Anzeige

21. Aug 2022•0 gefällt mir## 0 gefällt mir

•251 Aufrufe## Aufrufe

Sei der Erste, dem dies gefällt

Mehr anzeigen

Aufrufe insgesamt

0

Auf Slideshare

0

Aus Einbettungen

0

Anzahl der Einbettungen

0

Downloaden Sie, um offline zu lesen

Melden

Bildung

DLL MATH 9 WEEK 1

MelanieCalonia1Folgen

Anzeige

Anzeige

Anzeige

Solving problems involving direct variationMarzhie Cruz

Detailed Lesson Plan in MathematicsAbbygale Jade

Lesson plan in mathematics ivErwin Cabigao

Long and synthetic divisionJessica Garcia

Adding and subtracting rational expressionsDawn Adams2

Mathematics 9 Quadratic Functions (Module 1)Juan Miguel Palero

- GRADES 1 TO 12 DAILY LESSON LOG SCHOOL: TUOD INTEGRATED SCHOOL GRADE LEVEL: NINE (9) TEACHER: MELANIE D. CALONIA LEARNING AREA: MATHEMATICS TEACHING DATES & TIME: AUGUST 22 – 26, 2022 (Week 1) QUARTER: FIRST QUARTER I. OBJECTIVES MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY A.Content Standards: The learner demonstrates understanding of the key concepts of quadratic equations, inequalities and functions, and rational algebraic equations. B. 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. C. Learning Competencies/Objective s: Write the LC code for each. The learner… shall be able determine the schedule of classes, school and classroom rules and regulations, and to select class officers. 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. II. CONTENT Orientation 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 Pages Page 14 Pages 15-16 Pages 16 – 17 Pages 18 2. Learner’s Materials Pages Pages 11-12 Pages 12-14 Pages 14 – 15 Pages 16 – 17
- 3. Text book Pages Math III SEDP Series Capalad, Lanniene, et., al. 21st Century Math IIIpp. 167-172 Ho, Ju Se T. et., al Math PACE (Algebra II – 8)pp. 7 Accelerated Christian Education, Inc. 4. Additional Materials from Learning resources(LR)Portal Math Learner’s Module Math Learner’s Module Math Learner’s Module Math Learner’s Module B. Other Learning Resources School Handbook (if any) Grade 9 LCTG by DepEd, laptop, Monitor/Projector, Activity Sheets Grade 9 LCTG by DepEd, laptop, Monitor/Projector, Activity Sheets III. PROCEDURE A. Reviewing Previous Lesson or Presenting 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: √8,−√40 , √60 ,𝑎𝑛𝑑 − √90 . Are the numbers rational or irrational? How do you describe rational numbers? a. What are the factors that contribute to garbage segregation and disposal? 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 1. √16 = 6. −√289 = 2. −√25 = 7. √0.16 = 3. √49 = 8. ±√36 = 4. −√64 = 9. √ 16 25 = 5. √121 = 10. ±√ 169 256 =
- How about numbers that are irrational? B. Establishing a Purpose for the Lesson Another Kind of Equation! Below are different equations. Use these equations to answer the 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? What Would Make a Statement True? 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? Factor each polynomial. a. x2 – 9x + 20 b. x2 – 8x + 12 c. x2 + 14x +48 d. x2 – x – 6 e. x2 + 7x – 18 x2-5x+3=0 c=12n-5 9-4x=15 r2=144 8k-3=12 2s+3t=-7 6p-q=10 1.𝑥 + 7 = 12 6. −5𝑥 = 35 2.𝑡 − 4 = 10 7. 3ℎ − 2 = 16 3.𝑟 + 5 = −3 8. −7𝑥 = −28 4.𝑥 − 10 = −2 9. 3(𝑥 + 7) = 24 5.2𝑠 = 16 10. 2(3𝑘 − 1) = 28 t2-7t+6=0 9r2-25=0 r2=144 2s+3t=-7
- 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 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 Equations such as 𝑥2 = 9, 𝑥2 = 16, and 𝑥2 = 21 are the simplest forms of quadratic equations. To solve this equations, we extract the square roots of both sides. Hence we get, 𝑥2 = 9 𝑥 = ±√9 𝑥 = ±3 Example 2. Find the solutions of the equation 𝑥2 + 81 = 0 by extracting square roots. Write the equation in the form 𝑥2 = 𝑘. Adding both sides results in 𝑥2 = −81. Recall that the square of any real number, whether it is positive or negative, is always a positive number. For example (+6)2 = 36; (−6)2 = 36. Hence, there is no real number x which satisfies 𝑥2 = −81. Therefore, the equation has no real root. Illustrative Example: The quadratic equation x2 + 4x = 5 can be solved by factoring using the following procedure: Write the equation in 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 Illustrative Example: Find the solutions of 2x2 + x = 6 by factoring. a. Transform the equation into standard form ax2 +bx+ c = 0. 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.
