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- 1. GRADES 9 DAILY LESSON LOG School Dona Maria Laurel Platon School of Agriculture Grade Level 9 Teacher Ms. Janine A. Estolano Learning Area MATHEMATICS Teaching Dates and Time June 4-8, 2018 June 4- orientation; June 7-8 Pre-test Quarter FIRST Teaching Day and Time Monday Tuesday Wednesday Thursday Grade Level Section Session 1 Session 2 Session 3 Session 4 I. OBJECTIVES 1. Content Standards The learner demonstrates understanding of the 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. Illustrates quadratic equations. (M9AL-Ia-1) a. Write a quadratic equation in standard form. b. Identify quadratic equations. c. Appreciate the importance of quadratic equations. Solves quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; and (d) using the quadratic formula. (M9AL-Ia-b-1) a. Express quadratic equation in the form x2 = k . b. Solve quadratic equation by extracting square roots. c. Appreciate the importance of solving quadratic equations by extracting square roots. Solves quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; and (d) using the quadratic formula. (M9AL-Ia-b-1) a. Find the factors of quadratic expressions. b. Apply the zero product property in solving quadratic equations. c. Be attentive and cooperative in doing the given task with the group. Solves quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; and (d) using the quadratic formula. (M9AL-Ia-b-1) a. Find the factors of quadratic expressions. b. Solve quadratic equations by factoring. c. Appreciate how does solving quadratic equation help in making decision.
- 2. II. CONTENT Illustrations of Quadratic Equations Solving Quadratic Equations by Extracting Square Roots Solving Quadratic Equations by Factoring Solving Quadratic Equations by Factoring III. LEARNING RESOURCES A. References 1. Teacher’s Guide pp. 14-18 pp. 19-23 pp. 24-27 pp. 24-27 2. Learner’s Materials pp. 11-15 pp. 18-23 pp. 27-31 pp. 27-31 3. Textbook Math III SEDP Series Capalad, Lanniene, et., al. 21st Century Math III pp. 167-172 Ho, Ju Se T. et., al Math PACE (Algebra II – 8) pp. 7 Accelerated Christian Education, Inc. 4. Additional Materials from Learning Resource (LR) portal http://math.tutorvista.com/al gebra/quadraticequation.ht m http://library.thinkquest.org/2 0991/alg2/quad.htm http://www.purplemath.com/ moduleiquadraticform.htm http://www.algebrahelp.com/ lessons/equation/quadratic http://www.purplemath.com/ modules/solvquad.html http://www.webmath.com/qu adri.html https://cdn.kutasoftware.co m/worksheets/Alg1/Solving %20Quadratic%20Factoring .pdf B. Other Learning Resources Grade 9 LCTG by DepEd Cavite Mathematics 2016, laptop, Monitor/Projector, Activity Sheets Grade 9 LCTG by DepEd Cavite Mathematics 2016, laptop, Monitor/Projector, Activity Sheets Grade 9 LCTG by DepEd Cavite Mathematics 2016, laptop, Monitor/Projector, Activity Sheets Grade 9 LCTG by DepEd Cavite Mathematics 2016, laptop, Monitor/Projector, Activity Sheets IV. PROCEDURES
- 3. A.Reviewing previous lesson or presenting the new lesson Do You Remember These Products? Find each indicated product then answer the questions that follow. 1. 3(x2+7) 2. 2s(s-4) 3. (w+7)(w+3) 4. (x+9)(x-2) 5. (2t-1)(t+5) 6. (x+4)(x+4) 7. (2r-5)(2r-5) 8. (3-4m)2 9. (2h+7)(2h-7) 10.(8-3x)(8+3x) a. How did you find each product? b. In finding each product, what mathematics concepts or principles did you apply? Explain. c. How would you describe the products obtained? Find My Roots! Find the following square roots. Answer the questions that follow. a .How did you find each square root? b. How many square roots does a number have? c. Does a negative number have a square root? Why? d. Describe the following numbers: . Are the numbers rational or irrational? How do you describe rational numbers? How about numbers that are irrational? a. What are the factors that contribute to garbage segregation and disposal? b. As an ordinary citizen, what can we do to help solve the garbage problem in our community? Students are grouped into 2 (boys vs girls). Using flashcards, have each group give the factors of the following polynomials mentally. a. x2 + 8x – 9 = 0 b. x 2 + 9x = 10 c. x2 = 3 – 2x d. x2 – 6 = – 5x e. x2 + 6x – 7 = 0 f. x2 + x – 12 = 0 B.Establishing a purpose for the lesson Another Kind of Equation! Below are different equations. Use these equations to answer the What Would Make a Statement True? Factor each polynomial. a. x2 – 9x + 20 b. x2 – 8x + 12 1. 6. 2. 7. 3. 8. 4. 9. 5. 10.
