Mississippi Math C.N.2

MathGrades 9–12Number and Quantity (N) Compute and Determine the Reasonableness of Results in Mathematical and Real-world Situations

The Standard

Estimate numerical derivatives from graphs or tables of data.

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students estimate how fast a quantity is changing at one point on a graph or in a table. They find the slope of a tangent or calculate a slope from nearby table values, then give the rate with units.
What Mastery Looks Like: On a graph, a student draws a reasonable tangent and uses its rise and run to estimate the slope. In a table, they choose nearby values, calculate a rate, and explain why it is an estimate.
Common Misconceptions: Students may read the graph's height as the rate or use table values far from the target point. They may miss a negative slope or give meters as the unit instead of meters per second.
How to Assess It: A toy car travels 3.61 meters in 1.9 seconds, 4 meters in 2 seconds, and 4.41 meters in 2.1 seconds. Estimate its speed at 2 seconds and show your calculation.

Lesson moves

Give pairs a printed curve and ruler; have them draw a tangent at x = 2 and count its rise and run.
For y = x², ask why slopes from 1 to 2 and 1.9 to 2 differ when estimating the slope at 2.
Play a matching game with cards showing tables, graphed tangents, and estimated slopes; have students explain each match.
Show a bike's distance at minutes 4, 5, and 6 as 0.8, 1.1, and 1.4 miles; estimate its speed at minute 5.

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