GRADES 9 DAILY LESSON LOG School BONIFACIO R. TAGABAN SR. IS Teacher ARIEL JAY B. VELA Teaching Dates and SEPT. 27 AND 29 - 1:15 - 3:15 Time Session 1 I. OBJECTIVES Session 2 TUESDAY Grade Level 9 Learning Area MATHEMATICS Quarter FIRST Session 3 Session 4 THURSDAY 1. Content Standards The learner demonstrates understanding of key concepts of quadratic equations, inequalities and functions, and rational algebraic equations. The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life 2. Performance problems involving quadratic equations, inequalities and functions, and rational algebraic equations and solve them Standards using a variety of strategies. 3. Learning Models real-life situations Represents a quadratic Represents a quadratic Represents a quadratic Competencies/ using quadratic functions. function using: (a) table of function using: (a) table of function using: (a) table of Objectives (M9AL-Ig-2) values; (b) graph; and (c) values; (b) graph; and (c) values; (b) graph; and (c) equation. (M9AL-Ig-3) equation. (M9AL-Ig-3) equation. (M9AL-Ig-3) a. Model real-life situations using quadratic functions a. Differentiate quadratic a. Differentiate quadratic a. Differentiate quadratic b. Appreciate the functions from linear functions from linear functions from linear application of quadratic functions functions functions function in real-life b. Represent and identify b. Represent and identify b. Represent and identify situations quadratic function using: quadratic function using: quadratic function using: (a) table of values (b) graph c) general form into vertex c. Value accumulated c. Value accumulated form equation knowledge as means of knowledge as means of c. Value accumulated new understanding new understanding knowledge as means of new understanding II. CONTENT Introduction to Quadratic Introduction to Quadratic Introduction to Quadratic Introduction to Quadratic Function Function Function Function III. LEARNING RESOURCES A. References 1. 2. Teacher’s Guide pp. 85-96 pp. 85-96 pp. 85-96 pp. 85-96 Learner’s Materials pp. 125-126 pp. 127-129 pp. 127-129 pp. 127-129 Grade 9 LCTG by DepEd Cavite Mathematics 2016, activity sheets, laptop and monitor Grade 9 LCTG by DepEd Cavite Mathematics 2016, activity sheets, laptop and monitor Grade 9 LCTG by DepEd Cavite Mathematics 2016, activity sheets, laptop and monitor, graphing paper Grade 9 LCTG by DepEd Cavite Mathematics 2016, activity sheets, laptop and monitor 3. Textbook 4. Additional Materials from Learning Resource (LR) portal B. Other Learning Resources IV. PROCEDURES A. Reviewing previous What is your favourite team lesson or presenting in PBA? NBA? How about the new lesson your idol/favourite player in basketball? Have you ever asked yourself why PBA/NBA star Players are good in free throws? How do angry bird expert players hit their targets? Do you know the Many things we see everyday are modeled by QUADRATIC FUNCTIONS. Give at least 3 examples. 1.Water in drinking fountain. 2. the path of a basketball 3. McDonald’s logo secret key in playing this game? What is the maximum height reached by an object thrown vertically upward given a particular condition? B. Establishing a purpose for the lesson Let the students act their 1. Which of the mathematical ideas to show how sentences are quadratic PBA/NBA and Angry Birds functions? Players do a free throw and 2. Which of the mathematical hit their targets. sentences are NOT Let the students estimate quadratic functions? Why? the maximum height 3. How would you describe reached by the object those mathematical thrown vertically upward. sentences which are not quadratic functions? How are they different from those equations which are quadratic? How your example does modeled the quadratic functions? How do we represent and identify quadratic functions using a graph? 1. What are the differences of Quadratic equations and not Quadratic equation base on the activity? 2. How can you recognize a quadratic function when a set of equations are given? C. Presenting examples/ Illustrative Example 1: instances of the Who does not like pizza? lesson Nowadays, pizza seems to be the favorite snack of many teenagers. When pizza is served to a customer, it is already divided into 8 pieces, if it is regular size or into 12 pieces if it is family size. Observe the 8 pieces result from 4 straight cuts; the 12-piece from 6 straight cuts. Reasoning tells us that 3 straight cuts would result to 6 pieces and 5 straight cuts to 10 pieces. In other words, pizza-cutting this way can be described by the linear function where is the number of straight cuts and, the number of pieces that result. The previous activities familiarized the students with the general form y = ax²+bx+c of a quadratic function so if an equation was written in vertex form y = We know that a quadratic a(x-h)²+k we can express the equation into standard form equation will be in the that will be more convenient form: to use when working on problems involving the vertex y = ax2 + bx + c of the graph of a quadratic function. The graph of a quadratic function is a parabola. The parabola can either be in "legs