QUARTER I
Week 1
Subject:
GENERAL
MATHEMATICS
Grade Level: 11
Date:
________________
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
TG for SHS General Mathematics, pp. 11-13
2. Learner’s
Materials
Pages
LM in General Mathematics, pp. 10-12
3. Textbook
Pages
General Mathematics by Orland Oronce Series 2016
4. Additional
Materials
Slide Decks on the Topic
5. Learning
Resources
(LR) portal
B. Other Learning
Resources
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
B. Establishing a
purpose for the
lesson
Recall the definition of a function.
C.
Make a discussion about evaluating a function and say:
Presenting
examples of the
new lesson
Ask: What would happen if a sack of rice grains is poured into the opening
of a working milling machine?
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
at
Step 1.
Given
Step 1.
By substitution
Step 2.
Closure Property of Multiplication
Step 3.
Step 4. Thus, the function value is
4.
E. Discussing new
concepts and
practicing new
skills #2
Closure Property of Addition
Ask: What is the function value of f as defined in Example 1 if
evaluated at
?
Below is the thorough discussion of the solution.
Step 1.
Given
Step 2.
by Substitution
Step 3.
Property
Distributive
Step 4.
Property of Addition
Step 5. Thus, the function value is
Closure
.
F. Developing
Mastery
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
participate in the activity, say the first five groups earns extra
points.)
Evaluate
at
.
Solution:
Step 1.
Given
Step 2.
Substitution
by
Step 3.
Squaring, DPMA
Step 4.
terms
Combining similar
Step 5. Thus, the function value is
G. Finding practical
applications of
concepts and skills
in daily living
.
Seatwork:
1.
Mark started selling snacks in the nearby school. In one
dayhe 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
100-meter tall platform at time t seconds is approximated by s(t) =
-5(
𝑡�What is the height of the object after 2 seconds? after 4
seconds?2�+�100.�𝑇�ℎ𝑖�𝑠��𝑓�𝑜�𝑟�𝑚�𝑢�𝑙�𝑎��𝑖�𝑠��𝑏�𝑎�𝑠�𝑒�𝑑��𝑜�𝑛��𝑎�𝑛��
𝑎�𝑝�𝑝�𝑟�𝑜�𝑥�𝑖�𝑚�𝑎�𝑡�𝑒�𝑑��𝑣�𝑎�𝑙�𝑢�𝑒��
Answer:
80
H. Making
Generalizations
and abstractions
about the lesson
I.
Evaluating
learning
J. Additional
Activities for
application or
remediation
V.
VI.
and 20 meters, respectively.
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.
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.
REMARKS
REFLECTION
A. No. of learners who
earned 80% in the evaluation
B. No. of learners who
require additional activities
for remediation
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
C. Did the remedial lessons work? _____ No. of
learners who have caught up the lesson.
D. No. of learners who
continue to require
remediation
D. ___ No. of learners who continue to require
remediation
E. Which of my teaching
strategies worked well? Why
did these work?
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
F. What difficulties did I
encounter which my
___ Bullying among learners
principal and supervisor help ___ Learner’s behavior/attitude
Science/Computer/Internet Lab
me solve?
___ Colorful Ims
Works
___ Unavailable Technology
G. What innovation or
localized I used/discover
which I wish to share with
other teacher?
___ Equipment (AVR/LCD)
___
___ Additional Clerical
___ Reading Readiness
EVALUATION
WORKSHEET No. ___
1. Evaluate the following functions at x = 3.
a) f(x) = x – 3
b. g(x) = 𝑥�3�−�3𝑥��+�5
d. p(x) =c. h(x) = 3𝑥�1𝑥�+3423+�𝑥��+�3�𝑥�−
. For what values of x can we not evaluate the function f(x) =
𝑥�𝑥�2+−34�.
1
ANSWER KEY
2
.
3
. The domain of the function is given by {𝑥�:�𝑥�∈𝑅�,�𝑥�≠±2}