This morning I was trying to come up with some good problems for students to use to find local maxima and minima. It's an awesome feeling to be able to combine everything I know about graphs and polynomials and end behavior to create polynomials within the window that I want that do what I want. It's cool to think that I don't have to just guess random things. So the graph is too long and skinny? I can do a vertical compression or a horizontal stretch. I want two local maxes and one local minimum, so I know I need to give it a negative leading coefficient and an even degree. It might be neat to come up with some sort of guidelines and have the students come up with their own polynomials. I wouldn't want them to just guess and check though. I might have them write something that says what they would have to do to a graph to get the desired results. It really forces you to use everything you know about polynomials and graph behavior and actually apply it.
I read a post on facebook today about things in the real world that students don't learn in school. It got me thinking about how we spiral everything in Geometry and Algebra 2. Here's how it works... We teach a brand new unit for about 2 weeks. During that time, we review something from a particular previous unit each day so that by the end of those two weeks, they have learned all the new material a little bit each day and reviewed all the "spiral" material a little bit each day. Then we give two tests, one over the new material and one over the "spiral" material. By doing this, they will experience all material once as new and a second time as spiral. This will allow them to take two tests over every unit. Their first test score affects their grade, but if they score higher on the second test, they get to keep just the higher score. If they score lower on the second test, we average the two test scores. Most students score higher on the second test becau...
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