DLL Gen Math Week 4
September 13, 2022 | Author: Anonymous | Category: N/A
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School Teacher Teaching Dates and Time Week 4
GRADES 1 to 12 DAILY LESSON LOG
Day 1
Day 2
Grade Level 11 Learning Area MATHEMATICS Quarter 1
Day 3
Day 4
I. OBJECTIVES
Objectives must be met over the week and connected to the curriculum standards. standards . To meet the objectives, necessary procedures must be followed and if needed, additional lessons exercises and remedial activities activitie s may be done for developing content knowledge and competencies. competencies . These are assesse assessed d using Formative Assessment strategies. strategie s. Valuing objectives support the learning of content and competencies and enable children to find significance and joy in learning the lessons. Weekly objectives shall be derived from the curriculum guides. The learners demonstrates understanding of key concepts of inverse functions, exponential functions, and logarithmic A. Content Standards B. Performance Standards C. Learning Competencies/Objectives
II. CONTENT
functions.. The learner is able to apply the concepts of inverse functions, exponential functions, and logarithmic functions to formulate and solve real-life problems with precision and accuracy. Finds the domain and range of Represents an inverse Determine the inverse of a Represents Represen ts real - life an inverse function. M11GMone-one function. M11GM- function through its: situations using one – (a) table of values, and (b) one functions. M11GM- Id-2 Id-4 graph. M11GM-Id-3 Id-1 FUNCTIONS AND THEIR GRAPHS.
III. LEARNING RESOURCES
there is a List the materials to be used in different days. Varied sources of materials sustain children’s interest in the lesson and learning. Ensure that there mix of concrete and manipulative materials as well as paper-based materials materials.. Hands-on learning promotes concept development. A. References 69-75 77-86 1. Teacher’s Guide 66-67 pages 60-61 62-67 2. Learner’s Materials pages General Mathematics by General Mathematics by 3. Textbook pages Frelie B. Tan- Faylogna Oronce, pp. 40-45 4.
pp.76-79.. pp.76-79
5. Additional Materials from Learning Resource (LR) portal B. Other Learning Resources IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson
B. Establishing a purpose for the lesson
Let the students recall on the concepts of one- one function. Let them give examples showing oneone relationship?
What is the importance of having one- one relationship?
Ask the students if they still remember table of values that represent one-one function.
The concepts of one- one function is important for the next lesson because a function has an inverse if it is one- one. Give a real life situation Give an example of a table C. Presenting of values in the board. examples/instances to the students and let them identify if the given Consider the table of values of the new lesson relation is a function and for the function given by the equation y = 2x - 1 given if it is a function below: determine whether it is
Review: What is the inverse function of the following: 1.{ (1,2) , (2,4), ( 3,6), (4,8) } 2.{ (mom,dad), (sis,bro), ( tito, tita) } Describe the coordinates coordinates of your answer in 1 and 2.
The students are given jumbled words and let the student come to answer using the same group. The first group to answer with the highest number of correct are declared winner. Fucnoint- the set of ordered pairs such that for every x, there correspond a unique y. Mainod- the x- value of the ordered pair Geran- the y- value of the ordered pair Serevin- a function that is derived from a given function by interchanging interchang ing the 2 variables, x and y
Ask the students if they have an idea on how to graph the inverse of the given function.
After the preliminary activity the group is given set of equations and let them give the inverse of the function.
Present a word problem that will guide the students. Cooperative Learning (Group of 5) Present a
The students will make a table of values from the given equations and its inverse.
Situation: Rey’s Mother
one- one.(The teacher may refer to TG p.6467.)
X y
-3 -7
-2 -5
-1 --3 3
0 --1 1
1 1
2 3
3 5
is a domestic helper in Hong Kong. He wants to buy books books for his study. study. She sent dollars for the requirements. requireme nts. The exchange rate was 1.00 $ to P 44.00.the table by Complete converting Dollar into pesos. $ 1 5 10 50 100 P
D. Discussing new concepts and practicing new skills #1
Tell the students that A function f(x) is a
Let the students interchange the values of x and y in the
The students will answer the given guide
The students will give the domain and range of the given inverse
one-one function if no two elements in the domain of f corresponds to the same element in the range of f.
given table of values and they will create a new equation from the table of values.
