Department of Education Region III Schools Division of Zambales Botolan District BOTOLAN NORTH INTEGRATED SCHOOL DETAILED LESSON PLAN IN MATHEMATICS V I. OBJECTIVES Content Standard: The learners demonstrate understanding the concept of sequence Performance Standard: The learners should be able to apply the knowledge of sequence in various situations Learning Competency: The learners should be able to formulate the rule in finding the next term in a sequence (Code- M5AL-IIIf-6) . II. LEARNING CONTENT Subject Matter: Defining Sequence Formulating the Rule in Finding the Next Term in a Sequence Values Infusion: Appreciating the value of giving and receiving gifts References: 1. Teacher’s Guide pages 101-102 2. Learner’s Material pages 250-257 Materials: visual aids, flashcards, activity sheets, chart, gifts III. PROCEDURE: Teacher’s Activity A. Preliminary Activities 1. Greetings Good Morning class! 2. Checking of attendance Can you tell me who are absent today? Ok, Thank you! 3. Setting Standards Are you now ready on our discussion? Good! But before that, what will you do again if your teacher is discussing in front? That’s Good! Now, how about if you want to answer a question or if you want to tell something? You got it! What else? All right! Now. Let’s see if you carefully follow those things? Pupils’ Activity Good Morning Ma’am! Are you ready class? 4. Checking of assignment By the way, do you have an assignment? All right! 5. Drill Let’s now have a drill on basic multiplication of whole numbers. 1. 6 x 5 2. 9 x 9 3. 6 x 9 4. 8 x 5 5. 12 x 3 6. Review Have a review on the past lesson. (about the different kinds of solid figures) The pupils will tell the answers as the teacher shows the flashcards. 1. 2. 3. 4. 5. 30 81 54 40 36 The pupils will give the different kind of solid figures. B. MOTIVATION Are you familiar with these things? (The teacher will show gifts to the class.) Ask the following questions: 1. When do you usually receive gifts? Pupil 1: I receive gifts during my birthday. Pupil 2: I receive gifts during Christmas. Pupil 3: My parent send me a gift when I got high grades. 2. What do you feel when you are giving/ receiving gifts? Pupil 1: I feel happy and thankful Ma’am. Now let us try to have a simple impromptu skit. I need two volunteers who act as the mother and the daughter. Someone will come in front to act out the problem.) (Present the word problem below.) Seven days before her Mother’s birthday, Alyanna planned to give her gifts. On the first day, she sent one gift to her Mother. On the second day, she sent three gifts. On the third day, she sent five gifts, and so on. How many gifts did Alyanna sent her Mother on the seventh day? Consider the given problem. It can be represented in table form. What does the problem ask you to find? (Take a look at the table below) Day No. of Gifts 1st 1 2nd 3 3rd 5 4th ? 5th ? 6th ? 7th ? The first row represents the days and the second row shows the number of gifts that Lourdes sent each day. Upon observing the number of gifts 1, 3, 5, __, __, __, __ +2 +2 As the sequence continues: 1, 3, 5, 7, 9, 11, 13 +2 +2 +2 +2 +2 +2 We can now conclude that her Mother will receive seven gifts on the fourth day, nine gifts on the fifth day, eleven gifts on the sixth day and finally, her mother will receive thirteen gifts on the seventh day. Again, how many gifts did Alyanna sent to her mother on the seventh day? Alyanna sent 13 gifts to her Mother on the seventh day. C. DEVELOPMENTAL ACTIVITIES 1. Presentation Present the word problem below. Cardo loves to draw stars in his notebooks. He draws 6 stars on the first page, 10 stars on the second page, 14 stars on the third page and 18 stars on the fourth page. If this pattern continues, how many stars will be drawn on the fifth page of his notebook? To make it simple, let’s do the illustration. ? / 1 page st 2 nd page 3 page rd 4 page 5th page th D. DISCUSSION 1. Performing the Activities Now let’s try to answer the questions. Understand: 1. What does the problem ask you to find? The problem ask us to find the number of stars that will be drawn on the fifth page of Cardo’s notebook. 2. What are the given facts? The given are: 6 stars on the first page 10 stars on the second page Plan: What operation or strategy do we use in solving the problem? 14 stars on the third page 18 stars on the fourth page We can solve the problem by the use of illustration. (Lead the pupils to discover the pattern on the illustration) Solve: Considering the illustration, there are 6 stars on the first page, 10 stars on the second page, 14 stars on the third page, and 18 stars on the fourth page. By listing the number of stars, we have: 6, 10, 14, 18, _?