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\nAP Calculus AB Unit 6: Integration and Accumulation of Change\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nThe 14 lessons in the AP Calculus AB Unit 6: Integration and Accumulation of Change use informative videos to introduce the topic of each lesson and model procedures. Each resource packet includes a video, worksheets, practice solutions,...\n
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Lesson Plan
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\n\"Riemann\n\n
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\nCurated OER\n
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\nRiemann Sums\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nStudents 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.\n
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\n\nGet Free Access\n\nSee Review\n
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AP Test Prep28:02
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\n\"Calculus\n\n
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\nFlipped Math\n
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\nCalculus AB/BC - Approximating Areas with Riemann Sums\n

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\n\nFor Students\n\n10th - 12th\n
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\nThere are several ways to estimate the area if the curve does not create nice geometric figures. The presenter introduces the idea of using areas of rectangles to estimate the area under the curve. Pupils use four types of Riemann Sums,...\n
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Worksheet
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\n\"Errors\n\n
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\nCurated OER\n
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\nErrors in Riemann Sums\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Riemann Sums instructional activity, students use the Riemann Sums method to approximate the area under the curves. This two-page instructional activity contains three problems.\n
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\n\"Riemann\n\n
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\nRiemann Sums and the Definite Integral\n

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\n\nFor Students\n\nHigher Ed\n
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\nFor 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...\n
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Worksheet
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\n\"Riemann\n\n
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\nRiemann Sums and Error Stacks\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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....\n
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Worksheet
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\n\"Connecting\n\n
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\nConnecting Riemann Sums to the Definite Integrals\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this math learning exercise, learners examine the relationships between Riemann sums and definite integrals. They define the Riemann sums and find area using them.\n
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\n\"Evaluating\n\n
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\nCurated OER\n
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\nEvaluating Definite Integral Using Riemann Sums\n

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\nIn this integral learning exercise, students use the Riemann Sum to estimate the value of a function. This two-page learning exercise contains two problems.\n
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Worksheet
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\n\"Summation\n\n
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\nCurated OER\n
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\nSummation Notation, Area, Riemann Sums\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nFor this math worksheet, learners explore the concepts of summation notation, area, and Riemann sums. Then they apply them for the word problems.\n
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Lesson Plan
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\n\"Exploring\n\n
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\nCurated OER\n
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\nExploring the Area Under a Curve\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nUsing 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...\n
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\n\"InteGreat\n\n
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\nInteGreat\n

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\n\nFor Teachers\n\n9th - Higher Ed\n\nStandards\n
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\nHands-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...\n
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Lesson Plan
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\n\"Integration\n\n
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\nCurated OER\n
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\nIntegration Unit: Riemann Sum\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nStudents investigate Riemann Sums. In this calculus lesson, students solve problems involving Riemann sums and Right Riemann Sums.\n
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Worksheet
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\n\"Riemann\n\n
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\nRiemann Sums\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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. \n
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\n\"Riemann\n\n
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\nRiemann Sums\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn 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.\n
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AP Test Prep
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\n\"Approximation\n\n
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\nCollege Board\n
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\nApproximation\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nSometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...\n
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Activity
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\n\"Collecting\n\n
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\nHouston Area Calculus Teachers\n
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\nCollecting Driving Data\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nGive AP Calculus classes the opportunity to check the accuracy of their calculations! A calculus activity involves the collection of data, the application of mathematics, and the analysis of the accuracy of results. Young mathematicians...\n
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Worksheet
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\n\"Math\n\n
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\nCurated OER\n
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\nMath 155 Worksheet 11\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this college level calculus worksheet, students use Riemann Sums to evaluate the given integrals and compare the answer to the limit.  The two page worksheet contains four problems.  Answers are not provided. \n
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Worksheet
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 8 - Spring 1996\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn 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.\n
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Worksheet
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\n\"Understanding\n\n
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\nCurated OER\n
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\nUnderstanding and Computing Riemann Sums\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Riemann sum worksheet, students use the Riemann sum to determine the volume of a square pyramid and the estimates of area around a circle. This four-page worksheet contains 18 problems.\n
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\n\"Finding\n\n
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\nCurated OER\n
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\nFinding Area Using Geometry, Integrals, and Riemann Sums\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this area learning exercise, students calculate area in five problems using geometry and integrals and find patterns using Riemann sums in one problem.\n
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\n\"Limit\n\n
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\nCurated OER\n
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\nLimit Definition of the Definite Integral\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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.\n
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Worksheet
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\n\"Lab\n\n
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\nCurated OER\n
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\nLab 3: Length as an Application of Integration\n

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\n\nFor Students\n\nHigher Ed\n
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\nFor this integration worksheet, students graph a function that is a quarter circle curve. They calculate lengths of curves by approximation using the distance formula. Students use a computer program to calculate the approximation of the...\n
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Worksheet
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\n\"Using\n\n
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\nCurated OER\n
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\nUsing Riemann Sums\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn the Riemann sums worksheet, students use Riemann sums to estimate the area under a curve. They calculate intervals and subintervals. Students create a graph picturing the intervals. This seven-page worksheet contains explanations...\n
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Worksheet
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\n\"Area,\n\n
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\nCurated OER\n
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\nArea, Riemann Sums and Summation Notation\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this math worksheet, students solve four problems written in sigma notation. They use Riemann sums to find the areas in four problems involving rectangles. Students work in groups to compute the Riemann sum approximations for rectangles.\n
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