## Great Application Problems — A Rubric

July 29th, 2010 by Dan Meyer

Can we see the “sturdy rubric describing the beginning, middle, and end of great application problems?”

Sure. The following rubric arose (without much coercion!) as we tried to resolve the different instructional outcomes between these two variations on the same theme.

What did we miss? Where did we overreach?

**Beginning:**

- engage the students with multimedia — pictures, videos, sound.
- the students come up with the question.
- the students make predictions — “give me a guess.”
- the students establish a range around their answer — “give me a wrong answer. give me an answer that’s too high, that’s too low.”
- there isn’t information on the first image.
- “announce the problem’s constraints quickly and clearly.”
- ask questions that lend themselves to guesses: “how long? how many? how heavy? how far? how fast?”
- try to translate questions that are harder to guess into questions that don’t change the objective but which lend themselves to guesses: “what is the area? what is the circumference?”

**Middle:**

- ask: “what information do you need to solve this?”
- ask: “how do you know that?”
- ask: “why?” “how?” — even on right answers.
- encourage students to explain their reasoning to other students.
- ask students to collaborate — “what do you think about jerold did?”
- ask: “how would that help you?” after they tell you certain information is necessary.
- ask: “what
*isn’t*necessary to find the answer? what information*don’t*we care about?”

**End:**

- ask students to summarize the process.
**sequel technique #1**: change a variable. eg. change the height of the water tank. change the number of sides of the base. make it a hexagon or a dodecagon. change the rate of flow.**sequel technique #2**: turn the answer into a question. at first we asked, “how many tickets are on a roll with a particular diameter?” now: “what’s the diameter of a roll that has 1,000,000 tickets?”- ask: “does the answer make sense?” — have them compare their answer to their ranges.
- show, don’t tell, the answer — ie. the label said 2000 tickets; the timer said 8:12.
- discuss sources of error.

on 29 Jul 2010 at 9:52 am1 Chris RiesbeckIn the beginning, for WCYDWT developers, and at the end, for students, ask “what else could you do with this?” What will/have we learned about solving what other problems?

on 29 Jul 2010 at 7:52 pm2 blaw0013It is very interesting the confluence of what I would name curriculum and pedagogy that define a “great application problem.” It seems lots of conversation about correcting the woes of math education are about one or the other, hugely ignoring the interrelatedness of the two.

on 30 Jul 2010 at 7:30 am3 Debby Smith@blaw0013: Good point, there is much overlap between the two. This rubric is not so much a measure of the design of the problem, but of that plus the playing out of the process of wrestling with the (well-designed) problem. As Dan took us through this process, I was continually impressed with the quality and impact of his questioning. Note all the “asks” in the middle portion.

The power of quality questions–from the driving opening question, to helping students craft good questions, to asking challenging questions throughout, to ending with key summary questions–is common across the curriculum.

on 04 Aug 2010 at 1:24 pm4 The Passion of the WCYDWT or: Mistakes I Have Made, and Vindication by the Neuroscience of Curiosity « Sarcasymptote[...] where I hyped that and the use of blogs- nothing you haven’t seen Dan Meyer talk about or write about already, just a bit more crass and sarcastic. Then, I sat in on a panel for all of the new [...]

on 09 Oct 2010 at 6:58 pm5 The bus stops here | Mr Duncan's Blog[...] other online reading, I discovered the work of Dan Myer through the TED Talk Videos. His post on developing good problems provided me with a good starting [...]

on 02 Feb 2011 at 8:40 pm6 Things That Improved My Teaching This Month « shifting phases[...] lead where I wanted to go, I had to develop some lesson plans in a hurry. This rubric for application problems helped a lot. Developed by Dan Meyer for math classes, it helps students find the meaning behind [...]