Republic of the Philippines
DEPARTMENT OF EDUCATION
Region XI
Division of Davao del Norte
-o0oCARMEN NATIONAL HIGH SCHOOL
Ising, Carmen, Davao del Norte
A Lesson Plan on Teaching How to Solve Quadratic Equations by Completing the Sqaure
Quarter:
1st
Year & Section: Grade 9 – Mercury
Time: 1:30 PM - 2:30 PM
Date: July 3, 2019
Competency: Solves quadratic equations by (c) completing the square. M9AL-Ia-b-1
OVERVIEW: This lesson helps students to understand and able to illustrate situations that involve quadratic equations.
This also includes the features of terminologies and activities that able students to investigate thoroughly
mathematical relationships in various situations, formulate real-life problems involving solving quadratic equations
by completing the square.
LEARNING OBJECTIVES:
At the end of the lesson, the students are expected to:
1. Identify the steps in solving quadratic equation by completing the squares;
2. Solve quadratic equation by completing the square; and
3. Develop cooperative skills and accuracy through activity
(Indicator to be achieved: Indicator 5 – Plans, manages and implements developmentally sequenced teaching and
learning process to meet curriculum and varied teaching contexts)
I.
LEARNING CONTENT:
a. Topic:
Solving Quadratic Equations by Completing the Square
b. Pre-requisite Skills: Solving Quadratic Equations by Extracting the Square Roots and
Factoring
c. References:
Grade 9-Math Teaching Guide pages 28-32
Grade 9-Math Learners’ Material pages 27-36
http://www.mathguide.com/lessons2/CompleteSquare.html
https://www.purplemath.com/modules/sqrquad2.htm
d. Instructional Materials:
Activity Sheets, Laptop, TV, Chalk
e. Strategy: 4A’s, Logical and Critical Thinking, Cooperative Learning
II. LEARNING EXPERIENCES/PROCEDURE:
A. Mood Setting
1. Energizer
2. Recall/Review (3 minutes)
(Indicator to be achieved: Indicator 1 – Applies knowledge of content within and across the curriculum
teaching areas)
Within the Curriculum
 Given the following quadratic equation, identify what process/method will you able to solve
it.
a. 2𝑥 2 − 50 = 0
- Extracting the Roots
2
b. 𝑥 + 6𝑥 + 9 = 0
- Factoring
c. 3𝑡 2 = 12
- Extracting the Roots
d. 𝑠 2 − 100 = 0 -Factoring/Extracting the Roots
3. Unlocking of Difficulty/Motivation (5 minutes)
Title: Make it Perfect!
Materials Needed: Visual Presentation
Direction: Everyone is encouraged to answer the given quadratic equations. Determine a number that
must be added to make each of the following a perfect square trinomial.
a.
b.
c.
d.
e.
𝑥 2 + 2𝑥 + ______
𝑡 2 + 20𝑡 + ______
𝑟 2 − 16𝑟 + ______
𝑥 2 + 12𝑥 + ______
𝑥 2 − 30𝑥 + ______
Answer is 1
Answer is 100
Answer is 64
Answer is 36
Answer is 225
(Indicator to be achieved: Indicator 1 – Applies knowledge of content within
and across the curriculum teaching areas.)
(Indicator to be achieved: Indicator 2 – Applies a range of teaching strategies to develop critical and
creative thinking, as well as other higher-order thinking skills.)
4. Presentation of the Lesson
Extracting square roots and factoring are usually used to solve quadratic equations of the form 𝑎𝑥 2 −
𝑐 = 0. If the factors of the quadratic expression of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 are determined, then it is more
convenient to use factoring to solve it.
Another method of solving quadratic equation is by completing the square. This method involves
transforming the quadratic equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 into the form (𝑥 − ℎ)2 = 𝑘, where k ≥ 0.
B. LESSON PROPER
1. Pre-activity
Giving of materials, activity sheets, instructions, and rubrics.
RUBRIC
Group # _________
Level 1
Observed
(5)
Sometimes
(3)
Never
(1)
Totally Correct
(5)
Slightly Correct
(3)
Not Correct
(1)
Members participated in
the group work.
Maintained focus on the
task at hand.
Members contributed
ideas, opinions and
feelings.
Level 2
Presented the given task
correctly.
TOTAL SCORE
2. ACTIVITY (20 Minutes)
_________ / 20
(Indicator to be achieved: Indicator 2 – Applies a range of teaching strategies to develop critical and
creative thinking, as well as other higher-order thinking skills.)
(Indicator to be achieved: Indicator 3 – Manages classroom structure to engage learners,
individually or in groups, in meaningful exploration, discovery and hands-on activities within a range
of physical and learning environment.)
(Indicator to be achieved: Indicator 5 – Plans, manages and implements developmentally sequenced
teaching and learning process to meet curriculum and varied teaching contexts.)
Material Needed: PowerPoint Presentation, Manila Paper, Paper Strips, Permanent Marker,
Masking Tape
Direction: Everyone is encouraged to answer.
Title: Identify Me!
Directions: Using the given solution flash on the screen, identify what process/step is being performed
for each number. Choose your answer from the given paper strips and paste it on your manila paper.
Facts/Information on the paper strips in random:

