Can we see the “sturdy rubric describing the beginning, middle, and end of great application problems?”
What did we miss? Where did we overreach?
- 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?”
- 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?”
- 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.