Exponential functions are defined as relationships between two variables that have a multiplier for the independent variable. Exponential functions are an extension of geometric sequences where successive terms are generated by multiplying a constant number (constant multiplier) by the previous term .
Activity
Begin by working through the Paper Folding Problems. You’ll need two sheets of paper – scraps from the printer that you intend to recycle, or even yesterday’s grocery list, are perfect. 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
1.4_-Algebraic-Reasoning-SWTDownload Paper Folding Problems.
Reflect
On your own paper or digital document (or in your professional learning log!), answer these two questions.
- What do you notice about the successive ratios in each relationship?
- What relationship exists between the successive ratios in the dependent variable and the equations that you have written?
Why does that work?
Next, watch the video to see how common ratios relate to the bases of exponential functions.
Connections and Teaching Hints
Here’s a video showing connections to Algebra 1 as well as other hints for teaching this topic with your kids from the author’s perspective.
In this video, we will examine:
- Prior learning from Algebra 1
- Geometric sequences and exponential functions
- Calculator hints
