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This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, procedures, and reflections for lessons on factoring polynomials. Specifically, it covers factoring polynomials with common monomial factors, the difference of two squares, the sum and difference of two cubes, perfect square trinomials, and general trinomials. The procedures describe reviewing previous lessons, presenting new material with examples, discussing concepts, practicing skills, developing mastery through activities, and assessing learning. Reflections include the number of students who achieved mastery and require remediation on the topics.

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DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 1 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies  Orient the learners about the subject.  Set standards and class rules. To diagnose students' prior knowledge on 1st quarter coverage -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 Subtask -Factor polynomials with common monomial factor -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 Sub-task -Factor polynomials with difference of two squares II. CONTENT Orientation Conduct Diagnostic Test PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages 32-33 34-35 2.Learner’s Materials Pages 27-31 32-33 3.Textbook Pages Elem. Algebra pp.202-203 Elem. Algebra pp.208-209

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4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson -Provide information on classroom policies to create a welcoming environment that builds a sense of community among the class. -Be aware of the grading system so that they will know how much are they going to put forth in order to pass.  Give the test:  Check the test  Have an item analysis  Compute the MPS Let the students review the GCF, multiplication rule and quotient rule as a prerequisite for factoring polynomials. Review the students with the previous lesson through board work. B. Establishing a purpose for the lesson The students will identify common things that are present in the three pictures. Then, they will answer the guided questions. Refer to Activity 4 page 30 of Math LM. LOCALIZATION: Use at least 5 pictures of school activities and let the students spot the things common to the pictures. Investigate the number pattern by comparing the products then write your generalizations afterwards. NUMBER PATTERN: a. (11)(9) = (10 + 1)(10 – 1) = 100 – 1 = b. (5)(3) = (4 + 1)(4 – 1) = 16 – 1 = c. (101)(99) = (100 + 1)(100 – 1) = 10000 – 1 = d. (95)(85) = (90 + 5)(90 – 5) = 8100 – 25 = e. (n – 5)(n + 5) = This activity will help the students understand the concepts of difference of two squares and how this pattern is used to solve numerical expressions. C. Presenting examples/instances of the new lesson The next activity will give an idea to the students on how factors are associated with products. They will match the factors in column A with the products in column B to Based on the activity, how do you think products are obtained? What are the different techniques used to solve for the products? What is the relationship of the

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decode the secret message. Refer to Activity 3 page 29 of Math LM. product to its factor? Have you seen any pattern in this activity? D. Discussing new concepts and practicing new skills #1 The teacher will ask the students with the following questions based on the previous activity. 1. What are your observations on the expression in column A? Compare them with those in column B. 2. Do you see any pattern? 3. Are the two expressions related? 4. Why is it important to know the reverse process of multiplication? For you to have a better understanding about this lesson, observe how the expressions below are factored and observe the relationships of the term with each other. 4𝑥2 – 36 = (2x + 6)(2x – 6) 𝑥2 – 𝑦2 = (x + y)(x – y) Ask students to generate rule in factoring difference of two squares. E. Discussing new concepts and practicing new skills #2 The teacher will start the discussion by defining factoring first. Then introduce the first type of factoring which is factoring the greatest common monomial factor and give more examples. Based on the examples that are presented, ask the students when to use and not to use this type of factoring. Oral Recitation: 1. What is the first term of each polynomial? 2. What is the last term of each polynomial? 3. What is the middle sign of the polynomial? 4. How was the polynomial factored? 5. What pattern is seen in the factors of the difference of two terms? 6. Can all expressions be factored using difference of two squares? Why or why not? 7. When can you factor expressions using difference of two squares F. Developing mastery(Leads to Formative Have a group contest. Board work Call a student who can write as many pairs of difference of two

