So, Dan Meyer (@ddmeyer) recently introduced Makeover Mondays where we, as a math blog community, makeover a series of textbook problems that have some potential as usable contexts, but have low impact delivery for engagement or cognitive demand.

This is my first attempt to offer something to the conversation.

So, here’s the first target:

So, here’s where my mind went in terms of making over this problem: First, the idea of “biggest bedroom” is a fairly appealing idea, except I don’t recall competing for biggest room with my friends. So, insert a new plot twist. Rodney and Emile are brother and sister.

Second, most of the competition for biggest room comes when the rooms are both empty. That is, move-in day. Most of my students are fairly well-acquainted with the idea of moving. So, remove the detached rectangles and insert a floor plan.

Third, let’s add a bit of complexity. Both of the children move in with their own furniture, but, of course, with one being a girl and one being a boy, the furniture is not the same. Emile has this dresser and this bed. Rodney has a combo piece that includes both bed and dresser.

They are going to also move in with toys, a lamp, a chair for the bedtime book, among several other things.

Finally, the new task: You are the parent in charge of making the decision over who gets which room. Who gets which room?

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The idea of siblings fighting for a certain room in a new home is definitely real. I’m wondering though if the question in Dan’s textbook example is targeting the learning goal of converting between feet and meters.

The Amazon links for the products are in inches, so perhaps the floor plan that you have can be given in meters then?

Thanks, Andrew. These are fun to thinking about.

I think that would be a useful update. I did consider after I had published the post that perhaps I changed the focus of the problem a bit.

I had also considered the idea of not giving any dimensions for the rooms (at least not to start) and see how the students reasoned it out. Not sure if that would be too vague, especially since I can’t think of one apartment complex that wouldn’t provide those measurements.

I can say that when I was a kid, I was pressing for the biggest room going to the oldest, and I’m sure that was for reasons besides my being the first-born. We had a similar policy about who gets to pick what to watch on the TV.

You could come up with spinoff questions like working out per-person size if there’s two siblings who have to go in one room and one in the other, including a bit about how a hypothetical division of the shared room along the long or short direction (or the diagonal) affects the per-person area.

I’m a sucker for a good spin-off problem. I think that is why I like the question “who get which room?” Instead of “which room is bigger?”

One includes a variety of reasoning (some potentially non-mathematical, “like this one is closer to the bathroom…”) and one is simply two calculations of area for a rectangle, a unit conversion and a subtraction.

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