GNAW on Polynomial Functions

Description

In this GNAW on Polynomial Functions Activity you will find three different levels of polynomial practice where students will explore problems that can be represented graphically, numerically, analytically, and verbally. They will make connections among these representations.

The Rule of Four approach to analyzing functions is sometimes known by the acronym GNAW. Graphically, Numerically, Algebraically, and Verbally (Words).

LEVEL 1:

This is appropriate for an Algebra 1(first course) where students are beginning to make connections to polynomials and the language.

LEVEL 2:

The rigor for this GNAW activity is geared toward Algebra 2 Honors or Pre-Calculus students.

LEVEL 3:

This last level will meet the needs of your Calculus students as they practice applications of the derivative for polynomials.

What is GNAW and the Rule of Four?

The “Rule of Four” or G.N.A.W. Approach is a method of thinking about mathematics in order to make connections through multiple representations of our mathematical thinking. Students should be able to represent mathematics in graphic, numeric, algebraic, and verbal formats. G.N.A.W.

Why should you use the GNAW approach?

By implementing this process into your classes, students will gain a deeper understanding of the mathematics. The Rule of Four helps students connect and validate concepts and techniques.

How can you use the Rule of Four?

Teachers can model this approach during instructional time to set the “tone” for expected thinking and reasoning. Then, give your students many chances to practice the techniques. It is also important that students learn to make connections between the different representations.

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