Let Pythagoras Help You Home

1
Let Pythagoras Help You Home

• A Web quest For Middle School Algebra and
  Geometry About the Pythagorean Theorem

Original Web quest created by Tiffani S. Ellison
at Freed-Hardeman University School of Education
for Dr. Bruce Lewis on November 27, 2001. Adapted
by Mary Hammers, Wichita State College of
Education for Tonya Witherspoon.
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Let Pythagoras Help You Home

• Introduction
• Tasks
• Process
• Evaluation
• Conclusion

• Teacher Advice
• References
• Standards
• Credits

3
Introduction Grandmas House

• You and three friends have been to your
  grandmas house to help with a lot of chores.
  Although old, the house is sturdy because, thank
  goodness, the builder knew her stuff.

Click on grandmas house to see why !
4
Introduction Your Aunts Challenge

• Now, you and your friends want to walk home.
  Your Aunt Molly thinks its too far to go two
  miles south to your school and then east one mile
  to your house. You know a shorter way but you
  have to prove it to her. Your aunt wants the
  exact distance before you can leave. How can you
  figure this out?

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The Tasks
Why not let Pythagoras help you home?

• To find the shortest distance to your house, you
  and your group need to complete the following
  tasks.

Task 1 Find Three Facts About Pythagoras Task
2 State the Theorem and When It is Used Task 3
Demonstrate a Proof From Internet

• Task 4 Practice Using the Theorem
• Task 5 Sketch and Write the Proof For Your Aunt
• Task 6 Present A Real World Application
• Task 7 Super Challenge

6
Process Who

• Task 1 -Just WHO Was Pythagoras ?
• Where and when did he live? What did his
• famous theorem concern? Find the answers
• at this website. Take notes and write three
• facts about him.

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Process What

• Task 2 - WHAT is the Pythagorean Theorem?
• When does it apply? What can it be used for? All
  of
• your questions and more can be answered using
  this
• link. Pay close attention to the math terms and
  how
• they are used. First, you may want to review the
• Parts of the Right Triangle.

8
Process Why

• Task 3 - Lets look at some
• cool demonstrations of this
• theorem.
• Many people, including
• a U.S. president have done
• proofs to show WHY the
• theorem really works.
• The site
• Pythagorean Theorem Proofs
• gives 36 proofs. Follow the
• instructions for these
• Interactive proofs.
• Try 5 and choose one that you
• and your group can give.

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Process Practice

• Task 4
• Now Lets Practice !
• You will find two ways of using
• the theorem at the site called
• Pythagorean Theorem Tutorial.
• One way is to input 2 triangle leg
• values. The hypotenuse will be
• calculated for you. The second
• way is to input 1 leg and the
• hypotenuse. The other leg will be
• calculated for you.
• Fill out the table to the right
• with the missing values. You must
• show your calculations on 3 of the
• problems !

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Process Prove it to Aunt Molly

• Task 5 - Now you know that the legs of a right
  triangle form and L (right angle), its time to
  draw and write the proof for your aunt. Use this
  template and label each triangle vertex (point)
  with the school, grandma's house, and home. Also
  put in your solution for each side length.
• Hint Re-read the introduction.

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Process Real World Application

• Task 6 - The Pythagorean Theorem is used in real
  life in many ways. You saw one example at your
  grandma's house.
• Nova Online shows two real world applications
  found in baseball and getting to the roof of a
  house.
• Go to the site and try these. Then think of your
  own application. Write it on paper and tell how
  you would use it.

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Task 7 -Super Challenge

• If you have time in class, try this SUPER
  CHALLENGE.
• Otherwise, you may take it home and finish it
  there.
• Extra credit points will be given that are worth
  5 of the total possible project points.

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Evaluation

• Your grade for this assignment is based on
  meeting the requirements of 6 tasks and extra
  credit for the 7th task.
• Look at the next page to find out the points you
  can earn from doing all the tasks and their
  objectives.
• I hope you are in the green!

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Evaluation Rubric
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Conclusion

• So how did you do? I hope that Pythagoras was a
  big help getting you home. I also hope you chose
  to do the super challenge. Its fun! Dont forget
  the practical applications of the theorem. You
  never know when you may need this information for
  your house!

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Teacher Advice - Tasks

• This lesson is designed for eight grade
  pre-algebra or geometry but can be adapted for
  7th or 9th grades. It can be used for individual
  or group learning.
• Completion of all the tasks takes about two fifty
  minute class periods or one block period.
• Students need to have calculators and
  understanding of squares and square roots.
• A student survey is recommended to determine
  effectiveness of this web quest experience.

