Pythagorean Theorem

The following lesson was very successful in introducing and discovering the pythagorean theorem to my students. The developed a table that let students find what the a^2, b^2, c^2 and c, was for each triangle I gave them on a separate sheet(around 8 triangles with different sizes). For instance, the first column listed the number of the triangles referring to the sheet with all the triangles. The second and third column had the literal measurements of side a and side b for each corresponding triangle. The fourth column gave them room to measure the c (hypotenuse) and record it. The fourth and fifth column let them figure out what a^2 and b^2 were. The sixth column was a^2+b^2 (they had to fill it out). The next column was the square root of a^2+b^2 followed by the last column, which was the measurement of the hypotenuse, c (they had to measure it and record it). After the assignment was done, I asked them if they came up with any conclusions and one student said all of the square roots of a^2+b^2 equal c for each triangle. Then I asked them if they can come up with a general formula to figure out what the hypotenuse is if you are given the lengths a and b. After the application, I enforced the Pythgorean Theorem a^2 + b^2= c^2.

Why students should learn mathematics

 It is crucial to know some mathematics to be a functional member of a democratic society.  Math is everywhere; almost everything you encounter throughout your day has some relation to math.  For instance, once you wake up you may read a clock.  A clock may give you time only if you learn how to interpret it.  By doing so, you are using math, particularly addition or subtraction.  Throughout our day, we are constantly interpreting clocks.  While we drive cars, we do math.  If we are going 60 miles per hour on the highway to reach a destination, you can figure out the time it will take you to get from point a to point b.  We can also determine our average speed if it took you 20 mins to get to your location.  When you go out to eat and actually pay your waiter a tip, you are using math.  Same goes for shopping when there is a 25% off sale.  It wouldn't be good if you did not know how to find out how much you are supposed to save from the sale.  A salesperson can play with your money and you wouldn't even know it.  Some of these daily interactions are some examples of  why you should learn math.  If students do not learn math, they are prone to face much frustration for a simple task such as splitting the bill at a restaurant.  It may be hard to find something that does not relate to math in some way.