How to Use Construction Art Challenges in Geometry Class
One of the big themes of the When Math Happens Geometry curriculum and Geometry courses is Math is Art. That’s why you’ll find construction art challenges throughout the curriculum, with an art challenge included in every Geometry chapter.
But it wasn’t always this way.
When I first started teaching Geometry, I tried to avoid constructions as much as possible. They seemed confusing, difficult to teach, and even harder to make engaging for students.
Then I discovered that a compass was more than just a dangerously sharp object collecting dust in a supply cabinet.
After seeing Lisa Bejarano’s Construction Design project, and after a conversation with an artist who told me he wished someone had explained the connection between math and art when he was younger, I started thinking differently about Geometry.
If Geometry is about shapes, angles, symmetry, transformations, and patterns, why not let students create art with those same ideas?
That’s where construction art challenges came in.
Start With One Simple Construction
If you want to use construction art challenges in your Geometry classroom, I recommend starting with a single construction during the first week of school.
I intentionally plan a shorter lesson so I have 10–15 minutes at the end of class to teach students how to construct a hexagon.
Why a hexagon?
Because many of the art challenges students encounter throughout the year can be built from this construction. And there’s something surprisingly satisfying about realizing you just made a perfect hexagon using a compass, straightedge, and pencil.
High school students actually went home and told their parents about it.
We work through the construction together as a class. I display a video or step-by-step animation, pause as needed, and have students complete each step with me.
Students work with a partner or small group so they can help each other, while I circulate and provide support.
My basic routine is:
1. Display a video or step-by-step demonstration.
2. Work through each step together.
3. Let students help each other when they get stuck.
4. Circulate and support students who need help.
5. Color the finished construction when appropriate.
The goal isn't to make everyone an expert at constructions immediately. It’s to give students a foundation they can build on later.
Turn the Construction Into a Challenge
I don't wait long before introducing the first art challenge—usually just a day or two after students learn the hexagon.
I display the finished challenge and let students figure out how to create it.
At first, I give students a few moments to see if they remember how to construct the hexagon.
If they’re completely stuck, I’ll play the full hexagon construction animation without stopping. Sometimes seeing the construction again is enough to trigger the memory.
Then I back off.
I want students to figure out the rest.
Students work with their groups, experiment, make mistakes, and try again. Once they complete the construction, they can color their artwork.
That basic approach works throughout the year.
If the challenge is based on a hexagon, refresh students on the hexagon construction. If it uses a square, refresh them on the square construction. Then let students use what they know to figure out the rest.
And I strongly recommend trying each challenge yourself before class.
Some of them are tricky!
That’s actually part of the fun.
Try to resist the urge to immediately rescue students when they get stuck. You’ll be surprised by how much they can figure out when given the time and space to explore.
Students are naturally creative. Give them an opportunity to use that creativity in math.
When Should You Use Construction Art Challenges?
You don't need to dedicate an entire class period to construction art.
In fact, I never do.
Some of my favorite times to use construction art challenges are:
At the end of class when we finish a lesson early
On Fridays as a brain break after a week of hard work
On quiz days for students who finish early
During a particularly long or tiring week when students need a change of pace
When the challenge connects to the current Geometry unit
Anytime the class needs a break from the normal routine
One of my favorite uses is as a brain break.
Students often told me that construction art was a great way to decompress. And there are plenty of days when you can tell your class has simply run out of gas.
Maybe it’s the end of a long week. Maybe there was a big school event the night before. Maybe students have been working especially hard.
Sometimes the best move isn't pushing through another 45 minutes of content.
Sometimes it's giving students a compass and letting them make something.
Where Can You Find Construction Art Challenges?
If you want to try this in your own Geometry classroom, you can find construction art challenges throughout the When Math Happens Geometry curriculum. Use the Routines filter and select Art to see the days that include construction art challenges.
For construction demonstrations, we also have a growing Geometry Constructions playlist with videos and animations students can follow.
Another resource I used frequently when I was in the classroom was Math Open Reference. It’s an older website, but its step-by-step construction demonstrations are still incredibly useful.
A Digital Option
I still prefer good old paper-and-pencil construction art.
There’s something different about students physically using a compass and straightedge to create something.
But we also created an online construction art game that gives students a digital way to practice constructions and explore geometric designs.
Think of it as another tool in the toolbox—not a replacement for the pencil-and-paper experience.
Start Small
If construction art feels intimidating, don't try to redesign your entire Geometry curriculum.
Start with one construction.
Teach students how to make a hexagon. Give them a simple challenge a day or two later. Let them struggle with it. Let them be creative. Then bring another challenge into the classroom when the opportunity makes sense.
Over time, you’ll build a classroom routine where students understand that Geometry isn't just about solving for x or memorizing theorems.
Geometry can also be something you create.
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