# Recursive Formula Activities

Instructor: Clio Stearns

Clio has taught education courses at the college level and has a Ph.D. in curriculum and instruction.

A recursive formula for an arithmetic sequence requires the computation of each term in the sequence in order to properly calculate the subsequent term. This lesson provides activities that will help your students better understand recursive formulas.

## Teaching Recursive Formulas

As a math teacher, not only are you are communicating important content and concepts to your students in ways that they can remember and apply, you are also responsible for helping students remain engaged in, excited about, and motivated to learn mathematics.

One way to help meet both of these goals simultaneously is to teach using activities, which let students work from their strength to gain mastery of material. The activities in this lesson will help your students understand what is meant by a recursive formula in mathematics.

A recursive formula is one that requires the calculation of one term in the sequence in order to properly compute the subsequent term. Recursive formulas build on themselves and constitute examples of iterative mathematical formulas.

## Visual Activities

This section offers activities that appeal to students who do their best learning visually, using images and graphic organizers.

### Illustrate a Recursive Formula

This is a great activity for students to work on in small groups.

Begin by giving each group an example of the first three steps of a recursive formula. Explain that their job is to make a poster that shows these three steps as well as the next six steps in the sequence. They should compute the variables for each of the subsequent steps and use illustrations to show how they conducted their computations. Hang completed posters around the room and give students a chance to view each other's work and draw conclusions about recursive formulas.

### Recursive or Not?

This activity lets students organize their thoughts about what makes a particular formula for an arithmetic sequence recursive or not.

Break students into partnerships and ask each pair to look at two sequences. One sequence should represent a recursive formula, while the other should not. Then, ask students to create a two-column graphic organizer. In each column, they should write three to five characteristics of each sequence. When they are done, they will have a complete graphic organizer showing traits of a recursive or non-recursive formula.

## Tactile Activity

### Recursive Formula Tag

This is a fun activity to do in a gym or recess yard.

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