# Pythagorean Theorem

What began as reviewing the area of a triangle with my son, somehow led to a discussion about pythagorean theorem.  He seemed to understand it very well so I designed an activity to strengthen his knowledge and allow him to think about the application of what he learned.  My son happens to love math so he really enjoyed this activity!

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Day 1

This is how it started:

Click on the picture to enlarge

You can see the remnants of our pytahgorean theorem discussion on our whiteboard. I essentially introduced him to the formula (later in the day my husband added the proof).  After our talk, we read What’s Your Angle Pythagoras by Julie Ellis together.

Day 2

The activity:

My goal was for my son to practice finding the missing side of a right triangle using the pythagorean theorem.  I wanted it to be fun, not just sitting at a desk filling in a worksheet. I decided to create a big triangle on the floor using building toys that we had readily available.

For the problems, I used pythagorean triples. This made it easier to solve the problems (no decimals!). I found the triples here at mathisfun.com.

I cut index cards in half and wrote one number on each card, using a different color for each triple to help keep track of what numbers went together in case they got mixed up! For example, one triangle has sides 3, 4, 5.  I wrote the 3 on one card, 4 on another, and 5 on another.

The next step is simple! I placed two of three numbers of the triple on the corresponding sides of the triangle. This was approximate, given that I used the same triangle over and over again. It was not to scale! As long as you put the biggest number on the hypotenuse, you’re good.

My son had to solve for the missing number.  For example: for the 3, 4, 5 triangle I put down the 3 and 4 and left the 5 out. He had to solve for the missing side- 5. I made sure to change up which side I left out so he wasn’t always solving the problem the same way. Originally, I wrote out just the first 6 triples, but my son loved doing this and asked for more- twice! He ended up doing a ton of these.

To solve the problems I allowed him to write on our small whiteboard.  I think that played a part in his enjoyment. If he had to solve these on paper, I don’t think he would have liked it as much. He’s pretty good with numbers and likes to solve things mentally as much as possible. Feeling like he “has to” show his work creates a mental block sometimes. I also think the fact that he was free to walk around and work standing up helped him.  There is so much that goes into a lesson. Keep in mind what works for your child. Some kids like sitting down and writing out all the steps. If that’s what they like, go for it!

Here’s what it the activity looks like:

When he solved for a missing side, I put the number where it belonged.

We lined up the triples after he solved them!

Working on the small whiteboard

This is how many he did!

After he solved for the missing side, we lined up the triples like a chart.  This allowed him to see a pattern emerging.  The pattern is not consistent all the time, but it gave him a general idea of solving for the hypotenuse when given the other two sides.  It was very interesting when we came across at triple that did not follow the pattern! It reminded him that we have to do the math every time, we can’t count on the pattern.

Day 3

To put this new skill to use, I found some word problems that required knowledge of the pythagorean theorem to solve.  This time I allowed him to use a calculator to solve the problems. The word problems can be found here at mathworksheetland.com.

That was our lesson! I hope your mathematician enjoys it