MPM2D - Day 7: Frogs & Quadratic Scenarios

After playing Frogs with my kids at home yesterday, I now have the pattern down. I think there are a number of interesting patterns involved in the game. The goal is to switch all of the pieces from one end, with the pieces at the other end in the fewest moves possible. Moves are a slide forward or a jump over a single piece to an empty spot. I used pieces from my daughter's Pengaloo game last night:

My students started playing in class yesterday, but didn't have enough time to get very far. Today, they played for real:

They were proudly working together to figure these out, even taking videos when they got them! Many really wanted to do four pairs which was more than I expected them to do, but they were excited to have figured out the "trick". I demonstrated four pairs for some groups that were finding this more challenging so they could also add that to their data table. They then found the pattern in the number of moves which they used to determine the number of moves for 10 pairs.

Since we had done a fair amount of work around quadratic relationships, I thought it was time to summarize the connections between a scenario in words, the data, the equation and the graph and to introduce new vocabulary. Here is the handout.

Here is the whole process that we went through together: 

And then the vocab:

Next they worked on some quadratic scenarios on their own (well, in their groups). Here is that handout. The first scenario was: "A ball is thrown from 5 m, reaches a maximum height of 9 m after 2 seconds, and lands after 5 seconds." Translating this to a graph was proving to be challenging for many so we looked at it together:

I also provided the equations as I could not show them how to use Desmos to perform regressions (projector was not working) and that really wasn't the purpose of this exercise.

The homework will (hopefully) help them see the link between the graph and the equation (in factored form). And here is that homework for today.