I came across this problem reading Dan Meyer’s blog. The goal is to grab students’ attention with a problem they think is trivial, but actually connects to a new mathematical understanding. It is an interesting way to get students to experience disequilibrium but having something come out in a way you did not expect.

Here’s the problem:

Here are some points on the plane:

(4, 1), (17, 27), (1, -5), (8, 9), (13, 19), (-2, -11)
(20, 33), (7,7), (-5, -17), (10, 13)

Choose any two of these points. Check with your neighbor to be sure that you didn’t both choose the same pair of points. Now find the rate of change between the first and the second point. Write it on the board. What do you notice?

When students do it, they’ll see that the slope is the same no matter which two points anyone chose, which leads to the question of “Wait, what? How can that be? Why?”

From Henri Picciotto’s review of Farrand’s session:

Students are stunned to learn that everyone in the class gets the same slope. This sets the stage for proving that the slope between any two points on a given line is always the same, no matter what points you pick.

Students would need to know how to calculate the slope or this problem will just frustrate them and the “big reveal” will be lost on them. Try this problem after teaching Unit 3 of the CUNY HSE Framework on discovering rate of change. It could also work if they’ve worked with the formula for finding slope.