Average Rate of Change for Quadratics
I can find the average rate of change of a quadratic over an interval and say why the interval matters.
The problem this sheet solves
A quadratic has no single rate of change, and an answer given without an interval is not imprecise — it is unanswerable. Students carry the habit from a whole unit of linear functions where the rate genuinely IS a property of the function, and the habit was correct there. What changes is not the arithmetic but what the answer BELONGS to. The demonstration is the sheet: compute the same function's rate on two different intervals and get two different numbers, one line each. The worked example and two practice items are built as PAIRS for exactly that reason, and the last exit-ticket question asks what is missing from a question rather than for a number. The formula is not new, and the sheet says so — it is the slope formula in function notation, now measuring a secant.
The key rule
Average rate of change is f(b) − f(a)/b − a, and for a quadratic it belongs to the INTERVAL, not to the function.
No interval, no answer.
Watch out
The mistake: A student says the average rate of change of y = x2 is 2.
The fix: Over WHICH interval? On [0, 2] it is 2, but on [2, 4] it is 6 and on [10, 12] it is 22. Without an interval the question has no answer.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.