Pinning this so it’s the first thing my students will see if they follow me:

You've heard of elf on the shelf but have you heard of

Did this with Year 7 and blew their minds... told them they could start from the left because we didn't need to borrow anymore... consternation!! So exciting to do something new in a framework they are so familiar with

Discussing with other people and considering different ideas, that was the fun part (for me). Math can be social and collaborative, and, when it is, it can also be engaging in and of itself. At least, that’s the case from my perspective. I’d love to hear yours. (End thread)

Honestly, if all my teacher talked about was my first solution, I wouldn’t have been all that interested in this problem beyond that. What made it interesting to me was investigating and connecting different solution approaches, even misguided ones, to each other.

Maybe it’s that math is useful to get the right answer efficiently? Well, another teacher shared she got the answer (likely much more quickly than I did) with guess and check. So advanced algebra skills are totally unnecessary here; the complex math I did was not the best tool.

(4) What makes math engaging? Some argue relevance. But is it really a “real-world problem” that these sisters know the difference of their speeds but don’t know how fast they were going? Probably not. So I’d argue this problem isn’t actually all that relevant.

(3) The SMPs aren’t an add-on to the content standards. They are an essential part of mathematical thinking, learning, and problem-solving that are (or at least should be) entrained in all we do in math class. A balance between content and practice standards is key to the CCSS.

That scaffold isn’t just for beginners. Problem-solving is hard, and taking time to write out your steps helps even “pros” (like teachers) avoid making mistakes. I count on my fingers, etc., not just to model that it’s ok for my students but also because it genuinely helps me.

(2) I teach my Ss that one of the first things they should do when solving a word problem (after reading it and checking that they understand it) is to define their variable. Literally writing out “let x represent…” and finishing the sentence for what x means in the story.

Ok, so what’s the moral of the story? (1) No shade to the teacher who posted this third approach. We all make mistakes, and (as is expected) I though and learned a lot by considering her mistake. I can feel my brain growing!

I think my reasoning checks out, but I make mistakes, too, so my last sentence is genuine. If anyone here notices something I missed, please let me know! I’m very interested in this problem and its varied solution approaches. But that’s basically the end of the convo so far.

Spoiler alert! Here’s the rest of my comment. Paying attention to units (mph vs hr) also helps clarify things here. SMP 6, attention to precision, is especially important when decontextualizing and recontextualizing. (Note: “she” refers to Jessica.)

Hint: what are the two different things “J” meant again? What are the two different values that those quantities have in the actual solution?

Cropped pics are a great way to create curiosity, btw. So it’s time for another exercise for your math educator brain: WHY does it work? Using the same variable for different things is a no-no like having 0 in the denominator. How did it give the right answer?

Ready for the answer? Spoiler alert! … It doesn’t really mean anything, because the variable J in this equation wasn’t precisely defined. Here’s the first part of my comment to the person who posted this method: Upon further reflection…

Hint: I had an epiphany when thinking about the connection I made between the non-viable solutions in my two methods. A speed of x = -9 mph would get you to a distance of 36 mi in 36/-9 = -4 hr; i.e. t=-4. What does the non-viable solution in this third approach, J = -7, mean?

But (*checks notes*) that’s actually my first approach, just using J instead of x. So how did this turn out so different? Here’s where I encourage y’all to pause and think about it. Can you figure out what’s different about this other person’s approach?

But I’m never satisfied with just seeing someone else’s solution. I want to break it apart and see how it works (think SMP 3 - critique the reasoning of others). So I wanted to try it from her approach, using J to represent Jessica’s speed and comparing it to Janine’s.

My first thought:

Happy with my work, I submitted and refreshed the page. Some other teachers had posted their solutions. Some were variations of one of mine, but then I saw this (doing my best to maintain anonymity here):