- 4. questions that follow. 1. Which of the given equations are linear? 2. How do you describe linear equations? 3. Which of the given equations are not linear? Why? How are these equations different from those which are linear? What common characteristics do these equations have? Solve each of the following equations in as many ways as you can. Answer the questions that follow. a. How did you solve each equation? b. What mathematics concepts or principles did you apply to come up with the solution of each equation? c. Compare the solutions you got with those of your classmates. Did you arrive at the same answer? If not, why? d. Which equations did you find difficult? Why? c. x2 + 14x +48 d. x2 – x – 6 e. x2 + 7x – 18 C.Presenting examples/ instances of the lesson A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following standard form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. In the equation, ax2 is Equations such as , , and are the simplest forms of quadratic equations. To solve this equations, we extract the square roots of both sides. Hence we get, Illustrative Example: The quadratic equation x2 + 4x = 5 can be solved by factoring using the following procedure: Write the equation in Illustrative Example: Find the solutions of 2x2 + x = 6 by factoring. a. Transform the equation into standard form ax2 +bx+ c = 0. x2-5x+3=0 9r2-25=0 c=12n-5 9-4x=15 r2=144 8k-3=12 t2-7t+6=0 2s+3t=-7 6p-q=10 1. 6. 2. 7. 3. 8. 4. 9. 5. 10.
- 5. the quadratic term, bx is the linear term, and c is the constant term. Example 1 2x2 – 6x – 15 = 0 is a quadratic equation in standard form with a =2 b = -6 and c =-15. Example 2 2x (x – 4) = 18 is a quadratic equation. However, it is not written in standard form. To write the equation in standard form, expand the product and make one side of the equation zero as shown below. 2x(x – 4)= 18→ 2x2 – 8x = 18 2x2 – 8x – 18 = 18 -18 2x2 – 8x – 18 = 0 The equation becomes 2x2 – 8x –18 = 0 which is in standard form. In the equation 2x2 - 8x -18 = 0 a = 2, b = - 8, c = - 18. Example 2. Find the solutions of the equation by extracting square roots. Write the equation in the form . Adding both sides results in . Recall that the square of any real number, whether it is positive or negative, is always a positive number. For example . Hence, there is no real number x which satisfies . Therefore, the equation has no real root. standard form: x2 + 4x – 5 = 0 Factor the quadratic polynomial: (x + 5) (x – 1)= 0 Set each factor equal to 0: (x +5=0) or (x-1=0) Solve each equation: x = -5 or x = 1 Write the solution set:{ -5, 1} Each member of the solution set can be checked by substituting for x in the original equation. Let x = -5 Let x = 1 x2 + 4x = 5 x2 + 4x = 5 (-5)2 +4(-5)=5 (1)2 +4(1)=5 25 - 20 = 5 1 + 4 = 5 5 = 5 5 = 5 2x2 + x – 6 = 0 b. Factor the quadratic expression 2x2 +x–6. (2x – 3) (x + 2) c. Apply the zero product property by setting each factor of the quadratic expression equal to 0. 2x – 3 = 0 ; x + 2 = 0 d. Solve each resulting equation. 2x – 3 + 3 = 0 + 3 2x = 3 x = 3/2 x + 2 – 2 = 0 – 2 x = - 2 e. Check the values of the variable obtained by substituting each in the equation 2x2 + x = 6. For x = 3/2 2x2 + x = 6 2(3/2)2 + 3/2 = 6 2(9/4) + 3/2 = 6 9/2 + 3/2 = 6 6 = 6 For x = -2
