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GRADE 8 DAILY LESSON LOG School SURABAY NATIONAL HIGH SCHOOL Grade Level 8 Teacher B. CHIONG Learning Area MATHEMATICS Week 4 (October 14-18, 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 linear functions. 2.Performance Standards The learner is able to formulate and solve accurately real-life problems involving linear functions. 3.Learning Competencies / Objectives The learner illustrates a relation and a function. (M8AL-IIc-1) a. Define relation and function. b. Represent a relation in four ways: 1. Table 2. mapping diagram 3. graph 4. rule method c. Develop the value of perseverance in studying. The learner verifies if a given relation is a function. (M8AL-IIc-2) a. Differentiate a relation from a function. b. Determine if a relation is a function or not using the vertical line test. c. Appreciate the concept of relation and function in real-life situation. The learner verifies if a given relation is a function. (M8AL-IIc-2) a. Determine if a relation is a function given: 1. ordered pairs, 2. mapping, and 3. rules/equations. b. Express real-life situations into: 1. ordered pairs, 2. mapping, and 3. rules/equations. c. Appreciate the concept of relation and function in real-life situations. The learner performs determines dependent and independent variables. (M8AL-IIc-3) a. Define dependent and independent variables. b. Determine the dependent and independent variables. c. Appreciate new understanding on dependent and independent variables of a given function. The learner finds the domain and range of a function.(M8AL-IId-1) a. Differentiate domain from range. b. Identify the domain and range of a function given: 1. the ordered pairs, and 2. mapping. c. Appreciate the concept of domain and range in real-life situations. II. CONTENT Representations of Functions and Relations Representations of Functions and Relations Representations of Relations and Functions Dependent and Independent Variables Domain and Range of Function III. LEARNING RESOURCES A. References 1. Teacher’s Guide 155-182 168- 169 2. Learner’s Materials 138-144 151-152 pages148-152 pages 155-156 3. Textbook None None Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 22-23; Valtoribio, Advanced Algebra, Trigonometry and Statistics, pp. 4-5. Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 27-28 Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 11-12. 4. Additional Materials https://www.youtube.com/watch? https://www.youtube.com/watch?
from Learning Resource (LR) portal v=C5xcpNGeKCQ v=l4265qSL914 B. Other Learning Resources Laptop, Projector,Speaker LCTG Grade 8 by DepEd Cavite Mathematics,2016 Laptop, Projector,Speaker LCTG Grade 8 by DepEd Cavite Mathematics,2016 Grade 8 LCTG by DepEd Cavite Mathematics 2016, projector, laptop, power point presentation Grade 8 LCTG by DepEd Cavite Mathematics 2016, projector, laptop, power point presentation Grade 8 LCTG by DepEd Cavite Mathematics 2016, laptop, projector, powerpoint presentation, “Cabbage of Knowledge” IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson Where do I belong??? Description: This activity will enable you to write ordered pairs. Out of this activity, you can describe the relation of the products to its respective places. Directions: Group the following products in such a way that they are from the same places in Cavite. Kesong puti See weeds Pastillas de leche Smoked fish (tinapa) coconut Dried fish (tuyo) Coffee beans Fresh milk Banana shrimp Black pepper Choco milk Strawberry milk crab pineapple General Trias Rosario Amadeo SPOTTING ERRONEOUS COORDINATES Do the task as directed A. Lea indicated that A has coordinates (- 3,2) 1. Do you agree with Lea? 2. What makes Lea wrong? 3. How will you explain to her that she is wrong in a subtle way? B. Cris insisted that B has coordinates (-2,-4) while C has coordinates (-2,2). If yes, why? If no, state the correct coordinates of points of B and C “Find your Match!” Call on 8 volunteers. Give each student a strip of paper and instruct them to find their match. Teacher-students Boyfriend-girlfriend Parent-child God-creation 1. What did each pair represents? 2. How can you make your relationship with others work/function? Can you live without your  parents? Who among you lives with their  parents? Therefore, are you dependent or  independent individual? Cabbage of Knowledge Let the students pass around the “cabbage of knowledge” while a music is playing. Once the music stops, the student holding the cabbage will uncover a leaf and will have to define or describe the word written on each leaf. Dependent Function Independent Domain Relation Range B. Establishing Presentation of Objectives Presentation of Objectives A function is a relation where there is no Variables may be dependent or The domain of a function refers to