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Teacher Advice Super Challenge

• The super challenge can be completed in one 50
  minute class period.
• For advanced or older students, super challenge
  can be part of project grade.
• Students will need to print a page have a pair
  of scissors for cutting.

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Teacher Advice - Reteaching

• Parts of the web quest can be completed under the
  direction of teacher or Para.
• Copies of the sites used (references section) and
  the presentation worksheets will allow a student
  to (re)work without the Internet at his/her own
  pace.

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References In Order of Appearance

• http//www.rblewis.net/technology/EDU506/WebQuests
  /pythagoras/pyththeorem2.htm
• http//www.learnalberta.ca/content/mejhm/html/pyth
  agoras/pythagorasSmall.html
• http//www.utm.edu/research/iep/p/pythagor.htm
• www.ci.fullerton.ca.us/ graphics/focus133.gif
• http//www.emsl.pnl.gov2080/docs/mathexpl/pythag.
  html
• http//www.geom.umn.edu/demo5337/Group3/rttri.htm
  
• http//www.ies.co.jp/math/java/geo/pythagoras.html
  
• http//www.geom.umn.edu/demo5337/Group3/rttri.htm
  l

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References ContinuedIn Order of Appearance

• http//math.about.com/gi/dynamic/offsite.htm?zi1/
  XJsdnmathzuhttp//www.mste.uiuc.edu/dildine/tc
  d_files/program10.htm
• http//www.pbs.org/wgbh/nova/proof/puzzle/use.html
  
• http//www.pbs.org/wgbh/nova/proof/puzzle/baseball
  .html
• http//www.pbs.org/wgbh/nova/proof/puzzle/pyramid.
  html
• http//standards.nctm.org/document/appendix/numb.h
  tm
• http//www.ksde.org/outcomes
• http//jeff560.tripod.com/
• www.enchantedlearning.com/.../ 1/tiny.GIF
• cartoon woman.jpg

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Standards - NCTM

• Algebra Standard
• Represent and analyze mathematical situations
  and structures using algebraic symbols
• Use mathematical models to represent and
  understand quantitative relationships
• Geometry Standard
• Analyze characteristics and properties of
  two- and three-dimensional geometric shapes and
  develop mathematical arguments about geometric
  relationships
• Specify locations and describe spatial
  relationships using coordinate geometry and other
  representational systems
• Use visualization, spatial reasoning, and
  geometric modeling to solve problems

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Standards NCTM Continued

• Measurement Standard
• Understand measurable attributes of objects and
  the units, systems, and processes of measurement
• Apply appropriate techniques, tools, and formulas
  to determine measurements.
• Process Standards
• Problem Solving
• Reasoning and Proof
• Communication
• Connections

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Standards - Kansas

• Standard 2 Algebra -The student uses algebraic
  concepts and procedures in a variety of
  situations.
• Benchmark1 Patterns The student demonstrates
  an understanding of relationships in patterns in
  a variety of situations.
• Benchmark 2 Variables, Equations, and
  Inequalities The student demonstrates an
  understanding of variables, equations, and
  inequalities in a variety of situations.
• Benchmark 3 Functions The student demonstrates
  an understanding of functions in a variety of
  situations.
• Benchmark 4 Models The student demonstrates
  the use of models to show relationships in a
  variety of situations.

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Standards - Kansas Continued

• Standard 3 Geometry The student uses geometric
  concepts and procedures in a variety of
  situations.
• Benchmark 1 Geometric Figures and Their
  Properties The student demonstrates an
  understanding of geometric shapes and their
  attributes.
• Benchmark 2 Measurement and Estimation The
  student demonstrates an understanding of
  estimation and measurement using standard and
  non-standard units of measure in a variety of
  situations.
• Benchmark 3 Transformational Geometry The
  student demonstrates an understanding of spatial
  sense and relationships in a variety of
  situations.
• Benchmark 4 Geometry From An Algebraic
  Perspective The student identifies one or more
  points on a number line in a variety of
  situations.

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Credits

• I would like to thank Tiffani Ellison and
• Dr. Bruce Lewis of Freed-Hardeman University for
  allowing me to use a webquest titled Let
  Pythagoras Help You Home for adaptation for this
  presentation.
• The original web quest can be found at the
  following website http//www.rblewis.net/technol
  ogy/EDU506/WebQuests/pythagoras/pyththeorem2.htm
• A special thanks goes to Tonya Witherspoon, my
  instructor at Wichita State.

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The End