A few weeks ago, I took my daughter to the mall. Later, she complained that “Dad spent half the time taking math photos!” Five of one hundred twenty minutes is not half!¹

One of those photos:

I thought that this would make a great “Would You Rather…?” math task. I considered a few approaches. My preference is probably to just display the offer and have students make up their own prices and riff on “What if…?” That might be a tall order. I created a few combinations. (More on these in a sec.) But I wanted something more open.

Here’s where I landed:

.pdf

The idea is that students would mix & match specific combinations of board games to justify their decisions.

For example, consider Carcassonne ($43) and Blokus ($40). With “buy one, get a second 25% off” the discount is $10 (25% of $40). Add Othello ($35) and with “buy two, get a third 50% off” the discount is $17.50 (50% of $35). It looks like the second option is the clear winner. But if we think about the (total) percent discounts, we get about 12% ($10/$83) and 15% ($17.50/$118), respectively. Proportionally, the gap shrinks.

What if we replace Othello above with Spot it! ($20)? Again, the discount is $10 (50% of $20). But it’s not a tie. Saving $10 on $83 is better than saving $10 on $103 (about 12% vs. 10%).

There are a couple of combinations where we can’t justify the second option. For example, consider Catan ($63) and Pandemic ($60). With “buy one, get a second 25% off” the discount is $15. Add Rock Paper Scissors ($6) and with “buy two, get a third 50% off” the discount sinks to $3.

Beyond making and justifying a decision using mathematics, I’d push students to generalize: *When* would you rather…?

A couple more photos from the mall:

“Dad, stop taking photos of arrays! Are these like the paint splatter thing?” Yep. Partially covered arrays in the wild. Lack of fraction sense aside, it’s nice to know that she’s paying attention. And making connections.

¹BTW, I use Microsoft Office Lens to quickly crop, clean up, and colour these photos on the fly. An essential app for teachers using vertical non-permanent surfaces (#VNPS on twitter). Check it out.

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What a terrific conversation starter. This reminds me, but this is more sophisticated, of the question about applying a coupon before or after a discount membership card. This kind of numeracy is far too lacking in my curriculum. This is a nice remind to make space for these conversations.

Thanks, Jim! I think I know what you mean by “coupon before or after discount card.” Something like this? The “What do you notice?” — that the difference is always $2 no matter the original amount — and follow-up conversation re: why is interesting. Less sophisticated still is “In which order should I use 10% off and 20% off coupons?” Not immediately obvious to students (or teachers) even if they “know” the commutative property.

The question I was thinking of is whether you apply your 10% off or your $10 off first. Students seem surprised, at first, that it matters. Gets them thinking about percent as a portion based on size.