- 6. 2x2 + x = 6 2(-2)2 + (-2) = 6 2 (4) – 2 = 6 8 – 2 = 6 6 = 6 D.Discussing new concepts and practicing new skills #1 Tell whether each equation is quadratic or not quadratic. If the equation is not quadratic, explain. a. x2 + 7x + 12 = 0 b. -3x (x + 5) = 0 c. 12 – 4x = 0 d. (x + 7) (x – 7) = 3x e. 2x+ (x + 4) = (x – 3)+ (x – 3) Extract Me! Solve the following quadratic equations by extracting square roots. Have them find a partner and do the following. Solve each equation by factoring. 1. x2 -11x + 30 = 0 2. x2 – x – 12 = 0 3. x2 + 5x – 14 = 0 4. x2 + 2x + 1 = 0 5. x2 – 4x – 12 = 0 Solve each equation by factoring. 1. 2x2 -7x - 4 = 0 2. 3x2 + x – 2 = 0 3. 4x2 – 1 = 0 4. 2x2 - 3x + 1 = 0 5. 10x2 – 14x + 4 = 0 E.Discussing new concepts and practicing new skills #2 a. What is a quadratic equation? b. What is the standard form of quadratic equation? c. In the standard form of quadratic equation, which is the quadratic term? linear term? constant term? d. Why is a in the standard form cannot be equal to 0? 1. What is the simplest form of quadratic equation? 2. How do you get the solutions of these equations? 3. How many solutions/roots does the equation have if k > 0? k = 0? k < 0? Factor each of the following polynomials: a. x2 + 5x -6 Find the factors of -6 whose sum is 5 b. y2 – 6y – 27 Think of the factors of - 27 whose sum is -6 c. x2 + 14x + 49 Find identical factors of 49 and having the sum of 14 d. x2 – 5x – 14 Determine the factors of a. How do we solve a quadratic equation? b. What are the procedures in solving quadratic equation by factoring? c. How many solution/s does a quadratic equation have? d. How do you call each solution? e. How do we know if the solution is correct? 1. 6. 2. 7. 3. 8. 4. 9. 5. 10. 6.
- 7. -14 whose sum is -5 e. 2x2 - 7x + 6 Find the missing factors (2x __)(x __) F. Developing mastery (Leads to Formative Assessment 3) Write each equation in standard form then identify the values of a, b, and c. a. 2x2 + 5x – 3 = 0 b. 3 -2x2 = 7 c. x (4x + 6) = 28 d. (3x-7)(5x+2) “Extract then Match” Find the solutions of the following quadratic equations by matching column B with column A. Correct roots will also reveal the cities primary delicious fruits. A B Tagaytay Strawberry Davao Mangosteen Cebu Pineapple Zamboanga Durian Baguio Mango Banana Solve the following quadratic equation by factoring. 1. x2 + 9x – 36 = 0 2. x2 – 6x = 27 3. x2 + 4x – 60 = 0 4. 2x2 – 5x – 18 = 0 5. x2 + 6x = 16 Determine the solution set of each equation. 1. 7r2 - 14r = -7 2. x2 – 25 = 0 3. 3y2 = 3y + 60 4. y2 – 11y + 19 = -5 5. 8x2 = 6x - x2 G.Finding practical applications of concepts and skills in New houses are being constructed in CalleSerye. The residents of this new Solve the problem. Cora has a piece of cloth Solve the following problem: One positive number Solve the problem: The length of a rectangle
