measurement of geometic figures unit plan final version

Measurement of Geometric Figures

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Author Information

First and Last Name: Elton John B. Embodo

Email Address: [email protected]

Name of School: Gov. Alfonso D. Tan College

Division: Tangub City Division

Municipality/City, Province, Region:Tangub City, Misamis Occidental, Region X

Country: Philippines

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Unit Overview

Unit Plan Title:

Essential Question How do we deal with our limitations?

Unit Questions How could we know that we grow physically?

Content Questions

What is the perimeter of a triangle, square and rectangle?

What is the circumference of a circle?

What is the area of a triangle, square, and rectangle?

What is the area of a circle?

What is the surface area of a cube?

Unit Summary:

Subject Area(s): Click box(es) of the subject(s) that your Unit targets

Business Education

Engineering

Home Economics

Language Arts

Music

School to Career

Social Studies

Drama

Foreign Language

Industrial Technology

Mathematics

Physical Education

Science

Technology

Other: English

Other: Filipino

Other: Makabayan

Grade Level: Click box(es) of the grade level(s) that your Unit targets

Kindergarten

Grade 1 -3

Grade 4 - 6

1stYearHigh School

2nd Year High School

3rd Year High School

4thYearHigh School

English as a Second Language

Gifted and Talented

Resource

Other

Targeted Philippine Basic Education Curriculum Competencies


Student Objectives/Learning Outcomes:

a. Calculate the perimeter of a triangle, square and rectangle given its side;

b. Compute for the value of a side of a triangle, square and rectangle given its perimeter;

c. Create a rectangular bulletin board having a size of 1m by 2m;

d. Calculate for the circumference of a circle given its radius or diameter;

e. Solve for the value of a radius or diameter given its circumference;

f. Construct a diorama involving geometric figures as parts;

g. Determine the area of triangle, square and rectangle given its value of a side;

h. Find the value of a side given the area of a triangle, square and rectangle;

i. Produce an info graphic about the importance of triangle, square and rectangle in our daily living;

j. Calculate the area of a circle given its radius or diameter;

k. Match the area of a circle to its corresponding radius or diameter’

l. Make a Venn diagram about the similarities and differences of triangle, square, rectangle and circle.

m. Solve for the surface area of a cube given its value of an edge and its area of one surface.

n. Describe the relationship between the area of plane figure and surface area of solid figure.

o. Construct a cube having an edge equal to 10cm using cardboard material.


Day 1Procedures: Developmental MethodSubject Matter: Perimeter of a Triangle, Square and Rectangle

Teacher’s Activity Students’ Activity

A. Preparation

a. Review

Good morning class!

So, yesterday we discussed about the two-dimensional figures right?

So, what are those two dimensional figures that we discussed yesterday?

Yes, _________

Very good!

So, what do we call this two dimensional figure that has three sides and three angles?

Yes, ____________

Precisely!

How about this two dimensional figure that has four congruent sides and congruent angles?

Yes, _________

Fabulous!

Now, what do we call this two dimensional figure that has all right angles and two pairs of congruent sides?

Yes, _________

That’s right!

Good Morning sir!

Yes, sir

The two dimensional figures that we discussed yesterday are triangle, square and

rectangle.

A two dimensional figure that has three sides and three angles is a triangle.

A two dimensional figure that has four congruent sides and congruent angles is a square.

A two dimensional figure that has all right angles and two pairs of congruent sides is a

rectangle.


b. Motivation

So you already knew on how to identify those two dimensional figures based on their properties and characteristics.

I have now the illustrations of these following two dimensional figures.

‘

Class, observe these figures properly.

What have you observed from these figures?

Yes, __________

That’s right!

Another one!

Yes, __________

Very good!

So, class you observed that these three

(students do as told)

The figures have common characteristics.

They have angles inside them.


figures are all bounded by their sides.

Now, class do you know what do we call the distance around these figures?

Do you known about the total or sum of the sides of these three figures?

Do you know how to get the total of the values of the sides or the total distance around each of these figures?

B. Presentation

So, be with me this morning class because we are going to discuss about the perimeter of triangle, square and rectangle.

Everybody read!

a. Statement of the aim

Listen to me attentively this morning class because at the end of our discussion you are expected to calculate the perimeter of a triangle, square and rectangle given its side, compute for the value of a side of a triangle, square and rectangle given its perimeter and create a rectangular bulletin board having a size of 1m by 2m.

No, sir

No, sir

No, sir

Perimeter of a triangle, square and rectangle


C. Development Proper

Class, before we’ll determine the perimeter of triangle, square and rectangle, let’s define first what is a perimeter all about.

Everybody read!

So, perimeter class is the total or the sum of the values of the sides of a figure or in short, it is the total distance around the two dimensional figure.

Let’s discuss first the perimeter of a triangle.

To find the perimeter of a triangle, we have to use its formula.

Everybody read!

