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More Hands-On Math--Using the Pythagorean theorem

Updated on July 20, 2012
Janine Huldie profile image

Janine is a published author in Only Trollops Shave Above the Knees, appears on The Huffington Post and at Confessions of A Mommyaholic.

Hands On Math/Real Life Applications..

In Middle School Math, another topic that needs to be learned is the Pythagorean theorem. Before I explain what the Pythagorean Theorem is for those not familiar with it, I will give the reader a bit of background on why I planned two different lessons for this topic.

I taught this lesson using two different real life models. First, I taught it using the Super Bowl and how to solve for a side of a triangle and the other example utilized the Baseball World Series and solving for the hypotenuse of the triangle (say what..no worries I am about to explain this in detail)!

Thus, I designed two very distinct lessons that I used these scenarios to motivate my students knowing most kids love baseball and football. My classroom came equipped with a SmartBoard and Wifi internet. So I utilized both in teaching this lesson.

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What is the Pythagorean Theorem?

Years ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) and you made a square on each of the three sides, then the biggest square had the exact same area as the other two squares put together!

It is called "Pythagoras' Theorem" and can be written in one short equation:

a2 + b2 = c2.

Note:

  • c is the longest side of the triangle
  • a and b are the other two sides

Now, we also must redefine the word hypotenuse, because when teaching this topic, this word does come up quite often. So the hypotenuse is the longest side of the triangle or in the pythagorean theorem "C" is the hypotenuse.


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The simplest example when first demonstrating this...

I put this example up first, because when teaching this topic, this truly is the basic example shown universally.

Example: A 3,4,5 triangle has a right angle in it.

Let's check if the areas are the same:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

It works ... like Magic!

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Now to Use It, Lesson 1--The Super Bowl..

a2 + b2 = c2

So earlier, I stated that I taught two separate lessons on this topic to teach how to solve for a side or to solve for the hypotenuse. The first one teaches how to solve for a side.

My first lesson was actually taught using the Super Bowl and how most of the country is obsessed with watching the big game on a big screen TV. So I set up the lesson that the students wanted to each buy a TV for their home and also needed to purchase a cabinet/stand for the TV to sit on.

So now on my Smartboard, I went to Best Buy's website to look at the different TVs and compare a few models.


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Samsung - 55" Class - LED - 1080p - 120Hz - Smart - HDTV

So, the TV that was decided upon is a Samsung 55" LED 1080p. Gorgeous and definitely a very nice size to watch the big game on. But now even though this TV is 55", is it 55" long where it sits on the actual TV stand? The answer is no. So how do we find out how long it is so we purchase the right size stand to put this TV on?

Well think of the TV as two right triangles put together. If the diagonal or hypotenuse (remember that word from earlier) is 55", then how will we find the length. Well on Best Buy's site, we are given the height, which is 30".

How will we find the length then? You guessed it we will use the pythagorean theorem!!

So:

a2 + b2 = c2

(30)2 + (b)2 = (55)2

900 + (b)2 = 3025

(b)2 = 3025-900

(b)2 = 2125

√b = √2125

b = 46.0977 ≃ 47"

So, we need a TV stand that is at least 47" long.

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Now to Use It, Lesson 2--The Baseball World Series..

So for the second, we are supposedly in the middle of baseball playoff season and we have already learned in the past about setting up and solving one step equations. In New York, we all seem to be fans of the Mets or the Yankees. Say the Mets and Yankees end up playing each other in the World Series. If we are at Yankee Stadium and the total distance around a baseball diamond is 360 ft. What is the distance from third base to home plate? I put up a visual of the diamond on the smartboard and show that that there are 3 bases, plus home plate that gives us a total of 4 bases. Also, I will then illicit that the diamond is really a square drawn on an angle and 360 is the measurement of the outside of the square.

Next let's think about what we have been talking about so far with formulas for with geometric shapes, what formula measures only the outside of a square or rectangle? Perimeter!!!! 360 is the perimeter!!!! Then, how can I find what one side measures. Think about what you know about a square and the sides. Students should recall that are all 4 sides are equal. Now, have students, recall the formula for perimeter, which is L + L + W + W or 2L + 2W. However, all sides are equal, so how do you think we can set up the equation? Students should realize that 4S = 360 or 4 times the side = 360. Now, have them solve for s, to find out s = 90 ft. (All of this so far should be review, but what a great review to set up for our current scenario).

Now let's say it is the bottom of the ninth, two men are on base at 1st and 3rd. The batter has got a full count and the guy at first is trying to steal second. How can we use the Pythagorean Theorem to figure how the distance from the catcher at home plate to throw out the the player that is trying to steal 2nd base? Well the baseball field is a square as we said earlier and if you were to draw and imaginary line down from 2nd base to home plate, you would have two right triangles, now we know the length of both sides of the square, but are missing the diagonal or the hypotenuse.

So here we go:

a2 + b2 = c2

(90)2 + (90)2 = (c)2

8100 + 8100 = (c)2

16200 = (c)2

√c = √16200

c = 127.279 ≃ 127.3"

So the hypotenuse or the distance from 2nd base to home plate to throw the runner out is 127.3"!

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Summing This Lesson Up..

I love this lesson, because it is another hands-on lesson using two sports that most middle school students are not only aware of, but interested in. Now, when they watch both maybe they will remember a bit about the pythagorean theorem even after the topic and test are long over and behind them. And as a teacher that is truly something you hope for that the student takes away something from your lesson and doesn't just forget it once the test is long gone! Anyone who has read any of my other math teaching articles previously will know from them that I am a strong believer in using stuff that interests middle school students to help them learn many of the basic concepts that are a requirement. I truly enjoy engaging my students and showing them how we can use math in everyday life and believe this lesson is another one that does just that.