Divide both sides of the equation by a then simplify.

Write the equation such that the terms with variables are on the left side of the equation
and the constant term is on the right side.

Add the square of one-half of the coefficient of x on both sides of the resulting equation.
The left side of the equation becomes a perfect square trinomial.

Express the perfect square trinomial on the left side of the equation as a square of a
binomial.

Solve the resulting quadratic equation by extracting the square root.

Solve the resulting linear equations.

Check the solutions obtained against the original equation.
Solve the quadratic equation 2x2 + 8x – 10 = 0 by completing the square.
1. Divide both sides of the equation by a then simplify.
2x2 + 8x – 10 = 0
2x 2  8x  10 0

2
2
2
x + 4x – 5= 0

2. Write the equation such that terms with variables are on the left side of the
equation and the constant term is on the right side.
x2 + 4x – 5= 0

x2 + 4x – 5 + 5 = 0 + 5
x2 + 4x = 5
3. Add the square of one-half of the coefficient of x on both sides of the resulting equation.
The left side of the equation becomes a perfect square trinomial.
1
4  2

22 = 4

x2 + 4x = 5
x2 + 4x + 4 = 5 + 4
x2 + 4x + 4 = 9
4. Express the perfect square trinomial on the left side of the equation as a square of a
binomial.

x2 + 4x + 4 = 9
(x + 2)2 = 9
5. Solve the resulting quadratic equation by extracting the square root.
(x + 2)2 = 9
x  2  

x + 2 = ±3
6. Solve the resulting linear equations.
x + 2 = -3
x + 2 – 2 = -3 – 2
x = -5
x+2=3
x+2–2=3–2
x=1
7. Check the solutions obtained against the original equation
For x = 1:
For x = -5:
2x 2  8x  10  0
?
21  81 10  0
2
?
21 8  10  0
?
2  8  10  0
00
2x 2  8x  10  0
?
2 5  8 5 10  0
2
?
225 40  10  0
?
50  40 10  0
00
3. Analysis
(Indicator to be achieved: Indicator 2 – Applies a range of teaching strategies to develop critical and
creative thinking, as well as other higher-order thinking skills.)
Guide Questions:
1.
2.
3.
4.
5.
6.
7.
What is the first step in solving quadratic equation by completing the square?
What is the second step in solving quadratic equation by completing the square?
What is the third step in solving quadratic equation by completing the square?
How is the fourth step in solving quadratic equation by completing the square performed?
How is the fifth step in solving quadratic equation by completing the square performed?
How is the sixth step in solving quadratic equation by completing the square performed?
How is the last step in solving quadratic equation by completing the square performed?
4. Abstraction
(Indicator to be achieved: Indicator 1 – Applies knowledge of content within
and across the curriculum teaching areas.)
(Indicator to be achieved: Indicator 2 – Applies a range of teaching strategies to develop critical and
creative thinking, as well as other higher-order thinking skills.)
1.
2.
3.
4.
Guide Questions:
How did you find the solution for the given quadratic equation?
What mathematics concepts or principles did you apply in finding the solutions?
How did you apply the concepts or principles in finding the solutions?
Are there real-life situations where solving quadratic equation by completing the square is
applicable? Can you give examples?
Discussion:
To solve quadratic equation in the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 by completing the square,
the following steps can be followed:
1. Divide both sides of the equation by a then simplify.
2. Write the equation such that the terms with variables are on the left side of the equation and
the constant term is on the right side.
3. Add the square of one-half of the coefficient of x on both sides of the resulting equation. The left
side of the equation becomes a perfect square trinomial.
4. Express the perfect square trinomial on the left side of the equation as a square of a binomial.
5. Solve the resulting quadratic equation by extracting the square root.
6. Solve the resulting linear equations.
7. Check the solutions obtained against the original equation
EXAMPLE:
Solve the quadratic equation 2x2 + 8x – 10 = 0 by completing the square.
1. Divide both sides of the equation by 2 then simplify.
2x2 + 8x – 10 = 0
2x 2  8x  10 0