Example 1;

Perimeter of a two dimensional figure is the distance around the figure. It can be

determined by adding all the values of the sides of the given two dimensional figures.

Perimeter of a Triangle

It can be determined by adding the length of all of its sides

P = a + b + c

Where a, b and c are the sides of a triangle


c = 8cm

C = 16cm

The right triangle ABC has the following values of its sides.

To find the perimeter of a triangle, we will use its formula.

So how are we going to find the perimeter of a right triangle?

Yes, _________

P = a + b + c

= 8cm + 10cm + 16cm

= 32cm

Do you get it class?

Example 2;

P = 18cm

Class, if the perimeter and two sides of a triangle are given.

How are we going to find the value of the third side?

So to find the value of the third side we will add the two given sides and subtract the sum from the perimeter.

(Possible answer)

Yes, sir

(possible answer)


a = 10cm

x = 6cm y = 5cm

z =?

P = x + y + z

18cm = 6cm + 5cm + z

18cm = 11cm +

18cm – 11cm = z

7cm = z


So now let’s proceed to the perimeter of the square.

Everybody read!

So how are we going to obtain the perimeter of a square?

Since the sides of the square are all congruent, then we can arrive in his formula.

P = s + s + s + s

Where s is the value of one side or any side of the square.

To make it short, we will just simply multiply the value of one side by 4 then.

P = 4s

Yes, sir

Perimeter of a Square

It is obtained by getting the product of one side multiplied by 4.

P = 4s

(possible answer)


P = 4s

Example 1;

So how are we going to find the perimeter of this square?

Yes, ___________

So we will substitute the given side to the formula.

P = 4s

= 4(4cm)

= 16cm


How about if we are given the perimeter of a square, how are we going to find the value of its side?

Yes, _______

So by applying the formula we can get the value of its side.

Example 2;

P = 20cm

(possible answer)

Yes, sir

(possible answer)


s = 4cm

P = 4s

20cm = 4s

4 4

5cm = s


So let’s proceed to the perimeter of a rectangle.

Everybody read!

Example 3;

The length refers to the height and the width refers to the base.

To get its perimeter, we will apply the formula.

P = 2[L + w]

= 2L + 2w

= 2(2) + 2(8)

= 4 + 16

= 20cm


How about we are given the perimeter and the length of the triangle, how are we going to find its width?

Yes, ________

Yes, sir

Perimeter of a rectangle

It is equal to the twice the sum of the length and the width. The length is any; the width is

the side next to the length.

P = 2[L + W]

Yes, sir

(possible answer)


w = 8cm

L = 2cm

So by deriving its formula

P = 2L + 2W

P – 2L = 2W

P – 2L = 2W

2 2

P – 2L = w

2

Example 2;

P = 32cm

To find the value of the width.

P = 2[l + w]

= 2l + 2w

32cm = 2l + 2w

32cm – 2l = 2w

32cm – 2(6cm) = 2w

32cm - 12cm = 2w

20cm = 2w

2 2

10cm = w

Do you get it class? Yes, sir


L = 6cm

W =?

Values Integration

Class, a while ago we discussed about the distance around the triangle, a square and rectangle.

So class in a real world, have you observed that some of the things in our environment are in the form of triangle, square or rectangle?

So class, who can give some examples of the things that are triangular, square and rectangular in form?

Yes, ______

Very good!

All your answers are correct.

So class, are those things important to you?

Yes, _______.

That’s right!

Since, they are important to us because we are always utilizing them in our daily living, then of course we also need to value those things. We should not destroy them instead

Yes, sir!

The top of the table.

A sheet of paper.

A ceiling inside the room.

A door, window and floor.

A chalk board and bulletin board.

Those things for example the chalk board and bulletin are important for me and not just for me but also for us because we are

always using them in our daily living especially for us as students. We always

utilize the chalk board during the teacher’s discussion and bulletin board in posting

announcement to the people.


we will construct like them.

IV. Application.

Activity 1

Directions: Calculate the perimeter of a triangle, square and rectangle given the following sides.

1. One side of a triangle ACV has a value equal to 8m and the other two sides are equal to 10m and 12m respectively. What is the perimeter of the triangle ACV?

2. The side of a triangle WER is equal to 5.5 inches, the second side is equal to 2.5 inches and the third side is equal to 2.5 inches. What is the perimeter of a triangle WER?

3. One side of a square QWER is equal to 2.6m; find the area of a certain square.

4. A square JHGB has a side equal to 55inches. What is its perimeter?

5. The length of a rectangle is equal to 50inches and its width is equal to 59 inches. Find its perimeter.

Evaluation

Directions: Compute for the value of a side of a triangle, square and rectangle given its corresponding perimeter.

1. Triangle ABC has a perimeter equal to 34cm and it has the value of two sides equal to 8cm and 6cm respectively. What is the value of the third side?


