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Introduce the Pythagorean Theorem with a short video. Follow this with a discussion on its historical context and applications in real life.

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Use online platforms to find interactive activities or quizzes. These can reinforce the concept through engaging and hands-on experiences.

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Looking for ideas for teaching the Pythagorean Theorem? I'm so excited to share with you some of my favorite activities for this topic. This is one of my favorite things to teach all year, and it's probably my favorite geometry topic of all time. The Pythagorean Theorem is a very visual concept and students can be very successful with it. This list of 13 Pythagorean Theorem activities includes bell ringers, independent practice, partner activities, centers, or whole class fun. Be sure to grab the free download included in this post.You're sure to find a few activities from this list that are the perfect fit for your classroom:

Let's dive-in

Let's dig deeper into each of these activities. These ideas can be used to start a lesson, for practice, and for formative assessments. You'll find something to use in your classroom and add a little spark.

Math mazes are a simple twist on traditional worksheets. They provide students a means of practicing that's non-threatening. We use them almost everyday in my class. I used these three Pythagorean Theorem mazes the week after we learned this topic. Mazes become a way to reinforce what students have learned. They could also easily be used for math centers or homework.

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The Pythagorean QR code activity makes a great game, independent activity, center or even homework. It focuses specifically on the converse of the Pythagorean Theorem. Students have to identify if a triangle is a right triangle or not. If you use it as a game, then students can battle against each other for a little friendly competition.

To play the QR code game battle, students each answer a different question at the same time. Next, they check their answers using a QR code. You can find QR code readers on a phone, tablet, or computer. Then, students earn points based on the points assigned for each problem through the QR code. This is done randomly. Due to this aspect of them game you can get more points even if you answer questions slower or if you get one wrong. Students love the battle part. Many of my students are very competitive and this is a low-stakes game. Also, this is an opportunity for students to keep themselves accountable. (For more QR code tips, check out 5 Ways to Use QR Codes in the Math Classroom).

This version of the game doesn't have super complicated questions, so it won't take that long. But along the way, students will get immediate feedback on their progress. Playing this game, students experience a high rate of success.

This Pythagorean Theorem riddle is a quick practice for students right after you've completed notes and some practice problems. It has a cute and cheesy riddle and 12 problems for students to work through. My students found a lot of success with this activity and completed it rather quickly. It didn't take as long as some other topics, mostly due to their strong foundation from the Pythagorean Theorem Discovery Lab, so I had to speed up my schedule. They loved finding the answer to the riddle. The other day when we were doing this riddle it spawned a slew of cheesy riddles from my students. It also gave the kids that like to be performers a chance to show their personality.

This 4 minute video shows how the Pythagorean Theorem is relevant in football. I'm a huge football fan and I love bringing math into the real world. So this video seemed like a no-brainer. The students were very engaged watching this video. You could hear some of them react when they saw a big hit. Some of the kids who don't know a lot about football may have been a little lost, but it still was a great way to look at the Pythagorean Theorem in action. We also related this to soccer, which is also popular among my students. The concepts they talk about in this video can actually be related to most sports. After watching, you can ask students to explain how the Pythagorean Theorem can be applied to another sport.

I use this video for an anticipatory set after students have a background with the theorem. It gets them talking about the Pythagorean Theorem, and some kids who don't normally contribute much had a lot to say.

This short video shows a contestant on Who Wants to be a Millionaire who lost $15,000 because he didn't know the Pythagorean Theorem. 8th graders love to see situations where they're smarter than adults. What a great way to start a daily lesson. I think when you watch it you kinda feel like you could have saved this person from losing their money. This is a great anticipatory set and a real life example of math. Questions you could ask students to answer during the video:

How could he have used the Pythagorean Theorem to answer this question?

Why do you think the audience also chose the wrong answer?

What is another example of when not knowing math can contribute to you losing money?

This can be an excellent way to start a class period on day 3 or 4 of your unit. What conversations will it start with your students? How many of your students will figure it out?

This Shmoop video uses a silly story about Peter Pan and his shadow to illustrate the Pythagorean Theorem. If you haven't used Shmoop videos before in your class, you should know that they are a little silly and quirky. Most 7th and 8th graders seem to appreciate the ridiculousness in these videos. I love to use them as anticipatory sets, and this specific one is a quick review of the Pythagorean Theorem. Also, you can use it for students who have missed a day or two. It can help them see the Pythagorean Theorem in a different way.

