(Note: for the full lesson w/handouts click on the link at the bottom)
This lesson will challenge students to consider the different physical factors that affect real-world models (and you’ll probably be surprised when it challenges you, too!). Students are asked to figure out how long it will take a birdfeeder – with a constant flow birdfeed “customers” – to empty completely. To begin, explain to students that they will be watching over a neighbor’s home. This neighbor is an ornithologist (a scientist that studies birds) and, of course, there is a birdfeeder to be looked after. The challenge is that humans can’t come around too often because it will scare off the birds, but they also can’t come around too seldom because the birds will leave when they get frustrated that the feeder is frequently empty! The students need to figure out when to come back and fill the feeder to ensure that the neighbor and the birds are all happy!
Students should be very comfortable with basic algebra.
Required: (For a physical model) Cardboard box, sand, cylindrical plastic bottle (a Starbucks Ethos Water bottle, for example), scissors, stopwatches or timers.
Suggested: Graphing paper or a graphing utility.
Worksheet 1 Guide
The first three pages constitute the first day’s work. Students are given the opportunity to explore a physical model of a birdfeeder using a cylindrical, plastic bottle as the feeder and sand as the feed. Make sure the bottle is perfectly or very nearly cylindrical. Use scissors to cut “feed holes” (approximately 1cm in diameter) in the appropriate spots, as indicated in the lesson. Cover the holes so no sand falls out until the experiment is ready to begin (a few students “plugging up” the holes with their fingers is sufficient). Hold the model feeder over a cardboard box so the sand doesn’t make a mess. Use stopwatches or other timers to keep track of each of the total time it takes to empty as well as each of the times passed at each of the mathematically important moments.
Worksheet 2 Guide
The next two pages after Worksheet 1 constitute the second day’s work. Students need to figure out how to model various different situations; they’ll learn that each one has a mathematical tie-in to the birdfeeder problems. It turns out that the model they created for the birdfeeder is sufficient to solve each problem, but this is not obvious until connections are made as to how the problems are mathematically related.