Start with the answer is a twist on typical math class questions, opening up the question, allowing for a variety of responses, approaches, and knowledge levels.
For example, a typical, closed prompt: Find the mean of 5, 11, 7 and 1.
The related, open “start with the answer” prompt: I have four numbers with an average of 6. What might the numbers be?
Consider the kinds of responses each of the prompts might yield, what students might learn, and what the teacher can learn from the responses to each.
In the closed prompt, students may use whatever method they choose, but once they find their answer, they are done.
In the open prompt, students again may use whatever they know about mean to find four appropriate numbers. But, then they can be challenged find as many quadruples as they are able and share their methods with the class: 5, 11, 7, 1 or, 1, 2, 3, 18 or, 6, 6, 6, 6 or, 5, 5, 7, 7 or, 5.5, 7.5, 6.5, 6.5 or -6, 12, 18, -12 or, 0, 0, 0, 24… Classroom discussions might involve number sense, patterning, and the whole range of rational numbers.
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Some function examples: