School: BIRBIRA HIGH SCHOOL Teacher: AGOSTO C. BUNSAY Teaching Dates and AUGUST 22-26, 2022 Time: GRADES 1 to 12 DAILY LESSON LOG MONDAY I. OBJECTIVES A. Content Standards B. Performance Standards C. Learning Competencies/ Objectives Write the LC code for each II. CONTENT III. LEARNING RESOURCES A. TUESDAY Grade Level: 8 Learning Area: MATHEMATICS Quarter: 1ST QUARTER WEDNESDAY THURSDAY 1. Identify the expression that can be factored 2. Determine the process of factoring using greatest common monomial factor 3. Show appreciation in factoring 4. Find factors of a given polynomials The learners demonstrate understanding of key concepts of factors of polynomials The learners formulate real-life problems involving factors and solve these with utmost accuracy using a variety of strategies. Learning Competency: Factors completely different types of polynomials (polynomials with common monomial factor, difference of two squares, sum and difference of two cubes, perfect square trinomials, and general trinomials). M8AL-Ia-b-1 Factoring polynomials with greatest common monomial factor Curriculum guide, Teacher’s guide, Learner’s module Curriculum guide, Teacher’s guide, Learner’s module Factoring polynomials with greatest common monomial factor Curriculum guide, Teacher’s guide, Learner’s module Factoring polynomials with greatest common monomial factor Curriculum guide, Teacher’s guide, Learner’s module Module 1: Pages 29-33 Module 1: Pages 29-38 Module 1: Pages 29-38 Pages 27-31 Pages 27-31 Pages 27-31 Let the students recall the definition of factoring and the first type of factoring introduced to them. Review previous lesson by letting the students answer the exercises. 1. What are the two types of factoring being discussed and introduced to you? 2. What type of factoring can be applied if you are given 49-n2? What are the factors? Factoring polynomials with greatest common monomial factor References 1. Teacher’s Guide pages 2. Learner’s Materials pages 3. Textbook pages 4. Additional Materials from Learning Resource (LR) portal B. Other Learning Resources Pictures of Filipino celebrities IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson FRIDAY Getting to know each other and Subject Orientation The teacher lets the students recall about finding the greatest common factor (GCF) of the given numbers using flash cards. 1. 3 , 6 2. 4, 6 3. 24, 36 4. 14, 28, 35 Possible response: Factoring is the reverse of multiplication. The first type was factoring by greatest common monomial factor Factoring polynomials with greatest common monomial factor Curriculum guide, Teacher’s guide, Learner’s module 5. 9, 12, 24 Possible responses: 1. 3 2. 2 3. 12 4. 7 5. 3 He/she then ask the students if the given polynomial below has a common monomial factor and let them also describe the given polynomial 1. abc + abd 3. X2-y2 2. 24m2-12m 4. 25-b2 Possible response: numbers 1 and 2 have a common monomial factor numbers 3 and 4 don’t have any common monomial factor The given polynomials are binomials terms in numbers 3 and 4 are perfect squares numbers 3 and 4 are polynomial with difference of two squares 3. How about if you are given 36t2-8t? What are the factors? Possible responses: 1. Factoring polynomial with greatest common monomial factor and difference of two squares 2. Difference of two squares, (7+n)(7-n) 3. Factoring with greatest common monomial factor, 4t(9t-2) Then the teacher now ask the student : If given this kind of polynomial a3+b3, can we find the factor using greatest common monomial factor or difference of two squares? Why? Possible responses: No, because the given has no GCMF and is not a difference of two squares. Also, It is a sum two cubes. B. Establishing a purpose for the lesson C. Presenting examples/instances of the new lesson D. Discussing new concepts and practicing new skills #1 * State that after studying polynomials in grade 7 which are special products, that is, polynomials which are the results of multiplying polynomials of particular forms, we can now take a look at how to determine the factors of these special products. * Ask the student to recall what they have learned before about factors. * State that factoring is the process of obtaining the factors of a product. It is the reverse of the process of finding the product. *Show pictures of celebrities performing Superhero roles. Start the study of factoring with a discussion of Greatest Common Monomial Factor. The activity presented will be a springboard in the discussion of factoring by greatest common monomial factor. He/she tells the students when to Let the students , in group of two do the Activity 5 on page 32 of the Learner’s Module and answer the following questions: 1. How do you think the products are obtained? Discusse and illustrates thoroughly the steps in finding the factors of a polynomial with sum and difference of two cubes. Give examples: 1. 