That’s a nice link Dan, and I’ll definitely use some of it. It is a nice way to introduce writing variables, which is a problematic issue.

But it isn’t what I asked. I struggle to find situations I can give my kids in class that have them write variables into an equation that is simple enough, yet cannot be solved by numerical methods. So the situations invariably end up being “maths teacher world”, where we solve with variables something they can do quicker in their heads.

If you go through pretty much any textbook looking at this topic you will find pseudo-context, because the constraints are impossibly tight. When I write worksheets on this I am perpetually annoyed how sad my exercises look, but I’ve never seen it done much better elsewhere.

Dentistry/dental hygiene was also my first thought about the picture. Without the multiple choice, I wasn’t able to come up with any guesses about the textbook context.

It would be interesting to bring in an actual photo price schedule from Costco or something. Do kids even purchase photos anymore? (I do)

Also, some of the logic behind some of the psuedo-contexts are things I actually used in banking and credit industry analytics. Because of that I sometimes tell students that while the examples may be things you’d never actually do in day-to-day life, some of the methods and logic can be used on a larger scale in a work environment. But, that’s really still not good enough. Plus, most of what we did was way more detailed and an analysis program did much of it, of course. That said, you had to understand those algorithms.

You aren’t spoiling anything, Rebecca. You’re fixing the pseudocontext by adding the price constraint. Nice.

The problem here is that the customer has no use for a general equation, but the store owner might—she’s got to deal with people who call in with all kinds of crazy orders and questions. Still, it’s unlikely the store owner would write an equation for just small and large pictures. It’s much more likely that she’d come up with a pricing scenario for unusual picture sizes.

Nice, I buy it.

The expression is of little use to the customer, but there probably is an expression that’s of a lot of use to the owner. I’m imagining a fix-the-broken-cash-register activity. You either have to fix the register with an expression or calculate all the prices by hand.

PS. I featured this comment in the post.

Given our track record, I’m not sure we’ll sync up on this idea, but Evan Weinberg has a lesson that’s simultaneously simple enough for an introduction to variables, but which also illustrates their power. Notably, it lacks any real-world context.

I’m on to you, Rawr.

School pictures have been taken, and a parent receives the proofs with an order form. Exactly 12 photos need to be ordered for relatives, the child and yourself, but you’re budget conscious. You can order different packages with small (exchange), medium (wallet), and “large” (3×5). The unit price can be figured from the add-ons. What should the price be for each package? Is the package with 9 wallets, 2 3x5s, and 1 class photo a good deal?

By the way, in my “real” example, the add-ons that increased the photo package to the next package up didn’t obey the triangle inequality in that the combination came out cheaper than the next package up. That’s why the question is “Is this a good value? What do I compute the price/value to be in each case?”