# Ch 2: Common Core HS Functions - Sequences

With the help of this chapter, you can meet the requirements for the Common Core and teach your high school class about sequences. You can also use the suggestions on how to use the lessons and recognize when your students have grasped sequences.

Standard: 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 greater than or equal to 1. (CCSS.Math.Content.HSF-IF.A.3)

Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (CCSS.Math.Content.HSF-BF.A.2)

Standard: 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). (CCSS.Math.Content.HSF-LE.A.2)

Once students fully understand sequences, they'll understand the various ways of writing sequences and will be able to use them as examples for different circumstances. Your students will also be able to create different kinds of functions and read them from a table. These lessons help students understand and do the following:

• Identify a mathematical sequence
• Understand sequences as mathematical functions
• Classify arithmetic sequences
• Use writing rules to describe sequences
• Find and classify geometric sequences

You'll recognize when your students have a thorough knowledge of the standard when they're able to understand and use the rules for writing geometric and arithmetic sequences and recognize recursive sequences. The lessons combined with the standard could prove useful to students should they choose to apply for college, and it they could also be useful for such careers as finance, marketing, biochemistry and city planning.

### How to Use These Lessons in Your Classroom

Following are a few suggestions that you could include in your regular curriculum to help you meet the standards for the Common Core.

#### Let Students Create Quizzes

Watch the lessons that identify, classify and teach the writing rules for arithmetic and geometric sequences. Allow your students to help themselves and each other by creating quizzes for the class. Each student would write out a short quiz. Collect the quizzes and pass them out randomly. After the students have completed the quizzes, discuss the answers in an open forum.

Have the class watch the How to Find and Classify and Arithmetic Sequence lesson. Have them graph stadiums in the shape of a trapezoid, pentagram and circle. Black out the sections inside the shapes where the games will be played. Using the lines on the graph as 'rows', have them write equations to figure out how many people will fit in each row around the playing field for each shape.

#### Preview Lessons and use Quizzes as Homework

In addition to regular homework, assign the video lessons for students to watch as a refresher. Use the corresponding quizzes the next day in class to go over the basic principles of sequences. Identify areas where students could use more help, and review the video lessons together.

3 Lessons in Chapter 2: Common Core HS Functions - Sequences
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