Written by Sara at Classically Homeschooling.
One important mathematical concept kids run into sometime in middle school or high school is the Pythagorean Theorem. Pythagoras, an ancient Greek philosopher and mathematician, who was born around 569 BCE is credited with the discovery.
The Pythagorean Theorem is that theorem you probably remember from your own middle school and high school years: a² + b² = c². Today we’re going to teach our kids the theorem with a hands-on activity!
But first let’s take a look at what a mathematical theorem is.
Hands-On Math: The Pythagorean Theorem
A mathematical theorem is a statement that can be shown to be true by accepted mathematical operations.
This means you can’t just make up a proof and say it works. You have to use logic, reasoning, and accepted mathematical operations to show the theorem is true. Today we’ll be using squares and areas to show the Pythagorean Theorem is true.
So what exactly is the Pythagorean Theorem?
Pythagorean Theorem: The square of a square drawn on the hypotenuse of a right triangle equals the sum of the areas of the squares drawn on the other two sides.
Put another way: a² + b² = c².
In other words. If you have a right angle and measure each side, the square of side a plus the square of side b is equal to the square of the long slope we call the hypotenuse.
What You Need for This Activity:
- Graph Paper
According to the Pythagorean Theorem, if I draw a right triangle, the square of the two sides added together will equal the square of the hypotenuse. Let’s see if this actually works!
Step 1: Pull out your graph paper and draw a right triangle on it. I’m going to use sides with the length of 3 boxes and 4 boxes.
Step 2: Measure the hypotenuse.
Step 3: Remember square of a number is the area of a square with that length of side. So I’m now going to draw and cut out my squares. One square will have sides the length of 2 squares on the graph paper. One square will have sides the length of 3 squares, while the third will have the length I measured!
To make the next step more clear I’m going to highlight the squares in different colors. The small one will be yellow. The medium will be green. And the large one will be blue.
Step 4: Let’s see if the area of the two small triangles will equal the area of the large triangle! We’re going to do this by laying the medium square on top of the large square.
Now you have a choice. If you count the squares left over on the large triangle, you’ll notice there are 9 squares. And what’s 3²? 9! Or you can do what I did and cut the square to fit the left over area.
As you can see, the square of the hypotenuse is equal to the sum of the squares of the sides. The Pythagorean Theorem works!
Now let’s run through all 4 steps again with different numbers. This time I’m going to use sides with lengths of 6 and 8.
Step 1: Again we create the right triangle.
Step 2: Now measure the hypotenuse.
Step 3: Create the squares.
Step 4: Do the squares of the sides equal the square of the hypotenuse? The highlighter caused the sides of my squares to curl, so I used a touch of tape to force the squares to lie flat. Even so, as you can see the answer is yes!
Try the activity yourself using varying lengths for the sides.
No matter what the length of the sides of your right triangle, you’ll discover the squares always equal the square of the hypotenuse or a² + b² = c².
You’ve shown the Pythagorean Theorem works!
So what lengths did you use for your right triangles?
Teach math with these other fun homeschool activities!