Mississippi Math C.G.22

MathGrades 9–12Geometry (G) Geometry

The Standard

Demonstrate and explain the differences between average and instantaneous rates of change.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Employ Various Integration Properties and Techniques to Elevate Integrals

Teacher's field guide

What Students Need to Do: Students find how much one quantity changes for each unit of another. They compare the rate over an interval with the rate at one moment, using a graph or a familiar example such as speed.
What Mastery Looks Like: A student calculates an average rate from two points and estimates an instantaneous rate from the slope of a tangent line. They explain why the two rates can differ and include units.
Common Misconceptions: Students may average the two output values instead of dividing the change in output by the change in input. They may also assume the rate at one moment must equal the rate over a longer interval.
How to Assess It: Give students d = t², where d is meters and t is seconds. Ask them to find the average rate from 0 to 2 seconds, estimate the rate at 2 seconds using t = 1.9 and t = 2.1, and explain the difference.

Lesson moves

Graph d = t² on graph paper, then lay a ruler along a secant from 0 to 2 and a tangent at 2.
Ask, 'Why can a car average 30 mph on a trip while its speedometer reads 50 mph at one moment?'
Set out six distance-time graph cards with marked intervals or points; partners race to draw the correct secant or tangent.
Put '12 miles in 20 minutes' beside a drawn speedometer at 45 mph; students calculate the trip average and explain the mismatch.

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