Doodle Notes is a part of my "Try One Thing" for this month. My two colleagues have tried this as well. I would say that our first attempt didn't go very well. It wasn't horrible, but we didn't really understand how to make doodle notes work. We needed to do a little more upfront research before diving in. We embraced the concept of connecting doodling and learning, and for that reason we're giving it another try with the distance formula next week. Doodle notes are a cool concept because they let students be creative in math while taking notes. I would still use this again and I'll tell you how it goes next week. (update- I continue to use Doodle Notes, but have learned that it's important to be very specific with students and to give them more directions than I initially did).

There are a lot of ways to use task cards. Really, task cards are just a way to practice problems, but they can also be a powerful engagement tool. I use this set of 27 mini task cards for practicing with the Pythagorean Theorem. While there are many options in how to use task cards, we played SCOOT with them. SCOOT is a game where you put one task card on each desk. Then, students answer the question on their desk. Next, everyone moves one desk to the right and they are given time to do that problem. Finally, you just keep repeating until students are back to their desk. If you have a small class like me you could have two task cards on each desk. Kids love this activity. I don't exactly know why they love it so much, to be honest. But it's fast paced and gets them moving around the room.

One great way to review for test or to see how the class is doing is through playing whole class games. One game I love playing with my class is called knockout. It can be played with or without an interactive whiteboard. All you need to have is a projector. This is how it is played:

A student chooses from one of the objects on this screen. After that a question is revealed. Some of the questions have bonuses. The bonuses can be good or bad. Each question has a point value. Then, after you show the answer, you go back and choose another question.

This particular game has solving for a missing side problems. Also, it contains converse of the Pythagorean Theorem questions as well. Because students choose what's next, the questions come up in a random order. That makes it work really well to prep for the unit test.

I play this with all students using a whiteboard to work out each problem. Each student answers every problem, and then they keep track of their points for the problems they get right. I don't emphasize the points very much, but many students love the points side of the game. When needed, I coach students through the problems if they seem to be struggling. We play this type of game the day before or the day of a test. These games work as a final boost for students.

I use a lot of quarter sheet exit tickets. Many of them I've made myself by looking through resources and books and then adapting them. This "Explain it to an Alien Exit Ticket" is one of my creations for this unit. You can quickly see what students understand about the topic. I give out this exit ticket at the end of the lesson and have students return it to me as they walk out the door. A few of them will really get into character and act like they're talking to an alien. Other kids won't get into that part at all. Either way, students' responses give a great snapshot of what they're understanding. You can click here to get a free copy of this exit ticket to use with your class.

The push for performance tasks sometimes leaves us trying to come up with our own stuff. I don't really have that problem anymore even since I found Illustrative Mathematics. I've talked about this site before, but it's truly a go to destination for Common Core performance tasks. It's free and the tasks are so detailed.

My favorite performance task for the Pythagorean Theorem is called Bird and Dog race . Students have to figure out who will win a race between a Bird and a Dog. It has just the right amount of challenge. It includes a series of questions that students have to answer and isn't just asking for a right answer. Try this one with your students and see what they can do with it.

Sometimes you come across something really cool that you have never seen before when you search for resources. That is how I feel about this one. The website that it comes from is a paid website, but they have a promotional lesson. It happens to be about Pythagorean Theorem. It comes with a lesson, a manipulative, problems, and a challenge. You can use one part of it or the whole thing. I think it would work great for fast finishers. No matter what type of group you work with there will always be fast finishers. I feel like I always send my fast finishers to Prodigy, which is our intervention. The lesson from Braining Camp gives me a better alternative.

The Pythagorean Theorem Drawing Project from 123 Teach-Brittany Kiser is a fun activity I used last year as an activity for students when they finished their benchmark test. You can read all about it in this blog post. In this activity students get to be creative and show the Pythagorean Theorem in a real world setting. Due to the fact that I had students do it during testing, they weren't able to ask me a whole bunch of questions. All of them were able to understand the directions and complete the project on their own.

Try One Thing

I work part of my day as an academic coach with other math teachers. I've learned that most people can't make many changes to their instruction or classroom management at a time. That's why I created the "Try One Thing" philosophy. It will amaze you how many tools you can add to your teacher tool box if you try just one thing at a time. This post contains a long list of ideas for Pythagorean Theorem. My challenge to you is to just Try One Thing.

All of my resources and activities for teaching Pythagorean Theorem are also available in a bundle at a steep discount. Check them out 🙂 Thanks so much for reading. Until next time!

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13 Pythagorean Theorem Activities for Your Classroom

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Looking for ideas for teaching the Pythagorean Theorem? I'm so excited to share with you some of my favorite activities for this topic. This is one of my favorite things to teach all year, and it's probably my favorite geometry topic of all time. The Pythagorean Theorem is a very visual concept and students can...

