Lesson Plan For Mathematics 10 3b6o1f

Lesson Plan for Mathematics 10

I.

Objectives At the end of the lesson, the students are expected to:  identify and generate patterns;  find the nth term of a sequence;  find the general term of a sequence; and  differentiate a finite sequence from an infinite sequence.

II.

Subject Matter  Topic: SEQUENCE  References: E-Math 10 by Orlando A. Oronce and Marilyn O. Mendoza, pages 2-20 Intermediate Algebra II by Julieta G.Bernabe, pages 226-228 Global Mathematics 10 by Geraldo DG. Banaag, pages 2-5, 57  Materials: Chalk and board, work sheets, slide presentation

III.

Procedure A. Priming/Activating Prior Knowledge Action Song : “A Food Cheer” B. Presentation *Activity (Group Activity)  The class will be divided into four groups. Each group will be given a task to do Group 1: “Sequence Generator” Group 2: “Radio Tuning” Group 3: “Multiplication Table” Group 4: “Routine Ko ‘To” (see attachments for the mechanics for each group activity)  Every group will be given 10 minutes to do the task.  After finishing the group activity, a representative from each group will present their output. *Analysis Answer the following guide questions 1. How do you fell 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? *Abstraction 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 is called a finite sequence. A sequence that has an infinite number of is called an infinite sequence.

Sequences may be obtained with the provision of a general term. Example: Find the first five 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 )=1 0 a3 :for n=3 :2 ( 3+3 )=2 ( 6 )=1 2 a 4 : for n=4 :2 ( 4+3 ) =2 ( 7 )=1 4 a5 :for n=5 :2 ( 5+3 )=2 ( 8 )=16 ∴ The first five of the sequence are 8, 10, 12, 14, and 16 *Application Directions: Solve the given problem assigned to your group. Group 1: Jessica wanted to buy a monopod equipped with shutter for her selfie habits that cost Php 300 and started by saving Php 5 on June 15, Everyday from then on, she saved Php 3 more than she did the preceding day. On June 25, she checked her savings and found that she needed to save more to buy the monopod. How much does she still need to save? Group 2: Alex is a very athletic person. He usually s fun runs and marathons. Unfortunately, he got injured in one of his events when his ankle twisted. He was told to take some rest and was advised to return to his jogging program slowly. In the program, he needs to jog for 15 minutes each day for the first week, then an increase of 7 minutes per day on the succeeding weeks. How many minutes does Alex have to jog on the 10th week of the program? Group 3: Every month, Jose saves Php 115 more than what he saved the preceding month in his bank . If he initially put Php 925 in his , find a formula to find out how much he saved in his bank on the nth month. (note: neglect periodic interests) Group 4: A ball is dropped from a height of 24 feet and always bounces off to 1/3 of the height from which it falls. Express the height from which the ball falls as of a sequence. Write a formula for the nth term of the sequence.

IV.

Evaluation Directions: Read and analyze the given items carefully. Write on the spaces provided before each number the next two of each sequence. ____ ____ 1. 3, 7, 11, 15, . . . ____ ____ 2. 8, 11, 14, 17, . . . ____ ____ 3. -5, -2, 1, 4, . . . 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 ain action of the movie and how you can do the same to help your community.

Prepared by: JEMARJO E. SALANDANAN Kalayaan Christian School Mathematics

Checked and Evaluated by:

NENITA ADAME Dr. Juan A. Pastor MNHS Principal II

MARITES BONIFACIO Sta. Monica NHS Principal I

JACQUELINE ARIAS Itlugan NHS Teacher III

ELINO GARCIA Dacanlao G. Agoncillo NHS Head Teacher I

Sequence Generator 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

…

Pentagonal Numbers 1 5 12 22

…

Square Numbers 1

4

9

1. Use patterns to complete the table below. Figurate Number

1st

2nd

3rd

4th

5th

Triangular Square Pentagonal Hexagonal Heptagonal Octagonal

1 1 1 1 1 1

3 4 5 6 7

6 9 12 15

10 16 22

15 25

6th

7th

2. Add two consecutive triangular numbers. What kind of figurate numbers do you get?

3.

