TITLE: Planetary Pythagoras

SUBJECT: Grade 8-9 Algebra 1

TOPIC: Using the Pythagorean Theorem to find the missing sides of right triangles.

INTERACTIVITY: The students will begin by choosing which route they will start with, either the top route or bottom route. Once the route is chosen the student will remove the first planet on that route and place the spaceship on the Velcro piece where the planet was. On the back of the planet is a right triangle that has one of its side's lengths missing. The student is to find the length for the missing side using the Pythagorean Theorem. The students are to show all of their work on the provided worksheet and record the length for that segment in the appropriate blank. The student can then place the planet in the discard bin and continue to the next planet on the chosen route following the same procedure as above. Once the student has found the length of each segment in the route they are to add all of the lengths together to find the total length of the chosen route. They should record that number in the appropriate place on their worksheet. Once they have completed the first route the student should complete the same procedure for the second route. Once both routes have been completed the student should answer the last question on their worksheet, which asks which route is shorter? The student is then to return the spaceship and all planets to their original places. Each segment and planet is labeled to make this easier. The worksheet is then to be handed in to the teacher for a homework grade.

DIRECTIONS FOR USE: Pythagoras has been exploring the universe but his exploring must be cut short. There is a mathematics crisis back on his home planet and the people desperately need him as soon as possible. There are two routes that Pythagoras can take to get home and it is your mission to figure out which route is the shortest and thus the fastest route for him to take. Begin your mission by first picking up the corresponding worksheet. Then decide which route you will want to test first, either the top route or bottom route. Once you have a route selected find the appropriate place on the worksheet to begin your work. Gently remove the first planet from the selected route. On the back of the planet will be a problem in which you need to solve for *x* using the Pythagorean Theorem.

Copy the problem and your work down on the worksheet. Make sure to write what segment of the route you are working on in the space provided. The segment name is located on the back of the planet as well as on the route itself. Also, remember to record the length of x in the space provided. When done with the planet, place it in the worksheet/discard bin and move Pythagoras to the planets original spot. Continue this process until you have completed the entire route and Pythagoras is back on his home planet. Then add up the lengths of all of the segments from the first chosen route to find out what the total distance of the route is. Once the first route is completed, use the same process to find the length of the second route. Once the second route has been completed, determine which route is shorter and record your answer on the worksheet in the space provided. Return Pythagoras and all of the planets back to their original places, the planets as well as the segments are labeled. Once finished, turn the worksheet in to Ms. Hanford for a homework grade.

TIME: This bulletin board should take 15-20 minutes to complete.

CREDIT: The students must complete bulletin board and fill out worksheet. The bulletin board will be posted during the entire Pythagorean Theorem unit and the student must complete the bulletin board and hand in the worksheet before the day of the test on the unit. The worksheet will count as one homework grade.