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Assessment) square as they can create. (Note: Teachers must see to it that students must form difference of two squares). G. Finding practical applications of concepts and skills in daily living Appreciate the importance of knowing how to classify things with common characteristics. Apply concept of difference of two squares in real life. H. Making Generalizations and abstractions about the lesson How factoring Greatest Common Monomial Factor is being done? How factoring difference of two squares is being done? I. Evaluating learning Answer the following LOTS: Find the greatest common factor of the following pair of expressions. 1.) 8 & 12 2.) 3x & 6x 3.) 2xy4 & 4x2y2 MOTS: Factor the following expressions. 1.) 4x2 – 12x 2.) 9m2 – 15m3 3.) 4a2 + 12a + 8 HOTS: State the steps of factoring Greatest Common Monomial Factor. Answer: LOTS: 1. 4 2. 3x 3. 2xy2 MOTS: 1. 4x(x-3) 2. 3m2 (3-5m) Answer the following LOTS: `Give 3 pairs of perfect squares. MOTS: Factor each completely. 1. 1 − 16𝑥8 2. 25𝑦2-9 3. 𝑎4 − 625𝑏8 HOTS: State the steps of factoring the difference of two squares. Answer: LOTS: Answers’ Vary MOTS: 1. (1-4x4)(1+4x4) 2. (5y-3)(5y+3) 3. (a2+25b4)(a-5b)(a-5b) HOTS: Answers’ Vary

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3. 4(a2 +3a+2) HOTS: Answers’ Vary J. Additional activities for application or remediation V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation who scored below 80%. 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 Iwish to share with other teachers?

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DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 2 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies -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 -Factor polynomials with sum and difference of two cubes.  Independence Day -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 -Factor polynomials in a form of perfect square trinomial. Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1 II. CONTENT PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages pp.35-36 pp.39-40 pp.41-43 2.Learner’s Materials Pages pp.34-35 pp. 36-38 pp.39-41

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3.Textbook Pages Elem. Algebra pp.209-210 Elem. Algebra 206-207 Elem. Algebra 204-205 4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources Student-made bingo cards IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson Students will give examples of difference of two squares as many as they can. Review the students with the previous lesson through board work. How to factor perfect square trinomial? B. Establishing a purpose for the lesson Do you know how to factor the sum or difference of two cubes? What you need to just to get a perfect score in a quiz? Before you go to supermarket, did you list first the items you want to buy? C. Presenting examples/instances of the new lesson You have learned from the previous activity how factoring the difference of two squares is done and what expression is considered as the difference of two squares. We are now ready to find the factors of the Sum or difference of two cubes. To answer this question, find the indicated product and observe what pattern is evident. a. (a + b)(𝑎2 – ab + 𝑏2 ) b. (a – b)(𝑎2 + ab + 𝑏2 ) Let the students perform activity 10 on page 37. How to factor quadratic trinomial with numerical coefficient of the leading term 1? D. Discussing new concepts and practicing new skills #1 What are the resulting products? How are the terms of the products related to the terms of the factors? What if the process was reversed and you were Discuss the rules on how to factor perfect square trinomials. Discuss how to find factors of a general quadratic trinomial with numerical coefficient of the leading term 1 by listing possible factors. Cite examples.

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asked to find the factors of the products? How are you going to get the factor? Do you see any common pattern? E. Discussing new concepts and practicing new skills #2  Show and discuss to the students the step by step process on factoring the sum and difference of two cubes.  Give more examples for the deeper understanding of the students. Discuss using the examples on page 37-38 F. Developing mastery(Leads to Formative Assessment) Give group seat work. Board work Call a student who can supply the missing terms to make a true statement: 1. m2 + 12m +36 =(m+__)2 2. 16d2-24d +9 =(4d-__)2 3. a2b2 -6abc +9c2 =(a2b__ ____)2 4. 9n2+30nd+25d2 =(___ __5d)2 5. 49g2 –84g+36 =(___ __ ___)2 Factor Bingo Game(By Pair) G. Finding practical applications of concepts and skills in daily living What makes the task easier to do? H. Making Generalizations and abstractions about the lesson How factoring sum and difference of two cubes is being done? How factoring perfect square trinomial being done? Give emphasis to students that factoring quadratic trinomial is easy to do if you list down first the possible factor.

