Pythagorean Theorem

Pythagorean TheoremGrade 8 UnitRebecca Folz

Source of Image: http://www.mathkplus.com/Integer-Math/2D-Object-Area/Right-Triangle-Area.aspx1

Rationale for Technology IntegrationTechnology is everywhere! Children grow up with a lot more technology then we did. If teachers want their students to be engaged in the classroom, they must embrace technology. This PowerPoint Presentation will show both students and teachers how technology can be used in order to help students better understand the Pythagorean Theorem and keep them engaged. Blogs, podcasts, videos, and apps can all be used to achieve this goal.

Evaluation of Internet contentAll websites used in the making of this presentation are reliable and safe sources of information.They all relate to teaching and applying the Pythagorean Theorem.All videos and graphics have been linked to the original source on the internet.Please reference the notes sections for further citations.

BlogThis blog is written by a retired math teacher of 42 years named Henri Picciotto. He now spends his time sharing instructional materials on his blog and developing curriculum for teachers and schools.This page describes how the Pythagorean Theorem can be proved and has interactive graphics to help students arrive at the proof themselves.

Sources: http://blog.mathedpage.org/2014/10/pythagorean-proofs.htmlhttp://www.mathedpage.org/constructions/pythagore/

Teachers can utilize Picciottos interactive graphics to help the students who are visual learners understand where the Pythagorean Theorem comes from. Teachers can also use this blog as an introduction to the Pythagorean Theorem unit because it uses a lot of prior knowledge.4

Instructional VideoNo matter how much instruction and help teachers give students during lessons, there will still be students who do not understand while trying to complete their homework. This is where technology can come in!On Kahn Academy there is an instructional video that students will be able to reference while they are at home working on their homework.

Source: https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/pythag-theorem/v/the-pythagorean-theorem

Homework is helpful in making sure the students are practicing the material you taught them that day. But homework can also hinder the students learning if they think they are doing the problems correctly when they are actually doing them incorrectly. If students complete homework with the belief they know what they are doing but are incorrect, they are conditioning themselves to remember their incorrect way on how to complete the problems. As a result, they will remember incorrectly on the unit exams and their grade will suffer. For this reason, it is important to use technology as a way to avoid these issues. If your students have instructional videos to reference while at home, they will hopefully complete their homework correctly and better learn the material.5

Youtube VideoAll students learn differently. For this reason, it is important to have multiple instructional videos, used in addition to your own lesson, for students to be able to watch and reference at anytime.

Sources: https://www.youtube.com/watch?v=TYBTKQBNsUA

This video can be used in addition to the teachers own lesson and the video in the previous slide. Some students may prefer this video over the other because they may not be able to concentrate to the voice in the other video without seeing the person talking. However, other students may find the previous video more helpful than this video. Its all about giving students options in an effort to help all the different types of learners you have in your classroom.6

Internet resourcesNational Council of Teachers of Mathematics includes lesson plans that teachers can filter through by grade level and the mathematical skill desired.Scholastic has free printable lesson plans that include Common Core Standards.TeAch-nology and edHelper are both great internet resources for teachers who need new worksheet ideas. These resources allow teachers to print out their worksheets for free.

Sources: http://www.nctm.org/

https://www.scholastic.com/teachers/home/

http://www.teach-nology.com/

http://www.edhelper.com/7

Inspiration

In a Pythagorean Theorem lesson, this graphic organizer would be used after the lesson and theorem is introduced. A teacher can hand this graphic organizer out and have the students use it to take notes on the steps and examples of how to use the Pythagorean Theorem to discover the length of the hypotenuse or one of the legs of a triangle.I think this visual will be helpful for students who are more visual learners. Some students may learn well with simply taking down the steps on how to solve the problems in their notebooks but other students are more visual learners. This will help those students better understand the process of solving the problems as well as give them an example to go along with it.8

Teaching materialsMath-Aids allows for teachers to create free practice worksheets for different areas and grade levels.Here is a worksheet I made pertaining to the Pythagorean Theorem.

Sources: http://www.math-aids.com/9

Teaching materialsWordMint is a website teachers can use to find word searches or create their own. This word search is one I found on the site that had already been created.

Sources: https://wordmint.com/

https://wordmint.com/public_puzzles/3768110

Theres an App for that!In the app store, students can download Pythagorean Theorem and its Converse.It is an app that should be used after the Pythagorean Theorem unit, but before the test. First, it gives a quick overview of the theorem to remind the students. Then, there are four tests to test the students and help them understand what they are doing wrong if they are getting the wrong answers.Teachers can have the students show them their screen to see if they completed the practice using the apps results option that gives the teacher an overview at how well the student did.

Sources: https://itunes.apple.com/us/app/pythagorean-theorem-its-converse/id556317588?mt=811

Theres an App for that!Socrative Teacher is an app where teachers can create quizzes and games for review.This could be best used before a test as review and can give the teacher a better idea at how comfortable the students are with the material.Pythagorean Theorem problems involve showing a picture of a triangle which not all apps can do, but Socrative Teacher has an option to upload a picture to attach to a problem on the quiz or game.

Sources: https://itunes.apple.com/us/app/socrative-teacher/id477620120?mt=812

Internet based resourceThinkQuest has interactive activities for different areas within the subject of mathematics. It also contains lesson ideas that teachers can reference.On this subject-specific resource, there is a useful Pythagorean Theorem introductory page. Teachers can reference this page while creating their lesson plan for the theorem. It is important for teachers to use different resources in an effort to find the best way to help their students learn.

Sources: http://wayback.archive-it.org/3635/20140211214957/http://www.thinkquest.org/pls/html/think.library

http://wayback.archive-it.org/3635/20130901140340/http://library.thinkquest.org/04oct/01808/intro.html13

Use of internetMapQuest can be used in creating real-life examples on how the Pythagorean Theorem could be used. In my example below, I took a suggested route created by MapQuest from Macys in New York to Madison Square Park. Now if we were to get access to a jet that could take us there using the shortest distance possible, that creates the hypotenuse. Then the students can use the theorem to discover that distance the jet would have to travel.

Sources: http://classic.mapquest.com/

http://classic.mapquest.com/#e812c4f022fe82e04bee1760

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Use of internetColor Landform Atlas of the United States is a way to connect the Pythagorean Theorem to geography. Students can pick a state of their choice and create a Pythagorean Theorem problem using the maps provided on the website. Below is an example of what a problem would look like completed.

Sources: http://fermi.jhuapl.edu/states/states.html

http://fermi.jhuapl.edu/states/maps1/ct_c.gif15

Web 2.0Emodo is a site with a similar setup to Facebook. Teachers can use it to post assignments, quizzes, polls, and reminders.Students can also get the app on their phones which will increase communication between teacher and student based on convenience.

Sources: https://www.edmodo.com/home16