1+3 =? Multiply each 3+ 6 triangular number by 8.then, add 1. What kind of figurate numbers do you get? Triangular Number (x)

1

3

6

10

15

8x + 1 4. Square any two consecutive triangular numbers. Subtract the smaller square number from the larger. What kind of number do you get?

Radio Tuning The Philippines is tagged as home of great singers and stage performers. We always like to hear good music being played over the radio. It has become part of our daily living that we listen to music and sing with it whenever possible. Once you turn on the radio, it is necessary that you know the station you are going to listen to. These stations, better known as FM (frequency modulation) modulate or vary their frequencies to carry sound or information over an electromagnetic wave.

What is your favourite radio station? ___________________________________________ Do you know some Batanguenyo radio station? Can you give some? _________________ How do you identify these stations? ___________________________________________ Below is a table showing the list of different existing FM stations with their corresponding frequency modulation. Complete the table by filling in the blank spaces the correct frequency assuming that the given stations are arranged in increasing frequency.

Frequency

Station

Frequency

Station

88.3 FM 89.1FM 89.9 FM 90.7 FM 91.5 FM 92.3 FM 93.1 FM 93.9 FM 94.7 FM 95.5 FM 96.3 FM 97.1 FM 97.9 FM

Jam 88.3 Wave 89.1 Magic 89.9 90.7 Love Radio 91.5 Big Radio Radyo5 92.3 News FM Monster Radio RX 93.1 93.9 iFM Mellow 947 Pinas FM 95.5 96.3 Easy Rock Barangay LS 97.1 97dot9 Home Radio

98.7 FM

98.7 Master’s Touch 99.5 RT RJ 100 101.1 Yes FM Tambayan 101.9 102.7 Star FM 103.5 Wow FM 104.3 Business Radio 105.1 Crossover Radio High 105.9 106.7 Energy FM 107.5 Win Radio

Routine Ko ‘To A schedule is an example of routine that creates a pattern. People need patterns in their lives for two reasons: RELIABILITY and PREDICTABILITY. A person who is whimsical is often unreliable.

Discuss among your group how you are doing this task: cooking rice Examine each other’s answer, and then check if their answer is the same as yours. Illustrate the process of cooking rice based from the procedures that your group had discussed.

Multiplication Table You are very familiar with the multiplication table. The figures below illustrate part of a multiplication table.

X 1 2 3 4 5 6

1

2

3

4

5

6

1 2 3 4 5 6

2 4 6 8 10 12

3 6 9 12 15 18

4 8 12 16 20 24

5 10 15 20 25 30

6 12 18 24 30 36

Can you see any pattern in the multiplication table? _______________________ What is the pattern for the encircled numbers in each row in the table below? ___________________________________________________________________

X 1 2 3 4 5 6

1

2

3

4

5

6

1 2 3 4 5 6

2 4 6 8 10 12

3 6 9 12 15 18

4 8 12 16 20 24

5 10 15 20 25 30

6 12 18 24 30 36

What is the pattern for the encircled numbers along the diagonal in the table below? ___________________________________________________________________

X 1 2 3 4 5 6

1

2

3

4

5

6

1 2 3 4 5 6

2 4 6 8 10 12

3 6 9 12 15 18

4 8 12 16 20 24

5 10 15 20 25 30

6 12 18 24 30 36

What is the pattern for the numbers grouped in inverted “L” in the table below? ___________________________________________________________________

X 1 2 3 4 5 6

1

2

3

4

5

6

1 2 3 4 5 6

2 4 6 8 10 12

3 6 9 12 15 18

4 8 12 16 20 24

5 10 15 20 25 30

6 12 18 24 30 36