Pythagorean+Theorem+Resource+File

By: Kristen Leining

This Resource file is designed for 9th grade Algebra 1 students that are studying the Pythagorean Theorem, Distance Formula, and Midpoint Formula. This unit starts with outlining the Pythagorean Theorem, completing a proof, and discussing applications. It then moves into the distance formula and its applications and finally the midpoint formula and real world applications of that.

The purpose of this file is to give students extra information about Pythagoras, the theorem, and the distance and midpoint formulas. It includes a variety of sources that allow students to further develop their understanding of all three concepts as well as mathematics in general. My hope is that some of this will be extra credit assignments, practice problems or allow students to clarify topics they did not fully understand in class.

The culmination of this unit will be students understanding all three formulas and how to use them in context, particularly in applying to word problems and real life situations. They will also compete a final project in which they will research another ancient mathematician and present their findings to the class.

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5 Text Based

1. Proofs of the Pythagorean Theorem This site describes a variety of different proofs of the Pythagorean Theorem. This could be used for more advanced students to further develop their learning and understanding of the theorem. However, it is written at a lower reading level so less advanced students can also use it as a resource

Flesh Reading Ease Level: 70.8 Author: Angie Head

2. Pythagoras' Trousers This website explains the History of Pythagoras. It reviews the book called Pythagoras’ Trousers and gives a shortened version of the content. It outlines Pythagoras’ beginnings and the history of his life leading up to the development of his theorem. This has a higher reading level and would be for more advanced students. It allows students who are very interested in history to delve more into that topic.

Flesh Reading Ease Level: 52.4 Werthheim, M. 1996. Pythagoras’ Trousers. Math Horizons, 3(3), p 5-7.

3. Sports and the Pythagorean Theorem This is a newspaper article from the NBC Sports website and it describes how the coach of the Dallas Cowboys football team wants his players to all understand the Pythagorean Theorem. It is a fantastic way to show kids how relevant the formula is and where it can be used in real life.

Flesh Reading Ease Level: 70.2 Author: Michael David Smith

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">4. How to Understand Math Formulas <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This is a blog post in which the author explains strategies for using formulas. Many students have trouble with formulas and he gives a variety of excellent tips and tricks for understanding them more effectively. This is excellent for students in general to read and use in all aspects of mathematics.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Flesh Reading Ease Level: 55.6 <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Author: Murray Bourne on IntMath.com

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">5. PurpleMath Distance Formula <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This website provides information on the distance formula from purplemath.com, an excellent resource on simplifying complex mathematics. It outlines the formula, provides an example, as well as explaining common areas that students make mistakes. Included is a small quiz that students can use for extra practice.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Flesh Reading Ease Level: 73.2 <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Author: Elizabeth Staple

5 Web Based

<span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">1. Math is Fun - Pythagoras' Theorem <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This website outlines the Pythagorean Theorem, has examples, and also small animations that show different proofs of the theorem.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">2. Interactive Distance Formula <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">This website has an interactive graph where students can move points and see how the calculation of the distance formula is done at those individual points. It also reflects how the distance formula is applicable for any set of points.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">3. Pythagorean Theorem Proofs

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<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This is an algebraic explanation of the proof of the Pythagorean Theorem. It explains where the theorem comes from and is very easy to follow along with.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">4. The Distance Formula

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<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This video explains the distance formula and shows the derivation of it from the Pythagorean Theorem. It also performs an example. This can be used for students who would like to see more practice problems performed if they forgot how to use it for their homework.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">5. The Midpoint Formula

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<span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">Done by the same person who made the distance formula video, this video explains the midpoint formula and gives an example.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16pt;">5 Unique Sources

<span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">1. Distance and Midpoint Calculator <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This is an interactive calculator that allows students to plug in values and calculate the midpoint and distance between two points. It is very useful to demonstrate how the formula applies to any two points.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">2. Pythagorean Theorem Practice Problems <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This website has many practice problems for students who may need more practice, especially for test review. It has step by step explanations as to how problems are solved as well as hints to help students.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">3. Pythagorean Puzzles <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Taken from the National Library of Virtual Manipulatives, this is an interactive proof of the Pythagorean Theorem where students have to move the triangles themselves. This is a good tool for students who are either visual of kinesthetic learners.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">4. MyScript Calculator App <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This app allows students to write out problems and the calculator will translate it to text and then solve. This is a good way for students who have trouble entering values into calculators, especially when they are long and require sets of parenthesis.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">5. The Best Pythagorean Theorem Rap Ever

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<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">This fun video is a rap that outlines how to solve the Pythagorean Theorem and other important vocabulary terms related to right triangles and the theorem.