a purpose for the lesson repetition of the first element. dependent. Dependent variable depends on the independent variable while the independent variable controls the dependent variable. the first or x values in a set of ordered pairs, while the range is the set of the second or y values in a set of ordered pairs. C. Presenting examples/ instances of the lesson Exploratory Activity From the previous activity, form some ordered pairs using the format: ( product, place ) a. Column 1: __________ b. Column 2: __________ c. Column 3: __________ Based on the coordinates you have formulated, is there a repetition of the first coordinates? How about the second coordinates? Try to present the ordered pairs formed in table form. PRODUCTS MUNICIPALITY Now, try to make a mapping diagram to show the relation.  What can you say about the diagram you have formed?  What elements belong to the first set? To the second set?  Is there a repetition of the first Plot the following points in five separate Cartesian Plane. The relation between time and pay is an example of a function. Example: Notice that there is no repeated value for the first element. So, this is a function. This can also be represented through A. Ordered pairs {(2,200), (4,400), (6,600), (8, 800), (10, 1000)} B. Mapping This is an example of one-to-one correspondence. A correspondence may be classified as one- to-one, many-to-one, or one-to-many. One-to-One Correspondence Student I.D. No. - Developmental Activity If you study hard, what will  happen? If you spend much of your  allowance, what will happen? If you eat much, what will happen?  If you travelled long distance,  what will happen? From the previous questions given to you, we can determine the dependent and independent variable. In the first question, if you study hard, you said you will get high scores on tests, so you will get high grades. In the second question, if you spend much of your allowance, you said you will lose your money. In the third question, if you eat much, you said you will gain weight. In the fourth question, if you travelled long distance, there is larger amount of gasoline to be consumed. From those given situations, can you determine the dependent and independent variables? How did you identify the dependent and independent variables? Let’s have other examples. Classify the variables as dependent or independent. 1. cost of chicken and its weight 2. income of a worker and number of hours of work 3. perimeter of a square and its side Given the following set of ordered pairs, identify the x values and y values. 1. (4,5), (5,-4), (8,5), (-3,2), (6,1) 2. (0,3), (-1,5), (2,-4), (3,6), (4, -7) 3. (2,0), (0,9), (1,3), (-1,9), (3,7) 4. (-8,1), (4,-5), (6,0), (-7,8), (-5,2) 5. (-2,6), (4,-3), (-5,1), (4,0), (5,3) In the previous activity, how did you determine the domain and range? In mapping diagram, like What is the domain? What is the range?
coordinates? How about the second coordinates? The relations you have formed in the previous activities are all examples of a FUNCTION, as they are many-to-one correspondence. If the relation shows one-to-one correspondence it is also a function, but if the relation is one-to-many correspondence, then it is not a function. Aside from these three methods, function can also be represented by picture or graph, by equation and by rule. Situation: Suppose Tenten is working in Gen. Trias Dairy Raisers Multi-Purpose Cooperative at Santiago, Gen. Trias, Cavite and he earns ₱43 per hour. Questions: a. How much will Tenten earn if he works for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? b. Is his earnings related to the number of hours of work? How? Tenten’s earnings can be represented by some other way like graph, equation or rule. By graph By equation or by rule, Tenten’s earnings can be represented by y=43(h) Many-to-One Correspondence One-to-Many Correspondence C. Rule/Equation As the number of time (x) increases, the amount of pay (y) also increases. -What will be your pay if you worked for 1 hour? 15 hours? 20 hours? n hours? So, the rule for this function is y= 100x. 4. In mathematical equation, like for example, the linear function, y =3x- 5. If x=1, what will be the value of y? If x=0, what is y? If x=1, what is y? In these cases, which are the dependent and independent variables? D. Discussing new concepts and Video Presention diffentiating a relation and a function. From the previous activity, Is there a repetition of the first coordinates? The second coordinates?  Connect the given points from the first given point up to the last. 1. Among the types of correspondence, which ones are functions? Why? 2. Does one-to-one correspondence between elements always guarantee a function? How about one-to-one? What is dependent variable? What is independent variable? How can you differentiate the dependent and independent variable? How can you describe the domain and range of a function given the: a. ordered pairs b. mapping diagram?