questions: 1. State the procedure you performed on the number of Hong Kong dollars to obtain the number of pesos. 2. Let p represent pesos and d represent dollars. Write an equation for the
equations.
function dollars input andthat pesos as as output. 3. Write an equation that converts pesos to the dollars using the equation in (c). 4. Switch the role of P and $. E. Discussing new
Let the students go to
The students will be given
The students will present
After knowing the value of its
concepts and practicing new skills #2
F. Developing mastery (Leads to Formative Assessment)
G. Finding practical application of concepts and skills in daily living
H. Making generalizations and abstraction about the lessons.
another function in a form of equation and they will analyze how to get the inverse of this equation.
the table of values of the original function and its inverse. Let the students find the difference.
domain and range of the inverse function, let the students draw the graph of the two.
Let the students have their
From the table of values,
From the given graph, the teacher
the situation situation and present it to the class by group.
own ways to get the inverse of the function. The students may use different strategies as long as they arrive in the correct answer.
let the students sketch the graph of the original equation and on the inverse equation.. (The teacher may call a student to do this and let the other students observe.)
will ask the following questions: 1. What is the relationship of the domain of the given function to the range of its inverse function? 2. What is the relationship of the range of the given function to the domain of its inverse function?
The students will realize that there are many situations in real life that shows one- one functions.
Let the students give a mapping diagram of real life situations that illustrates inverse functions.
The students will observe the two graphs presented on on the board and they will write what their own insights from the lesson. Graphing inverse functions Given the graph of a
The students will have their own understanding on the concept of inverse function and they will relate it to the real-life.
their respective group. They will choose a real life situation in the community that shows one-one function. The students will act on
A function f(x) is a one-one function if no two
Let f be a one-to-one function with domain A and range B. Then the inverse of
elements in the domain of f corresponds to the same element in the range of f.
one-to-one function, the f, denoted f -1, is a function with graph of its inverse can be obtained by domain B and range A reflecting the graph denoted by f -1(y) = x if and about the line y = x. only if f(x) = y for any y in B. To find the inverse: Follow the following steps: 1.Replace f(x) with y 2.Interchange x and y 3.Solve for the new y from the equation in
1. Define and give examples of an inverse function. 2. Identifying the domain and range of an inverse function. 3. Find the relationship of the domain of the given function to the range of its inverse function? 4. Find the relationship of the range of the given function to the domain of its inverse function?
step 2. 4. Replace the new y with f -1(x). I. Evaluating learning
Identify if the given reallife situations represents a one- one function.
Determine the Fill up the table with the correct inverse of the range of the function : following table of 1. F ( x) = x – 10 10
1. Books to Authors 2. SIM cards to cell phone numbers numbers 3. True or False Questions to answers 4. A mother and father relationship
values and graph. (1) X Y
Determine the inverse of the
following functions if there’s any. 1. M(x) = x +2 2. R(x) = (x + 3) 2 3. D(x) = 2x – 7 7 4. f(x) = 2x + 1
X y
20 68 (2) 3 2
30 86
50 122
-3 -1
-6 3
(3)
100 212 6 -1
(4)
X F ( x)
10
11
12
13
2. F ( x) = 2x + 1 X F ( x)
1
2
3
4
Fill up the table with the correct domain of the function :
.
3. F ( x) = x + 10
3x - 4 .
X F ( x)
0
1
2
3
4. F ( x) = x – 1 1/ 2 X F ( x)
J. Additional activities for application or remediation
REMARKS
Which of the following relations is a one-to-one function?
Determine if f and g are inverses of each other. 1. f(x) = 3x +5 , g(x) = x-5
3 1. { (0,0),(1,1), (0,0),(1,1), (2,8), 2. f(x) = x3 , g(x) = 3√x (3,27), (4,64)} 2. {(-2,4), (1,1).(0,0),(1,1),(2,4)} 3. {(0,4),(1,5),(2,6),(3,7),...( n,n+4),...}
Let the students make their own table of values and let them draw the graph.
3
5
7
9
It is optional for the teacher to give additional activities.
REFLECTION
Reflect on your teaching and assess yourself yourself as a teacher. Think about your students’ progress this week. What works? What else needs to be done to help the students learn? Identify what help your instructional supervisors can provide for you so when you meet them, you can ask them relevant questions. questions .
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 with 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 or supervisor can help me solve?
G. What innovation or localized materials did I use/discover which I wish to share with other teachers?
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