
Picking Pythagoras
Alexander Sabatino, Jr. 


69 
Five 45minute classes 

This is an interactive mediarich lesson in which students examine the
Pythagorean Theorem. By experiment, students will discover that side measurement
is important in determining the angle classification of a triangle. By
squaring sides, they will predict whether triangles will be right, obtuse,
or acute. Using the Internet, students will prove the Pythagorean Theorem
and use it to solve problems. Finally, students will demonstrate their
knowledge of the Pythagorean Theorem by finding the perimeter of polygons
on the coordinate plane by triangulation. This lesson utilizes reading,
writing, and mathematical skills in an interdisciplinary format.
Students will be able to:
 Prove that the sum of two sides of a triangle must be greater than
the third
 Use the Pythagorean Theorem to predict triangle classification
by angle
 Use a calculator to find a square root to the nearest tenth
 Find the missing side of a right triangle
 Apply the Pythagorean Theorem in problem solving
 Use triangulation to find the perimeter of a polygon on the coordinate
plane
National
Council of Teachers of Mathematics grades K12
http://www.nctm.org/standards/standards.htm
Number and Operations
 Understand numbers, ways of representing numbers, relationships
among numbers, and number systems.
 Compute fluently and make reasonable estimates.
Algebra
 Represent and analyze mathematical situations and structures using
algebraic symbols.
 Use mathematical models to represent and understand quantitative
relationships.
Geometry
 Analyze characteristics and properties of two and threedimensional
geometric shapes and develop mathematical arguments about geometric
relationships.
 Specify locations and describe spatial relationships using coordinate
geometry and other representational systems.
 Apply transformations and use symmetry to analyze mathematical situations.
 Use visualization, spatial reasoning, and geometric modeling to
solve problems.
Measurement

Apply appropriate techniques, tools, and formulas to determine measurements.
Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data.
Problem Solving
 Solve problems that arise in mathematics and in other contexts.
 Apply and adapt a variety of appropriate strategies to solve problems.
Reasoning and Proof

Make and investigate mathematical conjectures.
Communication

Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
Connections

Recognize and apply mathematics in contexts outside of mathematics.
Web sites:
Nova:
The Proof, The Pythagorean Puzzle, Demonstrate the Pythagorean Theorem
http://www.pbs.org/wgbh/nova/proof/puzzle/papertriangle.html
This site has a printable right triangle on a grid.
Nova:
The Proof, The Pythagorean Puzzle, Demonstrate the Pythagorean Theorem
http://www.pbs.org/wgbh/nova/proof/puzzle/theoremsans.html
Students can prove the Pythagorean Theorem by drawing and cutting squares
on the sides of a right triangle and showing that the smaller squares
together equal the larger square.
International
Education Software, Pythagorean Theorem #1
http://www.ies.co.jp/math/Java/geo/pythasvn/pythasvn.html
A Japanese educational group maintains this site. They offer Java applets
demonstrating various mathematical topics. In Pythagorean Theorem #1,
students create a right triangle by moving a red dot. Squares are drawn
on all three sides. The two smaller squares are cut into polygons that
change shape as the triangle changes. Students move the polygons inside
the two smaller squares into the largest square proving the Pythagorean
Theorem. To run the demonstrations, you must have Java enabled on your
computer.
University
of Minnesota Geometry Center, Pythagorean Applications, Baseball Problem
http://www.geom.umn.edu/~demo5337/Group3/bball.html
This is a good site to get applications of math topics. The center presents
students a problem in baseball where they have to apply the Pythagorean
Theorem.
International
Education Software, Pythagoras Tree
http://www.ies.co.jp/math/Java/geo/pytree/pytree.html
Students create a right triangle by moving a red dot. Squares are drawn
on the triangle and each subsequent click on the button creates right
triangles and squares on the previous squares. In order to work, your
computer must be Javaenabled.
Nova
Online Adventure Web Site
http://www.pbs.org/wgbh/nova/pyramid/geometry/model.html
On this site, students assemble a scale paper model of the great pyramid
using a printable copy of a diagram. The measurements of two more Egyptian
pyramids are given for the class to scale down and assemble from scratch.
Students use the Pythagorean Theorem to obtain scale measures of the pyramid's
sides.
Per Class:
 Set of calculators
 Set of rulers
 Set of scissors
 12 to 15 Triangle Activity Packets
 12 to 15 paper clips
Per student:
 12 sheets of quarterinch graph paper
 Right triangle on grid paper
 Exploring Angles Activity
 Triangle Classification Organizer
 Triangulation Sampler Organizer

