Content Standards: The learner demonstrates understanding of key concepts of quadratic
equations, inequalities and functions, and rational algebraic equations.
Performance Standards: The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving
quadratic equations, inequalities and functions, and rational algebraic
equations and solve them using a variety of strategies.
Learning Competency and Code: Solves Problems involving quadratic equations and rational
algebraic equations (M9AL-le-1)
Quarter: FIRST
Week:
5th
Day: 17
I. Objectives:
At the end of 60 minutes, 85% of the learners are expected to:
1. Translate verbal phrases to mathematical expressions.
2. Give the equivalent equations for verbal statements involving quadratic equations.
3. Solve Number Problems involving quadratic equations..
II. Content:
Subject Matter: Solving Problems involving quadratic equations.
Integration:
(Learning Area):
Strategies: Learning through Discovery, Discussion, Interaction, paper and pencil
activities
Materials: Worksheets, chalk and chalk board, textbook
References:
*google: (Problem solving involving quadratic equations)
*Math 9 Learners Material, pp. 174-183
* Advanced Algebra, Trigonometry and Statistics
Math Ideas and life applications IV , pp. c. 2010
by ABIVA Publishing
* Advanced algebra, Trigonometry and Statistics 2nd Edition,
pp. 195-206
c. 2008 by Fernando Orines, et. Al.
Phoenix Publishing House
III. Learning Tasks:
A. PRELIMINARIES;
B. ELICIT: Answer the worksheets in just three (3) minutes.
How does each of the following mathematical expression be read/written in English?
1. X + 3
6. (n-5)2
2
2. X
7. 10- d2
2
3. 3f
8. (m + n)2
2
4. k – d
9. x2+ y2
5. 2(n2+6)
10. m2- 9
C. ENGAGE:
The teacher let the students give the answer by writing it on the board. Together, the
students would then try to check whether the English phrases / interpretation they give is
correct, letting them give the correct phrase if what they gave is wrong. Guide questions
can be thrown by the teacher in cases the students cannot really give the correct English
phrase.
ANSWERS (Note, answers may vary, depending on how the sentence is being constructed;
answers here are the nearest possible.)
1. sum of a number and 3.
2. square of a number
3. thrice the square of a number
4. a number decreased by a square of another number
5. twice the sum of the square of a number and six
6. the square of the difference of a number decreased by five
7. ten decreased by a square of a number
8. The square of the sum of two distinct numbers
9. The sum of the squares of two numbers.
10. the square of a number decreased by nine
D. EXPLORE:
Teacher: Ok, this time let’s try it on number problems:
One positive integer is one-half the other and the sum of their squares is 80.What
are these integers?
The teacher would then give the students time to solve and then present their
interpretation on the problem given. The students would are then given time to defend,
discuss their answers in front. While the teacher would only listen to the student’s
interaction, trying to take note important points for learning as well as the misconceptions
if there’s anything that would arise.
SOLUTION:
Let x be the bigger number
𝑥
𝑥 2 + (2)2 = 80
𝑥2+
𝑥2
4
= 80
4𝑥 2 + 𝑥 2
= 80
4
5𝑥 2 = 320
𝑥 2 = 64
X = ±8 ;note that the number we are looking for is a positive number, thus,
we take x = 8.
The smaller number is 8/2 = 4
Checking:
8
8 2 + ( )2 = 80
2
82 + 42 = 80
64 + 16 = 80
80=80
E. EXPLAIN
The teacher would then give the important points jotted at the Explore stage, and
let the students raise questions as well as letting the students answer questions/ parallel
situations thrown by the teacher.
F. ELABORATE
The teacher would let the students enumerate the steps (in their own words) they
found out earlier on how to solve Word problems involving quadratic equations,
eventually supplying ideas , may there be cases students could not trace or there are steps
not given/ left out. This list of steps would serve as their guide for the next activity.
G. EXTEND
The teacher let the students apply what they learned through the following
activity. (Note: this is an Individual activity.)
Solve the following number problems:
1. Find two consecutive positive integers having 145 as the sum of its squares.
2. Find two consecutive even integers whose product is 120.
3. Two Odd integers have 1023 when multiplied. What are these integers?
Solutions:
1. Let x
be the first positive number
x + 1 be the second positive number
x2 + (x+1)2 = 145
x2 + x2 +2x +1 = 145
x2 + x2 +2x +1-145 = 0
 Checking:
2x2 +2x -144 = 0
82 + 92 = 145
2x2 +2x -144 = 0
64 + 81 = 145
2
145=145
2
x + x -72 = 0
(x-8)(x+9)=0
x-8 =0 ;
x + 9 =0
x=8
;
x=-9
Since we are looking for two consecutive positive integer, we can only take
8 as our first number; -9 is the extraneous solution.
x + 1 = 8 + 1 = 9.
2. Let x
be the first positive even number
x +2 be the second positive even number
x ( x+2 ) = 120
x2 + 2x = 120
 Checking:
2
x + 2x – 120 = 0
x ( x+2 ) = 120
(x +12)(x – 10) = 0
10(12) = 120
x + 12 = 0 ; x – 10 = 0
120 = 120
x = -12 ;
x = 10
10 is the first positive even number; -12 is the extraneous solution.
x + 2 = 10 + 2 = 12
12 is the second positive even number
3. Let x
be the first odd integer
x +2 be the second odd integer
x ( x+2 ) = 1023
x2 + 2x = 1023
x2 + 2x – 1023 = 0
(x +33)(x – 31) = 0
x + 33 = 0 ; x – 31 = 0
x = -33 ;
x = 31
 Checking:
x ( x+2 ) = 120
10(12) = 120
120 = 120
31 is the first odd integer; -33 is the extraneous solution.
x + 2 = 31 + 2 = 33
33 is the second odd integer
H. EVALUATE
Evaluation is done by letting the students check their work, discussing the
answers of the problems given. The teacher should be quick in trying to know what
percentage of students got the correct answer/ solved the problem correctly to decide
(Reflection) if re-teaching or giving another topic will be done next meeting.
V. Assignment / Enrichment
1. Find two consecutive numbers whose product is 600.
2. Find two consecutive even numbers whose product is 80.
3. Two consecutive odd integers gives the product 2549 when multiplied.
What are these integers?
Reflection:
A. No. of learners achieve 80%: ____
B. No. of learners who require additional activities for remediation: ___
C. Did the remedial lessons work? ___
D. No. of learners who have caught up the lesson: ___
E. No. of learners who continue to require remediation: ___
F. Which of my teaching strategies worked well? Why did these work? ___
G. What difficulties did I encounter which my principal or supervisor help me solve? ___
H. What innovation or localized materials did I used/discover which I wish to share with other
teacher? ___