Grade / Section: Grade 10 – Italio Date / Time: July 31, 2019 / 8:40-9:40 a.m. Subject : Mathematics 10 Lesson Plan in Grade 10 – Mathematics I. Objectives General Objective: 1.) generates patterns. M10AL-Ia-1 Specific Objectives: At the end of the lesson, students are expected to: 1. generate and describe patterns; 2. find the general term of a sequence; and 3. appreciate the importance of a finite sequence and an infinite sequence. II. Subject Matter A. Topic: Sequence B. Key Question: What is the difference between a finite sequence from an infinite sequence? C. Reference: Learner’s Materials pages: 9 Teacher’s Guide pages: 15 Intermediate Algebra II by Julieta G.Bernabe, pages 226-228 Global Mathematics 10 by Geraldo DG. Banaag, pages 2-5, 57 D. Materials: PowerPoint Presentation, laptop, projector, Work sheets E. Strategies: 4As, Group Work, Multiple Teaching, Reflective Teaching F. Value Focus: Appreciation of one’s situation, group wor G. III. Learning Activities A. Preliminary Activities 1. Greetings 2. Arranging chairs, picking up of dirt 3. Checking of Attendance - The class beadle will be asked to report the class attendance. 4. Review (Q&A Method) - Question will be flashed on screen. - Select student will give the answer for each question that has (4) four choices. The PowerPoint presentation uses hyperlink that makes it interactive. Review Question: 1.) Look carefully at the sequence of symbols to find the pattern. 2.) Look carefully at the sequence of symbols to find the pattern. 3.) Look at this series: QAR, RAS, SAT, TAU,___ . What letter should fill the blank? a. UAV b. UAT c. TAS d. TAT 4.) Look at this series: XXIV, XX, __, XII, VIII, . . . What number should fill the blank? a.XXII b.XIII c.XVI d.IV 5.) Look at this series: J14, L16, __, P20, R22, . . . What number should fill the blank? a.S24 b.N18 c.M18 d.T24 6.) Look carefully at the sequence of symbols to find the pattern. 7.) QPO NML KJI _____ EDC a.HGF b.CAB c.JKL d.GHI 8.) 5. Motivation – Start the lesson by showing some pictures and asked the students their ideas about patterns. Let them realize that recognizing and extending patterns are important skills needed to understand the concepts of sequence. 6. Presentation of the Objectives - Objectives will be flashed on screen. - A student will be asked to read each of the objectives. 7. Short Reminder of the class rules on - cooperation and participation B. Lesson Proper 1. Activity (Group Activity) - Students will be grouped into three (3) - Each group will be performing differentiated activity. - Each group will choose a leader, a secretary and a reporter. - Each group will perform an activity as follows: o Group 1 – “Sequence Generator” o Group 2 – “What’s next?” o Group 3 – “Multiplication Table” o Group 4 – “Sequence Generator” o Group 5 – “What’s next?” o Group 6 – “Multiplication Table” - Each group will be given 10 minutes to perform the activity. - After finishing the group activity, a representative from each group will present their output. - An area will be assigned for each group; chairs will be arranged in a small circle. Activity Guide: Activity 1 – “Sequence Generator” (for Group 1) The Greek mathematician Pythagoras who lived during the sixth century BC was the founder of the Pythagorean brotherhood. The group studied numbers of geometric arrangements of points, such as triangular numbers, square numbers, and pentagonal numbers. The following illustrate the first few of each of these types of numbers. Triangular Numbers 1 3 6 10 15 … 16 25 … 22 … Square Numbers 1 4 9 Pentagonal Numbers 1 5 12 Then, answer the questions that follow. 1.) Use patterns to complete the table below. Figurate Number 1st 2nd 3rd 4th 5th 6th 7th Triangular 1 3 6 10 15 Square 1 4 9 16 25 Pentagonal 1 5 12 22 Hexagonal 1 6 15 Heptagonal 1 7 Octagonal 1 2.) Add two consecutive triangular numbers. What kind of figurate numbers do you get? 1+3=? 3+6=? 3.) Multiply each triangular number by 8.then, add 1. What kind of figurate numbers do you get? Triangular Number (x) 8x + 1 1 3 6 10 15 Activity 2 – “What’s Next” (for Group 2) Each item below shows a pattern. Answer the given questions. 