Imagine you’re at a store that lets you pull products apart and pay for as much or as little of them as you want. What will your total grocery bill be for these three items?
If a student has no idea where to start, you can prompt her to list a price that sounds fair to her for the three sodas or, failing even that, a price that seems unfair to her. (You’re basically asking her to give a wrong answer. It’s a lot easier to give wrong answers than right answers because there are a lot more of them.)
You’ll find students who divide all the way down to the unit rate (ie. each egg costs 19 cents) and then multiply back up. You may also find students who set up a proportion, which will disguise the unit rate in an interesting way.
You’ll find students who set up different but equivalent unit rates. (ie. 19 cents per egg and .05 eggs per cent.) You’ll find students who set up different but equivalent proportions.
One of your many challenges during this activity will be to select students to show work that highlights a) the different ways to find the unit rate, b) the different ways to set up the proportion, c) the equivalence within those methods, and d) the equivalence between those methods (ie. ask your students to help you find the unit rate within the proportions).
I’m with Christopher and, I think, Dan here: Toss it out with the understanding that students can use any method that makes sense to them. Then not only share those methods but compare them to see why they yield the same result. Love the word “catharsis” in this context.