2. The two sides of triangle CEX are both 18inches and it has a perimeter equal to 48inches. What is the value of the third side?

3. The two sides of an isosceles triangle are equal to 10inches and it has a perimeter equal to 30inches, what is the value of the third side?

4. A square window has a perimeter equal to 288inches. What is the value of each side of the window?

5. A certain rectangle has a perimeter of 54cm. The length has measure of 9cm. What is the value of the width?

Assignment

Directions: Construct a rectangular bulletin board having the length equal to 1m and with equal to 2m. You will do it by group and pass your work on Friday afternoon. That’s your final activity regarding our lesson this morning.


Output in Day 1Rectangular Bulletin Board


Day 2

Subject matter: Circumference of a Circle

Procedure: Deductive method


A. Preparation

a. Review

Good morning class!

So yesterday, we discussed about the two dimensional figures right?

Before we proceed to our new topic this morning, let’s first have a review.

So what is again a perimeter?

Yes, _________

That’s right!

So what is the formula in getting the perimeter of a triangle?

Yes, ______

Very good!

What is the formula in getting the perimeter of a square?

Yes, ____________

Precisely!

What is the formula in getting the perimeter of a rectangle?

Yes, ________

Fabulous!

Good morning sir!

Yes, sir

Perimeter is the distance around the two dimensional figure.

The formula in getting the perimeter of a triangle is P = a + b + c.

The formula in getting the perimeter of a square is P = 4s.

The formula in getting the perimeter of a rectangle is P = 2[2l + 2w].


So all your answers are correct.

b. Motivation

Class, at this moment I will show to you a hula-hoop.

Class what kind of figure is a hula-hoop?

Yes, ___________

That’s right!

Now, class do you know what do we call this curved line bounding the hula-hoop?

Do you know how to measure the length of the curved line bounding the hula-hoop?

Since a hula-hoop is a circle, do you know how to measure the length of the curved line around the circle?

Do you know about the Circumference of a circle?

B. Generalization

So be with me this morning class because we are going to discuss about the

It is a circle.

No, sir!

No, sir

No sir

No, sir


circumference of a circle.

Everybody read!

a. Statement of the Aim

Listen to me attentively class because at the end of our discussion, you are going to calculate for the circumference of a circle, solve for the radius of a circle, and create a diorama having geometric figures as parts.

Everybody read the definition of the Circumference of a Circle.

But class, since the diameter is twice the length of the radius.

d = 2r

we can also use this formula

C = 2πr

To get the circumference of a circle, we will use these following formulas;

C =πd or C = 2πr

Example 1;

“Circumference of a Circle”

Circumference of a Circle is the length of the curved line bounding the circle. It is equal to the product of the diameter multiplied by Л.

C = πd


r = 9cm

So to find the circumference of this circle given its radius, we will use this formula.

C = 2πr

C = 2π(9cm)

C= 18cmπ or 18πcm

Take note class that the value of a Л or “pie” is 3.1416, so we can also extract its value and multiply it to 18cm which can result into

C= 18cm(3.1416)

C = 56.5488cm

for more accuracy


Example 2;

A basket ring has a diameter of 20cm, find its radius.

So in this case class, how are we going to get the circumference of a basket ball ring?

Yes, _________

So we will use first the formula which is

Yes, sir

(possible answer)


c = 20cm

C = πd since the given is the diameter.

Who wants to solve it on the board?

Yes, ___________

Very good!

How about we are given the value of circumference, how are we going to find its radius or diameter?

Yes, _________

Okay, so we will use again its formula. We can use the two formulated in getting its circumference.

Example 3;

A fresh wheel has a circumference of 34πcm. Find its radius and diameter.

So, now how are we going to its radius and

d = 20cm

C = πd = π(20cm) = 20πm Or = 62. 832cm


C = 34πcm

diameter?

Yes, _________

Okay, so we will use again its formula either in the two because they are just similar.

Let us find its diameter,

C = πd

34πcm = πd

π π

34cm = d

So how are we going to find the radius?

Yes, _______

Who wants to solve it on the board?

Yes, _________

C. Inference

So class for your better understanding, I will give you more examples.

1. r = 3m ; find C and d

C = 2πr

= 2π(3m)

= 6πm or 18. 88496m

d = 2πr

= 2(3m)

(possible answer)

(possible answer)

C = 2πr34πcm = 2πr

2π 2

17cm = r


= 6m


2. d = 8cm ; find C and r

C = πd

= 8πcm or 25.132cm

r = d

2

= 8cm

2

= 4cm


3. C = 22πcm ; find d and r

C = πd

22Лcm = πd

ππ

22cm = d

r = d

2

r = 22cm

2

r = 11cm


4. R = 3. 1416cm ; find C and d

C = 2πr

= 2π(3.1416)

= 6. 2832cm or 19. 7393

Yes, sir!