_ +4 +4 +4 2. Processing Activities Let us go back to the problem. Upon observing the sequence, the number of stars increases by 4 each time. Therefore as the pattern continues, 18 + 4 = 22. Solution: Rule : Add 4 6 + 4= 10 10 + 4 = 14 14 + 4 = 18 18 + 4 = 22 Answer: There will be 22 stars on the fifth page of Cardo’s notebook. Check: 6, 10, 14, 18, _22_ +4 +4 +4 +4 What can you observe in the set of numbers? We have observed that the list of numbers is in logical order. And it is called sequence. Sequence is a list of numbers or objects in a defined or logical order. And each number in a sequence is called a term. Wherein, in Mathematics rule is a way to calculate or find any term in a sequence. There are many ways to figure out the rule, such as: Pupil: I’ve noticed that the list of numbers is arranged from lowest to highest. ( Call another pupils for more observations) a. Looking at the numbers and see if there is a pattern, like taking each number and multiplying by 3 or by simply adding 4. b. Think about common number pattern, like counting by 2s, 5s, or 10s and so on. c. Find the difference between the numbers. ( Give more examples for better understanding of the lesson.) Formulate the rule and find the next three terms in the sequence Sequence 1. 2, 5, 8, _____, _____, ______ 2. 3, 6, 12, 24, ___, _____, _____ 3. 1, 3, 7, 15 , _____, ______, ___ Rule _____ _____ _____ Answers: Sequence 1. 2, 5, 8, 11,14 , 17 2. 3, 6, 12, 24, 48, 96, 192 3. 1, 3, 7, 15 , 31, 63, 127 Rule Add 3 Multiply by 2 Multiply by 2 and add 1 E. GENERALIZATION What is sequence? Pupil 1: Sequence is a list of numbers or objects in a defined or logical order. How do you formulate a rule in finding the next term in a given sequence? There are many ways to figure out the rule, such as: a. Looking at the numbers and see if there is a pattern, like taking each number and multiplying by 3 or by simply adding 4. b. Think about common number pattern, like counting by 2s, 5s, or 10s and so on. c. Find the difference between the numbers. F. ENRICHMENT ACTIVITIES 1. Group Activities This time, I will group you into four. Name your group with “MATH” as its first syllable. For example, MATHinik. (The pupils will do the task) I have here four envelopes with problem inside. Select one representative from your group to pick one. Group I- Solve the problem. Princess is writing a poem. She writes 6 words on the first line, 12 words on the second line, 24 words on the third line, and 48 words on the fourth line. If this pattern continues, how many words will Princess write on the fifth line? I will give you five minutes to answer and two minutes to present your output in front of the class. Group II- Find the next three terms in each set of sequence. a. 13, 23,33,43,___, ______,______ b. 800, 700, 600, ____, _____, _____ c. 3, 8, 18, 38, _____, ______, ______ Group III- Give the rule in each sequence. a. 4, 12, 36 Rule : b. 1, 5, 25, 125 Rule: c. 1, 10, 100, 1000 Rule: Group IV-Make an illustration to answer the problem. While observing the audio visual room, Dalisay noticed that there were 2 chairs in the first table, 3 chairs in the second table, 6 chairs in the third table, 11 chairs in the fourth table, and 18 chairs in the fifth table. If this pattern continues, how many chairs will there be in the seventh table? 2. Individual Activities (Let the pupils answer the following on the board.) Formulate the rule in each sequence and write the missing term. 1. 1, 4, 7, 10, _____ Rule: _____ 2. 23, 31, 39, 47,55 , _____ Rule : _____ 3. 100, 80, 60 , 40, _______ Rule : _____ 4. 2, 8, 32, 128, _______ Rule : _____ 5. 5,11,23, 47, ________ Rule : _____ Expected answers: 1. 2. 3. 4. 5. 13 63 20 512 95 Rule : Add 3 Rule: Add 8 Rule : Subtract 20 Rule : Multiply 4 Rule : Multiply 2 and Add 1 IV. ASSESSMENT: Answer the following: 1. _________ is a list of numbers or objects in a defined or logical order. 2. In Mathematics, this is the way to calculate or find any term in a sequence. 3. – 4. Formulate the rule and find the next term in each sequence: a. 24, 30, 36, 42, ______ b. 60, 56, 52, 48, 44, _____ 5. Solve. Carla stored pens in small boxes. She put 1 pencil in the first box, 3 pencils in the second box, 9 pencils in the third box, and 27 pencils in the fourth box. If the same pattern was followed, how many pencils did Carla place in fifth box? V. ASSIGNMENT: Read, analyze and answer. An auditorium has 12 rows of seats. It has 30 seats in the first row, 35 seats in the second row, 40 seats in the third row and so on in the same increasing pattern. 1. How many seats are there in the 11th row? 2. All in all, how many seats are there in the theater? Prepared: ________________ Mentee Noted: ____________________ Adviser Checked: ________________ School Head/Principal
