A Detailed Lesson Plan in Mathematics for Grade 10

Combination (Illustrating combination of objects)

Prepared by:
Martinez, Allyssa Marie C.
Student Teacher

I. Objectives

At the end of 60-minutes discussion, 85% of the students should be able to

achieve the following:

a. Define combination in their own words;

b. Identify if the given situation illustrates combination or not;
c. Illustrates the combination of objects; and
d. Demonstrates cooperation and participation during discussion.

II. Subject Matter

A. Topic : Combination (Illustrating combination of objects)

B. Reference : Mathematics Learner’s Module, page 301-306

Combination in Math- Definition, Formula and

Example. https://byjus.com/maths/combination/

C. Materials : PowerPoint presentation, box containing students’

names

D. Values Integration: Reflect on one’s own personality/understanding and

participation

III. Procedures
 Teacher’s Activity Students’ Activity

A. Preliminary Activities
1. Classroom Management

Students will pick up some pieces of papers and

trash, arrange the chairs.

2. Greetings and Prayer

Good morning, Class!

Good morning, Ma’am.

Okay, let us stand for a prayer.

Student A, please led the prayer.

(All students will stand, and Student A will

lead the prayer)

3. Checking of Attendance
Okay for your attendance, kindly affix your
signature in the attendance sheet.

Students will sign the attendance sheet.

B. Review / Motivation
Before we proceed to the lesson
proper, let us have a game as a review to
your previous discussions which is about
permutations. Are you ready, grade 10?

Yes, Ma’am!
Before that, here is the mechanics of
the game.

Mechanics of the Game:

The teacher will randomly pick a

name from the box that consist names of the
students. The first one to be pick will
answer item number 1, second to be pick
will answer number 2, and so on. The
student will answer what is asked on the
given question.

Questions:

1. It is the arrangement of objects in a

definite order.
2. Permutation means the selection of
objects, where the _______ matters.
3. The formula for linear permutation is
________. Answers:

1. Permutation

2. order / arrangement of selection

3. P (n,r) = n! / (n-r)!

That game served as a review on

your previous lesson, now let us move on to
our next topic.
 C. Presentation of the Lesson

(The teacher will continue the game

played a while ago, she will pick 10
students’ name on the box, and they will
answer the questions 1 to 10)

Let us continue our game, I will pick

10 names here on the box and they will
answer questions 1 to 10. Are you ready?

Answer: Yes, we are, Ma’am!

Direction: Identify if order or arrangement

is important or not.
1. Choosing 5 questions to answer out
Answer Key:
of 10 questions in a test.
2. Opening a combination lock For numbers 2, 3, 6, 8, order or arrangement is
important.
3. Winning in a contest
4. Selecting seven people to form a For numbers 1, 4, 5, 7, 9, 10, order or arrangement
Student Affair Committee is not important.
5. Forming triangles from 6 distinct
points in which no 3 points are
collinear.
6. Assigning seats to guests at dinner
7. Drawing a set of 6 numbers in a
lottery containing numbers 1 to 45
8. Entering the PIN (Personal
Identification Number) of your ATM
card
9. Selecting 3 posters to hang out of 6
different posters.
10. Listing the elements of subsets of a
 given set

D. Development of the Lesson

(The teacher would emphasize that

in the previous activity, the situation where
order or arrangement is important is called
PERMUTATION, and the situation where
order or arrangement is not important is
called COMBINATION)

Situations 2, 3, 6, and 8 are permutations.

2. Opening a combination lock

3. Winning in a contest
6. Assigning seats to guests at dinner
8. Entering the PIN (Personal
Identification Number) of your ATM
card

Why do you think it is permutation?

Answers: Ma’am it is because order or

arrangement is important in those situations.

Very good! How about item 1, 4, 5,

7, 9, and 10, what did you noticed?

1. Choosing 5 questions to answer out of 10

questions in a test

4. Selecting 7 people to form a Student

Affairs Committee

5. Forming triangles from 6 distinct points

in which no 3 points are collinear
7. Drawing a set of 6 numbers in a lottery
containing numbers 1 to 45

9. Selecting 3 posters to hang out of 6

different posters

10. Listing the elements of subsets of a

given set

Answer: Order or arrangement on those items are

not important, Ma’am.

Nice observation! In the activity

you have just done, you were able to
identify situations where order is important
which is the concept of permutations.

The concept wherein orders or

arrangement not important. explains
COMBINATION, which will be our topic
for today.

As you noticed on the situations on

our activity, order is not important.

1. Choosing 5 questions to answer out of 10

questions in a test

4. Selecting 7 people to form a Student

Affairs Committee

5. Forming triangles from 6 distinct points

in which no 3 points are collinear

7. Drawing a set of 6 numbers in a lottery

containing numbers 1 to 45

9. Selecting 3 posters to hang out of 6

different posters

10. Listing the elements of subsets of a

given set

To understand more about the

concept of combination, let us have
examples.

Example:

Given 4 fruits; say an apple, an orange, a

pear, and a melon.

1. Get 2 fruits. (apple and orange)

a. Select a fruit one at a time and list all

possible selections

 an apple
 an orange

b. Illustrate or describe each selection you

made.

 an apple = 1 way
 an orange = 1 way
= 2 ways

c. Count the number of different selections

you have made.

 an apple = 1 selection
  an orange = 1 selection
= 2 selections

2. Get 3 fruits. (orange, pear, and melon)

a. Select 2 pieces, 2 at a time and list all

possible selections.

11. orange and pear

12. orange and melon
13. pear and melon

b. Illustrate or describe each selection you

made.