Yes, sir

Yes, sir


C = πd

19.7393 = πd

19.7393 = 3.1416d

19. 393 = 3. 1416d

3. 1416 = 3. 1416

6. 2832 = d

Or

6.2832Лcm = πd

Л Л

6.2832 = d


5. D = 16.15cm ; find c and r

C = πd

= π(16.15cm)

= 16.15πcm

Or

= 50.7368cm

r = d

2

= 16.15cm

2

r = 8.075cm


Yes, sir

Yes, sir


D. Verification

So, class since I had already given more examples, I’ll now test you on how far did you understand our discussion.

I need five students to give their own examples on the board and explain them later on. You will find circumference, radius and diameter. And the rest you will also write your own examples in a sheet of paper and you will pass them to me afterwards.

Very good!

Around of applause.

I will not check your work on the board.

(Verifying)

Values Integration

Class a while ago, we discussed about the distance around the circle right?

So, class in our environment, have you observed that some of the things that we see in our surroundings are in a form of circle?

So class, for you is circle important in our daily living? Is it useful today? Why and why not?

Yes, _______

(Students do as told)

Yes, sir

Yes, sir

For me, it is important sir and it is also useful because as we observe that there are

many things that involve the circle form, just like as stage, Ferris wheel, CD tape, hula-hoop, coins, plates, crown, the faces of the


Very good!

So, circle is important because there are some things in our surroundings that need to be formed in a circle, they could not be made if not in a form of circle.

Sometimes, we get it unnoticed but I tell you whether you know it our not, circle is important.

IV. Application

Activity 1

Directions: Calculate for the circumference of a circle given the radius or diameter.

1. A circle C has a radius equal to 5 inches, find its circumference.

2. A circle B has a radius equal to 9cm, find its circumference.

3. Circle Z has a diameter equal to 15inches, find its circumference.

4. Circle M has a diameter equal to 200m, find its circumference.

5. Circle O has a radius equal to 18dm, find its circumference.

Evaluation

Directions: Solve for the radius of a circle given its circumference.

balls and many other things that involve the circle form.


1. A circle has a circumference equal to 121πcm, find its radius.

2. Circle H has a circumference equal to 144πcm, find its radius.

3. 81πcm is a circumference of a circle t, what would be its values of diameter?

4. The circumference of a circle K is 64πcm, what is the value of its diameter?

5. 169πinches is the circumference of a circle P, finds its diameter.

Assignment

Directions: Create a diorama in which geometric figures especially circles are present as parts. You can choose any theme that you want for your diorama. You will pass your work on Friday afternoon.


Output in Day 2Diorama


Day 3

Subject Matter: Area of a Triangle, Square and Rectangle

Procedure: Developmental Method


A. Preparation

a. Review

Good morning class!

Yesterday and on the other past day we discussed about the distance around the two dimensional figure.

Am I right class?

So class, what do we call the distance around the circle?

Yes, _______

That’s right!

Who can recall its formula?

Yes, _______

Very good!

How about the distance around the triangle? What do we call it?

Yes, _________

Fabulous!

Now who can state its formula?

Yes, ________

That’s correct!

How about the distance around the square?

Good morning class!

Yes, sir!

The distance around the circle is called the circumference of a circle.

Its formula is C = 2Лr or C = Лd.

The distance around the triangle is called the perimeter of a triangle.

Its formula is P = a + b + c.


Yes, _______

Fabulous!

How about the formula in getting perimeter of a square?

Yes, ______

That’s correct!

So now who can recall the distance around the rectangle?

Yes, ______

Precisely!

How about the formula in getting the perimeter of a rectangle?

Yes, _________

Very good!

Everybody around of applause to those who were able to answer my questions.

b. Motivation

Class you already knew the distance around the two-dimensional figures just like circle, triangle, square and rectangle.

Now class I have here the illustrations of those figures.

The distance around the square is called the perimeter of a square.

Its formula is P = 4s.

The distance around the rectangle is called the perimeter of a rectangle.

The formula in getting the perimeter of rectangle is P = 2(W + L).


Class, observe these figures carefully.

So, class have you observed that there are spaces inside each two-dimensional figure?

Do you know what do we call the amount of space inside each figure?

Do you know how to get the amount of space within each figure?

B. Presentation

So class, be with me this morning because we will discuss on how to get the amount of space or the area of a triangle, square and rectangle.

Everybody read!


Listen to me attentively this morning class because at the end our discussion, you are expected to determine the area of a triangle, square and rectangle given its value of a side of a triangle, square, find the value of a side of square, triangle and rectangle given its area, and produce an info-graphic about the importance of triangle, square and rectangle.


Yes, sir

No, sir

No, sir

”Area of triangle, Square and Rectangle”


C. Development Proper

Class before we’ll determine the area of triangle, square and rectangle, let’s define first what area all about is.

Everybody read!

So class the area of two-dimensional figure is the amount of space within a certain figure. To find its area, we have to use its formula. Let’s discuss first the area of a triangle.

Everybody read!

Example 1;

Area of two-dimensional figure is the amount of space inside each figure. It is the total space within the figure. It expressed in square denominations such as square inches,

square centimeters and square miles.

The area of a triangle is equal to one-half of the product of the base and the height.

A = 1 (b x h)

2

Where b is the base h is the height


a = 10cm

To find the area of a triangle, we will use its formula.

A = 1 (b x h)

2

= (8cm) (10cm)

2

= 80cm 2

2

= 40cm2


Now class, is it possible to find the height of a triangle given its area and the value of base?

So let’s try whether it is possible or not.

Example 2:

How are we going to find the value of the

Yes, sir!

(possible answer)


b = 8cm

b =?

a = 12m

A = 30cm2

height?

Yes, _________

Let’s use again the formula.

A = 1 (b x h)

2

(2) 30cm2 = 12cm (h) (2)

2

60cm 2 = 12cm h

12cm 12cm

5cm = h

So it’s possible to find the height of the triangle given its area and its base.


So let’s move on to the area of a square.

Everybody read!

Take note class that the area of a square is always a perfect square.

Example 1:

We will simply utilize the formula in getting the area of a square.

(possible answer)

Yes, sir

The area of a square is equal to the square of the length of any side.

A = s2


s = 11cm

A = s2

= (11cm)2

= 121 cm2


Example 2:

We can also get the value of a side of the square given its area just like in this example.

A = s2

25cm2 = s2

√25 cm2 = √s2

5cm = s


So let’s move on to the area of a rectangle.

Everybody read!

Yes, sir

Yes, sir

The area of a rectangle equals the product of the length multiplied by the width.

A = l x w


A = 25cm2

To get the area of a rectangle let’s just simply multiply the value of the length to the value of the width.

Example 1;

How are we going to find the area?

Yes, ___________

Very good

A = l x w

= 6cm x 13cm

= 78cm2


So class, is it possible to find the value of the length given the width and its area?

Example 2

We will use the formula.

Yes, sir


l = 6cm

w = 13cm

w = 10cm

l =?

A = 120cm2

We will substitute the given area and width to the formula.

A = l x w

120cm2 = l (10cm)

120cm 2 = l (10cm)

10cm 10cm

12cm = L

So what’s the value of the length?

Yes, _________

Fabulous!

Values Integration

Class, is it important to know the formulas in getting the area of the triangle, square and rectangle?

Why?

Yes, ________?

In real life situation class, who can cite an example that needs to have a formula in order to get the accurate amount or value?

Yes, __________

The value of the length is 12cm2

Yes, sir

It is important so that we could really determine the exact or accurate area of a

certain figure.

In making some medicines, we need to have a formula so that we could get the accurate amount of a certain medicine and also to

avoid over dosage and in order to make them effective and won’t harm the patient.


IV. Application

Activity 1

Directions: Determine the area of triangle, square and rectangle given its value of sides.

1. Determine the area of a square given its side equal to 10m.

2. Determine the area of a triangle given the following values of sides: a = 12cm, b = 8cm and c = 10cm.

3. Determine the area of a rectangle given the length equal to 8inches and with equal to 9inches.

4. One side of an equilateral triangle has a value equal to 20cm, determine the area.

5. l = 21cm and w = 19cm, determine the area of a rectangle.

Evaluation

Directions: Find the value of a side of triangle, square and rectangle given their corresponding area and the other side.

1. Given the area and the height of the triangle equal to 40m2 and 10cm respectively, find the value of the base.


2. Given the area and the base of the triangle equal to 30cm2 and 5cm respectively, find the value of the unknown height.

3. Given the area of the square equal to 144cm2, find the side of the square.

4. Given the area and the width of the rectangle equal to 78cm2 and 13cm respectively, find the value of the unknown length.

5. Given the area and length of the rectangle equal to 120cm2 and 12cm respectively, find the unknown width.

Assignment

Directions: Produce an info-graphic about the importance of using formulas in getting the accurate measures of the mentioned geometric figures above.


Output in Day 3

Info graphic


Day 4

Subject Matter: Area of a Circle

Procedure: Developmental Method


A. Preparation

a. Drill

Class, yesterday we discussed the area of a triangle, square and rectangle.

Am I right class?

Before we proceed to our new lesson for this afternoon, let’s have first an activity. So, I will group you into two. The left side will be the group one and the right side will be the group two.

Now, class I have here a word box and five questions. Each group will have the same five questions. All you have to do is to identify the following statements or questions by selecting your answers on the blank before each number.

Is my instruction clear class?

So be in your group now for I will only give you three minutes to do it.

Yes, sir!

Yes, sir


______1. It is the amount of space inside each figure.

______2. It is the height of a triangle.


A = lw A = bh A = a2

Altitude 2 baseArea length height

b. Motivation

So you are familiar about the formulas in getting the area of triangle, square and rectangle.

