The modeling activities in this lesson center on electronic devices. This Warm-up activates students’ knowledge and personal experience with such devices, preparing them for the mathematical work ahead.

Students may not have a good sense for the answer to the last question (about comparing the lengths of charging time if the device started out with different levels of power). This is fine, as students will do some modeling with specific data later in the lesson.

Invite students to share their characterization of the time it takes to drain and charge the battery on their device. Students are likely to bring up different factors affecting how long their device would stay charged, such as how it is used and how long or how frequently it is used. They may also bring up factors that affect charging time, such as the age of the battery or the quality of the charging cable or wireless charger used.

Highlight that both the battery life of a device after each charge and the length of charging time can vary for many reasons.

In this activity, students analyze percentages of battery power as it is being charged, generalize how the quantities are changing, and use their generalization to predict when the battery will be fully charged. The values in the table change at a roughly constant rate, so students are likely to choose a linear model, reason about the average rate of change (which they could do in different ways), and extend that rate of change to make their prediction.

Students apply their understanding of average rate of change and linear relationships to reason about the data and to make a prediction (MP4). If students choose to use graphing technology to help with their analysis, they practice choosing appropriate tools strategically (MP5).

One variation to consider as a follow-up to this activity or to the lesson is to ask students to collect their own data on charging time. This would increase the modeling demand. If students collect their own data, they may find out that batteries tend not to charge linearly all the way to 100%. (Based on the full information, students may decide to use a piecewise function as a refined model and revisit the problem.)

Previously, students analyzed a set of data on the power levels of a battery as it was being charged. They looked for a model that enabled them to predict when the battery would be 100% charged. In this activity, they engage in a similar, yet more challenging, modeling exercise to determine when a battery would be completely out of power.

Here, students are asked to define a function and then use their function to make some predictions. Then, they evaluate their predictions and adjust the function to account for new information. Data about the situation are presented in a way that may be unfamiliar, so students need to persevere in making sense of quantities and the relationships among them (MP1).

As students work, monitor for those who use different reasoning strategies and representations as they find a model that describes how the battery power is decreasing over time. Select them to share their work later.

No time estimate is specified for this activity as the length would depend on decisions about how students' models are discussed, revised, tested, and presented. If students are to collect data using their own devices, or if they are to prepare a presentation that illustrates their results and their modeling process, additional time will be needed.

Making graphing and statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).