- 8. daily living housing project use a 17m long path that cuts diagonally across a vacant rectangular lot. Before the diagonal lot was constructed, they had to walk a total of 23 m long along the two sides if they want to go from one corner to an opposite corner. Write the quadratic equation that represents the problem if the shorter side is x. Identify the values of a, b, and c. whose area is 32 square inches. What is the length of the side of the largest square that can be formed using the cloth? exceeds another by 5. The sum of their squares is 193. Find both numbers. is 6 cm more than the width. If the area is 55 cm2 , find the dimensions of the rectangle. H.Making generalizations and abstractions about the lesson A quadratic equation is an equation of degree 2 that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. To solve an incomplete quadratic equation: 1. Solve the equation for the square of the unknown number. 2. Find the square roots of both members of the equation. Some quadratic equations can be solved easily by factoring. To solve such equations, the following procedure can be followed. 1. Transform the quadratic equation using standard form in which one side is zero. 2. Factor the non-zero side. 3. Set each factor to zero. 4. Solve each resulting equation. 5. Check the values of the variable obtained by substituting each in the original When solving a quadratic equation, keep in mind that: 1. The quadratic equation must be expressed in standard form before you attempt to factor the quadratic polynomial. 2. Every quadratic equation has two solutions. Each solution is called a root of the equation. 3. The solution set of a quadratic equation can be checked by verifying that each different root makes the original equation
- 9. equation. a true statement. I. Evaluating learning Write fact if the equation is quadratic and bluff if the equation is not quadratic. 1. x2 + x – 3 = 0 2. 24x + 81 = x2 3. x2 = 2x (6x2 + 4) 4. 2x2 = 7x 5. 5 – x + (2x - 3) = 12 Solve each equation by extracting square roots. 1. x2 = 81 2. 4x2 – 100 = 0 3. a2 – 225 = 0 4. 7p2 – 2 = 54p 5. 2r2+ 3 = 67 Group Activity: What Name is Given to Words That are Formed to Imitate Sounds? Find the solutions and write the letter of each solution set on top of the given answer in the boxes below to solve the puzzle. N x2 – 2x = 4 T x2 +4x– 21 =0 C x2 – 4x = 5 P x2 – 2x = 8 E x2 – 3x = 10 A x2 – x = 2 I x2 – 9x = -8 O x2 – 3x = -2 M x2 – 5x+6= 0 Solve each equation by factoring. 1. 3r2 – 16 r – 7= 5 2. 6b2 – 13b + 3 = -3 3. -4k2 – 8k – 3 = -3-5k2 4. 7x2 + 2x = 0 5. 15a2 – 3a = 3 – 7a Fact or bluff
- 10. J. Additional activities for application or remediation 1. Give 5 examples of quadratic equations written in standard form. Identify the values of a, b, and c. 2. Study solving quadratic equation by extracting the square root. a. Do you solve a quadratic equation by extracting the square root? b. Give the procedure. Reference: Learner’s Material pp. 18-20 Find the solutions of the following equations by extracting square roots. 1. 2(x+3)2 = 18 2. 4a2 – 147 = a2 3. 1 = ½ x2 4. 54a2 – 6 - 24 5. 3c2 – 5 = 25 Follow-Up 1. Find the solutions of (x + 3)2 = 25. 2. Do you agree that x2 + 5x – 14 = 0 and 14 – 5x – x2 = 0 have the same solutions? Justify your answer. Factor the following Quadratic Equation. 1. x2 + 4x + 4 = 0 2. x2 – 6x + 9 = 0 3. x2 – 8x + 16 = 0 4. x2 + 2x + 1 = 0 5. x2 – 10x + 25 = 0 What have you noticed with their factors? 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.
- 11. 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? 7. What innovation or localized materials did I use/discover which I wish to share with other teachers? Preparedby: JANINE A. ESTOLANO Teacher I Notedby: LEA H. SANGALANG Head Teacher I