# Explicit Formula Activities

Instructor: Clio Stearns

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

As you teach algebra to your students, you will want them to understand what an explicit formula is. This lesson offers activities that teach about different understandings of explicit formula.

## Teaching Explicit Formula

As a math teacher, you have many different responsibilities. You want your students to understand and be able to apply the concepts you are teaching them, as well as be engaged and motivated in their study of mathematics.

One good way to increase student engagement is to incorporate activities into your teaching. Activities make learning hands-on and help students take ownership over their own developing understandings.

As you teach the concept of explicit formula, you will be referring to a variety of interpretations, including:

• analytical expressions
• closed-form expressions
• algebraic expressions
• the L-function

The activities in this lesson will help you access different learning styles and strengths while addressing each of these phenomena with your students.

## Analytical Expressions

Analytical expressions are expressions that use well-known operations.

### Compare and Contrast

Ask your students to look at some examples of analytic expressions that are and are not considered closed-form expressions as well. Discuss the similar and different attributes of these expressions with your students, as well as the contexts in which they might be used. Then, ask your students to complete a Venn diagram with examples of closed-form expressions, analytical expressions, and those that might be considered part of both categories.

### Liouville's Theorem

One aspect of understanding analytical expressions is knowing that the integral of the expression might not be possible to express in closed form. This is known as Liouville's theorem.

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