practicing new skills #1  How can you describe each graph?  Draw vertical lines through the graph.  Does the vertical lines touch the graph?  How many times does the vertical line touch the graph? Justify your answer. 3. Does one-to-many correspondence between elements always guarantee a function? Justify your answer. E. Discussing new concepts and practicing new skills #2 A. What can you say about relation? B. Can you determine whether a relation is a function or a mere relation? How? C. What will be your reference that a relation is a function? D. Give real-life examples/ situations that can describe a function. A. Does each graph represent a function? Why or why not? B. If you are only given the graph, how can you determine if the graph represents a function? C. What do you call this method? Tell whether the following relations as function or not. 1. 2. 3. 4. y = 3x+9 5. x2 + y2 =16 6. (-1,2), (1,3), (1,5), (2,7) 7. (0,6), (-3,4), (3,5), (4,0), (6,-3) Fill in the blanks. 1. I consider the weight of chicken as a/an ________ variable because it ________ the cost of chicken. 2. I consider the cost if chicken as a/an ________ variable because it ________ on the weight of the chicken. 3. I consider the income of a worker as a/an _______ variable because it ________ on the number of hours the worker worked. 4. I consider the number of hours worked as a/an ________ variable because it ________ the income of the worker. 5. I consider the perimeter of a square as a/an ________ variable because it ________ on the length of its side. 6. I consider the length of the side of a square as a/an ________ variable because it ________ the perimeter of the square. Determine the domain and range given the following. 1. (2,0), (3,1), (3,7), (6,-1) 2. (3,0), (4,0), (5,0), (6,0) 3. (-1,9), (4,-1), (-4,1), (1,-1) F. Developing mastery Determine whether a given mapping diagram is a function or NOT a function. Given the following graphs of relation, determine whether each describes a function or not a function. Determine whether the following relations as functions or not. 1. (-6,-4), (-4,-2), (-1,0) , (1,1), (4,2), (3,3) (Group Activity) Think of two quantities related to each other. Identify the dependent Determine the domain and range given the following. 1. (9,10), (8,10), (-9,10), (6,10)
-5 -1 -9 10 (Leads to Formative Assessment 3) 2. (-4,0), (0,3), (4,0), (0,-3) 3. 3x + y = 4 4. 2x2 + y2= 8 6. 7. and independent variables. Give three examples. (You may choose real life situations.) 2. (3,2), (4,4), (5,6), (6,7) 3. (-7,9), (-6,-1), (-5,1), (-4,-1) G. Finding practical applications of concepts and skills in daily living. Situation: Suppose you are working in a fast food company. You earn ₱48 per hour. Questions: a. How much will you earn if you work for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? Plot the following points in five separate Cartesian Plane and use vertical line test to determine if is a function or not. If a kilo of mango costs ₱120, how much are 2 kilos? 3 kilos? 4 kilos? 5 kilos? Express this relation by a.) ordered pairs; b.) mapping; and c.) through equation. Determine if it describes a function. From the three examples you have made in “Independent Practice” (I Can Do This!) choose one and conduct an interview, then make a table of values and set of ordered pairs that will represent/illustrate the function. Rewrite the following ordered pairs in mapping form or diagram and vice versa and determine the domain and range. 1. (4,5), (6,6), (5,7), (6,8) 2. (-3,-2), (-4,-4), (-5,-6), (-6,-7) 3. (-7,2), (-6,2), (-5,2), (-4,2) 2 0 -2 1 2 3 0
b. Are your earnings related to the number of hours of work? How? ( The learners will be instructed to represent their answer in different ways.) Group 1 – by ordered pairs Group 2 – by table Group 3 – by mapping diagram Group 4 – by graph Group 5 – by equation/rule Questions to be used: How did you write the set of ordered  pairs? How did you make a table?  How did you make a mapping diagram?  How many elements are there in the set  of ordered pairs you have made? What elements belong to the first set?  second set? Is there a repetition of first coordinates?  How about the second coordinates? Domain Range 1. 2. 3. 4. 5. H. Making generalizatio ns and abstractions about the lesson A relation is any set of ordered pairs. The set of all the first coordinates is called the domain of the relation. The set of all the second coordinates is called the range. A function is a relation in which 1. for each first coordinate, there is exactly one second coordinate, or: 2. for every first element x, there corresponds a unique element y. NOTE: Every function is a relation, but some relations are not functions. A function can be represented by using a table, or a set of ordered pairs of numbers, by mapping, by picture or graph, by equation and by rule or correspondence A function is a relation where there is no repetition of the first element. The vertical line test is used to determine whether the graph is a function or not. If any vertical line drawn through the graph intersects the graph in exactly one point, then the graph represents a function. A function is a relation where there is no repetition of the first element. -A correspondence may be classified as one- to-one, many-to-one, or one-to-many. It is one-to-one if every element in the domain is mapped to a unique element in the range; or many-to-one if any two or more elements of the domain are mapped to the same element in the range; or one-to-many if each element in the domain is mapped to any two or more elements in the range.  Dependent variable is a mathematical variable whose value is determined by that of one or more other variables in a function. It depends on the independent variable.  Independent variable is a mathematical variable that is independent on the other variables in an expression or function and whose value determines one or more of the values of the other variables. It controls the dependent variable. -The domain of a function is the set of all possible values of its first coordinates and the range is the set of all possible values of its second coordinates. -The domain and range of a function or relation maybe identified from the set of ordered pairs, from mapping diagram, from the graph or from a rule or equation.
