Mississippi Math C.G.26

MathGrades 9–12Geometry (G) Geometry

The Standard

Analyze curves with attention to non-decreasing functions (monotonicity) and concavity.

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: Read a graph from left to right and find where it rises or stays level. Track how its steepness changes to tell where it bends up or down.
What Mastery Looks Like: Students mark non-decreasing intervals, including flat stretches, and label where a curve bends up or down. They explain their labels using changes in steepness.
Common Misconceptions: Students may think any rising curve bends up, even if it is leveling off. They may leave flat sections out of non-decreasing intervals or mistake a peak for a change in concavity.
How to Assess It: Exit ticket: Sketch y = −(x − 2)² for 0 ≤ x ≤ 4. Mark where it is non-decreasing and state whether it bends up or down.

Lesson moves

Give pairs bendable wire and grid paper; have them shape a rising curve that levels off, then mark where its steepness changes.
Draw a rising curve that levels off and ask, 'Can a curve rise while bending down? Explain using its steepness.'
Give pairs graph cards for y = x², y = −x², and y = √x; have them sort by non-decreasing intervals and concavity.
Plot a cyclist's distance each minute: 0, 100, 250, 450, 600, 700 meters; mark where distance rises and where gains shrink.

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