Functions and Non-functions (2/11/15)

Earlier this year in geometry we looked at examples and non-examples of different figures in order to let students develop their own definitions for the figures. I really enjoyed the process and felt like it was great for students, so I tried it again today when introducing functions to my 8th graders. I gave them one function and one non-function, and let them compare the two and try to figure out what distinguished the one as a function. After having the student discuss in their groups and then share out, I put another example of each up, which contradicted their first conjectures. For example, the first function I put up was linear, so a lot of students guessed that functions were linear. But then I put up a parabola, which threw that off. This went on for a while and I started putting up input/output tables and sets of coordinates. Finally, in both classes students began noticing that each x value, or input was only used once in the functions, and some were used twice in the non-functions. It was a great letting the students develop their own definition for functions based on exploration and discussion, rather than me just telling them what a function was. I want to do this more often.

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