Unit plan- Measurement of Geometric figures [email protected] originalfinal na final

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Name of the Unit Plan

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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 1

Procedures: Developmental Method Subject 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 figures are all bounded by their sides.

(students do as told)

The figures have common characteristics.

They have angles inside them.



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

a = 10cm

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)

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


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 we will construct like them.

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.



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.



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!

So all your answers are correct.

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].



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

circumference of a circle.

Everybody read!

It is a circle.

No, sir!

No, sir

No sir

No, sir

“Circumference of a Circle”



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 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

C = 𝜋𝑑 since the given is the diameter.

Yes, sir

(possible answer)

c = 20cm



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

diameter?

Yes, _________

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

d = 20cm

C = 𝜋𝑑 = 𝜋(20cm)

= 20𝜋m

Or = 62. 832cm

(possible answer)

C = 34𝜋cm



Let us find its diameter,

C = 𝜋𝑑

34𝜋cm = 𝜋𝑑

𝜋𝜋

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)

= 6m


(possible answer)

C = 2𝜋𝑟

34𝜋cm = 2𝜋𝑟 2𝜋 2

17cm = r

Yes, sir!



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



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

balls and many other things that involve the circle form.



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.

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:Createa 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.



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?

Yes, _______

Fabulous!

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.

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



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.

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

b = 8cm



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

A = 1 (b x h)

2

= (8cm) (10cm)

2

= 80cm2

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 height?

Yes, _________

Let’s use again the formula.

Yes, sir!

(possible answer)

(possible answer)

b =?

a = 12m

A = 30cm2



A = 1 (b x h)

2

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

2

60cm2 = 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.

A = s2

= (11cm)2

= 121 cm2


Yes, sir

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

A = s2

Yes, sir

s = 11cm



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

√25cm2 = √s2

5cm = s


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

Everybody read!

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

Yes, sir

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

A = l x w

A = 25cm2



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

A = 120cm2

We will substitute the given area and width

to the formula.

We will use the formula.

Yes, sir

l = 6cm

w = 13cm

w = 10cm

l =?



A = l x w

120cm2 = l (10cm)

120cm2 = 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.



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.

______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.

A = lw A = bh A = a2

Altitude 2 base Area 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?

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!


No sir,

No, sir

No, sir

“Area of a Circle”




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 = 𝜋𝑟2

= Л(3m)2

= 9m2Л

= 9Лm2

Take note class that we can also extract the

“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?

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 = 𝜋𝑟2

No, sir



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?

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

𝐴 = 𝜋𝑟2

= Л(7inches)2

= 49Лinches2

= 49Лsquared inches

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

Yes, sir



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 = 𝜋𝑟2

64Л𝑐𝑚2 =𝜋𝑟2

Л Л

√64𝑐𝑚2 = √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.

𝐴 = 𝜋𝑟2

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.

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.

(possible answer)



𝐶 = 2𝜋𝑟

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 = 2𝜋𝑟

Substitute the value of the circumference to

the formula.

𝐶 = 2𝜋𝑟

10Лm = 2𝜋𝑟

10Л𝑚 = 2𝜋𝑟

2Л 2Л

5m = r

Can we get now the area of a circle?

That’s right!

Since, we have now the value of radius.

𝐴 = 𝜋𝑟2

= 𝜋(5𝑚)2

= 25𝜋m2

D you get it class?

No, sir

Yes, sir

Yes, sir



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 = 𝜋𝑟2

36𝜋𝑚2 = 𝜋𝑟2

36𝜋𝑚2= 𝜋𝑟2

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

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?

(possible answer)

None, sir.

Yes, sir

Yes, sir

Yes, sir



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, _________

Fabulous!

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 usbecause if we will not consider the individual differences in dealing

with them, we might hurt them or we might violate their rights.



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.

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.



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?

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.

Good morning too sir!

Yes, sir

1 3 4 5

2

6

1

2 3 4

5

6



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!

So both groups formed a CUBE out from the

pattern given.

Class, observe the cube properly.

Yes, sir


Group 1 Group 2

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

We have also formed a CUBE.




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

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.

The plane figures that bounded the cube are

squares.

No, sir!

No, sir

“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, _______

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

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.

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




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

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

Yes, sir

Yes, sir



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

150cm2 = 6s2

6 6

25cm2 = s2

√25𝑐𝑚2 = √𝑠2

5cm = s


Yes, sir

Yes, sir.



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

√36𝑐𝑚2= √𝑠2

6cm = s

SA = 6s2

= 6(6cm)2

=6(36cm2)

SA = 216cm2


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

SA = 6s2 384cm2 = 6s2

6 6

64cm2 = s2

√64𝑐𝑚2 = √𝑠2

8cm = s

Yes, sir

Yes, sir



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!

Let’s now check your work

(checking)

Yes, sir




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!

Do you still have any question class?

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.

None, sir!



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.

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.

Approximate Time Needed:

300minutes in a week

Prerequisite Skills:

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

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:

Use APA Style

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.

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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.

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.

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.

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.

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).

Key Word Search:

Geometry

Measurement

Perimeter

Are

Surface Area

Produce the output of each lesson in a day…example day five (Bulletin Board)-produce a picture

and print. Include the Appendix for each output. March 24, 2015.

Unit plan- Measurement of Geometric figures [email protected] originalfinal na final

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