- which is in standard form. In the equation 2x2 - 8x -18 = 0 a = 2, b = - 8, c = - 18. 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 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 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? 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 𝑥2 = 𝑘 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 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 1. 𝑥2 = 16 6. 4𝑥2 − 225 = 0 2. 𝑡2 = 81 7. 3ℎ2 − 147 = 0 3. 𝑟2 − 100 = 0 8.(𝑥 − 4)2 = 169 4. 𝑥2 − 144 = 0 9. (𝑘 + 7)2 = 289 5. 2𝑠2 = 50 10. (2𝑠 − 1)2 = 225 6.
- d. Why is a in the standard form cannot be equal to 0? Determine the factors of -14 whose sum is -5 e. 2x2 - 7x + 6 Find the missing factors (2x __)(x __) equation have? d. How do you call each solution? How do we know if the solution is correct? 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 (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 𝑥2 − 64 = 0 𝑥 = ±6 Davao Mangosteen 2𝑥2 − 32 = 0 𝑥 = ±5 Cebu Pineapple 𝑥2 − 196 = 0 𝑥 = ±8 Zamboanga Durian 11𝑥2 + 17𝑥 = 106 𝑥 = ±4 Baguio Mango 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 8x2 = 6x - x2
- 𝑥 4 = 9 𝑥 𝑥 = ±14 Banana 𝑥 = ±3 G. Finding Practical Application of Concepts and Skills in Daily Living New houses are being constructed in CalleSerye. The residents of this new 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. Solve the problem. Cora has a piece of cloth whose area is 32 square inches. What is the length of the side of the largest square that can be formed using the cloth? Solve the following problem: One positive number exceeds another by 5. The sum of their squares is 193. Find both numbers. Solve the problem: The length of a rectangle is 6 cm more than the width. If the area is 55 cm2 , find the dimensions of the rectangle. H. Making Generalization 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. 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. 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
- 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 equation. two solutions. Each solution is called a root of the equation. The solution set of a quadratic equation can be checked by verifying that each different root makes the original 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 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 {1,2}{4,−2} {1,2}{3,2} {−1,2} {−7,3} 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
- {1,2} {−2,4} {1,2} {−2,5} {1,8}{−1,5 } 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 3c2 – 5 = 25 Follow-Up 1. Find the solutions of (x + 3)2 = 25. 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 The lesson shall be continued tomorrow. The lesson shall be continued tomorrow. The lesson shall be continued tomorrow. The lesson shall be continued on Monday. VI. REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who required additional activities for remediation C. Did the remedial lessons work? D. No. of learners who continue to require remediation
- E. Which of my teaching strategies work well? Why did this work? F. What difficulties did I encounter which my principal or supervisor can help me solve? G. What innovation or localized materials did I used/discover which I wish to share with other teachers? Prepared by: Noted : Melanie D. Calonia Jenefeir B. Denque Math Teacher Principal I

Anzeige