Students will learn how to find first and second differences given a table of values. If the first differences are constant, we have a linear equation. If the second differences are constant, we have a quadratic. If neither the first nor second differences are constant, the equation is neither linear nor quadratic. Students will also learn how to infer linear equations from constant first differences, and quadratic equations from constant second differences.
Conclude by giving your students these challenges:
- Hawaiian Earring by NRICH
- Light Blue - Dark Blue by NRICH
- 2008 AMC 8, Problem 11
- 2018 AMC 8, Problem 3
- 2005 AMC 8, Problem 11
- Squares in Space by Pierce School: Problem / Solution