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QUARTER I
Week 1
Subject:
GENERAL
MATHEMATICS
Date:
________________
Grade Level: 11
Day: 2 (Lesson 2)
Content Standard
The learner demonstrates understanding of key concepts of
functions.
Performance
Standard
The learner is able to accurately construct mathematical models to
represent real-life situations using functions.
Learning
Competency
M11GM-Ia-2
The learner evaluates a function.
I. OBJECTIVES
Knowledge:
Skills:
Affective:
II. CONTENT
The learner:
Finds the function value of f(x) at a specific value of x;
Evaluates functions given a specific value of x;
Shows accuracy in evaluating a function.
Evaluating Functions
III. LEARNING RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Materials
Pages
3. Textbook
Pages
4. Additional
Materials
5. Learning
Resources
(LR) portal
B. Other Learning
Resources
TG for SHS General Mathematics, pp. 11-13
LM in General Mathematics, pp. 10-12
General Mathematics by Orland Oronce Series 2016
Slide Decks on the Topic
Teacher’s Guide and Learner’s Material
General Mathematics, Diwa Publishing, Senior High School
Series. 2016
IV. PROCEDURES
A. Reviewing or
presenting the new
lesson
Recall the definition of a function.
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)
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B. Establishing a
purpose for the
lesson
Ask: What would happen if a sack of rice grains is poured into
the opening of a working milling machine?
C. Presenting
examples of the
new lesson
Make a discussion about evaluating a function and say:
If one thinks of functions as a function machine, evaluating a
function is analogous to providing our machines with a valid
input.
 Evaluating a function means replacing the variable in the
function, in this case x, with a value from the function’s
domain and computing for the result. To denote that we are
evaluating f at a for some a in the domain of f, we write f(a).
 If one thinks of functions as a machine, evaluating a function
is similar to providing our machines with a valid input.
D. Discussing new
concepts and
practicing new
skills #1
(See Example TG, p. 12). Take for example, (a) evaluate
f ( x)  2 x  1 at x  1.5 .
E. Discussing new
concepts and
practicing new
skills #2
Ask: What is the function value of f as defined in Example 1 if
evaluated at f (3x  1) ?
F. Developing
Mastery
Step 1. f ( x)  2 x  1
Given
Step 1. f (1.5)  2(1.5)  1
By substitution
Step 2. f (1.5)  3.0  1
Closure Property of
Multiplication
Step 3. f (1.5)  4
Closure Property
of Addition
Step 4. Thus, the function value is 4.
Proceed to Example 2 on the same page. Or you may opt to
change the values of x to find the function values.
Below is the thorough discussion of the solution.
Step 1. f ( x)  2 x  1
Given
Step 2. f (3x  1)  2(3x  1)  1
by Substitution
Step 3. f (3x  1)  6 x  2  1
Distributive
Property
Step 4. f (3x  1)  6 x  1
Closure
Property of Addition
Step 5. Thus, the function value is 6x 1 .
Let the learners work with a partner. Assign the problem below.
The solution is provided for you. The teacher will have to mill
around to facilitate the group activity. Call a representative to
discuss the solution in the class. ( A classroom reward system
could be used to further encourage and motivate the learners to
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)
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participate in the activity, say the first five groups earns extra
points.)
Evaluate q( x)  x 2  2 x  2 at q (2 x  3) .
Solution:
Step 1. q( x)  x 2  2 x  2
Given
Step 2. q(2 x  3)  (2 x  3)  2(2 x  3)  2 by
Substitution
Step 3. q(2 x  3)  4 x 2  12 x  9  4 x  6  2
Squaring, DPMA
Step 4. q(2 x  3)  4 x 2  8x  5
Combining
similar terms
Step 5. Thus, the function value is 4 x 2  8 x  5 .
Seatwork:
2
G. Finding practical
applications of
concepts and skills
in daily living
1. Mark started selling snacks in the nearby school. In one day
he spends P200 for rent and P25 for each snack item he prepares.
His expenses in a single day can be expressed as the function
C(x) = 25x + 200, where x is the number of items and C(x) is his
daily expenses in pesos. How much are his expenses if he
prepares 100 snack items? 150 snack items?
Answer:
P2,700 and P3,950, respectively.
2. The function for the height of an object dropped from 100meter tall platform at time t seconds is approximated by s(t) = 5(𝑡 2 +
100. 𝑇ℎ𝑖𝑠 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑖𝑠 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝑎𝑛 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡
100𝑚
𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦. ) What is the height of the object after 2
𝑠2
seconds? after 4 seconds?
Answer:
80 and 20 meters, respectively.
H. Making
Generalizations
and abstractions
about the lesson
I.
Evaluating
learning
Ask: How is evaluating a function done?
Evaluating a function can be done replacing the variable in the
function, in this case x, with a value from the function’s domain
and computing for the result. To denote that we are evaluating f
at a for some a in the domain of f, we write f(a).
See attachment.
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)
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J. Additional
Activities for
application or
remediation
For remediation, assign learners to pick 2 problems that they did
not worked on in the previous activity found in part I. Peer
tutoring is desired for this purpose.
For enrichment, assign Seatwork 5 on p. 11. The same rubric
should be used for grading the learners’ outputs.
V.
REMARKS
VI.
REFLECTION
A. No. of learners who
earned 80% in the evaluation
B. No. of learners who
require additional activities
for remediation
C. Did the remedial lessons
work? No. of learners who
have caught up the lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well? Why
did these work?
F. What difficulties did I
encounter which my
principal and supervisor help
me solve?
A. ____ No. of learners who earned 80% in the
evaluation
B. ____ No. of learners who require additional activities
for remediation
C. Did the remedial lessons work? _____ No. of
learners who have caught up the lesson.
D. ___ No. of learners who continue to require
remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Poweerpoint
presentation
Answering preliminary activities/exercises
___ Discussion
___ Differentiated
Instruction
___ Case Method
___Role Playing
/Drama
___ Think-Pair-Share (TPS)
___ Doscivery Method
___ Rereading of Paragraphs/Poems/Stories ___ Lecture Method
Why?
___ Complete Ims
___ Availability of Materials
___ Pupil’s eagerness to learn
___ Group member’s cooperation in doing their tasks
___ Bullying among learners
___ Equipment (AVR/LCD)
___ Learner’s behavior/attitude
___
Science/Computer/Internet Lab
___ Colorful Ims
___ Additional Clerical
Works
___ Unavailable Technology
___ Reading Readiness
G. What innovation or
localized I used/discover
which I wish to share with
other teacher?
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)
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EVALUATION
WORKSHEET No. ___
1. Evaluate the following functions at x = 3.
a) f(x) = x – 3
b. g(x) = 𝑥 3 − 3𝑥 + 5
3
c. h(x) = √𝑥 3 + 𝑥 + 3
d. p(x) =
𝑥 2 +1
𝑥−4
𝑥+3
2. For what values of x can we not evaluate the function f(x) = 𝑥 2 −4.
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)
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ANSWER KEY
1.
2. The domain of the function is given by {𝑥: 𝑥 ∈ ℝ, 𝑥 ≠ ±2}
Prepared by: MERCYDITHA D. ENOLPE
SHS Teacher (Zamboanguita-JMLMHS)