This year’s first Pre-Algebra Problem of the Week, “Duke is Missing,” is the story of a mean brother who “helps” his sister describe their lost dog’s length to the SPCA through a confusing math riddle. I have to confess I never much liked the problem. I think it’s because, as a dog lover, I find what the brother did to be REALLY mean! Seriously, what kind of jerk would do something like that in a time of crisis?

But… I do have a new puppy and the problem got me wondering… does my puppy have the same proportions as Duke? Are his proportions changing as he grows? In the picture below, from the day we got him, he weighed 13lbs and was 7 weeks old. I measured and got the following ratios:

- tail:body :: 8:20
- tail:head :: 23:20
- head:body :: 7:20.

Here’s a more recent picture if you’re curious about how the ratios have changed as he’s grown!

Wondering is one thing that we really focus on when we think about PoWs and problem solving. A good problem should lead you to think about something (puppies, for example) in a new way, or to want to discover more patterns and math.

Here’s something else I’m wondering about… at the beginning of a school year in Pre-Algebra, how do we support students to *make sense of* the relationships in a problem, whether they’re representing them algebraically or not? Here is some student work that I’m wondering how to respond to. What would you say?

2(6+(6+1/2B))=X. Im not quite sure how i got the answer

I’m looking forward to reading about your wonderings, noticings, mentoring ideas, and tips for PoWs in the blog comments!

**Some “Duke is Missing” links** in case you are interested:

- The problem [requires a Math Forum PoW Membership].
- Information about accessing “Duke is Missing” (and all our current PoWs) for two weeks with a free Math Forum trial account.
- Information about becoming a Math Forum Problems of the Week Member. Compare prices – consider starting with a $25 membership giving you access to all of this year’s Current PoWs — and now you can create 36 student logins as well!