Visual Patterns

I recently heard that math is composed of patterns and the equation represents the pattern.  I like that and I may put it up on my wall but why use visual patterns to teach math.

First, visual math teaches students to think about changes recursively and secondly rationally. 

The other day, I came across a web site called visual patterns.  The site has 240 different patterns for students to figure out the equation associated with the pattern.

Each activity shows the first three iterations of the pattern and then gives the value of the 42nd iteration so you know that total.  Using the given information, people are expected to arrive at the equation producing the pattern.

This is a cool site but if you are looking for the answers, you will not find them.  You will find a teachers page and a gallery with more information but you will not find all the answers.

These activities would make great warm-ups where students need to include their thinking process.  While searching for ideas on Visual patterns, I stumbled across a two volume Algebra Book which uses visual patterns to teach algebra.

I looked at the first few exercises in each volume.  The lessons come with everything including examples of ways students could solve the problems because students do not always use the same method to find the answers.  Yes it does use blackline masters so if you are a teacher who prefers letting students explore things for themselves, it isn't hard to set up a google doc or google slides for cooperation.

The books actually go hand in hand with the visual patterns activities.  I have some students who struggle with math.  I think  something like this may help them improve their understanding while making it a bit more interesting.

If you want students to learn more about finding the equation that expresses the pattern, Desmos has a lovely activity called "Visual Patterns Tribute" based on the first site I wrote about.  It makes the whole topic a game allowing students to choose their own adventure.  The activity comes with a teacher guide so the teacher can make notes as they try out the student preview.  In addition, it comes with a page for students to use as they work through it but the page is more like a data sheet for students to record their findings.

There are certain topics which may be harder for us to teach because we don't understand the visual patterns.  I freely admit visual patterns is not something used when I went through school.  It was never even mentioned when I went through my teacher's training class so I have no idea how to teach quadratics using visual representation.

MATA has two links on this page to teach linear and quadratic functions using visual patterns.  What I loved about the links is on the quadratic one, they included one or two for x^2 + 1 and even more complex quadratics.  Once I saw these, my mind went "Yes" so I have a way of using this in class for specific topics.

If you'd like to know about possible student misunderstanding for these types of problems check out this blog entry as it discusses this topic. 

I love finding new tools for my teaching arsenal. Let me know what you think!  I love hearing from people.  Have a great day.