After looking over my class' Linear Review homework, I decided to give my students some time at the beginning of class to go over their errors and make corrections. I wrote the answers on the board and let them work in their groups (they sit in groups or 4 or 5). I wanted to make it clear that correcting errors is a really important part of the learning process. I post the full solutions on Edmodo so they can also look at those if they get stuck.
We then started the High Five activity. Imagine that you are at a sporting event and as each player is introduced, they high five all of the previously introduced players. What will the total number of high fives be once all players have been introduced? I had a student volunteer to be the "announcer" and several more who came up, one at a time as players, each high fiving (that isn't really a verb) all of the other players. We recorded the TOTAL number of high fives after each player arrived.
They soon saw the pattern and my players and announcers were rewarded with a lollipop before returning to their seats. We recorded the pattern in the total number of high fives (1st differences) and then the pattern within the pattern (2nd differences). They created a scatter plot (the link to the handout is below) which I did using Desmos. We talked about the shape of the graph before they started working on finding its equation.
All that visual pattern work really paid off as they were able to find the "rule" for this quadratic. Many recognized the numbers 3, 6, 10, 15... and found that those were in pattern #11. That was the pattern where we had to double to find the rule.
They then had to use their rule to find the number of high fives for the whole school (approximately 1240 students). Once they had that answer, I asked how long they thought it would take. We estimated 1 second per high five, assuming that everyone was perfectly lined up and ready to go. They really had no idea how long that number of seconds was so we worked that out too, just for fun.
We spent the last little bit of class playing Frogs. They understand what they need to do and some were starting to get the pattern, but we will work on that more tomorrow. I'll fill in the details then.
Here are the handouts for High Fives, Frogs, and the pizza one that I assigned as homework.