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Provide a worksheet with a variety of Pythagorean Theorem problems. Include real-life scenarios to show its practical applications, such as in architecture or navigation.

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Group Assignment: Real-Life Problem Solving

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Group Assignment: Real-Life Problem Solving

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Divide the class into small groups and assign each a real-life problem to solve using the Pythagorean Theorem. Encourage creative presentations of their solutions.

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Incorporate math games that involve the Pythagorean Theorem to make learning fun. Look for games that can be played on computers.

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The Pythagoras theorem which is also sometimes referred the Pythagorean theorem is the most important formula of a geometry branch. According to Pythagoras, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle. In this lesson, you will learn about the Pythagoras theorem, its derivations, and equations followed by solved real-world problems on the Pythagoras theorem triangle and squares.

What Is Pythagoras Theorem?

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. In the given triangle ABC,we have BC ² = AB ² + AC ²​​. Here, ​​​​AB is the base, AC is the altitude or the height, and BC is the hypotenuse.

Pythagoras Theorem Equation

Pythagoras theorem equation helps you to solve right-angled triangle problems, using the Pythagoras equation: c ² = a ² + b ² ('c' = hypotenuse of the right triangle whereas 'a' and 'b' are the other two legs.). Hence, any triangle with one angle equal to 90 degrees will be able to produce a Pythagoras triangle. We can use this Pythagoras equation: c ² = a ² + b ² there.

History of Pythagoras Theorem

Pythagoras theorem was introduced by the Greek Mathematician Pythagoras of Samos. He was an ancient Ionian Greek philosopher. He started a group of mathematicians who works religiously on numbers and lived like monks. Finally, the Greek Mathematician stated the theorem hence it is called by his name as the "Pythagoras theorem." Though it was introduced many centuries ago its application in the current era is obligatory to deal with pragmatic situations.

Although Pythagoras introduced and popularised the theorem, there is sufficient evidence proving its existence in other civilizations, 1000 years before Pythagoras was born. The oldest known evidence dates back to between 20th to 16th Century B.C in the Old Babylonian Period.

Pythagoras Theorem Formula

The Pythagoras theorem formula states that in a right triangle ABC, the square of the hypotenuse is equal to the sum of the square of the other two legs. If AB, BC, and AC are the sides of the triangle, then: BC ² = AB ² + AC ²​. While if a, b, and c are the sides of the triangle, then ​c ² = a ² + b ². In this case, we can say that AB is the base, AC is the altitude or the height, and BC is the hypotenuse.

Pythagoras Theorem Proof

Pythagoras theorem can be proved in many ways. Some of the most common and most widely used methods are by using the algebraic method proof and using the similar triangles method to solve them. Let us have a look at both of these methods individually in order to understand the proof of this theorem.

Algebraic Method Proof of Pythagoras Theorem

Pythagoras Theorem Proof using Similar Triangles

Algebraic Method Proof of Pythagoras Theorem

Algebraic method proof of Pythagoras theorem will help us in deriving the proof of the Pythagoras Theorem by using the values of a, b, and c (values of the measures of the side lengths corresponding to sides BC, AC, and AB respectively). Consider four right triangles ABC where b is the base, a is the height and c is the hypotenuse. Arrange these four congruent right triangles in the given square, whose side is a + b.

The area of the square so formed by arranging the four triangles is c ². The area of a square with side (a + b) = Area of 4 triangles + Area of square with side c. This implies (a + b) ² = 4×1/2×(a×b)+ c ², a ² + b ² + 2ab = 2ab + c ². Therefore, a ² + b ² = c ². Hence Proved.

Pythagoras Theorem Proof using Similar Triangles

Two triangles are said to be similar if their corresponding angles are of equal measures and their corresponding sides are in the same ratio. Also, if the angles are of the same measure, then we can say by using the sine law, that the corresponding sides will also be in the same ratio. Hence, corresponding angles in similar triangles will lead us to equal ratios of side lengths.

In triangle ABD and triangle ACB:

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, triangle ABD and triangle ACB are equiangular, which means that they are similar by AA similarity criterion. Similarly, we can prove triangle BCD similar to triangle ACB. Since triangles ABD and ACB are similar, we have AD/AB = AB/AC. Thus we can say that AD × AC = AB ². Similarly, triangles BCD and ACB are similar. That gives us CD/BC = BC/AC. Thus, we can also say that CD × AC = BC ². Now, using both of these similarity equations, we can say that AC ² = AB ² + BC ². Hence Proved.

