In this lesson students are shown two different ways to solve/think about the Pythagorean Theorem. The first video is a teacher showing students one way to solve the Pythagorean Theorem. During this video clip the teacher will pause at certain points and ask the students questions. For example: during the video the teacher in the clip creates four right triangles into a square to demonstrate that the outer square equals the square and triangles on the inside. At the point the classroom teacher pauses the video and asks the students what is the equation for finding the area of a square and a triangle. This is a type of informal assessment on the students.
The second video clip is a shorter clip which shows that if you take the three sides of a right triangle, turn them into squares, the two legs added together will equal the hypotenuse of the given triangle. During this video clip students can see how each individual block making up the pieces of the square add together to equal the side of the hypotenuse.
After the video clips the teacher goes over what the students just watched, then splits them into small groups to do some example proofs on the white boards. One example the teacher might give the students would be giving the students a right triangle with one leg (a) equaling 3 and an area of a square on the other leg (b) equals 16, and ask the students to determine what the hypotenuse of that triangle is. Then taking the equation a2 + b2 = c2 the students can calculate that a=3 therefore a2=32=9 and they are given b2=16. 16 + 9 = 25 = c2 and the square root of 25 is 5 therefore c=5. Thus the hypotenuse is 5. After finding the answer each group will be asked to explain their procedure and how they agreed upon their answer.
Once the white board activity is done, the teacher will then pass out the worksheet Pythagorean Theorem and its Converse and have the students begin working on that.
The video clips and worksheet align with the Common Core State Standards:
CCSSMath.G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
CCSSMath.G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity
Using these particular video clips help the teacher have more than one voice teaching the students about the Pythagorean Theorem and allows the teacher to observe the students as they watch the clips, to see who is understanding and who seem to be struggling, at that time the teacher is able to pause and ask questions or ask who has questions without “throwing off” the rest of the lesson.
The Pythagorean Theorem and Its Converse worksheet and answer key