1.) What is the next shape? A, , A, , , A, , , , A, , , , , ______ 2.) What ct is the ct next number? ct ct th number? ____ What is the 10 iv iv iv iv 0, 4, 8, 12, 16, ____ it it it it 3.) What is the next number? y y y y What is the 7th number? ____ 4 80, 40, 4 20, 10, ____ 4 4 160, – – – – Activity 3 – “Multiplication Table” (for Group 3) “ “ “ “ R familiar R with the multiplication R You are very table.RThe figures below illustrate part of a multiplication o o o table. o ut ut ut ut X in 1in 2in 3 in 4 5 6 1 e 1e 2e 3 e 4 5 6 2 k 2k 4k 6 k 8 10 12 3 o 3o 6o 9 o 12 15 18 4 4 8 12 16 20 24 to to to to 5 5 10 15 20 25 30 ” ” ” ” 6 6 12 18 24 30 36 (f (f (f (f 1.) Can you see any pattern in the multiplication table? _______________________ or or in each row in the table below? 2.) Whatoris the pattern for theorencircled numbers G G G G ___________________________________________________________________ X ro 1 ro 2 ro 3 ro 4 5 6 1 2 u 3 4 5 6 u 1 u u 2 2 4 6 8 10 12 p p p p 3 3 6 9 15 18 4) 4) 4) 4) 12 4 5 6 4 5 6 8 10 12 12 15 18 16 20 24 20 25 30 24 30 36 3.) What is the pattern for the encircled numbers along the diagonal in the table below? ___________________________________________________________________ X 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36 2.) Analysis (Group Reporting) Answer the following guide questions: 1. How do you feel about the task given to your group? Why? 2. In doing the activity, what mathematics concepts or principles did your group apply? Explain how you applied these mathematics concepts or principles? 3. How would you describe the sequence? 3.) Abstraction -The teacher will deliver a lecturette using interactive PowerPoint. -Examples will be shown. Sequence is a logical order or arrangement of values defined by a general term or nth term. The general term of a sequence defines the characteristic of the whole sequence. Every element in a sequence is called a term. Examples: 1. 2. 3. 4. Set of counting numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . . . Multiples of 7: 7, 14, 21, 28, 35, 42, . . . Powers of 2: 2, 4, 8, 16, 32, 64, . . . Multiples of 5 between 11 and 60: 15, 20, 25, 30, 35, 40, 45, 50, 55 Finite Sequence and Infinite Sequence A sequence having a finite number of terms is called a finite sequence. A sequence that has an infinite number of terms is called an infinite sequence. Sequences may be obtained with the provision of a general term. Example: Find the first five terms of the sequence, given the general term 𝑎𝑛 = 2(𝑛 + 3). Solution: 𝑎1 : 𝑓𝑜𝑟 𝑛 = 1 ∶ 2(1 + 3) = 2(4) = 8 𝑎2 : 𝑓𝑜𝑟 𝑛 = 2 ∶ 2(2 + 3) = 2(5) = 10 𝑎3 : 𝑓𝑜𝑟 𝑛 = 3 ∶ 2(3 + 3) = 2(6) = 12 𝑎4 : 𝑓𝑜𝑟 𝑛 = 4 ∶ 2(4 + 3) = 2(7) = 14 𝑎5 : 𝑓𝑜𝑟 𝑛 = 5 ∶ 2(5 + 3) = 2(8) = 16 ∴ The first five terms of the sequence are 8, 10, 12, 14, and 16 4.) Application Directions: Solve the given problem assigned to your group. IV. Evaluation A- Directions: Read and analyze the given items carefully. Write on the spaces provided before each number the next two terms of each sequence. ____ ____ 1.) 3, 7, 11, 15, . . . ____ ____ 2.) 8, 11, 14, 17, . . . ____ ____ 3.) -5, -2, 1, 4, . . . B- Directions: Read and analyze the given sequence carefully. Complete the sequence by filling in the blanks the missing term/s. 5. 4, 8, ___, 16, 20 6. 13, ___, 33, ___, 53 7. 1.6, ___, 2.2, ___2.5, ___ V. Assignment Movie Review: “Pay it Forward” Watch the movie “Pay it Forward”, starring Kevin Spacey, Helen Hunt, and Haley Joel Osment. The movie is about a middle school student, Trevor McKinley, who was caught between the extensive complexities of life when he met his Social Studies teacher and provided them with an assignment: “Think of an idea to change our world – and put it into ACTION.” See how this student changes the lives of a lot of people. Realize how the concepts of sequences have been used to illustrate the aim action of the movie and how you can do the same to help your community. Prepared by: RIZZA MAE S. BAGSICAN Grade 10 Mathematics Teacher Checked by: ROMULO Q. MORATA School Head