Pythagoras Theorem Triangles

Right triangles follow the rule of the Pythagoras theorem and they are called Pythagoras theorem triangles. The length of all the three sides are being collectively called Pythagoras triples. For example, 3, 4, and 5 can be called as one of the sets of such triangles. There are a lot more right-angled triangles which are called Pythagoras triangles. All such triangles follow one common rule: c ² = a ² + b ².

Pythagoras Theorem Squares

As per the Pythagorean theorem Hypotenuse² = Perpendicular², which further justifies that the area of the square built upon the hypotenuse of a right triangle will be equal to the sum of the area of the squares built upon the other two sides. And these squares are known as Pythagoras squares.

Applications of Pythagoras Theorem

Though it is necessary to learn the basic concepts such as theorem statements and their mathematical representation, we would be more curious in understanding the applications of the Pythagoras theorem which we face in day-to-day life situations.

Here are some of the applications of the Pythagoras Theorem

Engineering and Construction fields

Most architects use the technique of the Pythagorean theorem to find the value as well as when length or breadth are known it is very easy to calculate the diameter of a particular sector. It is mainly used in two dimensions in engineering fields.

Face recognition in security cameras

We are more familiar with face recognition nowadays it reduces the turmoil in investigating the crimes in the security areas. It undergoes the concept of the Pythagorean theorem that is, the distance between the security camera and the place where the person is noted is well projected through the lens using the concept.

Woodworking and interior designing

As the main concept indicates if the cardboards being square can be made into a triangle easily by cutting diagonally then very easily the Pythagoras concept can be applied. Most woodworks are made on the strategy which makes it easier for designers to proceed.

It's a very amazing fact but people traveling in the sea use this technique to find the shortest distance and route to proceed to their concerned places.

Usually, surveyors use this technique to find the steep mountainous region, knowing the horizontal region it would be easier for them to calculate the rest using the Pythagoras concept. The fixed distance and the varying one can be looked through a telescope by the surveyor which makes the path easier.
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If you want to build more conceptual knowledge with the help of practical illustrations try Pythagoras Theorem Worksheets. Also, check out few more interesting articles related to Pythagoras Theorem for better understanding.

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FAQs on Pythagoras Theorem

What Is the Pythagoras Theorem in Math?

Right triangles follow the rule of the Pythagoras theorem and they are called Pythagoras theorem triangles. All such triangles will follow just one common rule: c ² = a ² + b ².

What is the Converse of Pythagoras theorem?

The converse of Pythagoras theorem is: If the sum of the squares of any two sides of a triangle is equal to the square to the third (largest) side, then it is said to be a right-angled triangle.

What Is the Use of the Pythagoras Theorem?

The Pythagoras theorem works only for right-angled triangles. When any two values are known, we can apply the Pythagoras theorem and calculate the other.

How Do You Find the Pythagoras Theorem for a Right Triangle?

The square of the hypotenuse of a right triangle is equal to the sum of the square of the other two sides. When any two values are known, we can apply the theorem and calculate the other.

What Are the Applications of the Pythagorean Theorem in Real Life?

The Pythagorean theorem helps in

Computing the distance between points on the plane.

Calculating the perimeter, the surface area, the volume of geometrical shapes, and so on.

In architecture and construction industries.

In surveys

How Do You Solve A Squared Plus B Squared Equals to C Squared Using Pythagorean Theorem?

A squared plus B squared equals to C squared implies c ² = a ² + b ², which is the formula of the Pythagoras theorem, for figuring out the hypotenuse in a right triangle when the other two sides are given.

Can We Apply the Pythagorean Theorem to Any Triangle?

No, you can't apply the Pythagoras or the Pythagorean theorem to any triangle. It needs to be a right-angled triangle only then one can use the Pythagoras theorem and obtain the relation where the sum of two squared sides is equal to the square of the third side.

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Pythagoras Theorem (Pythagorean) - Formula, Proof, Examples

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The Pythagoras theorem which is also sometimes referred the Pythagorean theorem is the most important formula of a geometry branch. According to Pythagoras, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

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Demonstrate the proof of the Pythagorean Theorem using cube a links. This hands-on activity helps students visually understand the theorem's concept.

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Guide students through calculating the sides of right-angled triangles using calculators. This reinforces their understanding and application of the theorem.

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Encourage students to research and present famous structures or places around the world that utilize the Pythagorean Theorem. Create a 'museum' in class where each student can display their findings.

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Assign students to create short videos explaining the Pythagorean Theorem or its application in an innovative way. This task will promote creativity and a deeper understanding.

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Challenge students to design their own game or puzzle that involves the Pythagorean Theorem. This encourages critical thinking and application of knowledge in a creative manner.