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Study Guide

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Learning Objectives

  • Compute average rate of change from formulas, tables, and graphs.
  • Interpret AROC with correct units and direction.
  • Compare average rates across intervals.
  • Connect AROC to secant-line slope.

Suggested Practice Sequence

1. Formula AROC with linear and quadratic $f$. 2. Table AROC with non-integer outputs. 3. Graph estimates using labeled points. 4. Applied rates (distance, temperature, cost) with units. 5. Interval comparisons and "largest average rate" questions. 6. Mixed sets that switch representations.

Classroom / Check-In Moves

  • Require the written AROC expression before the decimal answer.
  • Cold-call units on every applied item.
  • Show two intervals on one graph; vote which has larger AROC, then calculate.

Misconception Watch-List

  • Rate equals the function value.
  • Average of several rates always equals the big-interval AROC (not true in general).
  • Instantaneous rate language when only average rate is available.

Vocabulary to Own

  • average rate of change (AROC)
  • secant line
  • interval $[a,b]$
  • units of rate
  • increasing / decreasing on an interval (via sign of AROC)

Materials Map

  • Practice problems: formula, table, and graph AROC drills
  • Word problems: applied rates with interpretation
  • Mixed practice: representation switching
  • Multi-step / multi-standard: rates with change-in-tandem or function features
  • Review & practice test: timed AROC fluency
  • Interactive: quick MCQ/typed AROC checks

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