A New Method for Finding Lengths of Diagonal Lines (Finding our way to the Pythagorean Theorem)

Summary:

Students worked through constructing a table and diagram of right triangles with varying dimensions to see whether they could identify any patterns.
Most DID find a clear pattern.
When you take the areas of squares drawn on the legs of a right triangle and add them, you find the area of a square drawn on the hypotenuse. Why is this important? Because once you have the area of the square on the hypotenuse, you can take its square root to find its side length.

For instance, you are given a right triangle with legs 5 and 12 inches long. What is the length of its hypotenuse?
The squares drawn on the legs would have areas of 25 sq. in. and 144 sq. in. The sum of these areas is 169 sq. in. and represents the area of the square drawn on the hypotenuse. The square root of 169 is 13 in. so that the hypotenuse is 13 in. long.

Home Nugget #18
Assigned on Monday January 29, 2007
Due on Tuesday January 30, 2007
On sheet which includes a coordinate grid on the reverse side, problems 1 -5

Focus Correction Areas:
Be mindful that teachers correct a great deal of lessons nightly and sometimes have only a few moments to assess the quality of a student’s lesson. These correction areas help you to focus on specific qualities that the teacher is looking for and will increase the likelihood of you producing a lesson worthy of a 4.
2 points: you make every effort to provide explanations and evidence for solutions when appropriate.
1 point: the appearance of your work demonstrates that you have spent time and considerable effort on the lesson.
1 point: explanations are clearly written with attention to detail and inclusion of relevant math terminology.