This one was certainly a freeze-framer!

I agree with your larger point that sometimes we can find answers to some of these problems using common sense. We can google “how many pennies in the pyramid of pennies” and arrive at the answer pretty quick. Or, let’s just each walk to the taco truck by different routes each way and find out instead of doing all this math. But it’s only by calculating a unit rate after a purchase that we can feel more certain about the validity of the pump (or the sign on the corner). This assumes that the pump isn’t lying about the amount of fuel it’s dispensing. And gas pumps are highly regulated by inspectors and anti-tampering measures (like security tape). Which is probably the best argument a student could make that gas pumps don’t rip you off.

I may be missing something to your point however so let know if I am. I think though that Sally’s question shows a need to verify the sign on the corner with our experience at the pump. I suppose that finding the unit rate procedurally through division makes the graph less necessary. Hmmm. You have me wondering more. Thank you.

Otherwise, I am wondering if the lesson goes something like this: Me: Which gas station is ripping you off? Sally: What are the prices? Me: I don’t know. Sally: Doesn’t it say on the pump? Isn’t there a huge sign on the corner with the prices? Me: Shut up Sally. Obviously we need to gather data and make a graph to figure it out.