Hands-On Explorations of the Pythagorean Theorem

Mathematics, in part, are built upon constants. One of the most well known and fundamental constants is the Pythagorean theorem.

We all know it and a lot of us teach it every year. Although educators and even parents are pretty familiar with this, our students don’t always grasp it as easily.

We know that the uses for this theorem are practically limitless; from astronomy, geography, physics to engineering and more. The Pythagorean theorem is a constant in our lives. 

And in this day and age of interactivity or press of a button knowledge (AKA: Google), it is important to teach on a more hands-on level.

​This collection offers 4 different approaches for discovering the ins and outs of the Pythagorean Theorem. 

Why Bother Taking the Time to Go Hands-On?

​Dr. Ben Mardell, Phd with the Project Zero at Harvard University has said, "kids learn through all their senses and they like to touch and manipulate things."  Basically, hands-on activities activate more regions of student’s brains.
 
It’s actually pretty simple. As Judy Dodge author of 25 Quick Formative Assessments for a Differentiated Classroom states "The more parts of your brain you use, the more likely you are to retain information, if you're only listening, you're only activating one part of the brain," she says, "but if you're drawing and explaining to a peer, then you're making connections in the brain."

​That’s why things like doodle notes and hands on activities are so important. Activities like these are easy to implement and immensely beneficial to the students. 

1. Cut & Paste

It can sometimes sound rudimentary, but a simple cut and paste activity is a tried and true method of learning. Kinesthetic learning is a great way to engage your students. Have your students cut up diagrams or models from worksheets or even a photocopy of textbook samples.

Then have your students  arrange them on paper and scotch tape them down to create the original, then re-number and write/tweak the actual question (save time drawing the diagram or model yourself).
 
Here is a great example of a hands-on pythagorean classroom activity from Kyle Krafka.

2. Folding

Another great illustration of the Pythagorean theorem is through paper folding. By folding a plain sheet of paper your students get a first hand look on exactly how this theorem is applied.  This one moves fast, but is really spiffy! 

This origami-style activity will help your students see and remember how the theorem actually applies.  The great part is that it is a general proof that works for different right triangles, and you can actually fold further to get different versions.

3. Project: Create a 3-d Model

Have your students team up in pairs and create and actual 3D model of the theorem. They can use small balls, blocks, jelly beans, water, or even wadded up balls of paper to show how the side lengths work out. Here is an example that a few students came up with in their own math project.
 

Ideas for the squares for hands-on student projects (edible options are always a big hit!):

• crackers
• blocks
• chocolates
• paper squares
• dice
• game cards
• candies

Giant Versions on the floor as a full class! -

• square plastic plates
• cloth napkins
• carpet squares or ceramic tiles

4. Concept-Based Doodle Notes

This set of doodle notes is a great way for students to record and reference the basics of the Pythagorean Theorem.  Visual note-taking is a strategy that is as hands-on as notes can get, and has been proven to boost focus, learning, and long-term retention.

Pythagorean Theorem Doodle Notes

​Teaching fundamentals is extremely important. However, what you really your students to retain is the real meaning of it all.

​Taking concepts such as the Pythagorean Theorem out of the text (beyond just memorizing a formula) and into our hands is a wonderful way learn. Do you have any tips or tricks you use in your classroom? Let us know what you do in the comments below! 

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