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    • Sunshine625 profile image

      Linda Bilyeu 4 years ago from Orlando, FL

      Oh my!! This hubs contains numbers and math problems. So not my cuppa tea. I hope that when Faith starts kindergarten in August I'll be able to help her with her homework. Oh my! :))

      I'll send her your way!!

      Outstanding hub! Very impressive ;)

    • Lord De Cross profile image

      Joseph De Cross 4 years ago

      Excellent lessons Janine! I did a similar hub, 2 weeks ago. But your explanation is wonderful and deserves ot be shared for the sake of our kids. No wonder the human mind can learn better with practical examples; that 's the beauty of teaching with a heart. Great job!

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Linda, you just me lol, but seriously you sound just like my husband. He keeps making me promise to help our kids when the times comes, because he was never very good at math and feels he will be of no real help to them! If you ever need any help, please don't hesitate to ask, it would be my pleasure!

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Thank you Lord de cross for your comment here. I totally believe with math and any other subject taught that it si all about collaboration. When I was teaching, I would always try to share my thoughts with other teachers and also take the advice of others as well. Thank you though for your kindness and glad you enjoyed this one.

    • thougtforce profile image

      Christina Lornemark 4 years ago from Sweden

      Very good explanation and I like the examples on how useful Pythagorean theorem is. Math is beautiful presented like this!

      Voted up, interesting, useful and shared

      Tina

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Tina, thank you for stopping by and commenting. I totally agree that I love to be able to present math this way. There is nothing worse that the chalk and talk method that is so cut and dry. Doing math lessons this way is just so much more and interesting by far. Thanks again!!

    • josh3418 profile image

      Joshua Zerbini 4 years ago from Pennsylvania

      Janine,

      Excellent hub! I loved math in high school. But, it has been so long, so some of this stuff I am rusty on. :) Very informative job, Awesome! :) The practical examples were spot on, and I enjoyed the real life picture! LOL

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Josh, I too loved math in high school and that is what made me I the end decide to try my hand in teaching it. Glad you enjoyed this one and thank you so much for all your compliments. Totally appreciate and thank u again.

    • molometer profile image

      molometer 4 years ago

      Hello Janine,

      Great hands on math lesson for all. Must show this to the kids after the summer break.

      Voted up interesting and useful sharing.

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Thank you so much Molometer. Glad you enjoyed this and hope you can use it for your kids after summer is over. Appreciate the comment, votes and share too!

    • TToombs08 profile image

      Terrye Toombs 4 years ago from Somewhere between Heaven and Hell without a road map.

      Janine - I really love how you include a real world example of how to use the math. SO many teachers just throw the stuff at their students with a "you'll have to use this stuff someday" but never say WHEN! :) Great job.

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Terrye, I totally hated being taught that way and tried very hard not to teach that way myself, so as much as I could I would always try to bring in real life examples that the kids could relate to. Thank you so much for stopping by and all your continued support, it is truly appreciated.

    • Natashalh profile image

      Natasha 4 years ago from Hawaii

      I have a hub on fun math activities that shows you how to make an use a quadrant. It deals with triangles and I think this would be an ideal link! Do you mind if I place a link to your hub on that page?

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Oh please do link me to your hub and I will do the same for you too. Thank you so much for asking and doing this for me.

    • Nell Rose profile image

      Nell Rose 4 years ago from England

      Before I say how much I loved this, I have to mention the fact that math in any form slides over my brain and out the door! for some reason its the one subject that I just cannot get! and believe me I have tried, so I read this, twice to be honest, and eureka! it actually sunk in! haha! seriously! that's the art of a good teacher, thank you! wonderful stuff! cheers nell

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Oh Nell your comments mean the world to me. My husband is the same way with math a you described yourself and I have been told thank god I am good with math for our kids' sake. Seriously, you made my day that you understood this and that I got the math across to you. Believe me I when I taught this, I was always so happy if at Lear one of my student's walked away saying the same as you. Thanks again for all your support, it is much appreciated.

    • teaches12345 profile image

      Dianna Mendez 4 years ago

      You are the master of this type of learning skill! I enjoyed reading through this one, even though I cannot do it. WEll DONE! Voted up.

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Thank you so much teaches12345. I honestly loved teaching this lesson and writing about it made me miss teaching. I really do appreciate your kindness and votes. Thanks again!

    • midget38 profile image

      Michelle Liew 4 years ago from Singapore

      Interesting, Janine. Maths would have been more interesting if you had taught it to me! A very creative take on Pythagoras Theorem...something that is easily beyond many students! Thanks for sharing.

    • Janine Huldie profile image
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      Janine Huldie 4 years ago from New York, New York

      Thank you Michelle. I think the same of you as an English teacher. Seriously, I think the world needs more teachers like you and I, who do care about the kids and want to make learning more fun and enrich their learning experiences. That said, thank you so much for sharing and for always being so kind to me!!

    • SAQIB6608 profile image

      SAQIB 2 years ago from HYDERABAD PAKISTAN

      Wonderful, Although I know Pythagoras Theorem but the way its basics with diagrams and practical examples are given, Its great.

      Regards

      SAQIB

    • SAQIB6608 profile image

      SAQIB 2 years ago from HYDERABAD PAKISTAN

      Wonderful, Although I know Pythagoras Theorem but the way its basics with diagrams and practical examples are given, Its great.

      Regards

      SAQIB

    • Janine Huldie profile image
      Author

      Janine Huldie 2 years ago from New York, New York

      Thanks and so glad this helped with you with the Pythagorean Theorem.

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