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I. Evaluating learning Answer the following: LOTS: Find the cube root of the following: 1.) 64 2.) X3 3.) 27y3 MOTS: Factor each completely. 1. 64𝑐3 − 𝑑3 2. 8𝑒3 𝑓6 + 125𝑔3 HOTS: Your teacher asked Kenth to factor 8x3-27 and his answer is 2x-3. Is he correct? Explain your answer. Answer: LOTS: 1. 4 2. X 3. 3y2 MOTS: 1. (4c-d)(16c2+4cd+d2) 2. (2ef2+5g)(4e2f4- 10ef2g+25g) Answer the following: LOTS: Determine a number that must be added to make each of the following a perfect square trinomial. 1. X2+2x+_____ 2. T2+20t+_____ 3. R2-16r+_____ MOTS: Factor the following. 1. x2+12x+36 2. a2+6a+9 3. 4n2+12nx+9x2 HOTS: How do you describe a perfect square trinomial? Answer the following: LOTS: Give the factors of the following numbers: 1. 4 2. 10 3. 15 MOTS: 1. x2+9x+20 2. a2+8a+15 3. y2-3y-10 HOTS: How to factor quadratic trinomial whose leading coefficient is 1? J. Additional activities for application or remediation V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation

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B. No. of learners who require additional activities for remediation who scored below 80%. 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?

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DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 3 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1 Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1  Solve problems involving factors of polynomials. M8AL-Ib-2  Students will follow the standard operating procedure in taking test.  Students will be able to answer the summative test. II. CONTENT PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages pp.44-46 pp.46-47 2.Learner’s Materials Pages pp.43-44 pp.44-45 3.Textbook Pages Elem. Algebra pp. 210-211 Elem. Algebra pp. 212-216 4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources IV. PROCEDURES

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A. Reviewing previous lesson or presenting the new lesson How to factor quadratic trinomial with numerical coefficient of the leading term 1? Have a drill. How to factor quadratic trinomial using Grouping or AC Method? How to factor polynomials consist of more than 3 terms?  Recall the standard operating procedure in taking summative test  Distribute the test papers.  Start the test.  Collect the test papers  Let them check their answers  B. Establishing a purpose for the lesson Do you know how to group things? What is your ideal group? Do you believe that every problem has a solution? C. Presenting examples/instances of the new lesson How to factor quadratic trinomial with numerical coefficient of the leading term greater than 1?Try this: 2x2-5x-3. How to factor polynomials by grouping technique? Pose one problem. Then, let the students solve it. Do this in a group of 5. D. Discussing new concepts and practicing new skills #1 Discuss how to find factors of a general quadratic trinomial with numerical coefficient of the leading term not 1by grouping or AC Method. Cite examples. State the steps of factoring polynomials by grouping technique. Give more examples State to the students the steps of solving problems involving factors of polynomials. Cite examples. E. Discussing new concepts and practicing new skills #2 Teach them by group on how to factor polynomials by grouping techniques F. Developing mastery(Leads to Formative Assessment) Group the students into 5 and let them perform activity 13 on page 44. Famous Four Words(By Group) With your group mates, factor the following expressions by grouping and write a four - letter word using the variable of the factors to reveal the 5 most frequently used four - letter word. 1. 4wt + 2wh + 6it + 3ih 2. 15te – 12he + 10ty – 8hy 3. hv + av + he + ae 4. 10ti – 8ts – 15hi + 12hs 5. 88fo + 16ro – 99fm – 18rm Have board work.

