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Sequence, arithmetic sequence, common divisor
Grades/Course: 11, Algebra 2
Lesson Number: Arithmetic Sequences
Time Required: 40 minutes
Original Author: Marion Blanchard
Essential Question(s) for this Lesson
What patterns exist in Math?
How can you use Math to make problems simpler?
Addressed for this Lesson
A2.A.29 Identify an arithmetic or geometric sequence and find the formula for its nth term
A2.A.30 Determine the common difference in an arithmetic sequence
A2.A.32 Determine the specified term of an arithmetic or geometric sequence.
G.PS.2 Observe and explain patterns to formulate generalizations and conjectures
Math B – Modeling / Multiple Representations
-- 4A Represent problem situations symbolically …
-- Use symbolic form to represent an explicit rule for a sequence.
Evidence of Student Understanding (Assessment) for this Lesson
Worksheet in class
Student Preparation Prior to this Lesson
None, this is the first class in the unit
Number and Patterns worksheet – I per student
Challenge problem – 1 per student
Unit tile blocks for manipulative approach to sequences if necessary
Specific Purpose(s) or Objective(s)
Use of mathematical notation
See that tedious and repetitive math problems may have a simpler pattern / solution
Arithmetic sequence notation and usage
A rich relative is leaving you money. You get a penny today, 2 pennies tomorrow, 4 pennies the next day, this continues. On which day do you get $10.01?
Step by Step Explanation of Activities/Strategies
1. Do Now – (3 minutes)
Put these sequences on the board. Students to find the next 3 numbers:
2, 4, 6, 8, … (arithmetic)
1, 4, 9, 16, …
15, 13, 17, 15, 19, ….
5, 10, 20, 40, …. (geometric)
1, 1, 2, 3, 5, … (Fibonacci)
1, 7, 13, …
2. Talk about each sequence. (6 minutes)
Any pattern you can explain is valid, as long as you can explain it to me.
Mention Fibonacci sequence, geometric sequence.
Our lesson will be on arithmetic sequences”
What is the first term? What is the next term? What did you do to get there?
3. Hand out number patterns worksheet and challenge worksheet (5 minutes)
Class start working on them. Stop after 5 minutes. Save this worksheet. You will need it again
4. Introduce notation: a1, an, d (common difference) (15 minutes)
backwards terminology! – we are adding and the word refers to subtraction
Write out the a1, a2, a3,.. of some of the series from the worksheet. Go forward 2 terms, what is answer? Two more. Then ask for the 105th term.
Look for general definition of nth term: an = a1 + (n-1)d
So back to the starting problem – How do we set this up?
an = a1 + (n-1)d;
an = $10.01,
d = .02
10.01 =.01 + (n-1) * .02,
n = 501.
It takes more than 500 days to get to $10.00. When we start doing summations of sequences in a few days I will show you something interesting about this problem.
5. Define homework (2 minutes)
Homework will be to finish worksheet. Write these instructions on the worksheet. Next to each sequence write a big “A” if it is an arithmetic sequence. If it is - write the a1 term and the d term. Write that on the work sheet now so you don’t forget. The challenge problem is optional.
In class – everyone make up an arithmetic sequence. Give it to your partner to solve. The person who is solving: be sure to define a1, d. Find the 243rd term of your sequence. You will hand in to me as you leave. Put both of your names on the sheet.
I will use some of these as tomorrow morning’s do-nows.----
Accommodations for Students with Disabilities or Diverse Learning Styles
Auditory learning – repeat key words – Common difference, nth term, sequence
Manipulative learning – have small unit square tiles available. Students can create piles of blocks, each pile a term in a sequence.
Challenge problem for advanced students
help on how to format text
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