SWBAT plot data points on a graphing calculator. SWBAT use a calculator to approximate a line of best fit. SWBAT see the effects of adjusting starting values and rates of change to equations.

Can you find the best function? Students plot data on the graphing calculator and write linear functions to best approximate the data.

20 minutes

I begin class by telling students that today they will go back to a previous activity, **Battery Life**. We will be using the data from that activity in a slightly different way. I read through the activity with students and tell them that we'll go through the first group's data together. I use wabbitemu software to show students what to do on the graphing calculator so everyone can follow along. I show students how to plot points using the calculators** List** function. I have them enter the ordered pairs for the red class. I make sure they plot the x points vertically under L1 and the y points vertically under L2. I show them how to turn on **Stat Plots **and let them choose the type of mark they would like to see on the graph.

Students often need help setting a viewing window. I ask students how far they need to see along the x-axis. Students should realize they want to make a prediction about when the devices will run out of battery, so they should look at least as far as 60 minutes, but probably a little further. Then I ask, "How high do you think you will need to see on the y-axis?" Even though they have a highest y-value in the table, you might point out that the table starts after 10 minutes, so the devices would probably have had even battery life than that. This is also a good opportunity for students to figure out appropriate scales for the x- and y-axes on the graphing calculator.

Once all students can see the plotted points in their viewing windows, I tell students their task today is to find a function that best approximates this data. Students may be hesitant to get started so I encourage them to choose any starting value and and rate of change that seems reasonable. Although there are lots of clues to help them estimate here, I think it is best to have them enter *any *linear equation into the graphing calculator, even if it is far off. Once they can see the linear function on their screen, they can think about how to adjust it to best fit their data points. From there, I ask them to make a prediction about the smart phone. Will it run out of battery before the 45 minutes? Students can review how to use the **TRACE** feature on the calculator here.

30 minutes

Once I think students have the gist of using the graphing calculator to plot points and estimate functions, I let them work on their own or in small groups on the remaining set of data. I find that students LOVE this Plotting Data activity and get really excited about it. It gives them the opportunity to try to fit a linear function to the data as best they can and I might see students arguing and comparing possible equations to best fit the data. I think it's also a great opportunity to show how useful the calculator can be to them in a way they may have never seen before. As students work, I keep track of the equations they find and possibly call them out or show them on the Smartboard to show other students. Remember to remind students that once they have a function, they need to use it to make a prediction.

Issues I watch for:

- Students might struggle to remember how to enter a list of data. I might keep the steps up on the board or have them take notes as a reference point. I make sure they clear out the old data when they are finished with it.
- I make it a point to continue to connect the linear function with a prediction, make sure students see that they are using the linear function in service of something bigger.

10 minutes

I make sure to leave time at the end of class for students to share out their results. If I have the points plotted on a graph on the board, I can ask students to share out their best equations to fit the data. This is a great opportunity for students to see how the starting point (y-intercept) and rate of change affect the graphs. I make sure to relate this to the problem situation. I might ask questions like:

- So according to your equation, how much battery life did the smartphone start with?
- Where do you see that in the equation? In the graph?
- If the phone used the charge at a constant rate, how much did it use per minute? How do you know? Where do you see that in the graph? Where do you see that in the equation?
- When do you predict the smartphone will run out of battery? Why? Where do you see that in the graph? What would that mean in the context of the equation?

I give students some time to reflect on their learning today. I use an **Exit Ticket** to help them reflect. A possible prompt for them to write about is:

**Describe how you found a function to best approximate your data points. What strategies did you use?**

**Homework**:

IMP has a great follow up assignment to this activity. It is on page 230 of their **Year 1** textbook. It uses a scenario of college students on a budget and asks students to follow the same steps they did in today's lesson to predict who will be able to pay their rent.

Note: students will need access to a graphing calculator or similar technology in order to complete this homework.