Cubic functions are relationships between two variables that have a constant third rate of change (the change in the change in the rate of change is a constant rate) .
Activity
Begin by working through the Prism Problem. Download the document and either mark it up on your screen with your finger or a touch-pen or print it and use a pencil. Please pay particular attention to the number patterns in the table.
1.8_-Algebraic-Reasoning-SWTDownload the Prism Problem.
Reflect
On your own paper or digital document (or in your professional learning log!), answer these two questions.
- A cubic function is a function of the form f(x) = ax^3 + bx^2 + cx + d. What is the degree of this function (i.e., the power of the greatest exponent)?
- Keeping in mind that a linear function contains a polynomial with degree one and a quadratic function contains a polynomial with degree two, what relationship is there between the degree of the polynomial and the level of finite differences that are constant?
Why does that work?
Next, watch the video to see how finite differences relate to cubic functions.
Connections and Teaching Hints
Here’s a video with hints for teaching this topic with your kids from the author’s perspective, plus some wisdom learned from Algebraic Reasoning teachers in the field.
