Sample modified dll with activity sheet
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The document summarizes a mathematics lesson on the nature of the roots of quadratic equations. It includes the objectives, content, learning resources, procedures, and activities for the lesson. The lesson teaches students to characterize the roots of a quadratic equation using the discriminant. It establishes that the nature of the roots (whether they are real/not real, rational/irrational, equal/not equal) depends on whether the discriminant is zero, a positive perfect square, a positive non-perfect square, or negative. Students complete group activities to practice determining the nature of roots for different quadratic equations.
Sample modified dll with activity sheet
- 1. Annex 2B.1 to DepEdOrderNo.42 ,s. 2016 Time : 11:00 – 12:00 ARROYO Monday I. OBJECTIVES A. ContentStandard The learnerdemonstratesunderstandingof keyconceptsof quadratic equations. B. Performance standard The learnerisable to investigatethoroughlymathematical relationships invarioussituations,formulate real-lifeproblems involvingquadraticequations. C. LearningCompetencies Write the LC Code for each The learner characterizes the roots of a quadratic equation using the discriminant. M9AL-Ic-1 II. CONTENT The Nature of the Roots of a Quadratic Equation III. LEARNING RESOURCES A. References 1. Teacher’s Guide pages 2. Learner’s materialspages pp. 56-65 3. Textbook pages 4. Additional Materialsfrom Learning Resource (LR) portal B. Other Learning Resources PowerPoint Presentation, Student Activity Sheet and Black cartolina IV. PROCEDURES TEACHER ACTIVITY STUDENT ACTIVITY A. Reviewingpreviouslessonor presentingthe new lesson. Good MorningClass! House Rule: 1. Enter tolearn 2. Behave 3. Be responsible Do youunderstand? VeryGood! Our lessonfortodayisabout The Nature of the Rootsof Quadratic Equation.Butbefore we goon, let us have a short review. Rememberthatthe quadratic formulais, 𝑥 = −𝑏±√𝑏2−4𝑎𝑐 2𝑎 Andb2 – 4ac isthe discriminantof the equationax2 + bx + c = 0. Good morningsir!It’snice to see you! Yes sir! Smiling Listening DAILY LESSON LOG School PRESIDENT QUIRINO NATIONAL HIGH SCHOOL Grade Level GRADE 9 Teacher JOHN L. PADASAN Learning Areas MATHEMATICS Teaching Day JULY 08, 2019 (Day26) Quarter FIRST
- 2. B. Establishinga purpose for the lesson. (Lecture Method) Thisvalue can be describedthe nature of the rootsof quadratic equation.Itcan be, 1. Real numberandare equal if the discriminantisequal tozero. 2. Rational numberbutnotequal if the discriminantisgreaterthan zeroand a perfectsquare. 3. Irrational numbers andnotequal if the discriminantisgreaterthan zerobut not a perfectsquare. 4. Noreal roots if the discriminant islessthan zero. Like forexample, Listening C. Presentingexamples/instancesof the lesson. (Demonstrationand Socratic Method) 1. Describe the rootsof x2 – 4x + 4 = 0 a = 1, b = -4 , c = 4 b2 – 4ac = (-4)2 – 4 (1)(4) = 16 – 16 = 0 Since the value is0, thenthe roots are real and are equal. Another problemand letthe studentto answerit on the board. 2. Determine the nature of the roots of x2 + 7x + 10 = 0. Since the value isgreaterthan0 and perfectsquare then whatisthe nature of the roots? 3. Describe the rootsof x2 + 6x + 3 = 0 Since the value isgreaterthan0 and nota perfectsquare thenthe roots is? 4. Determine the nature of the roots of x2 + 2x + 5 = 0 Since the value islessthan0 then the equationhas?.... Understand? Is there anyquestion? VeryGood! Not yet. Now,proceed to yourgroup and do the following activities. Listeningandasksany clarification Givenproblemansweredbythe studenton the board. x2 + 7x + 10 = 0. a = 1, b = 7 , c = 10 b2 – 4ac = (7)2 – 4 (1)(10) = 49 – 40 = 9 Rational numberbutnotequal. Givenproblemansweredbythe studentonthe board. x2 + 6x + 3 = 0 a = 1, b = 6 , c = 3 b2 – 4ac = (6)2 – 4 (1)(3) = 36 – 12 = 24 Irrational numberandnot equal. Givenproblemansweredbythe studentonthe board. x2 + 2x + 5 = 0 a = 1, b = 2 , c = 5 b2 – 4ac = (2)2 – 4 (1)(5) = 4 – 20 = - 16 No real roots. Yes,sir! None sir! Quiz!Quiz!Quiz! Ugh… Proceedtotheirrespective groupand do the activities. D. Discussing newconcepts and practicing new skills#1 (ActivityMethod) (Concept) Activity5: Place Me on the Table! Do the activity by group
- 3. E .Discussing newconcepts and practicing new skills#2 (Process) Activity7: What IsMy Nature? Do the activity by group F. Developingmastery ( Leadsto Formative Assessment3) (Reflect) Activity9: How Well DidI Understand the Lesson? Do the activity by group G.FindingPractical applications of concepts and skillsin dailyliving (Transfer) Activity10: Will Itor Will ItNot? Do the activity by group H. Presentationof Activity (Socratic Method) Askthe studentsto presentto presenttheirwork. Present the work done. I. Making generalizationsand abstractions about the lesson The lessonprovidedyouwith opportunitiestodescribe the nature of the rootsof quadratic equationusingthe discriminant evenwithoutsolvingthe equation. Most importantly,youwere able to findouthow the discriminantof a quadraticequationisillustratedin real-lifesituation. Listening J. Evaluating learning Formative Answerthe formative exam K. Additional activities for application or remediation. Assignment Note the assignment V. REMARKS Achieved VI. REFLECTION A. No. of learnerswho earned (80%) in the evaluation 60 (Note: 80% in 0=60 transmutation formula is 1/2 of the highest possible score) B. No. of learnerswho require additional activitiesfor remediation. 