Exponential growth, on the counter.

The objective

Students see exponential growth in a jar on the kitchen counter: a sourdough starter doubling at its peak, and how a feeding ratio changes the pace.

The launch (5 minutes)

Hold up the jar. “A sourdough starter is a pet you feed flour and water. Every day it eats everything you give it, doubles, and waits for the next meal.” Then ask: if it doubles every time, how many days until it fills this room? Let the guesses fly.

The work (25 minutes)

• The doubling table (10 min): Start with 10 grams of starter. It doubles at its peak: 10 → 20 → 40 → 80 … Students fill the table to day 7 and mark the day it passes the jar’s size. The pattern is the lesson: adding a fixed amount grows in a line; doubling grows in a curve.
• The feeding ratios (10 min): A feeding reads starter : flour : water by weight. The daily rhythm is 1:1:1 (peak in about 12 hours). 1:2:2 buys more time; 1:5:5 is the once-a-day pace; 1:10:10 is the fridge bridge that survives a week away. Students compute: for 10 g of starter at 1:1:1, how much flour and water? (10 g and 10 g.) At 1:5:5? (50 g and 50 g.)
• The discard (5 min): Bakers keep the starter small on purpose. To hold it at 10 g starting from 80 g: keep 10, discard 70. The discard question — where does the rest go? — is the honest half of the lesson, and the answer is pancakes.

The close (10 minutes)

Exit question: “Your friend feeds a starter at 1:1:1 and you feed the same starter at 1:10:10. Whose doubles sooner, and why does the bigger ratio take longer?” (The 1:1:1. Its food is only twice the starter's weight, and the starter is already a third of the jar, so a couple of doublings eat it all and it peaks sooner. At 1:10:10 the starter is one part in 21, with twenty times its weight in food, so it needs several more doublings to get there. The big ratio is the slow lane.) Collect the doubling tables.

Extensions

• The curve: Plot the table (days on x, grams on y) and trace the curve — the shape that made the guesses in the launch so far off.
• Real starter: The ratios and the 12-hour peak are the same ones the sourdough guide carries; a class starter makes the lesson a month long. With a real starter: flour is a raw food that can carry E. coli and Salmonella, so no tasting or playing with raw starter, flour or discard, and discard is eaten only once it is fully cooked. Wash hands with soap and running water, and wash jars, spoons and counters with warm, soapy water after handling it (FDA on handling flour).
• The honest boundary: Exponential growth never fills the room — the starter runs out of food. Where the doubling stops is the lesson’s honest ending.

Teacher’s background

Everything above runs on paper. The ratios, the 12-hour peak and the fridge bridge are the guide’s own sourced figures — no starter required to teach it, only to prove it.