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G. Finding practical applications of concepts and skills in daily living How important is proper grouping in real life? Apply concept of grouping techniques in real life by classifying things found in school. Apply the process of solving problems involving polynomials by formulating real life problem involving factors of polynomials. H. Making Generalizations and abstractions about the lesson One of the methods of finding the factor of quadratic trinomial with numerical coefficient of the leading term not 1 is through grouping or AC method. Extend learnings in factoring through grouping techniques. You have to group terms with common factors. Some problems encountered in Algebra need to be expressed in terms of polynomials before they can be solved. Then, apply the different factoring techniques for finding correct solutions. I. Evaluating learning Answer the following: LOTS: Arrange the steps of grouping or AC method in factoring quadratic trinomial whose leading coefficient is greater than 1. ___Group terms with common factors. ___Factor the groups using greatest common monomial factor. ___Find the product of the leading term and the last term. ___Find the factors of the product of the leading term and the last term ____Rewrite the trinomial as four-term expressions by replacing the middle term by the sum factor. ____Factor out the common binomial and write the remaining factor as the sum or difference of binomial. MOTS: Answer the following: LOTS: Group the terms with common factors. 1. 7sm+35om+9se+45oe 2. 42wa+54wt+56ha+72ht 3. 72he+16we+27hn+6wh MOTS: Factor by grouping: 1. 3x2-2x+6x-4 2. 3ab+5b-3ac-5c 3. 5m-15+3m2-9m HOTS: Answer the following: LOTS: MOTS: Solve the problem: The square of a positive integer is 98 less than twice the square of the next consecutive positive integer. What are the integers? HOTS: Formulate 1 real life problem involving factors of polynomials.

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Factor the following: 1.) 2a2+a-15 2.) 3x2-8x-3 3.) 4x2+10x+6 HOTS: Formulate 1 quadratic trinomial whose leading coefficient is greater than 1, then find the factors. J. Additional activities for application or remediation JOURNAL WRITING: Instruction: Reflect on the activities you have done in this lesson by completing the following statements. Write your answers on your journal notebook. • I learned that I... • I was surprised that I... • I noticed that I... • I discovered that I... • I was pleased that I... V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation who scored below 80%. C. Did the remedial lessons work? No. of learners who have caught up with the

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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?

