Mississippi Math C.S.27

MathGrades 9–12Statistics and Probability (S) Adapt Integration Methods to Model Situations to Problems

The Standard

Apply integration to solve problems of area.

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 sketch a region bounded by curves and find where the boundaries meet. They write and evaluate a definite integral to find its area in square units.
What Mastery Looks Like: A student can identify the upper and lower curves and subtract in the right order. They split the integral where the curves cross and check that the result fits the sketch.
Common Misconceptions: Students may subtract the upper curve from the lower one and get a negative answer. They may also use one integral across a crossing, letting areas on opposite sides cancel.
How to Assess It: On an exit ticket, ask: Graph y=x and y=x² from x=0 to x=1. Write and evaluate the integral for the area between them. The area is 1/6 square unit.

Lesson moves

Draw y=x and y=x² on graph paper with ten squares per unit; shade the gap, estimate its area, then integrate.
Ask students to explain why the integral of x from −1 to 1 is zero, but the area between y=x and the x-axis is not.
Put two curve pairs on cards: y=x and y=x² on [0,1], and y=x and y=0 on [−1,1]; partners race to calculate each area.
Model a garden bed whose width in meters is 0.2x(10−x) along a 10-meter fence; integrate the width to find its planting area.

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