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daily lesson log

JosephSPalileoJrSuivre

- GRADES 9 DAILY LESSON LOG School Grade Level 9 Teacher Learning Area MATHEMATICS Teaching Dates and Time Quarter FIRST Teaching Day and Time Grade Level Section Session 1 Session 2 Session 3 Session 4 I. OBJECTIVES 1. Content StandardsThe learner demonstrates understanding of key concepts of quadratic equations, inequalities and functions, and rational algebraic equations. 2. Performance Standards The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving quadratic equations, inequalities and functions, and rational algebraic equations and solve them using a variety of strategies. 3. Learning Competencies/ Objectives Characterizes the roots of a quadratic equation using the discriminant. (M9AL-Ic-1) a. Evaluate the expression given the b2 – 4ac values of a, b, and c b. Use the discriminant in characterizing the roots of quadratic equations c. Appreciate the importance of discriminant Describes the relationship between the coefficients and the roots of a quadratic equation. (M9AL-Ic-2) a. Describe the relationship between the coefficients and the roots of quadratic b. Determine the sum of the roots of quadratic equations c. Value the knowledge as a means of new understanding Describes the relationship between the coefficients and the roots of a quadratic equation. (M9AL-Ic-2) a. Describe the relationship between the coefficients and the roots of quadratic b. Determine the product of the roots of quadratic equations c. Appreciate the importance of quadratic equation in real- life situation Solves equations transformable to quadratic equations (including rational algebraic equation). (M9AL-Ic-d-1) a. Transform quadratic equation into standard form b. Find the solutions of equations transformable to quadratic equations c. Show self-reliance and display interests when working independently II. CONTENT Nature of Roots of Quadratic Equation Sum of the Roots of Quadratic Equations Product of the Roots of Quadratic Equations Equations Transformable to Quadratic Equations
- III. LEARNING RESOURCES A. References 1. Teacher’s Guide pp. 39-44 pp. 45-49 pp. 45-49 pp. 50-53 2. Learner’s Materials pp. 56-63 pp. 66-72 pp. 66-72 pp. 77-87 3. Textbook Our World of Math pp. 21-25 21st Century Mathematics pp. 168-172 Ju Se T. Ho et.al 21st Century Mathematics pp. 168-172 Ju Se T. Ho et.al Intermediate Algebra pp. 58-60 Julieta G. Bernabe et.al. 4. Additional Materials from Learning Resource (LR) portal http://www.purplemath.com /moduleiquadraticform.htm http://www.algebrahelp.co m/lessons/equation/quadrat ic http://www.athometuition.com/ QuadraticEquationFormula.ph http://www.math-help- ace.com/Quadratic-Equation- Solver.html http://www.athometuition.co m/QuadraticEquationFormul a.ph http://www.math-help- ace.com/Quadratic- Equation-Solver.html B. Other Learning Resources 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 Grade 9 LCTG by DepEd Cavite Mathematics 2016, activity sheets, laptop and monitor IV. PROCEDURES A.Reviewing previous lesson or presenting the new lesson Preliminary Activity: 1. Evaluate the expression b2 – 4ac given the following values of a, b, and c. 1. a =1 , b = 5, c = 4 2. a = 2, b = 1, c = -21 3. a = 4, b = 4, c = 1 4. a = 1, b = -2, c = -2 Let’s Do Addition! Perform the indicated operation. 1. 7+15 = 2. -9 + 14 = 3. -6 + (-17) = Determine the roots of each quadratic equation using any method. 1. x2 + 7x + 12 = 0 = ____ , = ____ 2. 2x2 – 3x – 20 = 0 = ____ , = ____ Preliminary Activity: Showing different equations on the TV screen and letting each learner study the given equation. 1. 2. (x+1) (x – 2) = 12
- 5. a = 9, b = 0, c = 16 4. + = 5. + = Quadrati c Equation Sum of Roots Product of Roots x2 + 7x + 12 =0 2x2 – 3x – 20 = 0 3. x(x – 3) = 20 4. 5. B.Establishing a purpose for the lesson 1. Where you able to find the expression b2 - 4ac given the values of a, b, and c? 2. What do you think is the importance of the expression b2 – 4ac in determining the nature of the roots of a quadratic equation? 1. How did you determine the result of each operation? 2. What mathematics concepts and principles did you apply to arrive at each result? 