up" or "legs down" orientation. Our job is to find the values of a, b and c after first observing the graph. Sometimes it is easy to spot the points where the curve passes through, but often we need to estimate the points. D. Discussing new concepts and practicing new skills #1 Among the most wellknown of the physical situations represented by the quadratic function is that which involves velocity and force of gravity. In the 17th century, Isaac Newton discovered that the height (h) of an object thrown upwards with an initial velocity (v0) at time (t) would be v0t reduced by the force of gravity equal to . If the thrower’s hand upon the release of this ball was at a starting height (h0) above the ground, then, The symbol which stands for acceleration due to gravity is equal to 9.8 m/sec near the earth’s surface. Suppose a baseball pitcher throws a ball upward with an initial velocity of 20m/sec. 1. What equation will give Find the differences between adjacent y – values in each table, and write them on the blanks provided. 2. Using the table values, graph the two functions. 3. Compare the graph of linear function and quadratic function. the height of the ball for any time in seconds? Use 2. What is the greatest height the ball would reach before it starts to fall to the ground? 3. At what time would the ball reach the ground? E. Discussing new 1. Is quadratic function concepts and useful in real-life practicing new skills situations? #2 2. How can quadratic Function be used to solve real- life problems? 1. What do you observe with a. What kind of functions is f(x) = 3x +1 and the difference of each table g(x) = x²+2x-4? values? 2. How can you recognize a b. What do you observe about the graph of linear quadratic function when a function and quadratic table of values is given? function? Transform the given quadratic functions into the form y = a(x-h)²+k by following the steps below. 1. y = x² - 4x - 10 2. y = 3x² - 4x + 1 F. Developing mastery (Leads to Formative Assessment 3) Menggay maintains a small Consider the given functions retail store to help support f(x) = 2x + 1 and her family. Think of the g(x) = x²+2x-1. diagram below as rows of 1. What kind of functions is bath soap. f(x)? g(x)? 2. Complete the following table values using the indicated function, f(x) = 2x + 1 x -3 -2 -1 0 y 1 2 3 g(x) = x²+2x-1 x -3 -2 -1 0 y 1 2 3 3. What are the differences between two adjacent x – values in each table? 4. Find the differences between each adjacent y – values in each table. Derek is living in Tagaytay, Write a 1 paragraph G.Finding practical Cavite. He is thinking of statement explaining how to applications of growing vegetables in his recognize that the given concepts and skills in backyard. He has 100 m. mathematical sentence is a daily living long fencing material. He QUADRATIC FUNCTIONS wants to enclose as much using the table of values in of his backyard as possible. your own words. What dimensions of a rectangular lot will result to the greatest area? 1. How do you find transforming of general form into vertex form in general form? 2. How about transforming a vertex form y = a(x-h)²+k into general form. Think of the given length of the wire as the perimeter of the lot, so a length and a width is 50. If the length is denoted as , then the width is Area, if you recall, is length times width. Let us put some pairs of values for and and their corresponding areas in a table. H. Making generalizations and abstractions about the lesson There are many situations in the real world that can be modeled or mathematically described by the quadratic function. Skill to do this can be useful to make estimates of one variable from known values of the related variable or to make predictions of the relationship between the general form y = ax² + bx + c vertex form y = a(x-h)² + k I. Evaluating learning J. Additional activities for application or remediation same two variables in a different situation. In 2009, a strong typhoon Ondoy with heavy rains flooded some parts of Luzon for days including Cavite. Helicopters were used to bring food and other supplies to flood victims. A helicopter dropped packages of food and supplies to a group of people from a height of 100 meters. 1. Neglecting air resistance, how far would the package have dropped in 2 seconds? (Hint: Go back to Newton‟s formula) 2. When will the package touch the ground? Assignment: Assignment: Study represent a quadratic Bring graphing paper function using: a) table of tomorrow. values, b) graph, and c)equation a. What is a quadrati c function? b. What is the difference between quadratic function and linear Assignment: List the mathematical concept that you use to transform the given quadratic functions. function? Reference: Grade 9 Learning Module pp. 125-126 V. REMARKS VI. REFLECTION a. No. of learners who earned 80% on the formative assessment 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? Reference: Reference: Grade 9 Learning Module pp. Grade 9 Learning Module pp. 127-129 pp. 127-129 Reference: Grade 9 Learning Module pp. 127-129 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?