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DLLWeek1_3.docx

  • 1. DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 1 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies  Orient the learners about the subject.  Set standards and class rules. To diagnose students' prior knowledge on 1st quarter coverage -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 Subtask -Factor polynomials with common monomial factor -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 Sub-task -Factor polynomials with difference of two squares II. CONTENT Orientation Conduct Diagnostic Test PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages 32-33 34-35 2.Learner’s Materials Pages 27-31 32-33 3.Textbook Pages Elem. Algebra pp.202-203 Elem. Algebra pp.208-209
  • 2. 4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson -Provide information on classroom policies to create a welcoming environment that builds a sense of community among the class. -Be aware of the grading system so that they will know how much are they going to put forth in order to pass.  Give the test:  Check the test  Have an item analysis  Compute the MPS Let the students review the GCF, multiplication rule and quotient rule as a prerequisite for factoring polynomials. Review the students with the previous lesson through board work. B. Establishing a purpose for the lesson The students will identify common things that are present in the three pictures. Then, they will answer the guided questions. Refer to Activity 4 page 30 of Math LM. LOCALIZATION: Use at least 5 pictures of school activities and let the students spot the things common to the pictures. Investigate the number pattern by comparing the products then write your generalizations afterwards. NUMBER PATTERN: a. (11)(9) = (10 + 1)(10 – 1) = 100 – 1 = b. (5)(3) = (4 + 1)(4 – 1) = 16 – 1 = c. (101)(99) = (100 + 1)(100 – 1) = 10000 – 1 = d. (95)(85) = (90 + 5)(90 – 5) = 8100 – 25 = e. (n – 5)(n + 5) = This activity will help the students understand the concepts of difference of two squares and how this pattern is used to solve numerical expressions. C. Presenting examples/instances of the new lesson The next activity will give an idea to the students on how factors are associated with products. They will match the factors in column A with the products in column B to Based on the activity, how do you think products are obtained? What are the different techniques used to solve for the products? What is the relationship of the
  • 3. decode the secret message. Refer to Activity 3 page 29 of Math LM. product to its factor? Have you seen any pattern in this activity? D. Discussing new concepts and practicing new skills #1 The teacher will ask the students with the following questions based on the previous activity. 1. What are your observations on the expression in column A? Compare them with those in column B. 2. Do you see any pattern? 3. Are the two expressions related? 4. Why is it important to know the reverse process of multiplication? For you to have a better understanding about this lesson, observe how the expressions below are factored and observe the relationships of the term with each other. 4𝑥2 – 36 = (2x + 6)(2x – 6) 𝑥2 – 𝑦2 = (x + y)(x – y) Ask students to generate rule in factoring difference of two squares. E. Discussing new concepts and practicing new skills #2 The teacher will start the discussion by defining factoring first. Then introduce the first type of factoring which is factoring the greatest common monomial factor and give more examples. Based on the examples that are presented, ask the students when to use and not to use this type of factoring. Oral Recitation: 1. What is the first term of each polynomial? 2. What is the last term of each polynomial? 3. What is the middle sign of the polynomial? 4. How was the polynomial factored? 5. What pattern is seen in the factors of the difference of two terms? 6. Can all expressions be factored using difference of two squares? Why or why not? 7. When can you factor expressions using difference of two squares F. Developing mastery(Leads to Formative Have a group contest. Board work Call a student who can write as many pairs of difference of two
  • 4. Assessment) square as they can create. (Note: Teachers must see to it that students must form difference of two squares). G. Finding practical applications of concepts and skills in daily living Appreciate the importance of knowing how to classify things with common characteristics. Apply concept of difference of two squares in real life. H. Making Generalizations and abstractions about the lesson How factoring Greatest Common Monomial Factor is being done? How factoring difference of two squares is being done? I. Evaluating learning Answer the following LOTS: Find the greatest common factor of the following pair of expressions. 1.) 8 & 12 2.) 3x & 6x 3.) 2xy4 & 4x2y2 MOTS: Factor the following expressions. 1.) 4x2 – 12x 2.) 9m2 – 15m3 3.) 4a2 + 12a + 8 HOTS: State the steps of factoring Greatest Common Monomial Factor. Answer: LOTS: 1. 4 2. 3x 3. 2xy2 MOTS: 1. 4x(x-3) 2. 3m2 (3-5m) Answer the following LOTS: `Give 3 pairs of perfect squares. MOTS: Factor each completely. 1. 1 − 16𝑥8 2. 25𝑦2-9 3. 𝑎4 − 625𝑏8 HOTS: State the steps of factoring the difference of two squares. Answer: LOTS: Answers’ Vary MOTS: 1. (1-4x4)(1+4x4) 2. (5y-3)(5y+3) 3. (a2+25b4)(a-5b)(a-5b) HOTS: Answers’ Vary
