## Great Application Problems — A Rubric

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.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

1. #### Chris Riesbeck

July 29, 2010 - 9:52 am -

In 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?

2. #### blaw0013

July 29, 2010 - 7:52 pm -