Lesson plan in mathematics 8 (Factoring Perfect Square Trinomial)
1. WestVisayasStateUniversity
COLLEGE OF EDUCATION
Graduate School
Luna St. La Paz Iloilo City
Rachel Ann T. Tabieros M.A. Ed. Mathematics 1
Lesson Plan in Grade 8 Mathematics
Factoring – Perfect Square Trinomial
CONTENT STANDARD
The learner demonstrates understanding of key concepts of factors of polynomials,
rational algebraic expressions, linear equations and inequalities in two variables, systems of
linear equations and inequalities in two variables and linear functions.
PERFORMANCE STANDARD
The learner is able to formulate real-life problems involving factors of polynomials,
rational algebraic expressions, linear equations and inequalities in two variables, systems of
linear equations and inequalities in two variables and linear functions, and solve these problems
accurately using a variety of strategies.
LEARNING COMPETENCY
The learner factors completely different types of polynomials (polynomials with common
monomial factor, difference of two squares, sum and difference of two cubes, perfect square
trinomials, and general trinomials).
LEARNING COMPETENCY CODE
M8AL-Ia-b-1
I. OBJECTIVES
At the end of the lesson, the students must have:
a. defined a perfect square trinomial.
b. determined the steps in factoring perfect square trinomial.
c. solved and identified the factors of perfect square trinomial.
II. SUBJECT MATTER
A. Topic
Factoring Perfect Square Trinomial
2. WestVisayasStateUniversity
COLLEGE OF EDUCATION
Graduate School
Luna St. La Paz Iloilo City
Rachel Ann T. Tabieros M.A. Ed. Mathematics 2
B. Pre-requisite Concepts
a. Perfect squares
b. Definition and examples of trinomial.
c. Special Products (Square of a binomial)
C. Integration
a. Value/s Integration
Cooperation, Analytical Thinking, Accuracy, Objectivity, Perseverance
b. Subject Integration
ICT Integration
Vocabulary words (English)
D. Instructional Strategies
a. Materials
Chalk, Blackboard, Visual Aids
Power Point Presentation, Laptop and Projector
b. Instructional Strategy
1. Discussion Method
2. Oral Questioning
3. Constructive and Discovery Learning
4. Cooperative Learning
E. References
Grade 8 Mathematics Learner’s Module
III. PROCEDURES
A. Daily Routine
a. Prayer
b. Greeting
3. WestVisayasStateUniversity
COLLEGE OF EDUCATION
Graduate School
Luna St. La Paz Iloilo City
Rachel Ann T. Tabieros M.A. Ed. Mathematics 3
c. Checking of attendance
B. Priming/ Pre-activity
Given the table, students will identify and cross out all the perfect squares.
C. Activity
The students will be grouped having 5 members and each group will be given a piece of
paper with a puzzle. They are going to solved for the products of the given binomials and
encircle the expression obtained.
D. Analysis
5 7 70 9 60 20 85
8 23 16 15 25 82 37
12 4 17 40 33 36 73
1 34 29 65 82 76 49
17 100 61 32 48 81 56
43 67 121 18 64 11 89
50 45 19 144 3 6 53
𝟐𝟓𝒙 𝟐
10x 81 18x 𝒙 𝟐
4
15x
𝟏𝟔𝒙 𝟐
−𝟐𝟒𝒙 𝟐
9 10x 12x
𝒙 𝟐 -12x 36 15x 25 𝟗𝒙 𝟐
𝟏𝟔𝒙 𝟐 49 8x
16 𝟐𝟒𝒙 𝟐 25
25 14x −𝟖𝒙 40x −𝟏𝟎𝒙 10x
7x 𝒙 𝟐
12x 𝒙 𝟐
40 𝟏𝟐𝒙 𝟐
a. ( 𝒙 + 𝟗) 𝟐
b. ( 𝒙 + 𝟕) 𝟐
c. ( 𝒙 − 𝟓) 𝟐
d. ( 𝟑𝒙 + 𝟐) 𝟐
e. ( 𝒙 − 𝟒) 𝟐
f. ( 𝒙 − 𝟔) 𝟐
4. WestVisayasStateUniversity
COLLEGE OF EDUCATION
Graduate School
Luna St. La Paz Iloilo City
Rachel Ann T. Tabieros M.A. Ed. Mathematics 4
a. What have you observed with the expressions obtained?
b. What kind of polynomial are they? Are they trinomials?
c. What is a perfect square trinomial?
