The goal of this lesson is to encounter two different growth patterns—one pattern is linear and the other is exponential, though students don't need to use those words, yet. Students think about and compare the patterns by performing calculations and using graphs. This lesson contains many opportunities for students to notice and make use of structure (MP7), for example, noticing that can be expressed as . There is also an opportunity to use appropriate tools strategically (MP5), for example, if students choose to use a spreadsheet to perform many iterations of such calculations.

They see that the pattern that grows by repeatedly doubling starts off slowly but eventually overtakes the other pattern, which increases by repeatedly adding the same amount. Throughout the unit, students will study exponential patterns systematically (eventually viewing them as functions) before returning to this comparison with linear functions.

Some technology is required for this lesson, but there are opportunities for students to select appropriate technology in the lesson. We recommend making scientific calculators and spreadsheet technology available.