When students enter the room I show them another variation on the Mario theme: Mario 7 coins clip.mp4
Not to get redundant, but we return to the Mario scenario again to talk about misconceptions on "almost" linear functions and in this case, data collection.
As in previous lessons, I begin by asking students to write down their questions and share them with their partner and then their group. Throughout this process I am circulating and observing. I like to use the students ideas directly in group discussion, so I am "recruiting" ideas I want to use as I listen to the students discussions. As a start, I want students to notice that the coins are set up in repeating patterns of 7 coins. This time, the arrangement is 1 coin, 3 coins, and 3 coins
I want them to consider how Mario's speed, and the arrangement of the coins, each impact the rate of coin collection. I also want students to be able to explain why they feel that way. (In general, it is really a pleasure to run this conversation. After several Mario lessons, students are typically ready to discuss the variables that will effect the rate of coin collection and influence the model.)
In thinking ahead with the lesson, I want to keep in mind that unlike the previous three Super Mario lessons, today I give the students a clip of Mario to work with. The task that I pose to them is to choose the most reliable data points that they can with which to model the rate of collection.
In order to complete today's investigation, my students need to know the total time of Super Mario's run. I include this information on an image: time only shot.png
During today's partner work, I ask students to scan the 18 second video and to choose data points that "best represent" Mario's progress: Mario 7 coins clip (I keep the video online for them to browse as they work.)
If students struggle with the data collection, I give them these three supporting images:
As they work, I like to push them a bit to help them think. I will ask questions like, "will the last coin that Mario collects be a single coin or a pair?" Questions like this help students to think about the timing in terms of ending up on the single (or seventh) coin in the sequence.
As we work to bring this investigation to a close I ask students to share their reasonable ranges for the number of coins Super Mario would collect by the end of his run. I write these ranges on the board to get a sense of what the class is thinking. I check for understanding by asking routine questions.
I also record the student's data points on the board for the class to see. In this way, we informally build a data set to analyze the problem.
Then we watch answer unfold on this video: Mario 7 Coins Full.mp4
I also display a photo of the finish time and coin count:Screen Shot 2014-04-20 at 12.54.35 AM.png