Common Core Standards: Math
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Your students should be gaining fluency in mathematics, and be able to write and rewrite expressions. The spells of nausea, hyperventilation, and paranoia surrounding the beautiful language of mathematics should have subsided by now. If they haven't, you may want to consult the school nurse.
Rather than rewriting expressions for the fun of it (and it is fun, isn't it?), students should understand what these different expressions can tell us about the quantities they represent. These mathematical expressions can tell us the zeros (or roots or x-intercepts) and the maximum and minimum values of a function, and have plenty of other applications in the real world. Most of them involving money.
- Factor a quadratic expression to reveal the zeros of the function it defines.
- Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151⁄12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.