For today's Warm-Up, I have selected the following questions: 1. The cups of Koolaid in a pitcher after n people fill their glasses is shown by the expression: 12 - 1.5n How many cups of Koolaid will be left after 6 people fill their glasses? 2. How many glasses total can be filled with this pitcher? How do you know?
Although we have been working with functions for several weeks, students still struggle to substitute values in an expression or equation. For this reason, I thought these two questions would provide additional opportunities to build understanding, especially because most have experience filling glasses from a pitcher and recognize that it holds a finite amount of liquid.
To introduce today's activity, I display the classified ads from the student worksheet. I check for background knowledge by asking what each add is selling. I then explain that we are going to spend work time today, organizing this data, first in a data table, then in a scatter plot, so we can use the displays to answer questions at the bottom.
I then ask students to talk with their shoulder partner about how they are going to organize their data in the table, but ask them NOT to begin writing in the table yet. The different cars are listed by model year and students are not likely to think about this unless I call it to their attention. Once students have talked with their partners for about 30 seconds, I ask for volunteers to share their thoughts. Typically, the first student says they will use model year as the x-values and sale price as the y-values.
To model their thinking, I ask, "So which car will we list first in our data table?" This question usually generates answers like, "00" and "98", so I say, "You are giving me the model year, but does that tell me how old the car is? In other words, is a 98 Ford ninety-eight years old? This usually causes some cognitive discourse for students, so I continue by asking, "How can we list car data so it shows how old the car is in years?" Typically, a student has figured out that s/he will need to subtract the model year from the current year to find the age. Once this is settled, I ask for needed clarification. I then set the timer and begin circulating the room, questioning, assisting, and redirecting students when needed.
When the activity timer sounds after 35 minutes, I ask students to bring their attention to the smartboard.
When the timer sounds, I ask students to give me their attention at the smartboard. I explain that I would like to see if all our practice with organizing data is improving our precision. I ask students to look at question number 4 and write their answer on a sticky note. I then asked students, one table at a time, to place their sticky note on the smartboard to create a line plot.
I was interested in seeing the range of numbers, which would tell whether students were truly attending to precision during this task. Gratefully, the range was only 3 years with a a strong mode and no outliers. This told me that the students were getting more precise with their lines of best fit.
Next, I asked students to share their equations that represented the lines of best fit. While these varied in both slope and y-intercept, overall, they were very representative of the data.