  • 5. 3. 4(a2 +3a+2) HOTS: Answers’ Vary J. Additional activities for application or remediation V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation who scored below 80%. 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 Iwish to share with other teachers?
  • 6. DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 2 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies -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 -Factor polynomials with sum and difference of two cubes.  Independence Day -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 -Factor polynomials in a form of perfect square trinomial. Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1 II. CONTENT PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages pp.35-36 pp.39-40 pp.41-43 2.Learner’s Materials Pages pp.34-35 pp. 36-38 pp.39-41
  • 7. 3.Textbook Pages Elem. Algebra pp.209-210 Elem. Algebra 206-207 Elem. Algebra 204-205 4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources Student-made bingo cards IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson Students will give examples of difference of two squares as many as they can. Review the students with the previous lesson through board work. How to factor perfect square trinomial? B. Establishing a purpose for the lesson Do you know how to factor the sum or difference of two cubes? What you need to just to get a perfect score in a quiz? Before you go to supermarket, did you list first the items you want to buy? C. Presenting examples/instances of the new lesson You have learned from the previous activity how factoring the difference of two squares is done and what expression is considered as the difference of two squares. We are now ready to find the factors of the Sum or difference of two cubes. To answer this question, find the indicated product and observe what pattern is evident. a. (a + b)(𝑎2 – ab + 𝑏2 ) b. (a – b)(𝑎2 + ab + 𝑏2 ) Let the students perform activity 10 on page 37. How to factor quadratic trinomial with numerical coefficient of the leading term 1? D. Discussing new concepts and practicing new skills #1 What are the resulting products? How are the terms of the products related to the terms of the factors? What if the process was reversed and you were Discuss the rules on how to factor perfect square trinomials. Discuss how to find factors of a general quadratic trinomial with numerical coefficient of the leading term 1 by listing possible factors. Cite examples.
  • 8. asked to find the factors of the products? How are you going to get the factor? Do you see any common pattern? E. Discussing new concepts and practicing new skills #2  Show and discuss to the students the step by step process on factoring the sum and difference of two cubes.  Give more examples for the deeper understanding of the students. Discuss using the examples on page 37-38 F. Developing mastery(Leads to Formative Assessment) Give group seat work. Board work Call a student who can supply the missing terms to make a true statement: 1. m2 + 12m +36 =(m+__)2 2. 16d2-24d +9 =(4d-__)2 3. a2b2 -6abc +9c2 =(a2b__ ____)2 4. 9n2+30nd+25d2 =(___ __5d)2 5. 49g2 –84g+36 =(___ __ ___)2 Factor Bingo Game(By Pair) G. Finding practical applications of concepts and skills in daily living What makes the task easier to do? H. Making Generalizations and abstractions about the lesson How factoring sum and difference of two cubes is being done? How factoring perfect square trinomial being done? Give emphasis to students that factoring quadratic trinomial is easy to do if you list down first the possible factor.
  • 9. I. Evaluating learning Answer the following: LOTS: Find the cube root of the following: 1.) 64 2.) X3 3.) 27y3 MOTS: Factor each completely. 1. 64𝑐3 − 𝑑3 2. 8𝑒3 𝑓6 + 125𝑔3 HOTS: Your teacher asked Kenth to factor 8x3-27 and his answer is 2x-3. Is he correct? Explain your answer. Answer: LOTS: 1. 4 2. X 3. 3y2 MOTS: 1. (4c-d)(16c2+4cd+d2) 2. (2ef2+5g)(4e2f4- 10ef2g+25g) Answer the following: LOTS: Determine a number that must be added to make each of the following a perfect square trinomial. 1. X2+2x+_____ 2. T2+20t+_____ 3. R2-16r+_____ MOTS: Factor the following. 1. x2+12x+36 2. a2+6a+9 3. 4n2+12nx+9x2 HOTS: How do you describe a perfect square trinomial? Answer the following: LOTS: Give the factors of the following numbers: 1. 4 2. 10 3. 15 MOTS: 1. x2+9x+20 2. a2+8a+15 3. y2-3y-10 HOTS: How to factor quadratic trinomial whose leading coefficient is 1? J. Additional activities for application or remediation V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation
  • 10. B. No. of learners who require additional activities for remediation who scored below 80%. 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?
