Explaining Pythagoreans Theorem with Clay-animation

Using clay-animation is a creative way to teach students mathematics concepts, such as the Pythagorean theorem. For example, the Pythagorean theorem is a relation in Euclidean geometry among the three sides of a right triangle.

The theorem can be written as:

Note the demonstration shows how the two blocks start out with equal area (comprised of red triangles and blue squares). Taking away the 4 red triangles from each side of the equation, results in one large blue box (equal to C squared) and on the right side of the equation there are two blocks (A squared plus B squared). By manipulating the blocks, students can better understand how this physical relationship can be true. Enjoy!

When students ask "Where does math come from?"

Many times students will ask "Where does math come from?" Interestingly enough many math courses only teach about formulas and problem solving, and never address this fundamental question. According to Greenberg (2008) the Greek historian Herodotus (fifth century B.C.) credits Egyptian surveyors, also known as "rope stretchers" with having originated the subject of geometry. Did you know the Egyptian priestly leisure class kept their math secret from the public? The Egyptians are also known for finding the correct formula for a truncated pyramid. According to Greenberg, the Babylonians were even more advanced than the Egyptians. They developed arithmetic using the base 60 (hexagesimal system). Today we use a decimal (10 base) system. The Hindu civilization on ancient India developed geometric information related to shape and sizes of altars and temples, and the Sulbasutra is one of the oldest mathematics texts currently known (~2000BC). Later, the Indians actually invented the number zero!
The ancient Chinese civilization also used math. According to Greenberg ancient China was mainly concerned about "practical matters" and developed the Nine Chapters on the Mathematical Art which included hundreds of problems on surveying, agriculture, engineering, and taxation (yes even math for taxation!). However, the Greeks ultimately developed and debated rigorous proofs. However, it doesn't stop there. Pythagoras was a spiritual leader, and along with his followers pursued mathematical studies. The Pythagoreans developed the concept of whole numbers and made observations regarding the length of vibrating strings with respect to harmonious sounds. These are just a few facts in a long line of mathematics history. To learn more you may want to check out Chapter 1 from the book Euclidean and Non-Euclidean Geometry by Marvin Jay Greenberg.

Information referenced in this blog taken from:
Greenberg, M. (2008). Euclidean and non-Euclidean geometries: Development and history. New York: W. H. Freeman and Company