Viral, Splitting, and Shrinking: Discovering Exponential Growth
Shared by A STEM Educator
Students will distinguish linear from exponential growth, construct tables and graphs for exponential scenarios, identify the initial value (a) and growth factor (b), and write exponential expressions in the form y = a·b^x.
Lesson Overview
Students move from additive vs. multiplicative patterns (WODB warm-up) through thin-sliced exponential tasks at vertical surfaces, culminating in writing and interpreting y = a·b^x for growth and decay contexts.
Materials
- Vertical non-permanent surfaces (whiteboards, windows, chart paper)
- One dry-erase marker per group
- Visibly random grouping cards
- Desmos Classroom activity (Part 3)
- Four-Quadrant Note-Taking sheets (one per student)
- Exit slip half-sheets
Scaffolded Task Progression
Imagine you discover a fascinating secret at school. On Day 0, you are the only person who knows it. On Day 1, you share it with exactly 2 friends, so now 3 people know it. On Day 2, those 2 friends each share it with 2 new people. If this pattern continues perfectly, where every new person who hears the secret tells exactly 2 new people the next day, how many *new* people will find out the secret on Day 5? Track the number of *new daily recipients* using a table and a sketch of a graph.
Using the Viral Rumor pattern (each new person tells 2 new people the next day, starting with 1 person on Day 0), find the number of NEW people who hear the secret on Day 10 — WITHOUT extending your table row by row. Write your shortcut using a repeated mathematical operation. How does your shortcut connect to the table pattern?
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