expressed in words. When pictures and arrows are used in representing a function, the function may be called mapping. The kinds of pairing or matching are : one-to-one correspondence, many-to-one correspondence and one-to-many correspondence. Note: A one-to-one correspondence and a many-to-one correspondence are called functions while the one-to-many correspondence is not. The variable x is considered the independent variable because any value could be assigned to it. However, the variable y is the dependent variable because its value depends on the value of x. I. Evaluating learning State whether the given set of ordered pairs is a function or NOT. Give the reason for your answer. 1. ( 1 ,2 ), ( 2, 3 ), ( 3 , 4 ), ( 4, 5 ) 2. ( -1, 6 ), ( -2, 7 ), ( -3, 8 ), ( -4, 9 ) 3. ( 1, 2 ), ( 0, 8 ), ( 1, 3 ), ( 2 , 7 ) 4. ( -3, 8 ), ( -1, 8 ), ( 3, 8 ), ( 7, 8 ) 5. ( 5, 4 ), ( 5, 8 ), ( 7, 2 ), ( 7, 3 ) If a kilo of mango costs ₱120, how much are 2 kilos? 3 kilos? 4 kilos? 5 kilos? 6 kilos? Express this relation by graphing and through vertical line test determine if it describes a function. True or False. 1. All functions relations. 2. Some relations are functions. 3. A many-to-one correspondence is a function. 4. A one-to-one correspondence is a relation. 5. A relation is a function if there is a repeated value in the first element. Answer the following: 1. At a grocery store, the amount of dressed chicken is Php 110 per kilogram. a. Find the cost of dressed chicken for 3 kilograms, and 2.5 kilograms. b. Which is the dependent variable? 2. In a Rice Productivity Program, a hectare of land in Buenavista, General Trias, Cavite yields an average of 120 cavans. What is the dependent and independent variable? True or False. 1. The range in {(3,5), (2,6), (1,7), (0,8)} is (5, 6, 7, 8). 2. The domain is the set of all x values. 3. In {(6,2), (-6,2), (-5,0), (5,0)}, the domain is (-6, 6) 4. The first values in a diagram below are called as range. 5. The correspondence in number 4 is many-to-one. J. Additional activities for application or remediation. Give a real life situation that can be an example of function. Select any of the methods to represent it. On a piece of an oslo paper draw a figure illustrating a relation and label it with function or not function. 1. Follow Up: On a piece of an oslo paper draw a figure illustrating a relation and label it with function or not function. 2. Study: Define the following: a. Dependent variable b. Independent variable 1. Follow Up: Give a situation that can help you determine the dependent and independent variables. 2. Study: Define: a. Domain b. Range Thumbs Up-Down-Sideways 1. How well can I determine the domain and range given a set of ordered pairs? 2. How well can I determine the domain and range given a mapping? Remediate on those who answered “down”. 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

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daily lesson plan math grade 8 Week-4.docx

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    GRADE 8 DAILY LESSON LOG SchoolSURABAY NATIONAL HIGH SCHOOL Grade Level 8 Teacher B. CHIONG Learning Area MATHEMATICS Week 4 (October 14-18, 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 linear functions. 2.Performance Standards The learner is able to formulate and solve accurately real-life problems involving linear functions. 3.Learning Competencies / Objectives The learner illustrates a relation and a function. (M8AL-IIc-1) a. Define relation and function. b. Represent a relation in four ways: 1. Table 2. mapping diagram 3. graph 4. rule method c. Develop the value of perseverance in studying. The learner verifies if a given relation is a function. (M8AL-IIc-2) a. Differentiate a relation from a function. b. Determine if a relation is a function or not using the vertical line test. c. Appreciate the concept of relation and function in real-life situation. The learner verifies if a given relation is a function. (M8AL-IIc-2) a. Determine if a relation is a function given: 1. ordered pairs, 2. mapping, and 3. rules/equations. b. Express real-life situations into: 1. ordered pairs, 2. mapping, and 3. rules/equations. c. Appreciate the concept of relation and function in real-life situations. The learner performs determines dependent and independent variables. (M8AL-IIc-3) a. Define dependent and independent variables. b. Determine the dependent and independent variables. c. Appreciate new understanding on dependent and independent variables of a given function. The learner finds the domain and range of a function.