2
2
2
x + 4x – 5= 0

2. Add 5 to both sides of the equation then simplify.
x2 + 4x – 5= 0

x2 + 4x – 5 + 5 = 0 + 5
x2 + 4x = 5
3. Add to both sides of the equation the square of one-half of 4.
1
4  2

22 = 4

x2 + 4x = 5
x2 + 4x + 4 = 5 + 4
x2 + 4x + 4 = 9
4. Express x2 + 4x + 4 as a square of a binomial.

x2 + 4x + 4 = 9
(x + 2)2 = 9
5. Solve (x + 2)2 = 9 by extracting the square root.
(x + 2)2 = 9
x  2  

x + 2 = ±3
6. Solve the resulting linear equations.
x+2=3
x+2–2=3–2
x=1
x + 2 = -3
x + 2 – 2 = -3 – 2
x = -5
7. Check the solutions obtained against the
original equation 2x2 + 8x – 10 = 0.
For x = 1:
For x = -5:
2x 2  8x  10  0
?
21  81 10  0
2
?
21 8  10  0
?
2  8  10  0
00
2x 2  8x  10  0
?
2 5  8 5 10  0
2
?
225 40  10  0
?
50  40 10  0
00
Both values of x satisfy the given equation. So the equation
2x 2  8x  10  0 is true when x = 1 or when x = -5
Answer:
The equation 2x 2  8x  10  0
has two solutions: x = 1 or x = -5
5. Application
(Indicator to be achieved: Indicator 1 – Applies knowledge of content within
and across the curriculum teaching areas.)
Represent then Solve!
Directions: Using the figure, write a quadratic equation that represents the area of the
shaded region. Then find the solutions to the equation by completing the square.
.
5 cm
.
t
t
Area = 176
t
t
ANSWER:
IV.
t t  5  176 or t 2  5t  176 or t 2  5t  176  0; t = 11
Note: The negative solution is disregarded since the problem involves measures of length.
Assessment
(Indicator to be achieved: Indicator 1 – Applies knowledge of content within and across the curriculum teaching
areas.)
(Indicator to be achieved: Indicator 4 – Manages learner behavior constructively by applying positive and nonviolent discipline to ensure learning focused environments.
(Indicator to be achieved: Indicator 5 – Plans, manages and implements developmentally sequenced teaching
and learning process to meet curriculum and varied teaching contexts.)
Directions: Find the solutions of the given quadratic equations by completing the square.
2x2 + 8x – 10 = 0
V.
Reflection
(Indicator to be achieved: Indicator 2 – Applies a range of teaching strategies to develop critical and creative
thinking, as well as other higher-order thinking skills.)
(Indicator to be achieved: Indicator 4 – Manages learner behavior constructively by applying positive and nonviolent discipline to ensure learning focused environments.
Students will be asked to fill in
the reflection sheet which will be
distributed to them. The
reflections sheet will be then
pasted on their notebook. Some
will be called to share their
reflections.
Prepared by:
JONEL F. MUYCO
Teacher I
Observer:
LLOYD S. BRAVO
Master Teacher I
Reflection
What I have learned so far…
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