Introduction to the Pythagorean Theorem

We finished up our introduction to geometry unit, and moved into coordinate geometry and the Pythagorean Theorem last week. First, we reviewed plotting coordinates. Then, we found lengths of vertical and horizontal segments in the coordinate plane. This week, students will learn about the Pythagorean Theorem and calculate diagonal segment lengths.

Since it has been a while since my students have plotted points in the coordinate plane, we started the unit with a fun coordinate plane secret codes activity.

Students got a code sheet to reference during the secret codes presentation. The presentation asked students to figure out what letter each symbol pair represented, then what 3-letter words. Above is one of the words questions.

The presentation is scaffolded with the x coordinates colored black for the first few slides to remind students to look at the x-axis first. Then, this extra coloring is taken away to better mimic the real coordinate plane.

As an aside, my classroom aide and I were talking about why students have trouble plotting points. My best guess (after trying to figure this out for the last 20 years) is that points are plotted x then y, but slope is found y then x. I think students confuse these two.

Then we moved into distance in the coordinate plane. I gave students a little segment lengths reference sheet for their notebooks.

We completed this distance in the coordinate plane worksheet together on the board that covers the lengths of vertical and horizontal segments. Students started to see the relationship between integers when finding distance. I let students know that they can always count the spaces between the coordinates, but that if they're feeling lazy, they can always subtract (like me!). We spent extra time on this because integers can often be a sticking point for students.

Pythagorean Theorem video

After this, we are moving into the Pythagorean Theorem with a presentation of videos from this Pythagorean Theorem YouTube playlist and interactive diagrams from Geogebra:

• Geogebra Pythagorean Theorem link 1: Pythagorean Theorem animation showing the areas of a and b squared equal c squared with a slider
• Geogebra Pythagorean Theorem link 2: Lets you click and drag the sides of a right triangle to see the square areas made by the legs and hypotenuse.
• Geogebra Pythagorean Theorem link 3: This one lets you click and drag the vertices of a right triangle looking for Pythagorean triples

The template from the video is here in my Google Drive. I printed the second page in 3 different colors for the video. If there is time, students will use the template to build 3-4-5 Pythagorean Theorem diagrams.

As a reminder, students will get this Pythagorean Theorem reference sheet for their notebooks.

We then did some practice with right triangles on this Pythagorean Theorem graphic organizer. My co-teacher last year told me about 1/2-page page protectors, so I slipped the graphic organizer into those. Once everyone is pretty solid solving for C given two leg lengths, we'll complete a couple Pythagorean Theorem activities to solidify things.

Then students will complete this Pythagorean Theorem in the coordinate plane activity, where they'll record coordinate points as a review and calculate diagonal segment lengths of right triangles. There's a more advanced version here where most triangle side lengths are all diagonals.

> Browse all Pythagorean Theorem activities