(M8AL-IId-1) a. Differentiate domain from range. b. Identify the domain and range of a function given: 1. the ordered pairs, and 2. mapping. c. Appreciate the concept of domain and range in real-life situations. II. CONTENT Representations of Functions and Relations Representations of Functions and Relations Representations of Relations and Functions Dependent and Independent Variables Domain and Range of Function III. LEARNING RESOURCES A. References 1. Teacher’s Guide 155-182 168- 169 2. Learner’s Materials 138-144 151-152 pages148-152 pages 155-156 3. Textbook None None Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 22-23; Valtoribio, Advanced Algebra, Trigonometry and Statistics, pp. 4-5. Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 27-28 Lapinid and Buzon, Advanced Algebra, Trigonometry and Statistics: Patterns and Practicalities, pp. 11-12. 4. Additional Materials https://www.youtube.com/watch? https://www.youtube.com/watch?
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    from Learning Resource (LR) portal v=C5xcpNGeKCQv=l4265qSL914 B. Other Learning Resources Laptop, Projector,Speaker LCTG Grade 8 by DepEd Cavite Mathematics,2016 Laptop, Projector,Speaker LCTG Grade 8 by DepEd Cavite Mathematics,2016 Grade 8 LCTG by DepEd Cavite Mathematics 2016, projector, laptop, power point presentation Grade 8 LCTG by DepEd Cavite Mathematics 2016, projector, laptop, power point presentation Grade 8 LCTG by DepEd Cavite Mathematics 2016, laptop, projector, powerpoint presentation, “Cabbage of Knowledge” IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson Where do I belong??? Description: This activity will enable you to write ordered pairs. Out of this activity, you can describe the relation of the products to its respective places. Directions: Group the following products in such a way that they are from the same places in Cavite. Kesong puti See weeds Pastillas de leche Smoked fish (tinapa) coconut Dried fish (tuyo) Coffee beans Fresh milk Banana shrimp Black pepper Choco milk Strawberry milk crab pineapple General Trias Rosario Amadeo SPOTTING ERRONEOUS COORDINATES Do the task as directed A. Lea indicated that A has coordinates (- 3,2) 1. Do you agree with Lea? 2. What makes Lea wrong? 3. How will you explain to her that she is wrong in a subtle way? B. Cris insisted that B has coordinates (-2,-4) while C has coordinates (-2,2). If yes, why? If no, state the correct coordinates of points of B and C “Find your Match!” Call on 8 volunteers. Give each student a strip of paper and instruct them to find their match. Teacher-students Boyfriend-girlfriend Parent-child God-creation 1. What did each pair represents? 2. How can you make your relationship with others work/function? Can you live without your  parents? Who among you lives with their  parents? Therefore, are you dependent or  independent individual? Cabbage of Knowledge Let the students pass around the “cabbage of knowledge” while a music is playing. Once the music stops, the student holding the cabbage will uncover a leaf and will have to define or describe the word written on each leaf. Dependent Function Independent Domain Relation Range B. Establishing Presentation of Objectives Presentation of Objectives A function is a relation where there is no Variables may be dependent or The domain of a function refers to
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    a purpose for thelesson repetition of the first element. dependent. Dependent variable depends on the independent variable while the independent variable controls the dependent variable. the first or x values in a set of ordered pairs, while the range is the set of the second or y values in a set of ordered pairs. C. Presenting examples/ instances of the lesson Exploratory Activity From the previous activity, form some ordered pairs using the format: ( product, place ) a. Column 1: __________ b. Column 2: __________ c. Column 3: __________ Based on the coordinates you have formulated, is there a repetition of the first coordinates? How about the second coordinates? Try to present the ordered pairs formed in table form. PRODUCTS MUNICIPALITY Now, try to make a mapping diagram to show the relation.  