Distance "The Pythagoras Way"

Before:

1. Type the following scenario on the interactive whiteboard before the students enter the room.  “Steve asked his parent if he could borrow the car to go to Jim’s house to study. His parents said that he could, but he could only drive to Jim’s house and back. They went to the movies instead of studying. The next morning Steve was grounded! How do you think that Steve’s parents knew that he went to the movies?” While students are working to answer the question, hand out two sheets of graph paper to each student.
2. Tell the students to write down their answers but do not share their answers with anyone.
3. After two minutes, tell the students to discuss their answers with one person without getting out of their seats.
4. After two minutes, call the students back together.
5. Call on a student to write the possible answers on the interactive whiteboard.
6. The correct answer is: ”Steve's parents knew the number of miles from their house to Jim’s. They multiplied by 2 and added the result to the car's previous mileage. Guess what? Steve put more miles on the car than he should have...busted!”
7. The teacher can relate this problem to the concept that subtracting the values is part of the distance formula. In comparison, the two formulas are identical, but different names.
8. State the lesson's objective: to be able to demonstrate the Pythagorean Theorem in the coordinate plane.

During:

1. Ask the students to go to the website https://www.geogebra.org/m/jmMXpzuM
2. Let the students practice putting points on the graph. The graph has three boxes at the top left corner. You can put points on the graph and connect the points to make lines. The arrow box will change the cursor back to the plus sign.
3. As you demonstrate the process to students, make sure they are writing the information from the graph on their graph paper.
4. Randomly pick two points on the graph [such as (-2, 3) and (4, 6)].
5. Put the two points on the graph
6. Change the point to a line and connect the two dots. Tell the students to make this line red on their paper.
7. Make a horizontal line including (-2, 3) and make it blue.
8. Make a vertical line including (4, 6) and make it blue.
9. The students should see where the two blue lines cross. They should also know this is a right angle.
10. The teacher can ask questions about right triangles as an informal assessment.
11. Ask the students to count the distance around the right angle. Write the answer beside each line.
12. Ask the question “Why would this not work for a slanted line?” Answer: The lines go through the boxes on the graph.
13. Using the Pythagorean Theorem (a² + b² = c²), Fill in ‘a’ and ‘b’ with the distance and solve the equation.
14. Guide the student through more points that you make up. Then, use the worksheet “Points for Pythagorean Theorem” to practice applying this equation.
15. After working on number one as a class, allow the students to work on 2 through 5 independently. Call on students to write the answers on the interactive whiteboard. The teacher should have a picture of the graph paper saved to the desktop of his or her computer so that the students can show how they got their answers.

 After:

1. Students will complete problems 6 through 10 individually. The teacher can take this assignment up for a formal assessment.
2. If some are falling behind, the teacher should put them with a partner or reteach the concept in small groups.
3. If students finish early, then they can complete the acceleration activity called “Distance to the Moon”.

Exit Slip: “Exit Slip Pythagorean”

While students are working on problems 6 through 10, the teacher should distribute the worksheet titled “Exit Slip Pythagorean.” This is another method of formal assessment.

Students should turn in the exit slip at the end of class.