I'm working with high school students, who are not currently enrolled in a math class, as they work through lessons on math-teaching software. There is a round of "benchmark testing" coming up and the principal wants to see the numbers go up. Originally this was conceived of as a relatively painless was to keep students' math skills current but now this expectation has emerged that I will give a 10-minute "mini-lesson," then students will master several methods of factoring quadratic expressions in the remaining 80 minutes.
A lot of the work so far has been in areas students are familiar with. But none of these students (freshmen) have done much with nonlinear functions.
I can show them the trick to factoring as they may see it on the test, but I am supposed to cover at least 4 techniques, without any time for students to learn why quadratic function are useful or even what they actually are. I can show them on a graphing calculator that the factored version is the same as the non-factored, and I probably can take a minute to two (literally) to give them examples. I would also like them to learn the FOIL technique for checking their answers.
I have 2 questions - can I make substantive headway in the one 90-minute session I have with my groups before the benchmark test? And, what are the merits of an overview that basically shows them the tricks, with virtually no real-world idea of what these functions are or why they are useful?
OK, three questions: What is the best way to go about this?
A lot of the work so far has been in areas students are familiar with. But none of these students (freshmen) have done much with nonlinear functions.
I can show them the trick to factoring as they may see it on the test, but I am supposed to cover at least 4 techniques, without any time for students to learn why quadratic function are useful or even what they actually are. I can show them on a graphing calculator that the factored version is the same as the non-factored, and I probably can take a minute to two (literally) to give them examples. I would also like them to learn the FOIL technique for checking their answers.
I have 2 questions - can I make substantive headway in the one 90-minute session I have with my groups before the benchmark test? And, what are the merits of an overview that basically shows them the tricks, with virtually no real-world idea of what these functions are or why they are useful?
OK, three questions: What is the best way to go about this?
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