson! Can you eplain

each one of them with one of your classmates? Check those you understood well and

cross out those where you need further eplanation!

! 'hen constructing routine problems involving circumference of a circle8 then

the answer to this problem is defined or there is ,ust one possible answer!

'hen this routine problem is solved8 we use the following as guide uestions:

• 'hat is asked in the problem?

• 'hat are given?

• 'hat is the hidden information or uestion?

• 'hat operation or process will you use?

• 'hat is the mathematical sentence?

• 'hat is the final answer?

• Is the final answer reasonable?

$! 'hen constructing non-routine problems involving circumference of a circle8

then the answer to this problem is open to many possible answers! 7o solve it8

we analy>e the problem using the same guide uestions for routine problems!

Construct one routine and another one non-routine problems

considering the following situations then solve each one of them:

! 4*icture of circular table5

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Enrich

Evaluate

$! 4*icture of a circular picture frame5

&! 4*icture of a circular garden5

2! 4*icture of a circular cover of food on the table5

"! 4 picture of a circular pool5

 

! (urf the internet! ;ook for more information and eercises about the adding fractions and

mied numbers that you have ,ust learned! *rovide the following information taken fromyour source!

• 'hat information did you get?

• 'here did you get this information?

• 'hat eercises did you find? In what website did you get them?

• 'hat additional information did you learn?

 A Test our !"#W$%&'% ( )"&%*+TA"&,"'

'ith reference to the problem below8 ,udge each statement if 7rue or False!

*roblem:

7he circular fish pond has a radius of # meters long! How long should be the barbed wire

that could be used to fence the entire edge of this fish pond?

! 7he diameter of the fish pond is ## meters! F

$! 7he problem reuires computation of the circumference of the circular fish pond! 7

&! 7he formula to compute the length of the barbed wire is $01! F

2! 7he circumference of the fishpond is 3$!6&$ suare meters! F

"! 7he diameter of the fishpond is $# meters! 7

 ! +how our +!,$$+ P*#&).T or P%*/#*0A".%

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Expand

Reflect

Construct routine or non-routine problems involvingcircumference of a circle then solve them. Give ve problemswithout repeating what have been shown in the class. Eachitem gets 2 points. 1 point for the problem constructed andanother 1 point for the correct use of circumference in the

problem constructed.

  Pause " Answer 

Are you happy with the result of your evaluation? 'hy?

'hat concepts are clear to you?

'hat concepts are still not clear to you?

Construct 2 routine and 2 non-routine problemsinvolving circumference of a circle using the same facts. Thenshow the solution for each problem you constructed.

In your notebook8 write your reflection of your lesson using the following

uestions as your guide!

What

 parts ofthe

lesson do I like

the most ? Why?

What parts

of thelesson do I 

like the least ?

Why?

What is themost 

challenging 

 part  in this

lesson? Why?

 In what 

 situation/sdo I find 

this lesson most 

useful?

What is

the most desirable

value or attitude

that I havedeveloped in this

lesson?

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