daily lesson plan for math 8 Week-2.docx

dll week 2

1. GRADE 8
DAILY LESSON
LOG
School SURABAY NATIONAL HIGH SCHOOL Grade Level 8
Teacher B. CHIONG Learning AreaMATHEMATICS
Week 2 (September 30- October 4, 2024) Quarter SECOND
Session 1 Session 2 Session 3 Session 4 Session 5
I. OBJECTIVES
1.Content Standards The learner demonstrates understanding of key concepts of factors of linear inequalities in two variables, systems of linear inequalities in two
variables and linear functions.
2.Performance
Standards
The learner is able to formulate and solve accurately real-life problems involving linear inequalities in two variables, and linear functions.
3.Learning
Competencies /
Objectives
Illustrates linear inequalities in two variables
(MBAL-IIa-1)
a. Identify linear inequality
from linear equation.
b. Translate verbal phrases
to mathematical
inequality.
c. Appreciate the concept of
linear inequality in
two variables.
Differentiate linear inequalities in two variables
from linear equations in two variables.
(MBAL-IIa-2)
a. Identify the solution of a
linear equation or
inequality in two
variables.
b. Determine whether a
point is a solution of a
linear inequality or not.
c. Appreciate the concept of linear inequality in
two variables.
Graph linear Inequalities in two variables
(MBAL-IIa-3)
a. Determine the solution
set of a linear inequality
in two variables.
b. Draw the graph of the
solution set of linear
inequalities in two
variables.
c. Appreciate the concept of
graphing of linear
inequalities in two
variables and apply in a
real life situation.
II. CONTENT CIVIL SERVICE
ACTIVITY
Linear Inequalities In Two VariablesLinear Inequalities In Two VariablesLinear Inequalities In Two VariablesDISTRICT TEACHERS’
DAY CELEBRATION
III. LEARNING
RESOURCES
A.References
1. Teacher’s
Guide
pages 200-203 pages 200-203 pages 204- 206
2. Learner’s
Materials
pages 220-222 pages 220-222 pages 222 – 225
3. Textbook Next Century Mathematics: Intermediate Algebra,
pages 83 - 84
Bernabe, Julieta G, et al.,
Next Century Mathematics: Intermediate Algebra,
pages 83 - 84
Next Century Mathematics: Intermediate Algebra,
pages 83 - 84

2. Intermediate Algebra, pages 38-39
Herrera Lucia D, et al Elementary Algebra Il, pages 411
– 413
4. Additional
Materials
from Learning
Resource (LR)
portal
http://lrmds.deped.gov.ph/. http://lrmds.deped.gov.ph/. http://lrmds.deped.gov.ph/.
B.Other Learning
Resources
Grade 8 LCTG by Dep Ed Mathematics 2016Grade 8 LCTG by Dep Ed Mathematics 2016Grade 8 LCTG by Dep Ed Mathematics 2016
Laptop, LCD, Graph Board, Graphing paper, Ruler and
Pencil
IV. PROCEDURES
A.Reviewing
previous
lesson or
presenting
the new
lesson
LESS WORDS, MORE POINTS
Fill in the appropriate words that will make each
statement true. Each group should defend their
answer to become acceptable. The group, who can
get the most number of points, will win the game.
Which of the following points is a solution to the
following linear inequalities? Explain your
answer.
1. 2x – y > - 3
(3, 6) (4, 11) (2, 7)
2. y ≥ -6x + 1
(2, -11) (-3, -8) (-5, 6)
3. 5x + y > 10
(0, -3) (3, -5) (4, 8)
4. y ≤ x - 9
(2, -5) (9, -3) (12, 3)
5. y < 5x -3
(3, 5) (2, 7) (3, 0 )
In an Entrepreneurship class, Joanna will receive
3 points for every graham balls that she can sell
and 2 points for every yema candy that she can
sell. Identify five combinations of graham balls
and yema candies that she can sell to earn exactly
30 points. Write your answer in the table then
graph it. Did you form a line?
B.Establishing
a purpose for
the lesson
Can we use “less’ and “more” in mathematics?
How can you translate these words in
mathematical sentence?
The solution of a linear equation is the set points
which lie on the line.
What differences are there between the graph of
a linear equation and the graph of a linear
inequality?

