# Battery Life

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## Objective

SWBAT develop awareness of the connection between rate and starting point and a linear function. SWBAT to make predictions and estimates based on limited data.

#### Big Idea

Will the digital devices run out of charge on the way to school? Students reason and make predictions based on a graph and compare the charge of a cell phone and a video game player.

## Opening

5 minutes

I begin today's class with the activity that students will work on for the bulk of the lesson. I start class by asking students, "What percentage of the battery life of your phone goes down every minute you use it?"  I let students share their estimates and justifications.  I usually have to be careful here about side conversations about phones! I let students know that today they will continue to make predictions from graphs and that in today's task they will graph two relationships on one set of axes. We read through the activity Battery Life together and I clarify any questions students may have.

Sometimes I include a discussion about how to scale the axes for this problem. I remind students that although the problem gives data only until 30 minutes, they need to be able to see all the way to the full hour (and perhaps a little beyond) in order to make a prediction about which device will last the whole trip.  I may also lead them in some questioning about how to scale the y-axis. I try to elicit these points from students rather than telling them how to set their scales.

## Investigation

35 minutes

Next, students work in pairs or small groups on the Battery Life task.  As I circulate around the room, I watch for the following issues:

• I make sure students are putting all the points on the same set of axes. They can differentiate devices by using colored pencils. It will be interesting to note which groups connect the points to make lines and which leave the ordered pairs.  It will also be interesting to note which groups use straight lines when they connect the points and if any groups use curves.  I note differences that I might want to have groups share out in the Discussion section of the class.
• I ask students to explain in writing whether or not they predict each device will last the one hour trip.  I try to get them to focus on explaining their reasoning. I help them to use the word "rate" to describe how quickly a device is using its battery.

## Discussion + Closing

20 minutes

I have different groups share out their graphs and approaches to answering the questions. You can see if there is agreement in the class about which device will have enough power to the last the trip (neither do). I ask students to describe how they made predictions. I expect that many groups will use linear models to make predictions but some may use nonlinear models as well.  Some students will reason using the graphs while others will reason numerically.  I draw attention to both of these methods as equally valid. It's important to show students that there is no one right answer here.

I introduce the term x-intercept here in relationship to running battery.  Students should realize that the x-intercept for each line will represent when the battery has run out. It's also important to note the downward trend in this graph. Students have previously looked at graphs that grow larger as the x-values increase.  Ask them to relate this downward trend to the problem situation.  You can also bring in the idea of "using up" the battery as a way to explain the downward trend.

Students have now done a series of graphing activities.  I like to give them the opportunity to reflect on graphing. In my experience, students often have a negative view of creating graphs.  I try to counter this negativity by asking students something they like about graphing. I also want to give them the space to vent about graphing if they need that too!  A reflection prompt for this lesson might be:

What part of the graphing process are you best at? Why?

What part of graphing is most challenging for you? Why?

These reflections might be fun to share with students at the start of the next class.

## Citations

1. Battery Life is adapted from 8-F Battery Charging. 8-F Battery Charging is licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License  https://www.illustrativemathematics.org/illustrations/641