  • 11. DAILY LESSON LOG School Grade Level Grade 8 Teacher Learning Area Mathematics Week/Teaching Dates and Time 3 Quarter First Quarter SESSION 1 SESSION 2 SESSION 3 SESSION 4 I.OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learning Competencies Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1 Factor completely different types of polynomials-general quadratic trinomials using special formulas, grouping and other techniques. M8AL-Ia-b-1  Solve problems involving factors of polynomials. M8AL-Ib-2  Students will follow the standard operating procedure in taking test.  Students will be able to answer the summative test. II. CONTENT PATTERNS & ALGEBRA III. LEARNING RESOURCES A. References 1.Teacher’s Guide Pages pp.44-46 pp.46-47 2.Learner’s Materials Pages pp.43-44 pp.44-45 3.Textbook Pages Elem. Algebra pp. 210-211 Elem. Algebra pp. 212-216 4.Additional Materials from Learning Resource(LR) Portal B. Other Learning Resources IV. PROCEDURES
  • 12. A. Reviewing previous lesson or presenting the new lesson How to factor quadratic trinomial with numerical coefficient of the leading term 1? Have a drill. How to factor quadratic trinomial using Grouping or AC Method? How to factor polynomials consist of more than 3 terms?  Recall the standard operating procedure in taking summative test  Distribute the test papers.  Start the test.  Collect the test papers  Let them check their answers  B. Establishing a purpose for the lesson Do you know how to group things? What is your ideal group? Do you believe that every problem has a solution? C. Presenting examples/instances of the new lesson How to factor quadratic trinomial with numerical coefficient of the leading term greater than 1?Try this: 2x2-5x-3. How to factor polynomials by grouping technique? Pose one problem. Then, let the students solve it. Do this in a group of 5. D. Discussing new concepts and practicing new skills #1 Discuss how to find factors of a general quadratic trinomial with numerical coefficient of the leading term not 1by grouping or AC Method. Cite examples. State the steps of factoring polynomials by grouping technique. Give more examples State to the students the steps of solving problems involving factors of polynomials. Cite examples. E. Discussing new concepts and practicing new skills #2 Teach them by group on how to factor polynomials by grouping techniques F. Developing mastery(Leads to Formative Assessment) Group the students into 5 and let them perform activity 13 on page 44. Famous Four Words(By Group) With your group mates, factor the following expressions by grouping and write a four - letter word using the variable of the factors to reveal the 5 most frequently used four - letter word. 1. 4wt + 2wh + 6it + 3ih 2. 15te – 12he + 10ty – 8hy 3. hv + av + he + ae 4. 10ti – 8ts – 15hi + 12hs 5. 88fo + 16ro – 99fm – 18rm Have board work.
  • 13. G. Finding practical applications of concepts and skills in daily living How important is proper grouping in real life? Apply concept of grouping techniques in real life by classifying things found in school. Apply the process of solving problems involving polynomials by formulating real life problem involving factors of polynomials. H. Making Generalizations and abstractions about the lesson One of the methods of finding the factor of quadratic trinomial with numerical coefficient of the leading term not 1 is through grouping or AC method. Extend learnings in factoring through grouping techniques. You have to group terms with common factors. Some problems encountered in Algebra need to be expressed in terms of polynomials before they can be solved. Then, apply the different factoring techniques for finding correct solutions. I. Evaluating learning Answer the following: LOTS: Arrange the steps of grouping or AC method in factoring quadratic trinomial whose leading coefficient is greater than 1. ___Group terms with common factors. ___Factor the groups using greatest common monomial factor. ___Find the product of the leading term and the last term. ___Find the factors of the product of the leading term and the last term ____Rewrite the trinomial as four-term expressions by replacing the middle term by the sum factor. ____Factor out the common binomial and write the remaining factor as the sum or difference of binomial. MOTS: Answer the following: LOTS: Group the terms with common factors. 1. 7sm+35om+9se+45oe 2. 42wa+54wt+56ha+72ht 3. 72he+16we+27hn+6wh MOTS: Factor by grouping: 1. 3x2-2x+6x-4 2. 3ab+5b-3ac-5c 3. 5m-15+3m2-9m HOTS: Answer the following: LOTS: MOTS: Solve the problem: The square of a positive integer is 98 less than twice the square of the next consecutive positive integer. What are the integers? HOTS: Formulate 1 real life problem involving factors of polynomials.
  • 14. Factor the following: 1.) 2a2+a-15 2.) 3x2-8x-3 3.) 4x2+10x+6 HOTS: Formulate 1 quadratic trinomial whose leading coefficient is greater than 1, then find the factors. J. Additional activities for application or remediation JOURNAL WRITING: Instruction: Reflect on the activities you have done in this lesson by completing the following statements. Write your answers on your journal notebook. • I learned that I... • I was surprised that I... • I noticed that I... • I discovered that I... • I was pleased that I... V.REMARKS VI.REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation who scored below 80%. C. Did the remedial lessons work? No. of learners who have caught up with the
  • 15. 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?