What can you say about the diagram you have formed?  What elements belong to the first set? To the second set?  Is there a repetition of the first Plot the following points in five separate Cartesian Plane. The relation between time and pay is an example of a function. Example: Notice that there is no repeated value for the first element. So, this is a function. This can also be represented through A. Ordered pairs {(2,200), (4,400), (6,600), (8, 800), (10, 1000)} B. Mapping This is an example of one-to-one correspondence. A correspondence may be classified as one- to-one, many-to-one, or one-to-many. One-to-One Correspondence Student I.D. No. - Developmental Activity If you study hard, what will  happen? If you spend much of your  allowance, what will happen? If you eat much, what will happen?  If you travelled long distance,  what will happen? From the previous questions given to you, we can determine the dependent and independent variable. In the first question, if you study hard, you said you will get high scores on tests, so you will get high grades. In the second question, if you spend much of your allowance, you said you will lose your money. In the third question, if you eat much, you said you will gain weight. In the fourth question, if you travelled long distance, there is larger amount of gasoline to be consumed. From those given situations, can you determine the dependent and independent variables? How did you identify the dependent and independent variables? Let’s have other examples. Classify the variables as dependent or independent. 1. cost of chicken and its weight 2. income of a worker and number of hours of work 3. perimeter of a square and its side Given the following set of ordered pairs, identify the x values and y values. 1. (4,5), (5,-4), (8,5), (-3,2), (6,1) 2. (0,3), (-1,5), (2,-4), (3,6), (4, -7) 3. (2,0), (0,9), (1,3), (-1,9), (3,7) 4. (-8,1), (4,-5), (6,0), (-7,8), (-5,2) 5. (-2,6), (4,-3), (-5,1), (4,0), (5,3) In the previous activity, how did you determine the domain and range? In mapping diagram, like What is the domain? What is the range?
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    coordinates? How aboutthe second coordinates? The relations you have formed in the previous activities are all examples of a FUNCTION, as they are many-to-one correspondence. If the relation shows one-to-one correspondence it is also a function, but if the relation is one-to-many correspondence, then it is not a function. Aside from these three methods, function can also be represented by picture or graph, by equation and by rule. Situation: Suppose Tenten is working in Gen. Trias Dairy Raisers Multi-Purpose Cooperative at Santiago, Gen. Trias, Cavite and he earns ₱43 per hour. Questions: a. How much will Tenten earn if he works for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? b. Is his earnings related to the number of hours of work? How? Tenten’s earnings can be represented by some other way like graph, equation or rule. By graph By equation or by rule, Tenten’s earnings can be represented by y=43(h) Many-to-One Correspondence One-to-Many Correspondence C. Rule/Equation As the number of time (x) increases, the amount of pay (y) also increases. -What will be your pay if you worked for 1 hour? 15 hours? 20 hours? n hours? So, the rule for this function is y= 100x. 4. In mathematical equation, like for example, the linear function, y =3x- 5. If x=1, what will be the value of y? If x=0, what is y? If x=1, what is y? In these cases, which are the dependent and independent variables? D. Discussing new concepts and Video Presention diffentiating a relation and a function. From the previous activity, Is there a repetition of the first coordinates? The second coordinates?  Connect the given points from the first given point up to the last. 1. Among the types of correspondence, which ones are functions? Why? 2. Does one-to-one correspondence between elements always guarantee a function? How about one-to-one? What is dependent variable? What is independent variable? How can you differentiate the dependent and independent variable? How can you describe the domain and range of a function given the: a. ordered pairs b. mapping diagram?