At this moment, I will show you again a picture of a circle.

Now class, observe the circle carefully.

I’ll ask you some questions class

Do you now what do we call this amount of space inside the circle?

Do you know about the area of a circle?

Do you know how to get the area of a circle?

______3. The formula in getting the area of rectangle.

______4. It is used to determine the area of a triangle.

______5. A formula used to get the area of a square.


No sir,

No, sir

No, sir


B. Presentation

So class, be with me this afternoon because we are going to discuss on how to get the area of a circle.

Everybody read!


Listen to me attentively class because at the end of our discussion, you are going to calculate the area of a circle given its radius and diameter, match the areas of circles to their corresponding radius and diameter and you are going to create a Venn diagram about the similarities and differences of triangle, square, rectangle and circle.

Now class lets define first the area of a circle.

Everybody read!

Now class let’s consider come examples.

1. Find the area of a circle given the radius equal to 3m.

To find its area, we have to use the formula.

A=π r2

= Л(3m)2

= 9m2Л

= 9Лm2

Take note class that we can also extract the

“Area of a Circle”

Area of Circle

- It is the amount of space within the circle. It is equal to the radius

squared multiplied by “pi” or Л.

A=π r2


“pi”, it is equal to 3.1416.

2. Given the diameter equal to 14 inches, find the area of a circle.

Now class, can we directly use the formula to get the area of a circle?

Why?

Yes, _____

That’s right!

So what are we going to do with the diameter? Remember class that the radius is always the half of the diameter.

Yes,_______

Precisely!

The formula to find the radius given the diameter is ,

d = 2r

14inches = 2r

2 2

7inches = r

So the value of a radius is 7inches.


Can we now get the area of a circle?

No, sir

We can’t directly use the formula because the given is diameter and not the radius.

We will divide the diameter by 2 to get the value of radius.

Yes, sir

Yes, sir


Since we now have the radius which is equal to 7inches.

A=π r2

= Л(7inches)2

= 49Лinches2

= 49Лsquared inches

Do you understand class?

What if class, the given is the area of a circle, we will try whether it is possible?

Yes, _______

Let’ find it out!

I have here another example.

3. Given the area of a circle equal to 64Лcm2, find the radius.

In this case class, we will still use the formula and then substitute the given to the formula

A=π r2

64 Л cm2 =π r2

Л Л

√64 cm2 = √r2

8cm = r

So what’s the value of the radius?

So always remember class that, whether we wil find the area or the radius of a circle, we will always use it formula.

Yes, sir

It is possible to find the radius because we use the radius to get the area of a circle so,

we can also use the area of a circle to get the value of the radius.

The value of the radius is 8cm.


A=π r2

Now class let’s have another twist, what if we have the circumference, is it possible to get the Area of a circle out from the given circumference?

Remember class that w have the formula for circumference.

C=2 πr

Let’s consider this example.

4. Given the circumference equal to 10Лrm, find the area of a circle.

Can w directly use the formula for the area of a circle?

So lets’ use first the formula of the circumference to get the value of a circle.

C=2 πr

Substitute the value of the circumference to the formula.

C=2 πr

10Лm = 2 πr

10 Л m = 2 πr

2Л 2Л

5m = r

Can we get now the area of a circle?

That’s right!

(possible answer)

No, sir

Yes, sir


Since, we have now the value of radius.

A=π r2

= π (5 m)2

= 25πm2

D you get it class?

Is it possible to get the value of diameter class, given the area of a circle?

Let’s find it out!

5 given the area of a circle equal to 36πm2, find the diameter.

A=π r2

36πm2 = π r2

36 πm2= π r2

Л Л

d = 2r

= 2(6m)

= 12m

So the value of the diameter is 12m.

Do you have questions class?

Values Integration

Now, class you already knew on how to get the area of a circle right?

And you already knew on how to get the

Yes, sir

(possible answer)

None, sir.

Yes, sir


area of square, triangle and rectangle.

Am I right?

As you noticed class that we used different formulas in getting the areas and perimeters of those figures.

Am I right?

So why did we use different formulas in measuring the perimeters and areas of those figures?

Yes, _________

That’s a good idea!

Who has another idea?

Yes, _______

Very good!

Now class, how about in real life situation, since no two individuals are alike, why do we need to consider the individual differences in dealing with the people around you?

Yes, _________

Yes, sir

Yes, sir

We used different formulas in getting the measures of those figures because those

figures are different from each other, so we did use different formulas.

We used different formulas in getting the measures of those figures since those figures have different form and shape. Even though those figures have similarities but all in all they are still distinct to each other thus, we

used different formulas.

As we all know that we need to consider the individual differences in dealing with the people around us because if we will not


Fabulous!

IV. Application

Activity 1

Directions: Calculate the area of a circle given its radius or diameter.

