Study Guide

Learning Objectives

• Determine AROCs for linear and quadratic functions (and sequences) on given intervals.
• Recognize constant AROC as the linear hallmark.
• For equal-length intervals, recognize that quadratic consecutive AROCs follow a linear pattern.
• Describe change in AROCs: rate 0 for linear; constant rate for quadratic.
• Connect AROC to secant slope.

Suggested Practice Sequence

1. Linear: verify AROC $=m$ on varied intervals. 2. Quadratic: compute AROC on $[a,a+h]$, $[a+h,a+2h]$, $[a+2h,a+3h]$. 3. Find the common difference of those AROCs. 4. Table identification: linear vs quadratic from rate patterns. 5. Applied contexts with constant vs changing rates. 6. Mixed sets linking 1.1/1.2 language to 1.3 patterns.

Classroom / Check-In Moves

• Require a two-interval check for any "constant rate" claim.
• Have students build a "rate of rates" row under a quadratic table.
• Ask: "If AROCs change by 4 each hour-step, what function type is plausible?"

Misconception Watch-List

• One AROC proves linearity.
• Quadratic outputs change at a constant rate (no: AROCs do, over equal steps).
• Unequal intervals still must show arithmetic AROCs for a quadratic.

Vocabulary to Own

• constant average rate of change
• consecutive equal-length intervals
• change in the average rates of change
• secant line / secant slope
• linear pattern of AROCs (for quadratics)

Materials Map

• Practice: linear constancy + quadratic consecutive AROCs
• Word: applied constant vs changing rates
• Mixed / multi-*: identify type from patterns; link to 1.1/1.2
• Review & practice test: timed pattern recognition
• Interactive: quick checks on constancy and common differences