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    practicing new skills #1  Howcan you describe each graph?  Draw vertical lines through the graph.  Does the vertical lines touch the graph?  How many times does the vertical line touch the graph? Justify your answer. 3. Does one-to-many correspondence between elements always guarantee a function? Justify your answer. E. Discussing new concepts and practicing new skills #2 A. What can you say about relation? B. Can you determine whether a relation is a function or a mere relation? How? C. What will be your reference that a relation is a function? D. Give real-life examples/ situations that can describe a function. A. Does each graph represent a function? Why or why not? B. If you are only given the graph, how can you determine if the graph represents a function? C. What do you call this method? Tell whether the following relations as function or not. 1. 2. 3. 4. y = 3x+9 5. x2 + y2 =16 6. (-1,2), (1,3), (1,5), (2,7) 7. (0,6), (-3,4), (3,5), (4,0), (6,-3) Fill in the blanks. 1. I consider the weight of chicken as a/an ________ variable because it ________ the cost of chicken. 2. I consider the cost if chicken as a/an ________ variable because it ________ on the weight of the chicken. 3. I consider the income of a worker as a/an _______ variable because it ________ on the number of hours the worker worked. 4. I consider the number of hours worked as a/an ________ variable because it ________ the income of the worker. 5. I consider the perimeter of a square as a/an ________ variable because it ________ on the length of its side. 6. I consider the length of the side of a square as a/an ________ variable because it ________ the perimeter of the square. Determine the domain and range given the following. 1. (2,0), (3,1), (3,7), (6,-1) 2. (3,0), (4,0), (5,0), (6,0) 3. (-1,9), (4,-1), (-4,1), (1,-1) F. Developing mastery Determine whether a given mapping diagram is a function or NOT a function. Given the following graphs of relation, determine whether each describes a function or not a function. Determine whether the following relations as functions or not. 1. (-6,-4), (-4,-2), (-1,0) , (1,1), (4,2), (3,3) (Group Activity) Think of two quantities related to each other. Identify the dependent Determine the domain and range given the following. 1. (9,10), (8,10), (-9,10), (6,10)
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    -5 -1 -9 10 (Leads to Formative Assessment 3) 2. (-4,0),(0,3), (4,0), (0,-3) 3. 3x + y = 4 4. 2x2 + y2= 8 6. 7. and independent variables. Give three examples. (You may choose real life situations.) 2. (3,2), (4,4), (5,6), (6,7) 3. (-7,9), (-6,-1), (-5,1), (-4,-1) G. Finding practical applications of concepts and skills in daily living. Situation: Suppose you are working in a fast food company. You earn ₱48 per hour. Questions: a. How much will you earn if you work for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? Plot the following points in five separate Cartesian Plane and use vertical line test to determine if is a function or not. If a kilo of mango costs ₱120, how much are 2 kilos? 3 kilos? 4 kilos? 5 kilos? Express this relation by a.) ordered pairs; b.) mapping; and c.) through equation. Determine if it describes a function. From the three examples you have made in “Independent Practice” (I Can Do This!) choose one and conduct an interview, then make a table of values and set of ordered pairs that will represent/illustrate the function. Rewrite the following ordered pairs in mapping form or diagram and vice versa and determine the domain and range. 1. (4,5), (6,6), (5,7), (6,8) 2. (-3,-2), (-4,-4), (-5,-6), (-6,-7) 3. (-7,2), (-6,2), (-5,2), (-4,2) 2 0 -2 1 2 3 0
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    b. Are yourearnings related to the number of hours of work? How? ( The learners will be instructed to represent their answer in different ways.) Group 1 – by ordered pairs Group 2 – by table Group 3 – by mapping diagram Group 4 – by graph Group 5 – by equation/rule Questions to be used: How did you write the set of ordered  pairs? How did you make a table?  How did you make a mapping diagram?  How many elements are there in the set  of ordered pairs you have made? What elements belong to the first set?  second set? Is there a repetition of first coordinates?  How about the second coordinates? Domain Range 1. 2. 3. 4. 