## Patterns and Pre-Algebra

Yesterday I was able to get outside and walk around a local park.  While soaking up the sun I started to notice a variety of patterns on the sides of the path.  The patterns changed depending on the vegetation and location.  As I searched for additional patterns I started to find more and and then looked for consistency among the sequences. I took out my phone and started taking pictures of the patterns that I saw thinking that I might use them next school year. After collecting a few I started thinking about how this connects to the math strand of algebra.

Taking the pictures had me thinking of a class I had a few years ago.  I remember reading a district-adopted fourth grade text that introduced pre-algebra to students as patterns and solving for the unknown.  This simple kid-friendly definition was explained to elementary students in a short paragraph. After thoroughly discussing the definition of a pattern (yes, that took time), students took that definition and ran with it.  They started to find patterns (number and otherwise) in and outside of the classroom. If a pattern didn’t seem to exist, students would make a prediction based on the prior sequence.  A completed pattern seemed to make sense and an uncompleted sequence didn’t have meaning.  Students started to put on their “pattern glasses” to identify sequences.  Students would argue whether something was a pattern or not.  I distinctly remember one student saying that to complete the pattern you need to find the missing puzzle piece. These discussions were interesting to observe as students were developing their own rules to the patterns and offering their suggestions to others.

After uploading the pictures from the walk I started to think of how students make meaning out of patterns.  This past year my students were able to find patterns in nature, use Which One Doesn’t Belong, and then transition that idea to Visual Patterns.  Understanding the rule or rules behind the pattern can lead to different levels of pre-algebra moving forward. It’s amazing when students start to realize that there can be more than one rule to a pattern or question.  Simple patterns can allow students multiple entry point to access pre-algebra concepts.  Before the school year starts I’ll be pondering the question below.

How do students identify patterns and does that help them become better problem solvers?

I’ll leave you with one more picture:

## Visual Patterns

My third #MTBoS post is about the visual pattern resource, visualpatterns.org.  Generally, patterns (numerical and object-based) are some of the first concepts taught to introduce algebra and number characteristics.   Initially, patterns may seem simple, but they often allow opportunities to enrich and extend instruction into more challenging concepts

My third grade class has been studying patterns and rules during the past two weeks.  One of the activities that we used can be found here.   We’re using math tasks to uncover different type of numerical patterns.   I’ve had the opportunity to visit this site multiple times during the algebra unit.  One of my classes tackled the problem below last week.

The students loved that this problem was created by a sixth grade student.  I think this added to their motivation and bonus! … also had them thinking of how they could create their own problems.  The students were given whiteboards and worked with a partner to find the fourth pattern. During that time I asked questions that helped guide the students towards a solution.  With enough time, most groups were able to find a solution.  The class then had a discussion on how the solution was derived.  Then came the fun part …  the partners decided to answer “How many lego pieces are in step 43”?  Student groups then presented their answers to the class.

At some point I’d like to have my students create and submit their own patterns to visualpatterns.org.