3. C.Presenting
examples/
instances of
the lesson
The words used in the activity are some of the
“Inequalities” that we use in a real life situation.
Let us study more examples and see its
translation in mathematical sentence.
The underlined words in the example above are
just few of the examples of inequalities that are
evident in a real life situation. These words can
be expressed using mathematical symbol.
A linear inequality in two variables is simply a
linear equation but instead of having an equal
sign (=) it will be replaced by an inequality sign.
The points (2, 7), (0, 3) and (-1, 1) are the points on
the line y = 2x + 3 and the solutions to the given
equation. To determine if it is true, substitute the
coordinates in the equation.
y = 2x + 3:
(2, 7)
x = 2 and y = 7
7 = 2(2) + 3
7 = 4 + 3
7=7 True
y=2x+3;(-1,1)
x=-1 and y=1
1=2(-1)+3
1=(-2)+3
1=1 True
y =2x + 3: (0,3)
x=0 and y=3
3=2(0)+3
3=0+3
3=3 True
Likewise, in determining if a point is a solution to
the linear inequality in two variables, substitute
the coordinates to the inequality and apply the
Law of Trichotomy.
Example: Determine if the points (5, 8), (0, 0), and
(10, 10) are solutions to the linear inequality
2x + 5y > 10.
2x + 5y ≥ 10;(5,0)
x = 5 and y = 0
2(5) + 5(0) ≥ 10
10 + 0 ≥ 10
10 ≥ 10 False
Thus, (0, 0) is a solution to 2x + 5y > 10
Let us now try to replace “=” to ≥, so it becomes
y ≥ 2x + 3. We can notice that the points on the
line are still part of the solution therefore we will
still use a solid line. Points (-6, -2), (-3, 3), (-2, 0),
(1, 7), and (-5, -4) are also solutions to the
inequality y ≥ 2x + 3. Observe the example
below:
The graph of the inequality y ≥ 2x + 3 is half of
the plane. It means that all the points on the left
side of the line is part of the solution and as well
as the points on the line.
Let us now try to replace “=” to ≥, so it becomes
y ≥ 2x + 3. We can notice that the points on the
line are still part of the solution therefore we will
still use a solid line. Points (-6, -2), (-3, 3), (-2, 0),
(1, 7), and (-5, -4) are also solutions to the
inequality y ≥ 2x + 3. Observe the example

4. -----------------------------
2x + 5y ≥ 10;(0,0)
x = 0 and y = 0
2(0) + 5(0) ≥ 10
0 + 0 ≥ 10
0 ≥ 10 False
Thus, (0, 0) is not a solution to 2x + 5y > 10
--------------------------------
2x + 5y ≥ 10;(-2,3)
x = -2 and y = 3
2(-2) + 5(3) ≥ 10
(-4) + 15 ≥ 10
11 ≥ 10 True
Thus, (5, 0) is a solution to 2x + 5y > 10
below
D.Discussing
new concepts
and
practicing
new skills
#1
1. Why do you think the following inequality
symbols are appropriate to use in each
example?
2. What are the different
inequality symbols?
3. How does a linear
inequality differ from
linear equation?
4. What are the other
translations for each
inequality symbols aside
from the listed in
above example?
1. What can you say about
the solution of a
linear equation?
2. When can you say that a
point is a solution to
a linear inequality in two
variables?
3. How can you solve if a
point is a solution to a
linear equation or
inequality in two
variables?
For the given example y ≥ 2x + 3
1. What can you observe about the points
2. Identify the 5 points from the left side of the
line, are they also solutions to the inequality?
3. Take a point on the right side of the line, is it
part of the solution?
4. What can you conclude?
E.Discussing
new concepts
and
practicing
new skills
#2
Tell whether a given mathematical sentence is a
linear inequality or not. If it is, encircle the
inequality symbol used.
1. 2x – 3y > 5
2. x + 4y = 6
3. a +8 < 6b
4. 100 ≥ s + 2r
5. 5( x + 5) ≠ 14p
Fill in the blanks then state whether each given
ordered pair is a solution of the inequality.
1. x + 2y ≤ 8; (6,1)
x = ___ and y = ___
___ + 2 (___) ≤ 8
6 + ___ ≤ 8
___ ≤ 8
________
Graph the following linear inequalities in two
variables. The points on the line are already
given. In (a) check the line that you are going to
use; in (b) using the origin (0, 0) tell whether it is
a solution or not; and in (c) shade the half plane of
the solution.

5. Thus, __________
_______________
identify x and y
substitute the values
of x and y
simplify
True or False
Write your conclusion
2. x - ≥ -2: (-6, -8)
x + ___ and y = ___
___ - ( ___)≥-2
-6 + ___≥-2
___≥-2
___________
Thus, _______
____________

3. 2x – y 7: (3, -1)
x = ___ and y = ____
2(___)- ___< 7
___ + ___< 7
___< 7
____________
Thus, _______
____________
4. 3x – y > 6;(0,0)
x = ___ and y = ____
3(___) + ___>6
____ + ___>6
___
__________
Thus, ______
___________
5. x + y ≤ 8; (5,4)
x = ___ and y = ___
___ +___ ≤ 8
___ ≤ 8
__________
Thus, _____

6. __________
F.Developing
mastery
(Leads to
Formative
Assessment
3)
Translate the following verbal sentences to
mathematical inequalities.
1. Five is less than thrice a
number b added to c 2.
Twenty-four added by a
certain number y is
not less than a number z.
3. Twice a number w is
greater than or equal to
a number z.
4. A certain number g
subtracted from 12 is less
than or equal to four
times a number h.
5. A certain number r is not
equal to twice a
number u added by 8.
Connect the following coordinates to the linear
inequality that makes them a solution. Show your
solution.
1. (8,2) •
2. (-1, 2) • • 2x – y > 5
3. (0, 5) •
4. (0,0) • • x + 2y ≤ 1
5. (2, 5) •
Graph the following linear inequalities in two
variables.
1. 4x – 3y < 12
2. x – 2y ≥ 4
3. x + 4y < 4
4. y > 2x – 6
5. y ≤ ½ x – 3

