Can we see the “sturdy rubric describing the beginning, middle, and end of great application problems?â€
What did we miss? Where did we overreach?
- engage the students with multimedia â€” pictures, videos, sound.
- the students come up with the question.
- the students make predictions â€” â€œgive me a guess.â€
- the students establish a range around their answer â€” â€œgive me a wrong answer. give me an answer thatâ€™s too high, thatâ€™s too low.â€
- there isn’t information on the first image.
- â€œannounce the problemâ€™s constraints quickly and clearly.â€
- 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: â€œwhat information do you need to solve this?â€
- ask: â€œhow do you know that?â€
- ask: â€œwhy?â€ â€œhow?â€ â€” even on right answers.
- encourage students to explain their reasoning to other students.
- ask students to collaborate â€” â€œwhat do you think about jerold did?â€
- ask: â€œhow would that help you?â€ after they tell you certain information is necessary.
- ask: â€œwhat isnâ€™t necessary to find the answer? what information donâ€™t we care about?â€
- 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, â€œhow many tickets are on a roll with a particular diameter?â€ now: â€œwhatâ€™s the diameter of a roll that has 1,000,000 tickets?â€
- ask: “does the answer make sense?” â€” have them compare their answer to their ranges.
- show, don’t tell, the answer â€” ie. the label said 2000 tickets; the timer said 8:12.
- discuss sources of error.