Start with discussion, brainstorming, estimation.
You run a Dollar Tree franchise. Everything costs a dollar.
You sell shampoo for a dollar – a popular brand called “White Rain.”
Problem: times are tough and the people who sell you the shampoo need to raise their prices higher than a dollar. What are your options at this point?
Teacher: write down student suggestions on the board. When someone suggests “sell less shampoo for the same price” resist the urge to declare, “Ahhh … that one’s eeeeenteresting,” thereby cluing your students to the fact that they weren’t really brainstorming, they were playing another game of “guess what the teacher wants to talk about.”
Spend a few seconds talking about, for instance, the student’s suggestion to rename the store. To what? Somewhere Around A Dollar Tree? You’re getting students all across the spectrum to invest in the problem and it’s costing you – what? – a few minutes.
Lower a little more structure onto the problem.
It turns out that “sell less shampoo for the same price” is exactly how that went down.
Teacher: “So what’s an interesting question we could ask here?”
Teacher: “How much extra are you actually paying here? What should the smaller bottle actually cost?”
Teacher: take guesses.
Your location in the scope and sequence of proportions will determine how much direct instruction your students will need here. That’s on you.
I dug through the entire Consumerist collection. The most valuable entries included both price and quantity.
Some of the others are great for discussion, though. Notice Dial’s effort to conceal the decrease with a taller, thinner container:
Tropicana’s opaque containers offer them enormous flexibility in the quantity of orange juice they give you:
And, if your class feels like venturing into some 3D geometry, ask your students how Yoplait has managed to shrink the amount of yogurt by 33% in a new container that looks nearly the same as the old.
The answer to that question (along with all the lesson materials) is located in this zipped archive.
[h/t MPG for the idea]