5 C. Did the remedial lessonswork? No. Of learnerswho have caught up with the lesson. 5 D. No. of learnerswho continue to require remediation. 0 E. Whichof my teachingstrategies worked well?Whydidthese work? Lecture method, Demonstration method, Activity Method and Socratic method. F. What difficultiesdidIencounter which my principal or supervisorcan helpme solve? None G. Whatinnovation or localized materialsdid I use/discoverwhich I wish to share with otherteachers? Used of black cartolina and chalk as student/group work sheet for presentation. Preparedby: JOHN L. PADASAN Math Teacher Checkedby: NIEVA B. COSTALES, MT-I Math DepartmentHead
- 4. ACTIVITY SHEET July 08, 2019 Rule: Work in group. After doing the following activities the group leader will pick a number from which of the following activities will be presented by the group. The leader shall also assign rate to the members from 1-5 based on participation. The fraction hereof is multiplied to the group score by the teacher for individual score in performance tasks. Name of Group: ____________________ Leader: ___________________________ Members: Rate: 1. _________________________ __________ 2. _________________________ __________ 3. _________________________ __________ 4. _________________________ __________ 5. _________________________ __________ A. Activity 5: Place Me on the Table! Answer the following. 1. Complete the table. Equation b2- 4ac Roots 1. x2 + 5x = 4 2. -4 x2 = 8x - 3 3. 10x - 1 = 4x2 4. 15 + 8x - 3x2 5. 3x(x – 14) = 12 2. Which quadratic equation has roots that are…. a) Real numbers and equal? __________________________ b) Rational numbers? _______________________________ c) Irrational numbers? _______________________________ d) Not real numbers? ________________________________ B. Activity 7: What Is My Nature? Determine the nature of the roots of the following quadratic equations using the discriminant. 1. x2 + 6x + 9 = 0 discriminant:__________ nature of the roots: __________ 2. 2x2 - 10x + 8 = 0 discriminant:__________ nature of the roots: __________ 3. x2 + 5x + 10 = 0 discriminant:__________ nature of the roots: __________ 4. 3x2 - 2x - 5 = 0 discriminant:__________ nature of the roots: __________ 5. 9x2 - 6x = -9 discriminant:__________ nature of the roots: __________ a. How didyoudetermine the nature of the rootsof each quadraticequation? _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ b. Whendo yousay that the rootsof a quadraticequation isreal or not real numbers?Rational or irrational numbers?Equal ornotequal? _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ c. How doesthe knowledgeof the discriminanthelpyouindeterminingthe nature of the rootsof any quadraticequation? _____________________________________________________________________________________ _____________________________________________________________________________________
- 5. _____________________________________________________________________________________ _____________________________________________________________________________________ C. Activity 9: How Well Did I Understand the Lesson? Answer the following questions. 1. Describe the roots of the quadratic equation when the discriminant is a. Zero. ____________________________________________________________ b. Positive perfect square. _________________________________________________ c. positive but not perfect square. ___________________________________________ d. negative. _____________________________________________________________ 2. Danica says that the quadratic equation 2x2 + 5x - 4 = 0 has two possible solutions because the value of its discriminant is positive. Do you agree with Danica? Justify your answer. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ D. Activity 10: Will It or Will It Not? Answer the following. 1. When a basketball player shoots a ball his hand at an initial height of 2 m with an initial upward velocity of 10 meters per second, the height of the ball can be modeled by the quadratic expression -4.9t2 + 10t + 2 after t seconds. a. What will be the height of the ball after 2 seconds? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ b. How long will it take the ball to reach the height of 4.5m? How long will it take to touch the ground? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ c. Do you think the ball can reach the height of 12 m? Why? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ d. Will the ball hit the ring if the ring is 3 m high? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________