Mathematics Resource Package: I. Objectives
Mathematics Resource Package: I. Objectives
Mathematics Resource Package: I. Objectives
I. OBJECTIVES
Knowledge Identifies whether the given systems of linear
equations in two variables is a solution or not.
Skill Solves systems of linear equations in two
variables by graphing.
Attitude Collaborates to the other students during group
work activity.
Solving systems of linear equations in two variables
II. CONTENT
using graphing.
A. References
1. Teacher’s Guide DepEd Mathematics Teacher’s Guide 8. pp. 297-299,
Pages 302,307
2. Learner’s DepEd Mathematics Learners Module 8, pp. 264-271
Materials Pages
3. Textbook Pages Intermediate Algebra II, pp. 12 - 13
4. Additional Graphing Board, Graphing Paper
Materials
5. Learning Resources
(LR) portal
B. Other Learning GeoGebra Application
Resources
IV. PROCEDURES
A. Reviewing or ACTIVITY: Exploration
presenting the new
Answer:
B. Establishing a
purpose for the lesson Motive Questions:
1. How do you describe the graph of the system of
equations? (The graph is either a system of consistent and
independent equations, system of consistent and
dependent equations, and system of inconsistent
equations.)
2. Are the graphs intersecting lines? If yes, what are the
coordinates of the lines? (Yes, the coordinates are (-2, 5).)
3. What do you think do the coordinates of the point of
intersection of the lines mean? (The coordinates of the
point of the intersection of the lines mean the solution of
the equations.)
C. Presenting examples EXAMPLES:
of the new lesson Find the solutions of the following systems of linear
equations graphically.
(a) {2 x+ y=7
−x + y=1
(b) { 3 x+ y=4
3 x− y=−5
(c)
{ x−2=−5
2 x−4 y=−10
Answer:
1. Solution: (1, 1) 2. Solution: (4, -2)
Solution:
(1) 2x + 3y = 16 (2) 3x – y = 2
2(2) + 3(4) = 16 3(2) – 4 = 2
4 + 12 = 16 6–4=2
16 = 16 2=2
1. {xy=x+
+ y =−7
1
4. {2 x−3
x + y=4
y=3
2. {x +5x−y=−7
y =5
5. {5 x−3
y=5 x−2
y =−14
3. {23y=4−6
x+ y=2
x
6. {32yx−3 y=5
=10+2 x
Answer:
1. Solution: (-4, -3) 4. Solution: (3, 1)
Answer:
Let y = age of Mother
x = age of her son
Mother is three times as old as her son so, we have
y = 3x (1).
In ten years, Mother will be two times as old as her son.
Thus, we have y + 10 = 2(x + 10) (2).
Solve for y in terms of x in equation (2).
y = 2x + 10
Thus, we have the system
{ y=3 x (1)
y=2 x+10( 2)
Answer:
1. Solution: (1,0) 2. Solution: (1/2, 1/3)
J. Additional
Activities for A. Identify whether the given ordered pair is the solution
application or of the given system.
remediation
1. (6, -8) x +2y + 10 = 0
2x – 3y + 30 = 0
2. (3, -2) 2x – y = 8
y + 3x = 7
3. (5, 2) 4x + 3y = 26
3x + 7y = 29
y+2=0
Answer:
1. not a solution
2. solution
3. solution
4. solution
5. solution
V. REMARKS
VI. REFLECTION
A. No. of learners who A. ___ No. Of learners who earned 80% in the evaluation
earned 80% in the
evaluation
B. No. of learners who B. ___ No. of learners who require additional activities
require additional for remediaton
activities for remediation
C. Did the remedial C. Did the remedial lessons work? ____ No. of learners
lessons work? No. of who have caught up the lesson
learners who have caught
up the lesson
D. No. of learners who D. ___ No. of learners who continue to require
continue to require remediation
remediation
E. Which of my teaching Strategies used that work well:
strategies worked well? ____ Group collaboration
Why did these work? ____ Games
____ Powerpoint Presentation
____ Answering preliminary activities/exercises
____ Discussion
____ Case Method
____ Think-Pair-Share (TPS)
____ Rereading of Paragraphs/Poems/Stories
____ Differentiated Instruction
____ Role Playing/Drama
____ Discovery/Method
____ Lecture Method
Why?
____ Complete IMs
____ Availability of Materials
____ Pupil’s eagerness to learn
____ Group member’s Cooperation in doing their tasks
F. What difficulties did I ____ Bullying among pupils
ATTACHMENT
Day: 1 and 2
DISCUSSIONS:
SUPPLEMENTARY ACTIVITIES
Note: The activities included here will be used only when needed.
DIRECTION: Find the solution of the system of linear equations by graphing. Use a
graph paper.
1. {xx+− y=−4
y=8
6. {53x−
x + y =5
y =3
2. {xx−=−2
y=0
7. {22x−y−x=0
y =−6
3. { x+y−x=0
y=2
8. {3xx+2+2y=3
y=5
4. {2xx−+ y=4
y =8
9. {23xx+3+2y=−2
y=2
Answer:
1. (2, 6) 6. (1, 2)
3. (1, 1) 8. (1, 1)
REFERENCES
C. INTERNET SOURCES: