GRADES 1 to 12 DAILY LESSON LOG School: Mary Belle Montessori School-Mayapa Inc. Teacher: Mr. John Kenneth P. Silloriquez Teaching Dates and Time: DAY 1 DAY 2 DAY 3 Grade Level: 10 Learning Area: Math Quarter: first DAY 4 DAY 5 I. OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of sequences, polynomials and polynomial equations. B. Performance Standards The learner is able to formulate and solve problems involving sequences, polynomials and polynomial equations in different disciplines through appropriate and accurate representations. C. Learning Competencies/Objectives The learner illustrates other types of sequences (harmonic). (M10AL-If-1) Write the LC code for each II. CONTENT The learner illustrates other types of sequences (harmonic). (M10AL-If-1) The learner illustrates other types of sequences (e.g., harmonic, Fibonacci). (M10AL-If-1) The learner solves problems involving sequences. (M10AL-If-2) Section 1.4 pages 29-31, 33 Section 1.4 pages 31-32 Section 1.4 page 33 Patterns and Algebra III. LEARNING RESOURCES A. References 1. Teacher’s Guide Pages 2. Learner’s Materials Pages 3. Textbook Pages Section 1.4 pages 28-29, 32 4. Additional Materials from Learning Resource (LR) Portal B. Other Learning Resources https://www. quora.com/ What-are-some-interesting-applications-of-the-harmonic-series Section 1.4 pages 32-33 IV. PROCEDURES A. Reviewing Previous Lesson or Presenting the New Lesson Present new lesson: Harmonic Sequences Review previous lesson: Present new lesson: Fibonacci Sequences Ask the students: When do you say that a given set of numbers forms a harmonic sequence? Give an example of harmonic sequence. How do you find the nth term of a harmonic sequence? Review previous lesson: End-of-the-Lesson Test: Harmonic and Other Sequences Ask the students: What is Fibonacci sequence? How do you find the sum of the terms of a Fibonacci sequence? How can you findthe nth term of a recursively-defined sequence? Discuss homework: Items from Matched Problem 1.4.5 (31), Matched Problem 1.4.6 (32), Matched Problem 1.4.7 (32) B. Establishing a Purpose for the Lesson There are several types of sequences. In this session, one type of sequence will be discussed – harmonic sequence. Number/s can be inserted between two numbers in order to form a harmonic sequence. In this session, we will discuss these terms called This session will also harmonic mean/s. tackle finding out the term/s of a harmonic sequence. There are several sequences. In this session, one type of sequence – Fibonacci will be discussed. This session will also include finding the nth terms and sum of Fibonacci sequence. C. Presenting Examples/Influences of the Lesson Introduce and Introduce and explain harmonic explain arithmetic sequence or progres- mean/s. sion Refer to Our World of Refer to Our World of Math 10 page 29 Math 10 page 28 Introduce and explain Fibonacci sequence This session is intended to solve problem involving sequences. Not applicable Post the problems from: Exercises 1.4 (page 33) Refer to Our World of B #’s 13, 15, 17 Math 10 page 31 Not applicable D. Discussing New Concepts and Practicing New Skills #1 Identifying if the given numbers are terms of a harmonic sequence: Discuss Example 1.4.1 a-c (page 28) Finding the harmonic mean/s between two given numbers: Discuss Example 1.4.3 (page 30), Example 1.4.4 (page 30-31) Finding the sum of the terms of a Fibonacci sequence: Discuss Example 1.4.5 (page 31), Example 1.4.6 (page 31) Discuss Exercises 1.4 (page 33) B #’s 13, 15, 17 Not applicable E. Discussing New Concepts and Practicing New Skills #2 Finding the nth term of a harmonic sequence: Discuss Example 1.4.2 (page 29) No new concept Finding the nth term of a recursively-defined sequence: Discuss Example 1.4.7 (page 32) No new concept Not applicable F. Developing Mastery (Leads to Formative Assessment 3) Board work/ Seatwork: Use items from Matched Problem 1.4.1 a-c (page 29), Matched Problem 1.4.2 (page 29) Board work/ Seatwork: Use items from Matched Problem 1.4.3 (page 30), Matched Problem 1.4.4 (page 31) Homework: Use items from Matched Problem 1.4.5 (page 31), Matched Problem 1.4.6 (page 32), Matched Problem 1.4.7 (page 32) Board work/ Seatwork: Use items from Exercises 1.4 (page 33) B #’s 14, 16, 19 Not applicable G. Finding Practical Applications of Concepts and Skills in Daily Living * To be discussed next session Cite some real-life situation involving harmonic sequence from: https://www. quora.com/ What-are-some-interesting-applications-of-the-harmonic-series * To be discussed next session Ask the students: Not applicable What attitude were you able to develop from these lessons about sequences? How can you use that attitude in daily living? (example: being keen observant, being detail-oriented) H. Making Generalizations and Abstractions about the Lesson Ask the students: When do you say that a given set of numbers forms a harmonic sequence? How do you find the nth term of a harmonic sequence? Ask the students: What is harmonic mean/s? How can you find the harmonic mean/s of a sequence? Ask the students: Not applicable What is Fibonacci sequence? How do you find the sum of the terms of a Fibonacci sequence? How can you findthe nth term of a recursively-defined sequence? Not applicable I. Evaluating Learning J. Additional Activities for Application or Remediation IV. REMARKS V. REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation C. Did the remedial lessons for 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 work well? Why did these work? F. What difficulties did I encounter which my principal or supervisor can help me solve? G. What innovations or localized materials did I use/discover which I wish to share with other teachers? Seatwork: Use items from Exercises 1.4 (page 32) A #’s 1-3 Seatwork: Use items from Exercises 1.4 (page 33) B #’s 5, 7 * To be given next session Announce End-ofthe-Lesson Test to be given next session End-of-the-Lesson Test: Harmonic and Other Sequences Use items from Exercises 1.4 (page 32-33) A #’s 4-5 B #’s 1, 2, 6, 8, 18