# Riemann Sums Teacher Resources

Find Riemann Sums lesson plans and worksheets
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#### Riemann Sums

For Teachers 9th - 12th Standards
Mathematicians use their calculators to investigate Riemann sums. Your learners will explore the relationship between the limit of two Riemann sums and the definite integral of the function.
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#### Riemann Sums

For Teachers 10th - 12th Standards
Students calculate the area under a curve. In this calculus lesson, students use Riemann Sums to find the area under a curve. They apply the boundaries of intervals as they solve for each area.
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#### Connecting Riemann Sums to the Definite Integrals

For Students 11th - Higher Ed
In this math worksheet, students examine the relationships between Riemann sums and definite integrals. They define the Riemann sums and find area using them.
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#### Riemann Sums

For Teachers 11th - 12th
Students explore Riemann Sums.  In this Calculus lesson, students investigate Riemann Sums as an approximation of the value of the definite integral.
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#### Integration Unit: Riemann Sum

For Teachers 11th - 12th Standards
Students investigate Riemann Sums. In this calculus lesson, students solve problems involving Riemann sums and Right Riemann Sums.
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#### Riemann Sums

For Teachers 11th - 12th
Students explore the concept of Riemann Sums.  In this Riemann Sums lesson, students find left and right Riemann Sums of the cubic function.  Students find the Riemann sum of the cubic function on the interval 0 to 3.
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#### Exploring the Area Under a Curve

For Teachers 9th - 12th Standards
Using TI-89, mathematicians explore and investigate Riemann sums to estimate the area under the graphs of intervals by drawing and illustrating rectangles. They review and practice the concepts of summation notation and area formulas to...
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#### Riemann Sum Investigation

For Teachers 10th - 12th
Students investigate left, midpoint and right Riemann sums. In this calculus lesson, students use trapezoidal sums to approximate areas. They use the computer lab and GeoGebra.
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#### Worksheet 8 - Spring 1996

For Students 11th - Higher Ed
In this math worksheet, students sketch the graphs of the functions 1/x 2 and 1/(x2 − 1) over the interval [2, ∞). They rewrite the series using the Riemann sum.
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#### InteGreat

For Teachers 9th - Higher Ed Standards
Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and midpoint...
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#### Limit Definition of the Definite Integral

For Students Higher Ed
In this integral worksheet, students compute the Riemann sum that is defined by the given equation. They use a step by step process for computing an integral.
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#### Evaluating Definite Integral Using Riemann Sums

For Students Higher Ed
In this integral learning exercise, students use the Riemann Sum to estimate the value of a function. This two-page learning exercise contains two problems.
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#### Summation Notation, Area, Riemann Sums

For Students 11th - Higher Ed
In this math worksheet, students explore the concepts of summation notation, area, and Riemann sums. Then they apply them for the word problems.
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#### Lab 2: Euler's Method and Riemann's Sums

For Students Higher Ed
In this Euler's Method and Riemann's Sum worksheet, students identify the best situation in which to use Euler's Method and Riemann's Sum. They identify the initial value of a problem and use the accumulation formula to determine the...
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#### Errors in Riemann Sums

For Students Higher Ed
In this Riemann Sums worksheet, students use the Riemann Sums method to approximate the area under the curves. This two-page worksheet contains three problems.
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#### Lesson #94 Exact Area Under a Curve

For Teachers 10th - 12th
Students research Riemann Sums. In this area lesson students listen to a lecture on finding the area under a curve. Links to a song about Riemann Sums, and a song titled "Failing My Calculus" are included.
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#### Riemann Sums and the Definite Integral

For Students Higher Ed
In this integral worksheet, students use Riemann sums to estimate their answers. They answer story (or word) problems about distance/speed. Students are given a defined interval and use the Riemann sum to find the endpoints of the graph....
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#### Riemann Sums and Error Stacks

For Students Higher Ed
In this Riemann sums worksheet, students use accumulation to find the estimate for the area of a given shape. Students use Riemann sums to estimate the area under the curves and error stacks to bound the error of their approximation....
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#### Riemann Sums

For Students 11th - Higher Ed
In this Riemann Sums worksheet, students solve and complete 12 various types of problems. First, they find the given sum for each. Then, students use the upper and lower sums to approximate the area of the given region using the...
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#### Sum of Rectangle Areas to Approximate Integrals

For Teachers 11th - 12th
Students explore the concept of approximating integrals.  In this approximating integrals lesson plan, students approximate integrals by finding the area of rectangles.  Students use a graphing calculator to find the left, right, and...
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#### Riemann Sums

For Students Higher Ed
In this college calculus worksheet, students write the Riemann Sum for the indicated partition and sub-intervals.  The two page worksheet contains five problems.  Answers are not included.
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#### Riemann Sums

For Students 12th - Higher Ed
In this calculus worksheet, students solve prolbem in which they estimate double integrals by using Riemann sums. The three page worksheet contains four questions. Answers are not included.
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#### Approximating Integrals with Riemann Sums

For Teachers 9th - 12th
Students practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger.
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#### Finding Area Using Geometry, Integrals, and Riemann Sums

For Students 11th - Higher Ed
In this area worksheet, learners calculate area in five problems using geometry and integrals and find patterns using Riemann sums in one problem.