5. H. Making generalizatio ns and abstractions about the lesson A relation is any set of ordered pairs. The set of all the first coordinates is called the domain of the relation. The set of all the second coordinates is called the range. A function is a relation in which 1. for each first coordinate, there is exactly one second coordinate, or: 2. for every first element x, there corresponds a unique element y. NOTE: Every function is a relation, but some relations are not functions. A function can be represented by using a table, or a set of ordered pairs of numbers, by mapping, by picture or graph, by equation and by rule or correspondence A function is a relation where there is no repetition of the first element. The vertical line test is used to determine whether the graph is a function or not. If any vertical line drawn through the graph intersects the graph in exactly one point, then the graph represents a function. A function is a relation where there is no repetition of the first element. -A correspondence may be classified as one- to-one, many-to-one, or one-to-many. It is one-to-one if every element in the domain is mapped to a unique element in the range; or many-to-one if any two or more elements of the domain are mapped to the same element in the range; or one-to-many if each element in the domain is mapped to any two or more elements in the range.  Dependent variable is a mathematical variable whose value is determined by that of one or more other variables in a function. It depends on the independent variable.  Independent variable is a mathematical variable that is independent on the other variables in an expression or function and whose value determines one or more of the values of the other variables. It controls the dependent variable. -The domain of a function is the set of all possible values of its first coordinates and the range is the set of all possible values of its second coordinates. -The domain and range of a function or relation maybe identified from the set of ordered pairs, from mapping diagram, from the graph or from a rule or equation.
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    expressed in words.When pictures and arrows are used in representing a function, the function may be called mapping. The kinds of pairing or matching are : one-to-one correspondence, many-to-one correspondence and one-to-many correspondence. Note: A one-to-one correspondence and a many-to-one correspondence are called functions while the one-to-many correspondence is not. The variable x is considered the independent variable because any value could be assigned to it. However, the variable y is the dependent variable because its value depends on the value of x. I. Evaluating learning State whether the given set of ordered pairs is a function or NOT. Give the reason for your answer. 1. ( 1 ,2 ), ( 2, 3 ), ( 3 , 4 ), ( 4, 5 ) 2. ( -1, 6 ), ( -2, 7 ), ( -3, 8 ), ( -4, 9 ) 3. ( 1, 2 ), ( 0, 8 ), ( 1, 3 ), ( 2 , 7 ) 4. ( -3, 8 ), ( -1, 8 ), ( 3, 8 ), ( 7, 8 ) 5. ( 5, 4 ), ( 5, 8 ), ( 7, 2 ), ( 7, 3 ) If a kilo of mango costs ₱120, how much are 2 kilos? 3 kilos? 4 kilos? 5 kilos? 6 kilos? Express this relation by graphing and through vertical line test determine if it describes a function. True or False. 1. All functions relations. 2. Some relations are functions. 3. A many-to-one correspondence is a function. 4. A one-to-one correspondence is a relation. 5. A relation is a function if there is a repeated value in the first element. Answer the following: 1. At a grocery store, the amount of dressed chicken is Php 110 per kilogram. a. Find the cost of dressed chicken for 3 kilograms, and 2.5 kilograms. b. Which is the dependent variable? 2. In a Rice Productivity Program, a hectare of land in Buenavista, General Trias, Cavite yields an average of 120 cavans. What is the dependent and independent variable? True or False. 1. The range in {(3,5), (2,6), (1,7), (0,8)} is (5, 6, 7, 8). 2. The domain is the set of all x values. 3. In {(6,2), (-6,2), (-5,0), (5,0)}, the domain is (-6, 6) 4. The first values in a diagram below are called as range. 5. The correspondence in number 4 is many-to-one. J. Additional activities for application or remediation. Give a real life situation that can be an example of function. Select any of the methods to represent it. On a piece of an oslo paper draw a figure illustrating a relation and label it with function or not function. 1. Follow Up: On a piece of an oslo paper draw a figure illustrating a relation and label it with function or not function. 2. Study: Define the following: a. Dependent variable b. Independent variable 1. Follow Up: Give a situation that can help you determine the dependent and independent variables. 2. Study: Define: a. Domain b. Range Thumbs Up-Down-Sideways 1. How well can I determine the domain and range given a set of ordered pairs? 2. How well can I determine the domain and range given a mapping? Remediate on those who answered “down”. V. REMARKS VI. REFLECTION
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    1.No.of learners whoearned 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