The Pythagorean Theorem is one of the culminating standards in my 8th grade class. It takes some of the other topics and concepts that we have learned and brings it all together. Some examples of concepts it involves are square numbers, formulas, triangles, and coordinate graphs. There are 3 Common Core standards dedicated to this theorem. Plus, it is something that 8th graders can really get! When I am planning my teaching for this topic, I like to chunk it with “I can” statements. Then I use those with students to help them keep track of their progress. Below I’ll share with you the “I can” statements I used to prepare & teach this unit, and how my students used them in their math interactive notebooks to reflect on their learning.
What I want my students to be able to do with the Pythagorean Theorem
We get two weeks of class to teach all things Pythagorean Theorem. Ultimately, I want students to be to explain and be able to apply the Pythagorean Theorem. This is a concepts that is completely new to all my 8th grade students. But, if you chunk it out right, even the kids who struggle the most can get the hang of it rather quickly. Here are the I can statements that I use as a path for teaching and learning for this topic:
- I can explain a proof of the Pythagorean Theorem.
- I can solve for a missing leg in a right triangle using the Pythagorean Theorem.
- I can solve for a missing hypotenuse in a right triangle using the Pythagorean Theorem.
- I can prove if a triangle is a right triangle or not using the Pythagorean Theorem
I find that using these I can statements, and having students review them on a daily basis, helps students to be more accountable for their learning. At the end of each day’s work, they have to think about what they learned and do a self-reflection with the I can statements in their interactive notebook. Reviewing and talking about what they are learning on a daily basis gives students more confidence about what they are learning. This chunking sequence has worked for me over the years. This year my kids learned it so fast that I got ahead by one day, which was awesome! (If you want to learn more about using I can statements in math interactive notebooks, read this post).
You can get your own print and go copy of the Pythagorean Theorem I Can interactive notebook insert, as well as 23 other 8th grade math concepts and a blank template, right here. They are a great addition to your interactive notebook.
I can explain a proof of the Pythagorean Theorem.
The first I can statement gets students an understanding of what exactly the Pythagorean Theorem is by explaining a proof. You can teach your students the formula for the Pythagorean Theorem and maybe go through the process of showing them how Pythagoras derived it. Or, even better, have them discover it themselves. I have the students work through a discovery lab for the Pythagorean Theorem to start the unit. This gets them gaining an understanding about it before ever giving them notes or examples. You can read more about the discovery lab in this post. In short, it is a lesson where the students get different squares with different side lengths. Then, they find the ones that make right triangles. After that, they draw conclusions and write a rule for the Pythagorean Theorem
In my experience discovery learning leads to better conceptual understanding and more engagement. If you want students to be able to explain the proof of the Pythagorean Theorem, then they need to understand it. If you give discovery a chance you will see students be able to explain things in a way you never thought possible. I am glad that we get to teach the Pythagorean Theorem because it is such a natural topic to have students discover a math concept through modeling.
I can solve for a missing leg in a right triangle using the Pythagorean Theorem.
To learn how to solve for a missing leg using the Pythagorean Theorem, we take notes in our interactive notebooks. Then, we do some practice problems together with a lot of guidance. I make sure that they are really solid on solving for a or b in the Pythagorean Theorem before moving on to solving for c. We also emphasize writing the formula at the beginning of each problem and not trying to do it in your head. So many of my students want to find a faster way. Unfortunately, often they are willing to use the faster way even if it means they are less accurate. Hmmmm. It must be something about the programming of the teenage brain.
I can solve for a missing hypotenuse in a right triangle using the Pythagorean Theorem.
After students are proficient at solving for a and b we shift to solving for the length of the hypotenuse. Students should have extensive practice solving for a variable, so I draw on those skills. Usually, my students are very proficient so it is just a matter of getting them to see that they have to move the value of one leg length to the other side by subtracting it from both sides. Once they see they get it, they are ready to practice. They can become comfortable with this very quickly.
Here’s where I found myself a day ahead of my original plans (and that NEVER seems to happen!) Students moved so quickly through solving for the hypotenuse that I could move right into the next day’s materials and lessons (thank goodness I already had those ready!) Once students are comfortable solving for any of the missing variables using the Pythagorean Theorem, they are ready for the final step.
I can prove that a triangle is a right triangle or not by using the Pythagorean Theorem.
Proving whether or not a triangles is a right triangle can kind of throw kids for a loop. They are so used to finding a right answer. But these questions don’t have a number at the end, so some of my students struggled at first. I love this topic because it doesn’t have a “right answer” and the students are forced to do reasoning instead of quickly doing a calculation. The students plug the numbers into the three variables, calculate, and then simplify. They are looking to see if the two sides are equal or not. Then, students have to evaluate if this make a right triangle or not.
This is fairly straightforward and students become proficient at it quickly. I work with students who struggle with math and this is one of the easier topics we do. Students really seem to enjoy learning about the Pythagorean Theorem and I think one reason is because they feel very confident about it.
The misconceptions are not too major on this topic. One thing that my students used to do was not find the square root at the end. This is an easy one to overcome by having students check to make sure that that would be a reasonable answer. For example, it would not be reasonable to have a triangle with side lengths of 3 and 4 to have a hypotenuse of 25. I show them how long that would be compared to the triangle and they kinda laugh at how ridiculous that would be. After every example that I do with them we check for reasonableness. Also, I have them explain why the c squared equation in the problem is not reasonable. My students don’t make this mistake anymore.
Take-aways and getting started
Chunking the learning through these I can statements keeps me and the students on track as we go. This week, as we were reviewing the I can statements in their notebook, I told them to put a check next to the ones they felt like they had mastered. One well-meaning boy told me he just checked them all at the beginning of the unit. Um, no. This made me chuckle because I think he was trying to be efficient and missing the point. I love how they keep me on my toes and remind me that I have to keep an eye on them at all times. We had a great conversation about what it means to check something off and feel confident that you really know how to do something new.
I hope you try this out in your classroom. Have students write I can statements in their notebook and see how it works for you. Can’t wait to hear about your experience!
Join the Maze of the Month Club
Join to get exclusive free math mazes every month!