Mississippi Math C.S.29
The Standard
Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Apply Appropriate Techniques, Tools, and Formulas to Determine Values for the Definite Integral
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split an interval into equal widths and add the areas of rectangles based on function values. They explain why the sums approach a fixed value as the rectangles get narrower. They connect that value to the definite integral.
What Mastery Looks Like
- Given a graph and interval, students find the width of each rectangle and write a sum using left or right endpoints. They explain why the limit gives signed area, with regions below the x-axis counting as negative.
Common Misconceptions
- Students may use unequal widths but multiply every height by the same width. They may treat one rectangle sum as the exact answer or count regions below the x-axis as positive.
How to Assess It
- Exit ticket: For y = x from 0 to 2, write a right-endpoint sum using n equal rectangles and find its limit. What does the limit represent?
Lesson moves
Ways to Teach It
Use graph paper to draw four and eight right-endpoint rectangles under y = x² from 0 to 2; compare the summed areas.
Ask students to explain what happens to rectangle width and the area estimate when the number of rectangles doubles.
Give pairs cards with a function, interval, and rectangle count; have them write right-endpoint sums, then swap cards to check.
Show a bike ride speed-time table; estimate distance using equal time intervals, then discuss how shorter intervals might improve the estimate.
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Printable C.S.29 Worksheet
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Related Standards
- C.A.21
Apply the power rule and u-substitution to evaluate indefinite integrals.
- A3.A.14
Decompose a rational function into partial fractions.
- A3.N.3
Calculate limits based on convergent and divergent series.
- C.S.28
Utilize integrals to model and find solutions to real-world problems such as calculating displacement and total distance traveled.
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