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Creating Tessellations in Middle School Math

Great End of School Year Activity!

This post was taken from my old blog and revised…with much more detail added:-) Originally posted in June of 2014!

Tessellations in middle school math – one of my all-time favorite activities! I especially love using tessellation activities at the end of the school year….art projects like these keep students engaged:-)

We normally take several days to work on tessellations…sometimes more, depending on how much time we have.

What Are Tessellations?

First off, what is a tessellation? I show students a few examples and ask what they believe a tessellation is. They typically come up with the idea that a tessellation is the repeating of a shape or shapes in a pattern. I usually have to add the idea that there are no gaps or overlaps in a tessellation.

Creating Tessellations with Regular Shapes

$tessellation with regular shapes$

We start with using regular shapes, so students understand the idea of tessellations in general.

We were fortunate to have pattern blocks of hexagons, triangle, squares, etc. in the classroom, so students could use those to trace and make their shapes as precise as possible.

After using regular shapes, we extend to creating Escher-like tessellations. I share several example of these with students so they can study them and see the different types of animals, objects, etc found in them.

Creating Tessellations with Irregular Shapes

$tessellation step 1, cutting and taping to create a shape$

For our tessellation templates, we use two-inch squares cut from oaktag, so they’ll be sturdy enough to be traced numerous times (the templates end up being pretty worn out by the end!).

Step 1: Draw lines on the left side and top of the square. These can be curved or pointed….whatever the students feel like. The more the detailed the line, the more complex the tracing becomes.
Step 2: Cut along the lines that were drawn.
Step 3: Tape the shape cut from the left side of the square onto the right side of the square. This step can be tricky. I encourage student to slide the shape over to the right, to be sure they don’t change the orientation of the shape.

The shape must be aligned as precisely as possible so the tracing doesn’t get ‘thrown off.’ (This is shown in the video below)

Step 4: Tape the shape cut from the top of the square onto the bottom of the square.

Deciding on the Tessellation Design

$tessellations - shapes rotated in different directions$

Once the shape is created, I encourage students to rotate it and look at it from different perspectives to try to see something in the shape, like an animal or object. Sometimes students can easily see a bird or a ghost or a face, but other times, it’s hard for them (and me!) to see anything, so I’ll have students ask others what they see, to get a few ideas.

This is always fun because the students are so creative, and we learn how we might all see something different depending on the perspective:-)

Creating Tessellations with Individual Shapes

$seahorse and seashell tessellation$

The next step is to actually create the tessellation!

When my math periods were longer (when I taught 5th grade) and we had a little more flexibility in the day, we would trace the templates onto colored paper, and draw the details onto each individual shape, and then glue them to a background.

One thing I liked about this method was that if the shapes weren’t perfect, we could adjust them and overlap them a tiny bit as we glued them onto a background paper, so the tessellation would then appear pretty perfect.

Creating Tessellations by Tracing

$tessellation example$

When my class periods were shorter (middle school vs elementary), I changed the process from gluing the individual shapes to tracing. This typically went much more quickly, unless the pattern got thrown off.

Sometimes when students trace directly onto the background, if the shapes weren’t taped precisely enough or the student doesn’t trace precisely enough, students get half-way done and the shapes don’t ‘fit’ where they should in the tracing any more….the space for the new shape is too big or too small for the tracer. Sometimes it gets so ‘off’ that they need to start over.

Tracing steps:

$completed tessellation of lizards on rocks$

1) Trace the template over and over in pencil, as precisely as possible.
2) Go over pencil with thin black Sharpie.
3) Add the details to each shape.
4) Color the pattern (colors should be in a pattern as well).