E. Abstraction
a. The students will share their ideas about perfect square trinomial and will come up
with this possible definition.
A perfect square trinomial is an expression with both first and last terms that are
perfect squares and the middle term is twice the product of the square root of
the last and first terms.
Hence, the expressions obtained earlier by the students are perfect square trinomials.
b. Now, the teacher can proceed on factoring a perfect square trinomial by giving 3
examples on the board.
Example 1. Find the factors of, 𝑥2 + 16𝑥 + 64 .
The answer would be, ( 𝑥 + 8)2.
Example 2. Factor: 𝑥2 − 6𝑥 + 9
The factors are, ( 𝑥 − 3)2.
Example 3. What are the factors of 4𝑥2 + 8𝑥 + 4?
The factors are, 4 ( 𝑥 + 1)2 or (2𝑥 + 2)2.
The students will analyze the three given examples and come up with possible steps or
procedure on how to solve for the factors of a perfect square trinomial.
The following are the expected steps pointed out by the students:
1. Get the square root of the first and last terms.
2. List down the square root as sum/difference of two terms.
The students could also come up with these relationships to factor perfect square
trinomial.
a. ( 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚)2 + 2( 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚)(𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)+ (𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)2 = ( 𝑓𝑖𝑟𝑠𝑡 + 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)2
b. ( 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚)2 − 2( 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚)(𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚) + (𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)2 = ( 𝑓𝑖𝑟𝑠𝑡 − 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)2
c. The teacher will give practice exercises to the students.
5. WestVisayasStateUniversity
COLLEGE OF EDUCATION
Graduate School
Luna St. La Paz Iloilo City
Rachel Ann T. Tabieros M.A. Ed. Mathematics 5
Practice Exercises:
1. 𝑓𝑎𝑐𝑡𝑜𝑟( 𝑥2 + 16 𝑥 + 64)
2. 𝑓𝑎𝑐𝑡𝑜𝑟( 𝑥2 + 12 𝑥 + 36)
F. Generalization
a. What is a perfect square trinomial? Give one example.
b. What are the steps on solving the factors of perfect square trinomial?
c. What are the relationships you observed and used in finding the factors of
perfect square trinomials?
G. Application
Find the factors of the following.
1. ( 𝑥2 + 26 𝑥 + 169)
2. ( 𝑥2 + 28 𝑥 + 196)
3. ( 𝑥2 + 10𝑥 + 25)
4. ( 𝑥2 + 12 𝑥 + 36)
5. ( 𝑥2 + 20 𝑥 + 100)
6. (4 𝑥2
+ 24 𝑥 + 36)
H. Assignment
Solve the following perfect square trinomials.
1. 𝑓𝑎𝑐𝑡𝑜𝑟(25 𝑥2 + 20 𝑥 + 4)
2. 𝑓𝑎𝑐𝑡𝑜𝑟(16 𝑥2 + 144 𝑥 + 324)
3. 𝑓𝑎𝑐𝑡𝑜𝑟(169 𝑥2 + 260 𝑥 + 100)
4. 𝑓𝑎𝑐𝑡𝑜𝑟(64 𝑥2 + 304 𝑥 + 361)
5. 𝑓𝑎𝑐𝑡𝑜𝑟(4 𝑥2 + 80 𝑥 + 400)
Answers:
1. ( 𝑥 + 13)2
2. ( 𝑥 + 14)2
3. ( 𝑥 + 5)2
4.( 𝑥 + 6)2
5. 4 ( 𝑥 + 3)2
Answers:
1. (5 𝑥 + 2)2
2. 4 (2 𝑥 + 9)2
3. (13 𝑥 + 10)2
4. (8 𝑥 + 19)2
5. 4 ( 𝑥 + 10)2
