Visual Patterns as Function Types

What are the differences between linear and nonlinear functions? This lesson activity will help students experience the differences themselves.

The Visual Patterns site contains over 150 patterns to use with students of all ages.  There are loads of ways to integrate visual patterns into your instruction. By reading through the "teacher" menu, you will get the idea.



Screen Shot from the website

What I appreciate about this site is its open ended/open mindedness. As a teacher you can take this resource in a bunch of different directions. Offered here is how I did it with my students. The activity shared above helps the teacher lead students through finding, extending, graphing and then classifying the pattern as either linear or nonlinear. Intuitively, students will begin making predictions and then look for common threads between the different classifications.


This gives a better idea of how I ask students to organize their work and what their product may look like.

In this blog entry and the other ones I write, I intend to show how I weave technology applications into my math classes. It's a joy to share. That's why I make all of the documents editable. Feel free to use them in any form that suits you and your students.




An Algebraic and Graphical Approach to Inverse Functions

This lesson outline allows the teacher to guide students through 2 very different ways to think about inverse functions. I usually begin with the algebraic approach because it is more challenging to students, and they seem more willing to strain their brains at the start of a lesson.
 
In the first four examples, students get a chance to determine whether the functions are inverses or not by determining if their compositions are equivalent.
 
After that, the students are introduced to the algorithm that enables them to find the "potential" inverse function of any given function. I say, "potential" because sometimes what seems to be the inverse of a function isn't a function at all; it's a relation.
 
The next part of the lesson involves graphing functions and their inverses simply by reversing the domain and range for each point. It becomes even clearer when they graph the functions and inverses in two colors. At this point, I have them sketch in the line of symmetry just by looking at the lines/curves they graphed, but I stop short of identifying the equation of the symmetry line.
 
All of this leads up to graphing a few more pairs of functions and inverses using Desmos. Even though the students are required to have and use TI-84 graphing calculators in my school, working with Desmos gives them a much clearer picture of the relationship between functions, inverses and their line of symmetry.
 
Here is the lesson outline. Go ahead and tailor it to your students' needs.