7. G.Finding
practical
applications
of concepts
and skills in
daily living.
Classify whether the situation illustrates an
inequality or not. If yes, then write the inequality
model.
1 A kilo of grapes (g) in
more expensive than a
kilo of oranges (o)
2.The number of males (m)
less the number of
females (f) in the
classroom is 8.
3. The municipality of Tanza
(t) has less
population than the
municipality of Silang (s).
4. Trece Martires City
Gynasium (m) can
accommodate at most
5000 people.
5. The minimum wage (w) of the employees in
EPZA is 315 Php per day
Determine 2 solution for each of the following
linear inequalities. Show your solution.
1. 5x + 2y < 17 ; x = 3
2. 3x - 8y ≤ 12 ; x = 0
3. - 10x - 2y > 7 ; x = -2
4. x + 5y ≥ 20 ; y = -1
5. 3x +2y < 21 ; y = 4
H.Making
generalizatio
ns and
abstractions
about the
lesson
A linear inequality in two variables is a
mathematical expression similar to linear
equation that makes use of inequality symbols
such as >, <, ≥, ≤, and ≠ instead of =.
The solution of a linear equation is the
set of points which lies on the line.
A solution of a linear inequality in two
variables is an ordered pair (x, y)
which makes the equation or inequality
true.
The steps in graphing a linear inequality in two
variables are as follows:
1. Get the corresponding
equation by replacing
the inequality sign with an
equality sign.
2. Graph the equation using
broken line if the
inequality is > or <.
However, if it is ≥ or ≤,
then use a solid line. 3.
Use the origin as a
test point to determine the
shaded region. If the
origin is a solution to the
equation then shade the
half plane where the
origin lies;

8. I.Evaluating
learning
Rewrite the following situations in to a linear
inequality model.
1. The sum of a fifty peso
bill (f) and a hundred
peso bill (h) is not more
than five hundred pesos.
2. Martha bought 3 boxes of
buko pie (p) and 2
boxes of buko tart (t) in a
store in Tagaytay.
She paid greater than
500 pesos.
3. Michael’s average grade
in Math (m) and
English (e) should be at
least 78 for him to
pass.
4. The cost of two blouses
(b) and three pants
(p) is less than 1000 Php.
5. In a river resort in Indang,
Cavite the entrance
fee for 1 adult (a) and 1
kid (k) is less than
250 Php.
Which of the following points is a solution to the
following equations/ inequalities? Encircle your
answer/s.
1. 3x + y > - 6
(3, 6) (4, 11) (2, 7)
2. y > 5x + 2
(2, -11) (-3, -8) (-5, 6)
3. -3x + 6y ≥ 10
(0, -3) (3, -5) (4, 8)
4. y ≤ 2x - 5
(2, -5) (9, -3) (12, 3)
5. 2y < 5x + 3
(3, 5) (2, 7) (3, 0)
From the graphs below, identify the graph that
will satisfy each inequality. Write the letter of the
correct answer.
1. y > x + 2
2. x + 3y < 6
3. 4x – 2y ≥ 8
4. x – y ≥ 3
5. y < -2/3x + 2

9. J.Additional
activities for
application
or
remediation.
1. Look around the school
and write at least 3
situations where in linear
inequality is being used.
Take a picture of it and
write the situation below.
2. Solve the following
inequality if x = 2 and
y = 3:
a. 2x + 3y = 7
b. 5x – 3y > 8
1. a. Which ordered pair
satisfies the inequality
3/2 x - 1/4y ≤ 1 ?
a. . (0, -5) b. (3, -5)
c. (0, 1) d. (6, 0)
b. Graph x + y = 6 in a
Cartesian plane
Identify 5 points which
are solution of the
inequality x + y > 6,
then plot them on the
same plane. Make a
conjecture about it.
2. Study how to graph linear
inequality in two
variables. Write the step
Explain the difference between the graph of
4x – 3y = 12, 4x – 3y > 12 and 4x – 3y < 12.

10. by step process on your
notebook.
V. REMARKS
VI. REFLECTION
1.No.of learners who earned
80% on the formative
assessment
2.No.of learners who require
additional activities for
remediation.
3.Did the remedial lessons
work? No.of learners who have
caught up with the lesson.
4.No.of learners who continue
to require remediation
5.Which of my teaching
strategies worked well? Why
did these work?
6.What difficulties did I
encounter which my principal
or supervisor can help me
solve?
Prepared By:BEN YHAZEER S. CHIONG
Teacher-III
Checked By: Attested By: Noted By:
ARNOLD C. AYAON VENJIE G. BALIDAD RIZA D. MORADOS
Master Teacher I Head Teacher III Principal IV