8-d3 2. k6+125 use and not to use this type of factoring. Emphasize that this type of factoring should be use first before applying any type of factoring. 2. 3. 4. What are the different techniques used to solve for the products? What is the relationship of the product to its factor? Have you seen any pattern in this activity? Answer key: 1. (2-d)(4+2d+d2) (k2+5) (k4-5k2+25) Possible responses : 1. E. Discussing new concepts and practicing new skills #2 F. Developing mastery (leads to Formative Assessment 3) G. Finding practical applications of concepts and skills in daily living H. Making generalizations and abstractions about the lesson Illustrate now on how to obtain the greatest common monomial factor of a given polynomial. He/she can use the examples found in learner’s module at page 31. the product are obtain by making the given numbers into sum and difference of binomials 2. by multiplying the sum and difference of binomials 3. the factors of difference of two squares are sum and difference of binomials. Students give varied answers Discuss with students using the given number pattern of activity 5 to see the relationship of factors to product. He/she may bring back the students to multiplying sum and difference of binomials in special product to see how factors may be obtained. Students should realize that factors of difference of two squares are sum and difference of binomials. Summarize the concept of factoring polynomials with difference of two squares by asking the following questions: 1. What are the factors of polynomials with difference of two squares? 2. How to find the factors of a given polynomial with difference of two squares? Summarize the steps in finding the factors of a given polynomial with sum and difference of two cubes through questions like: A. What are the steps in finding the factor of polynomial with sum of two cubes? B. What are the steps in finding the factor of polynomial with difference of two cubes? Answers shall be drawn from the students. Answers shall be drawn from the students. Possible responses: 1. It is the sum and difference of binomials 2. Get the square roots of the two squares, then write the product of the sum and difference of the square roots Possible response: Remember: The factored form of a polynomial that is a difference of two squares is the sum and difference of the square roots of the first and last terms. A. Steps in finding the factor of polynomial with sum of two cubes Step 1: Find the cube root of the first and last terms. Step 2: Write their sum as the first factor Step 3: For the second factor, get the trinomial factor by: a. Squaring the first term of the first factor; b. Subtracting the product of the first and second terms of the first factor. c. Squaring the last term of the first factor Step 4: write them in factored form B. Steps in finding the factor of polynomial with difference of two cubes Step 1: Find the cube root of the first and last terms. Step 2: Write their difference as the first factor Step 3: For the second factor, get the trinomial factor by: a. Squaring the first term of the first factor; b. Adding the product of the first and second terms of the first factor. c. Squaring the last term of the first factor Step 4: write them in factored form I. Evaluating learning Find the factors of the given polynomials 1. 7r4h5+14rh6 2. 32m3-24mn5-64m2n 3. 120a2b4c7+50abc10 Answer key: 1. 7rh5(r3+2h) 2. 8m(4m2-3n5-8mn) 10abc7(12ab3+5c3) J. Additional activities for application or remediation V. REMARKS Let the students answer individually the formative assessment. Find the factors of the given polynomials. 1. c3-d3 2. w6+1 3. 216-h9 Answer key: 1. 2. 3. (c-d)(c2+cd+d2) (w2+1)(w4-w2+1) (6-h3)(36+6h3+h6) VI. REFLECTION A. B. C. D. E. F. G. No. of learners who earned 80% in the evaluation No. of learners who require additional activities for remediation Did the remedial lessons work? No. of learners who have caught up with the lesson No. of learners who continue to require remediation Which of my teaching strategies worked well? Why did these work? What difficulties did I encounter which my principal or supervisor can help me solve? What innovation or localized materials did I use/discover which I wish to share with other teachers?
