LESSON PLAN

Name of the Teacher : Saranya P                                                              Std : X

Name of the Subject : Mathematics                                                        Duration : 30 mts

Name of the unit: Arithmetic Sequences.                                             Age level: 15+                                                                   

Name of the subunit: Arithmetic Sequence                                         Date: 11/09/14

                                                                                                               

Curricular Statement

Students will examine the concept of arithmetic sequence and learn to find the sum of arithmetic sequence.

Objectives

Applies special number relationships such as sequences and series to real-world problems.

Content Analysis

Terms

Terms, sequence, number sequence, arithmetic sequence, first term, second term, common difference, number of terms, nth term

Facts

·         A sequence is an ordered list of numbers.

·         Terms are elements in a sequence.

·         An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such  that the difference between the consecutive terms is constant.

·         5,7,9,11,13,15….. is a number sequence.

·         First term is a first number of sequence.

·         Second term is a second number of sequence.

·         Nth term is a nth number of sequence.

·         Number of terms are the total element of a sequence.

·         The difference between each number in an arithmetic sequence is called common difference.

 Concept

Definition of the sum of an arithmetic sequence: Sn = n/2[2a1 + (n ­ 1) d].

Formula

an = a1 + (n – 1) d

Sn = n/2[2a1 + (n ­ 1) d].

Symbol

an=nth term

a1=first term

sn=sum of nth term

n=no of terms

d=common difference

Learning outcomes

I. The pupil remembers about the progression, number progression, arithmetic progression, common difference, terms, concepts of nth term.

The pupil

a) Retrieves relevant knowledge about different types of numbers, arithmetic sequence, terms, progression, arithmetic progression, common difference etc.

b) Identifies different types of arithmetic sequences, its terms and common difference etc

 II. The pupil understands about sum of arithmetic progression

The pupil

a) Classifies the sum of different arithmetic sequence.

b) Generates the major points and finding the sum of arithmetic progression

III. The pupil applies the equation of nth term of AP to new and unfamiliar situation

The pupil

a) Uses appropriate formula to solve sum of terms of an AP.

b)Executes the procedure to a given problem

IV. The pupil analyses and check how to find the sum of AP

The pupil

a)  Distinguishes the given problem as to what is given and whats to be found out.

 Related Knowledge

·         Knowledge about different types of digits.

·         Knowledge about different types number sequence.

·         Knowledge about arithmetic sequence.

·         Knowledge about first term and common difference of A.P

Teaching learning resources

·         Text book and hand book of class X

·         Chart

·         Activity card

·         Usual class room equipments

Strategies followed

·         Discussion and lecture method

Teacher Activity	Expected Response
After Classroom interaction procedure teacher tells following story.  “A long time ago, there was a student in a math class. Now, his classmates were being very noisy and disruptive, so the math teacher got very, very angry. To punish his students, the teacher told them to add all the integers from 1 until 100. No student could leave the class until he or she was finished with the problem. So everyone began to add the numbers, 1 + 2 = 3. 3 + 3 = 6. 6 + 4 = 10, and so on and so forth. However, this one math student just sat there and thought for a long time. He didn’t write anything down, but after a while, he wrote down the answer and showed it to his teacher. Then, his teacher was amazed that the answer was correct, and the student got home early. So, how did this student figure out how to solve this problem?”	Most Students are puzzled by the story
Introduction of topic "arithmetic sequence”.	Understanding arithmetic Sequence
Give the definition of an arithmetic sequence. A sequence is said to be arithmetic if each term, after the first, is obtained from the preceding term by adding a common value. Eg: 2,4,6,8,.... Teacher shows a chart based on definition for better understanding for students	Pupil reads carefully the charts and understands the definition
Give examples of arithmetic sequences on the laptop.	Students understand different arithmetic sequences.
Find the general term of an arithmetic sequence-the nth term of an arithmetic sequence is an = a1 + (n – 1) d, where a1 is the first term and d is the common difference. Derivation of arithmetic sequence: a1 a2 = a1 + d a3 = a2 + d = (a1 + d ) + d = a1 + 2d a4 = a3 + d = (a1 + 2d ) + d = a1 + 3d . . an = a1 + (n – 1) d	Students understand the equation to find the nth term of arithmetic sequence.
Example: 1. Find the nth term of the arithmetic sequence 11, 2, -7… Solution : 1. an = a1 +(n – 1) d = 11 + (n – 1)(-9) = -9n + 20	With examples students understand how to find the nth term of arithmetic progression.
“Now that you have recognized the pattern of an arithmetic sequence. We can figure out the sum to the problem above. First we have to know the formula for figuring out the sum of an arithmetic sequence.” Definition of the sum of an arithmetic sequence: Sn = n/2 [2a1 + (n - 1) d].	Students understand the equation for finding the sum of arithmetic progression.
Example: 1. Find S20 for the arithmetic sequence whose first term is a1 = 3 and whose common difference is d = 5. Solution : 1. S20 = 20/2 [2(3) + (20 - 1)5]. = 1010	Students understand how to find the sum of arithmetic progression after solving the example
“Now that you have practiced how to find the sum of an arithmetic sequence, let’s find the solution to the problem i told in the story.” - The student who told the answer was the famous mathematician Gauss	Class surprised to understand the student was famous mathematician Gauss and motivated that they also able to understand the same.

Review question

·         Retrieves (R): What is an A.P?

·         Identifies(R):2, 5, 6,8,10 is an A.P?

·         Uses (A): How to find sum of n terms for an A.P?

FOLLOW UP ACTIVITY

1. Which of the following is/are example(s) of arithmetic sequence?

A) 1, 3, 5, 7, …

B) 2, 4, 8, 16, …

C) –3, -2, -1, 0, …

D) 1, 2, 3, 5,

2. Find the 30th term of the sequence 120, 126, 132, 138, .