Gotta Love Math!

When presenting information to middle school students, engaging them is the key.  Using Internet resources can help the students take responsibility for their own learning. They can learn at their own pace, and try the applets over and over until they have experimented with them in every way necessary to satisfy their curiosity.  One strategy that the teacher might use is to present the web resources to the students in a progression that allows their understanding to build.  This way, students move from doing concrete through abstract, leading to a deeper understanding of the concept.

The Math is Fun site has a nice applet on the front page showing that the area of the two squares adjacent to the legs of a right triangle are equal in area to to the square adjacent to the hypotenuse, and it explains it in writing, too, helping visual and verbal linguistic learners understand the concept behind Pythagoras’ Theorem.  This page walks students through the visual proof, into the definition, through an algebraic proof, and adds two additional proofs that students can do using paper cutouts of the squares.  This would make an excellent introductory lesson for the students, utilizing concrete and abstract activities to gain a greater understanding of Pythagoras’ Theorem.

In the NCTM Illuminations site, students have the opportunity to watch an applet demonstrating Pythagoras’ theorem.   This applet offers a different proof of the theorem, which is attributed to Bhaskara, I a mathematician who lived in the 12^th century.   This would give students an opportunity to look at the theorem from a different perspective, and teach them that there is more than one way to offer proof that .

The University of Minnesota has an excellent site that includes real-world examples of problem solving using Pythagoras’ Theorem.   It provides “examples and contexts in which this invaluable theorem influences and can be involved in our everyday affairs.”  One problem involves a hot air balloon ride where three friends are in a ticklish situation.  They are in the air at right angles to each other (according to the diagram).  One is running low on fuel.  The other needs to decide if he has enough fuel to save his friend.  Students will use the information in this puzzle to determine a solution, which can then be checked.  The other puzzle on this page involves builders using the theorem to determine if their building has square corners.  This is a standard use for the theorem, put into action every day by builders.  This puzzle gives students enough information to solve, and then they can check their solutions on another page.  Both of these examples offer a terrific way to apply the theorem to real-world situations and would make wonderful follow-up lessons.

A third site that offers hands-on experience for middle school students who are studying the Pythagorean Theorem is this Pythagorean Theorem Webquest. This page offers a web quest for pre-algebra students in seventh or eighth grade.  Students can create their own scenario for the problem which involves traveling the shortest distance to your home. Students use the information on the website to find out about Pythagoras, then move into demonstrating proofs of their problem, giving them practice in applying the theorem.  The problem will appeal to students as it is directly applicable to their lives.

While there are many websites available on the Internet. The above set provides a sample progression.  When students can follow the progression at their own pace, learning is deeper, and the resources help the student understand the information that is available at their fingertips.