#anyqs is the Twitter hashtag for an idea spinning from Dan Meyer’s work with multi-media, engaging, narrative problem-launches. The challenge is to use a single photo or <15 second vide clip to get students asking a good math question, something they’d be engaged in solving. Note that you don’t say to kids, ideally, “hey, what math does this make you wonder about?” You just show the media and say, “what are you wondering?”

This summer I’m hoping to enlist rising 6th and 7th graders with the task of finding images. I’m hoping that they at least can do what most of us teachers on the Twitter-verse have done, which is capture and image and say, “math!” Then, they have college-age mentors and I, not to mention each other, who can help them choose the most compelling images with the clearest questions. We’ll see…

To warm up, in our first hour together on Saturday, we started by looking at some images and playing, “What do you Notice? What do you Wonder?” Here are the three images, with what we noticed/wondered about each (I’m paraphrasing, I didn’t get a chance to photograph our exact noticings and wonderings).

Photo 1:

Noticed: 8 slices cost more than 1 whole pizza. Toppings for the whole pizza cost $1.75 (7 quarters) more than a slice. The “A” is missing. Toppings cost different amounts ($2.00 vs. $0.25).

Wondered: Why the “A” is missing. Why toppings cost more sometimes. How many slices are in a pizza? Is it 8?

Overall outcome: the math is all there and noticeable, comparing whole pie costs to slice costs. Both toppings and plain pizza costs were noticed. However, I think the sign itself was confusing and not everyone knew what the $2.00 vs. $0.25 were referring to (the cost of toppings for a whole pizza vs. a slice). Sadly, the whole, “best deal” question didn’t really emerge, other than the noticing that 8 slices cost more than a whole pizza. I think that question is a little too math-book-y. There was too much going on and the question took a lot of organization to pose. When I showed the sign to a bunch of math geeks around the office (and a programmer), the best deal question emerged for some, though at least one person found that the question got obscured by the amount of stuff going on. Wonder if this version would have been better or worse:

Photo 2:

We noticed: the gas prices go up as the grades go up. The gas prices are mostly odd numbers. They all end in 9. They all start with 3. The grades go up by 2 or 3. The gas prices go up by about 20 cents. They don’t go up consistently.

We wondered: can the grades keep going up? Can they be above 100? What do they mean? Do higher grades make your car go faster?

Overall outcome: I loved that the students immediately saw this as table-like. The looked for and compared rates of change and noticed inconsistency. I don’t think we could have gotten much bang for our buck if we had covered up one price, since I don’t think price as a function of octane rating is predictable enough for 6th and 7th graders. My favorite question was “Do higher grades make your car go faster?” and I think this would have been a great launch for a little organic chemistry…

Photo 3:

via @MathBratt

We noticed: Both cups say “Dad,” both are coffee cups, one is bigger than the other. The small one costs $5.95

We wondered: Does the big one cost $10.95? Is the big one twice as big? How many of the little one can the big one hold? How much water does each one hold? Does the big one cost more? Does it cost $40? Is one more breakable? What are they made of?

Overall outcome: #anyqs gold. The students zeroed in quickly on the question of, “how much does the big one cost” and were able to establish a range (assuming it’s not made of gold or useless at holding water): $5.95 – $40 (though someone pointed out they both look cheap and she wouldn’t pay more than a couple bucks for either). Then I asked them, “how would you decide on a fair price for the big cup” and answers ranged from “$40.00!” to “measure the inches, divide, and multiply” to “see how many times the little cup fits in the big cup” to “either measure how much water each can hold or how many inches long each one is, and compare.” This is an amazing launch for thinking about ratio and proportion, linear vs. area vs. volume measurements, volume of cylinders, etc. I want to own these cups, or at least get measurements.

Final thoughts:

I messed up by not leaving any time to talk about what made for good photos. We got caught up in logistics of getting their photos turned in for the next session, as well as running short on time and attention span. What I should have done is done all 3 photos (and more) quicker and then had them in their small groups rate how interesting each one was, say why, and then talk about their plans for getting photos. We’ll see what (if anything) they come in with. I’ve got quite a collection in my back pocket if the kids don’t do their homework so they can at least choose photos with questions they like.