Geometric and Arithmetic Sequences and Series Review

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Objective

SWBAT represent arithmetic and geometric sequences/series verbally, visually, in lists/tables, graphically, as a recursive rule/pattern, an explicit rule, and in summation notation using Cornell notes in a review activity.

Big Idea

Represent arithmetic and geometric sequences/series with various models (MP#4) using a cooperative learning review activity (MP#3).

Lesson Author

Kelli Ireton

Junction City, KS

Grade Level

Ninth grade

Tenth grade

Eleventh grade

Twelfth grade

Subjects

exponential function

Math

Algebra

Summation Formulas

Patterns (Algebra)

Standards

HSF-IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

HSF-IF.A.3

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

HSF-BF.A.1a

Determine an explicit expression, a recursive process, or steps for calculation from a context.

HSF-BF.A.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*

HSF-LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

Quick Write

10 minutes

The point of this QW is to get them thinking of the what they need improvement on for this introductory unit.

Students will enter the classroom and answer the following question in their binder or on a piece of paper (teacher choice, I have a required binder with Quick Write section they are graded on)

"I am still struggling with the concept of ____________________. I plan on getting assistance during __________________."

So far in this unit I can see students struggling with creating explicit rules and writing functions. I plan on spending time reviewing this concept further depending on their Quick Write answers.

Review Sunken Treasure Game

70 minutes

Connections

I like to play this sunken treasure game for reviews, especially when there is a series of questions involved. Instead of just handing them a series of questions, they get to play a game involving the questions. They can work at their own pace and still win a prize, which is also important to me.

Students will be playing a game with the below attachments. They will receive the series of questions face down and told to not turn it over until stated. The Sunken Treasure Smartboard Game will be shown on the board. Students answer each question as a team, one team member brings all of the packets to the teacher/co-teacher/para to check answers. Once all of the questions have been checked and approved, the team chooses a number on the board. If even one is incorrect, I will let them know that they have not all agreed upon an answer and will have to discuss and come to a consensus (MP#3). Behind one number is a "treasure". You can choose for the treasure to be what you want, I give candy (mints, red hots, dumdums, gum) or extra credit points. There are 10 different scavenger board hunts that they can play, so when a treasure is found you can simply choose a different board. The game keeps going until time runs out. Explanation of the game can be found here.

There is flexibility in this lesson since whatever questions are not answered during the game can be assigned as homework.