3. Compare your answers with those of your classmates. Did you arrive at the same answers? If NOT, explain why. 1. What do you observe about the sum and product of the roots of each quadratic equation in relation to the values a, b, c? 2. Do you think a quadratic equation can be determined given its roots or solutions? Justify your answer by giving 3 examples 1. Which of the given equations are written in Standard Form? 2. How do you describe standard form of equation? C.Presenting examples/ instances of the lesson Examples: 1. x2 – 2x + 1 = 0 D = b2 – 4ac D = (-2)2 – 4(1)(1) D = 4 – 4 The sum of the roots of the quadratic equation ax2 + bx + c = 0 can be determined using the coefficients a, b, and c. Remember that the roots of a quadratic equation can be determined using the formula The product of the roots of the quadratic equation + bx + c = 0 can be determined using the coefficients a, b, and c. Remember that the roots of a quadratic equation can be determined using the formula Solving Quadratic Equations That are Not Written in Standard Form Example 1: Solve x(x – 5) = 36
- D = 0 Therefore the roots are real, rational, and equal. 2. 3x2 – x – 2 = 0 D = b2 – 4ac D = (- 1)2 – 4(3)(-2) D = 1 + 24 D = 25 Since D ˃ 0 and a perfect square Therefore the roots are real, rational, and unequal. 3. x2 – 6x + 7 = 0 D = b2 – 4ac D = (-6)2 – 4(1)(7) D = 36 – 28 D = 8 Since D ˃ 0 and not a perfect square. Therefore the roots are real, irrational and unequal. 4. x2 – 4x + 5 = 0 From the quadratic formula, let and be the roots. Example 1. Find the sum of the roots of + 8x – 10 = 0 Sum of the roots = The sum of the roots of + 8x – 10 = 0 is - 4 Example 2. Use the values of a, b and c in finding the roots of the quadratic equation. The values of a, b, and c in the equation are 1, 7 and -18, respectively. Use this value to find the sum and the product of the roots of the equation. Sum of the roots = The sum of the roots of + From the quadratic formula, let and be the roots. Example 1. Find the sum of the roots of + 8x – 10 = 0 Product of the roots = The product of the roots of + 8x – 10 = 0 is -5 Example 2. Use the values of a, b and c in finding the roots of the quadratic equation. The values of a, b, and c in the equation are 1, 7 and - 18, respectively. Use this value to find the sum and Example 2: Find the roots of the equation (2x - 2)(x + 4) = 0 2x – 2 = 0 or x + 4 = 0 X = 1 or x = -4
- D = b2 – 4ac D = (-4)2 – 4(1(5) D = 16 – 20 D = - 4 Since D ˂ 0 therefore the roots are not real or imaginary. 7x – 18 = 0 is -7 the product of the roots of the equation. Product of the roots = The product of the roots of + 7x – 18 = 0 is -18 D.Discussing new concepts and practicing new skills #1 Using the values of a, b, and c, write the quadratic equation ax2+bx+c= 0. Then find the roots of each resulting equation. 1. a =1 ,b = 5, c = 4 2. a = 2,b = 1,c =-21 3. a = 4,b = 4, c = 1 4. a = 1,b = -2,c = -2 5. a = 9, b = 0, c = 16 Direction: Determine the sum of the roots by using . - 2x – 3 = 0 = 10x – 25 + 2x – 5 = 0 + 8x + 3 = 0 – 2x – 7 = 0 Direction: Determine the product of the roots by using c/a - 2x – 6 = 0 = 10x – 36 + 2x – 5 = 0 + 8x + 6 = 0 – 2x – 14 = 0. View Me in Another Way! Transform each of the following equations into a quadratic equation in the form . 1. x (x + 5)= 2 2. 3. 4. 5.
- E.Discussing new concepts and practicing new skills #2 Follow-up Questions: 1. Can we determine the nature of the roots of a quadratic equation without solving the equation? 2. Can we identify whether the roots are real, rational, or irrational, equal or unequal? 3. When will the equation have no real roots? Follow-up Questions: 1. What is the relation between the coefficients and the roots of quadratic equation? 2. How can the sum of the roots be obtained? 3. How do you check your answer? Follow-up Questions: 1. What is the relation between the coefficients and the roots of quadratic equation? 2. How can the product of the roots be obtained? Follow-up Questions: 1. How did you transform each equation into a quadratic equation? 2. What mathematics concepts or principles did you apply? 3. Did you find any difficulty in transforming each equation into a quadratic equation? Explain. F. Developing mastery (Leads to Formative Assessment 3) Solve for the discriminant of the following quadratic equation and determine the nature of the roots. 1. + 5p – 3 = 0 2. + 9r + 14 = 0 3. + 5x + 10 = 0 4. – 7x = 30 5. + 6x + 9 = 0 Direction: Find the sum of the roots. + 4x + 3 = 0 + 12x – 18 = 0 – 6x = 8 – 3x = 0 = 25 Direction: Find the product of the roots. + 4x + 9 = 0 + 12x – 36 = 0 – 6x = 18 – 16x = 0 = 36 Solve and Find the roots of the following equations. 1. 2. (x – 10)(x + 3) = 0 3. x(x + 12) = 10 4.