Who wants to try answering this Student A:

item? Okay student A, what is your answer?
14. We have 3 ways to choose ma’am, it can
be orange and pear; orange and melon; and
pear and melon.

Thank you, student A. Let us

proceed to number 2, letter c.

c. Count the number of different selections

you have made.

I will pick a name here on the box to

answer this item. Student B: There are 3 possible selections made,
I picked Student B, what do you think is the Ma’am.
answer? 15. orange and pear
 16. orange and melon
17. pear and melon

That is correct! There are 3 possible

selections made when you select 2 pieces at
a time.

Next is item number 3.

3. Get 3 fruits. (orange, pear, and melon)

a. Select 3 pieces, 3 at a time and list all

possible selections.

 Orange, Pear, and Melon Student D: By selecting 3 fruits, 3 at a time, there

b. Illustrate or describe each selection. is only 1 way we can make, Ma’am.

Student D, can you tell what how
many ways can you make if you select 3
pieces or fruits, 3 at a time?

(Students will raise their hands)

Student D is correct. How about the Student F: There is only 1 selection made, Ma’am.
number of selections made?
 Yes, Student F?

Correct! Thank you, student F!

Now I will give you 2 minutes, to

answer this. And then later we will see if
your answers are correct.

4. Get 4 fruits. (apple, orange, pear and

Answers:
melon)

a. Select 2 pieces of fruits, 2 at a time. a.

b. Illustrate or describe each selection.

Apple - Apple - Pear Apple - Melon
c. Count the number of different selections
Orange
you have made, using 2 at a time from the
given 4 fruits.
Orange - Pear Orange - Melon - Pear

Melon

b. There are 6 ways to select 2 pieces of fruits, 2 at

a time.

c. There are 6 possible selections.

5. Get 4 fruits. (apple, orange, pear and
melon)

a. Select 4 pieces of fruits, 4 at a time.

When we select 4 pieces of fruits, 4 at a

time we will have:

 apple, orange, pear and melon

b. Illustrate or describe each selection.

 After selecting 4 fruits, 4 at a time,

we can see that there is only 1 way
to make it.

c. Count the number of different selections

you have made, using 4 at a time from the
given 4 fruits.

 There is only 1 selection made using

all the 4 fruits at a time.

We have here a table and we are

going to answer the number of possible
selections needed.

Number of Number of Number of

Objects Objects possible
Taken at a
 (n) time selections

(r)

2 1 2

3 2 3

Answer: No ma’am.
3 3 1

4 2 6

4 4 1

After doing this activity, does the

order of selecting objects matter?

Yes, correct, it does not matter.

In mathematics, combination is
defined as “an arrangement of objects
where the order in which the objects are
selected does not matter.” The combination
means “selection of things”, where the order
of things has no importance.

Let us explore more examples.

Answer: No ma’am because the list still refers to
1. You were assigned by your teacher to be
the leader of your group for your project. the same people you have chosen.
You were given the freedom to choose 4 of
your classmates to be your group mates.
 (The teacher will call students in front to
show the concept of combination)

If I will choose Student A, B, C, and D,

does it make difference if I choose Student Answer: Yes Ma’am. It is different from the first
D, A, B, and C?
combination cited; it is another combination of

students in a group.

Very good! How about when I

choose Student A, B, D and E? does it make
a difference?

Nice answer! Let have another

example.

2. Lloyd has three donuts, chocolate,

strawberry, and milky. He wants to eat two
donuts during his breaktime and eat the
other one for his lunch. What two flavor of
donuts will he eat?

There are three combinations of two

that can be chosen from the set: it can be
chocolate and strawberry; chocolate and
milky; or strawberry and milky.
 There are 3 combinations made, and
Lloyd can choose what he is going to eat
during his breaktime.

3. If you play cards, you know that in most (Students will give their own examples)
situations, the order in which you hold cards
is not important.

4. Choosing 3 desserts from a menu of 10,

order of choosing the dessert is not
important.

Can you give more examples of

combination on your own?

Possible answer:

E. Generalization A combination is a way of selecting items from a

(The teacher asks the students to collection where the order of selection does not
share to the class their understanding of matter.
combination. The teacher will randomly
pick one or two names on the box of names
of the students to share in front of the class)

What have you learned about our

lesson for today?
 F. Fixing Skills

The students (by pair) study the following

situations and identify if the situation
suggests combination or not. Write your
answer on any sheet of paper.

1. Forming a 3 - digit number out of 0, 1, 2,

…,9.

2. Choosing three of your classmates to

attend to your birthday party.

Answers:

1. Not a combination

2. Combination
G. Evaluation

Identify if each situation below illustrates combination or not. Write your answer on
your Mathematics notebook.

1. Determining the top three winners in a Math Quiz Bowl

2. Assigning 3 different tasks to 5 students

3. Choosing 5 representative from in each class to attend a symposium

4. Picking two different fruits form a fruit basket that contains guava, apple, avocado,
banana, and orange

5. Selecting a pair of blouse and a skirt as your OOTD.

Answer:

1. Not combination

2. Not combination

3. Combination

4. Combination

5. Combination

Assignment:

After identifying if each situation below illustrates combination or not (on your evaluation
task) give a short explanation for your answer.

1. Determining the top three winners in a Math Quiz Bowl

2. Assigning 3 different tasks to 5 students

3. Choosing 5 representative from in each class to attend a symposium

4. Picking two different fruits form a fruit basket that contains guava, apple, avocado, banana,
and orange

5. Selecting a pair of blouse and a skirt as your OOTD.