8th Grade Pre-Algebra: Connecting Pythagorean Theorem to Novel Situations

Goals and Objectives: Have students relate their knowledge of the Pythagorean Theorem to new situations through critical thinking skills.

SOLs Covered: 8.10 The student will a) verify the Pythagorean Theorem and b) apply the Pythagorean TheoremMaterials: Paper and Pencil

Dry Erase Markers and White BoardsMotivation: Start students with a review question on how to find the missing length of a side using Pythagorean Theorem

A ladder is 10 feet from a wall and the ladder is 13 feet long. If the ladder touches at the exact top of the wall, how tall is the wall?

Lesson Procedure: Today’s lesson will focus on one large question:o A man is riding a bicycle up a ramp. We know the horizontal distance of the ramp is 35 feet. The

diameter of the bicycle tire is 26 inches. If the bicycle tire makes exactly 7 full rotations from the moment it begins up the ramp until it reaches the top, how TALL is the ramp? (Note: The question does NOT ask how LONG is the ramp)

Diagram of problem is belowo Students will be given five minutes to think about the problem by themselves, in silenceo After this, the students will be paired with their neighbor and be given twenty minutes to work on

the problem Due to the difficulty of the problem, each group will be allowed to ask the teacher one

question during these ten minutes, but only one (put a check on their scratch work when they have asked a question to keep track)

o Questions To Help Students: Why does the problem tell us how many rotations it takes to get up the ramp? Why is the diameter of the tire important in the problem? How long is the ramp? How can we find out? If the tire makes a full rotation, is there a way to find out how far it has travelled? How can we make a diagram of this problem?

o Extension (if groups figure out the problem): Find the radius of the tire needed if the ramp is exactly 28 feet tall and the tire makes 11 rotations to get up the ramp

o With the last fifteen minutes of class, the students will be pulled together and be allowed to compile their ideas

Students can now ask any questions they have about the problemClosure: If time allows, go into the extension question with the entire class