Introduce Taylor polynomials in the first semester! If your students understand tangent line approximation, simply extend it to "quadratic approximation," then "cubic approximation," etc. This activity builds understanding through color-coded graphing and algebraic reasoning, NOT substituting into formulas. Includes color-coded answer key and a satisfying connection and pleasant surprise at the end (Euler's identity!). Recommended: work through one or two examples in class, then let student