- 5. (x – 4)(x + 5) = 0 G.Finding practical applications of concepts and skills in daily living Directions: Study the situation below and answer the questions that follow. Lola Nidora asks Rogelio to make a table which has an area of 6m2. The length of the table has to be 1 m longer the width. 1. If the width of the table is p meters, what will be its length? 2. Form a quadratic equation that represents the situation. 3. Without actually computing for the roots, determine whether the dimensions of the table are rational numbers. Explain. 4. Give the dimensions of the table. Answer the following problem. 1. Suppose the sum of the roots of a quadratic equation is given, do you think you can determine the equation? Justify your answer. 2. The sum of the roots of a quadratic equation is -5. If one of the roots is 7, how would you determine the equation? Write the equation. Read and understand the situation below to answer the questions that follow. 1. Lola Nidora is informed that his bodyguard Rogelio owns a rectangular lot. The perimeter of the lot is 90m and its area is 450 m2. a. What equation represents the perimeter of the lot? b. How about the equation that represents the area? c. How is the given situation related to the sum and the product of the roots of quadratic equation? d. What quadratic equation can be formed that describes the problem? e. What are the dimensions of the rectangular lot? My understanding of Equations Transformable into Quadratic! Answer the following. 1. In a water refilling station, the time that a pipe takes to fill a tank is 10 minutes more than the time that another pipe takes to fill the same tank. If the two pipes are opened at the same time, they can fill a tank in 12 minute. How many minutes does each pipe take to fill the tank? 2. A flare is launched from a life raft with an initial velocity of 80 meters per second. How many seconds will it take for the flare to return to the sea?
- 2. The perimeter of a rectangular bulletin board is 20ft. if the area of the board is 21ft. What are its length and width? H.Making generalizations and abstractions about the lesson If b2 –4ac = 0, the roots are real, rational and equal. If b2 –4ac ˃ 0 and a perfect square, then the roots are real, rational and unequal. If b2 –4ac ˃ 0 and not a perfect square, the roots are unequal and irrational. If b2 –4ac ˂ 0 the roots are not real or imaginary. Sum of the Roots of Quadratic Equation + The sum of the roots of quadratic equation is . Product of the Roots of Quadratic Equation ) The sum of the roots of quadratic equation is . There are equations that are transformable to quadratic equations. These equations may be given in different forms. Hence, the procedures in transforming these equations to quadratic equations may also be different. Once the equations are transformed to quadratic equations, then they can be solved using the different methods of solving quadratic equations, such as extracting square roots, factoring, completing the square and using the quadratic formula. An extraneous root of an equation can be derived from an original equation. However, it is not a solution of the original equation. I. Evaluating learning “Where do you like to go in Cavite?” Direction: Characterize the nature of the roots of the following quadratic Using the values of a, b, and c, find the sum of the following equations. – 4x – 21 = 0 Using the values of a, b, and c, find the product of the following equations. – 4x – 12 = 0 Let’s Be True! Find the solution set of the following. 1. x(x+3)=28
- equations using the discriminant. Use the legend below. Taal Volcano Water Camp Kaybiang Tunnel Aguinaldo Shrine (real,rational,equal) (real,rational,unequal) (real,irrational, unequal) (not real, imaginary) 1. + 9x + 20 =0 2. + 6x + 13 = 0 3. – 5x = - 4 4. – 2x – 5 = 0 5. + 8x + 16 = 0 – 8x = 48 = 1 – x + 6 = 0 -8x + 1 = 0 – 8x = 24 = -6 – x + 12 = 0 -8x + 3 = 0 2. 3s(s-2) = 12s 4. =65 J. Additional activities for application or remediation Assignment: Follow-up Find the value of k in each quadratic equation in order to have: Equal roots a. + 2x + 1 = 0 b. + 4x + k = 0 2. Study the sum and product of the roots of the Assignment: Study 1. Product of Roots of Quadratic Equations Assignment: Determine the sum and the product of each equation. 1. = 3c 2. (x – 2 =9 3. – 9b = 0 4. ( n – 7 = 6 5. 3(a + 7 + 4 = 49 Assignment: Study the steps in transforming rational algebraic expressions into quadratic equation.
- quadratic equation. a. How do you get the sum and product of quadratic equation? b. Give the formula 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?
- 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?