1. Circle C has a radius equal to 56m, what is the area of the given circle?

2. Circle Z has a radius equal to 45inches, calculate its area.

3. Circle A has a diameter equal to 90inces, calculate its area.

4. Calculate the area of a Circle having a diameter equal to 25dm.

5. Calculate the area of a circle having the radius equal to 7.5inches.

Evaluation

Directions: Match the areas of circles in column A to their corresponding diameter or diameter in column B.

consider the individual differences in dealing with them, we might hurt them or we might

violate their rights.


Column A Column B

1. 225πkm2

2. 60πm2

3. 121πinch2

4. 36πcm2

5. 400πm2

a. 6m

b. 40m

c. 15km

d. 25km

e. 11inc

f. 16m

Assignment

Directions: Create a Venn diagram about the similarities and differences and of triangle, square, rectangle and circle.


Output in Day 4

Venn diagram


Day 5

Subject Matter: Surface Area of a Cube

Procedure: Deductive Method

Teacher’ Activity Students’ Activity

A. Statement of the Problem

a. Drill

Group 1

Group 2

Good morning class!

Last days, we discussed about the perimeter and area of a triangle, square and circle.

Am I right?

Good morning too sir!


1 3 4 5

2

6

1

2 3 4

5

6

So, before we proceed to our new topic for this afternoon, let’s first have a drill.

So now, I will group you into two, the left side will be the group one and the right side will be the group two. Each group will have three representatives to do the task.

I have here patterns of certain solids made in cardboard material. All you have to do class is to make these patterns into their possible solid forms.

Is my instruction clear class?

I will only give you two minutes to do the task.

Okay class, your time starts now!

b. Motivation

So group 1 what solid figure you have formed out from the pattern?

Very good!

How about the group 2, what solid figure you have formed out from the pattern?

Very good!

Yes, sir

Yes, sir


Group 1 Group 2

The solid that we’ve formed out from the pattern is a CUBE.


So both groups formed a CUBE out from the pattern given.

Class, observe the cube properly.

So class, what plane figures that are bounding the cube?

Yes, _____

Precisely!

So every face of the cube is a square.

Class, do you know what do we call the total area of the squares bounding the cube?

Do you know how to get the total area of the squares bounding the cube?

B. Generalization

So be with me this morning class because we are going to discuss about the Surface Area of a Cube.

Everybody read!


Listen to me attentively this morning class

We have also formed a CUBE.


The plane figures that bounded the cube are squares.

No, sir!

No, sir

“Surface Area of a Cube”


because at the end of our lesson, you are going to solve for the surface area of a cube given its value of the edge or its area of one surface, describe the relationship between the area of plane figures and surface area of solid figures, and last is you are going to construct a cube using cardboard material.

I have here a definition of the Surface Area of a cube.

Everybody read!

Who has an idea about this formula?

How did we arrive at this formula?

Yes, _________

You have the idea.

How many faces does the cube have?

Yes, _________

Precisely!

What kind of plane figures each face of the cube?

Yes, ________

Who can recall the formula in getting the area of a square?

Yes, _______

Surface Area of a Cube is equal to the sum of the areas of squares bounding or covering

around the cube.

SA = 6s2

(possible answer)

There are six faces.

It is a square.


So class remember that each surface of a cube is a square, so in getting the surface area of a cube is just like adding the area of six surfaces covering the around the cube.

SA = s2 + s2 + s2 + s2 + s2 + s2

Let’s add each area of the squares, the sum is;

SA = 6s2


Example 1;

Find the surface area of a cube given the edge equal to 4cm long.

Given: s = 4cm

Find: SA

SA = 6s2

= 6(4cm)2

= 6(16cm)2

SA = 96cm2


Example 2:

Find the surface area of a cube given the perimeter of one surface of a cube equal to 36cm.

Given : P = 36cm

Find: SA

The formula in getting the area of a square is A = s2

Yes, sir

Yes, sir


In this case, we can’t directly use the formula of the surface area of the cube. Let’s find first the value of the side or the edge of a cube.

P = 4s

36cm = 4s

4 4

9cm = s

So we can now find the surface area of the cube.

SA = 6s2

= 6(9cm)2

= (81cm2)

SA = 486cm2


Example 3:

The SA of the cube is 150cm2, what is the edge of the cube?

Let us solve for the edge of the cube.

Given: SA = 150cm2

SA = 6s2

150cm 2 = 6s 2

6 6

25cm2 = s2

Yes, sir


√25 cm2 = √s2

5cm = s


C. Inference

Class for your better understanding. I’ll give you more examples:

1. Given: s = 7cm, Find A and SA

A = s2

= (7cm)2

A = 49cm2

SA = 6s2

= 6(49cm2)

SA = 294cm2


2. Given: A = 36cm2, find s and SA

A = s2

36cm2 = s2

√36 cm 2= √s 2 6cm = s

SA = 6s2

= 6(6cm)2

=6(36cm2)

SA = 216cm2

Yes, sir.

