### Integral Limit Game

This year when I was in my intro to integrals unit, I tried to look back at this blog for the second integral game I know I played (besides this one), and saw I hadn’t blogged about it. I had tweeted about it, but now I’m thinking, you know, I should, uh, archive things that I only tweeted about in a more permanent place, in guess Twitter doesn’t last much longer.

Anyway, this game is based on The Product Game, with the same structure of turns – players take turns moving a token on the bottom rows, that then determine which square in the top section, where the first player to get 4 in a row is the winner. (I usually have students play in teams of 2, but I’ll keep saying “player” go forward.)

The idea here is that the bottom rows represent the limits of a definite integral. One player plays as the Upper Limit, and the other as the Lower Limit. Once both limits are placed, the player who most recently went calculates the value of the definite integral on the accompanying graph, then covers the square in the top section with the area. (Remember that if the lower limit is greater than the upper limit, the sign is switched!)

Making the function that would give a variety of answers was a fun challenge. After coming up with a graph I thought looked good, I wound up making an excel sheet to calculate all the possible definite integrals to see how balanced it was, and adjusted.

I’ll include that excel sheet as well, as it’s useful for checking answers (as a teacher), although of course each team should be checking each other. After doing a bunch of different integrals on the same function, students often realize they can use their previous work to help them find new answers, reinforcing the cumulative nature of integrals.