Mississippi Math C.G.25

MathGrades 9–12Geometry (G) Geometry

The Standard

Identify and apply local linear approximations.

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 use a tangent line at a known point to estimate a nearby function value. They use the slope and the change in input to estimate the change in output.
What Mastery Looks Like: Given f(25)=5 and f'(25)=0.1, a student estimates f(26) as 5.1. They can explain why the estimate is less reliable farther from 25.
Common Misconceptions: Students may use the slope as the estimated value instead of multiplying it by the input change. They may subtract inputs in the wrong order or expect the estimate to stay accurate far from the known point.
How to Assess It: Exit ticket: Given f(9)=3 and f'(9)=1/6, estimate f(9.6). Show the input change and explain why your answer is an estimate.

Lesson moves

On graph paper, plot y=x² near x=2, draw its tangent, and use a ruler to estimate (2.1)².
Ask students to write why the tangent at x=2 estimates (2.1)² better than 3².
Deal cards marked f(4)=8, f'(4)=3, and x=4.2; have pairs estimate f(4.2) and check each other's work.
A square garden grows from 100 to 101 square meters; have students estimate its new side length using a tangent at 100.

Free download

$Preview of the C.G.25 printable worksheet$

A ready-to-print activity worksheet aligned to C.G.25, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.