Yes, sir



3. Given: SA = 384cm2, find A and s

SA = 6s2

384cm 2 = 6s 2 6 6

64cm2 = s2

√64 cm 2 = √s 2

8cm = s

A = s2

= (8cm)2

A = 64cm2


D. Verification

So class, since I had already given you more examples, I’ll now test you on how far did you understand our discussion.

I need five students to give their own examples on the board and explain them later on. You will find the surface area of the cube. The rest on your seats will also write your own examples on a scratch paper and later on you will pass that to me.

Do you get me class?

Very good!

Yes, sir

Yes, sir


Let’s now check your work

(checking)

Values Integration

Class, a while ago, we discussed about Surface area of a cube.

You noticed class that all the faces of the cube are equal.

Am I right!

Do you think class if the faces of the cube are not equal, we can still form a perfect cube?

That’s right!

Thus, they should be all equal.

Now class, is equality important today?

Yes, _____

Very good!


Yes, sir

No, sir

Equality in all aspects is very much important. It is important in the sense that it prevents some unnecessary things to happen.


Do you still have any question class?

E. Application

Activity 1

Directions: Solve for the surface area of a cube given its value of an edge and its area of one surface.

1. Solve the surface area of a cube having an area of one surface equal to 49m2.

2. Solve the surface area of a cube having a value of an edge equal to 18cm. Determine also the area of one surface of a cube.

3. Solve for the surface area of a cube having the area of one surface equal to 36inch2.

4. Solve the value of an edge of a cube having the surface area equal to 486m2.

5. Solve for the area of one surface of a cube having the surface area equal to 600cm2.

None, sir!


Activity 2

Directions: In a one-fourth sheet of paper, describe the relationship between the area of a plane figure and the surface area of a solid figure (square-cube).

Activity 3

Directions: Construct a cube having the value of an edge equal to 10cm using cardboard material.

IV. Assignment

Directions: Do an advance study about the surface area of other solid figures. We will have a quiz next meeting.


Output in Day 5Object of a Cube


Approximate Time Needed:

300minutes in a week

Prerequisite Skills:

1. The students should have the prior knowledge about the definitions and properties of geometric figures.

2. The students should be familiar with the basic parts of each geometric figure.

Materials and Resources Required For Unit

Technology – Hardware: (Click boxes of all equipment needed)

Camera

Computer(s)

Digital Camera

DVD Player

Internet Connection

Laser Disk

Printer

Projection System

Scanner

Television

VCR

Video Camera

Video Conferencing Equipment.

Other:

Technology – Software: (Click boxes of all software needed.)

Database/Spreadsheet

Web Page Development

Image Processing

Encyclopedia on CD-ROM

Multimedia

E-mail Software

Word Processing

Web Browser

Desktop Publishing

Other:

Printed Materials:


Supplies:Wood, nails, hammer, plywood, Styrofoam, pictures, paint, internet connection, cardboard

Internet Resources:

Mathematics Skills For The Auto Body Repair Trades:

Calculation of Perimeter, Area and Volume of Geometric

Figures. © Houghton Mifflin Company. A. Retrieved on March

6, 2015 from

www.geogiancollege.ca/coned09/wp-content/uploads/09-M13-

ABRT-Calculation-of-Perimeter-Area-and-Volume-of-

Geometric-Figures1.pdf.

Others:

Accommodations for Differentiated Instruction

Resource Student:

To cope up with the lessons, he or she must do following:

Attend a remedial class. Answer the activity sheets intended for the remedial

class. Do a research about the lesson.

Gifted Student:He or she must make additional activity that is related to the lesson.

Make a module about the lessons.


Student Assessment:

Assessment for the first day class.

The students will calculate the perimeter of a triangle, square and rectangle given the following sides.

The students will compute for the value of a side of a triangle, square and rectangle given its corresponding perimeter.

The students will create a rectangular bulletin board having a size of 1m by 2m.

Assessment for the second day class.

The students will calculate for the circumference of a circle given the radius or diameter.

The students will solve for the radius of a circle given its circumference.

The students will create a diorama having geometric figures as parts.

Assessment for the third day class.

The students will determine the area of triangle, square and rectangle given its value of sides.

The students will find the value of a side of triangle, square and rectangle given their corresponding area and the other side.

They students will produce an info-graphic about the importance of triangle, square and rectangle.

Assessment for the fourth day class.

The students will calculate the area of a circle given its radius or diameter.

Match the areas of circle to their corresponding diameter or diameter.

The students will create a Venn diagram about the similarities and differences of triangle, square, rectangle and circle.

Assessment for the fifth day class.

The students will solve for the surface area of a cube given its value of an edge and its area of one surface.

The students will describe the relationship between the area of a plane figure and the surface area of a solid figure (square-cube).

They students will construct a cube using cardboard material.


Key Word Search:

Geometry

Measurement

Perimeter

Are

Surface Area


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