Common Core Standards: Math
8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
We never understood why teachers assign their students detention in the form of writing one particular sentence over and over and over again. For instance, making Tommy rewrite the phrase, "I will not kick soccer balls at the P.E. teacher," doesn't guarantee a bruise-free Coach Gibson and it doesn't teach Tommy anything he doesn't already know.
Instead, math teachers should make students rewrite algebraic expressions in different but equal forms as punishment. It'll get Tommy to see functions in different ways and make him think critically about the consequences of his actions, or the output of his input.
Taking care of the Coach Gibson situation and teaching a bit of algebra in the process? Two birds with one stone.
- Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
- Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t⁄10, and classify them as representing exponential growth or decay.