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\n\n38\nItems in Topic\n\n
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\nLesson Planet Curated\n
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\nAP Calculus AB\n

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\n\nFor Students\n\n11th - 12th\n
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\nPrepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...\n
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\n\n73\nItems in Unit\n\n
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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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\n\n28\nItems in Unit\n\n
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\n\"TeachEngineering:\n\n
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\nTeachEngineering: Android Acceleration Application\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nIntroduce young engineers to the software development design process used in app building. After watching a video tutorial, groups are challenged to build an accelerometer app for an Android device and design an app utilizing the GPS...\n
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Instructional Video16:11
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\nFinding The Area Under a Curve Using Rectangles\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nHere's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of...\n
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Lesson Plan
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\n\"Area\n\n
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\nCurated OER\n
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\nArea Under A Curve\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nCalculus students use the derivative and integral to solve problems involving areas. They calculate the area under a curve as they follow a robot off road making different curves along the drive, using Riemann Sums and...\n
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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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Instructional Video5:38
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\n\"Approximating\n\n
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\nBrightstorm\n
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\nApproximating Area Using Rectangles\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nFinding area using rectangles—isn't that a little too simplistic for a calculus course? Viewers learn how to approximate area under a curve using rectangles in the first installment of a seven-part video series on the definite integral....\n
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Lesson Plan
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\n\"Finding\n\n
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\nFinding the Area Under A Curve with Random Probability\n

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\n\nFor Teachers\n\n11th - Higher Ed\n
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\nStudents explore the concept of area under a curve. In this area under a curve lesson, students find the area under a curve using the Monte Carlo method using random points and probability. Students calculate the area under the same...\n
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\nCurated OER\n
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\nThe Definite integral and Area Under a Curve\n

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\nStudents define integrals and explore how they relate to the areas under a curve. In this calculus instructional activity, students solve word problems relating curves and integrals. They sing a song to help them remember the formula for...\n
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\n\"Filling\n\n
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\nFilling The Urn\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nStudents calculate the area under a curve. In this calculus lesson,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.\n
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\nCurated OER\n
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\nLesson #94 Exact Area Under a Curve\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nYoung scholars research Riemann Sums. In this area instructional activity 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.\n
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Instructional Video14:56
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\n\"Area\n\n
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\nCorbett Maths\n
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\nArea under a Graph\n

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\n\nFor Students\n\n8th - 12th\n\nStandards\n
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\nWhat? The calculation of area is a linear distance? A short video shows how to use the areas of simple polygons to estimate the area under a graph. Pupils divide the area under a curve into figures to easier calculate the area. Given...\n
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\nShodor Education Foundation\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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AP Test Prep11:21
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\n\"Calculus\n\n
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\nFlipped Math\n
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\nCalculus AB/BC - Exploring Accumulation of Change\n

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\nAdd up area to find total change. Pupils learn what it means to find the area under a curve and how to calculate it geometrically. They first find the accumulation of change given a rate of change function. Scholars then apply that...\n
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Interactive
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\n\"Area\n\n
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\nArea Sums: Estimation with Rectangles\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nThe more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.\n
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Instructional Video12:39
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\nWhat Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9\n

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\nIt seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.\n
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AP Test Prep
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\n\"2010\n\n
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\nCollege Board\n
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\n2010 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nKeep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...\n
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\n\nGet Free Access\n\nSee Review\n
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AP Test Prep
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\n\"2009\n\n
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\nCollege Board\n
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\n2009 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nLet them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...\n
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AP Test Prep
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\n\"2003\n\n
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\nCollege Board\n
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\n2003 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nBe integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...\n
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AP Test Prep
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\n\"2003\n\n
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\nCollege Board\n
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\n2003 AP® Calculus AB Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nGet a better grasp of the intended content. The six free-response questions provide insight into the purpose of the AP® Calculus content. Two questions have real-world context while the remaining are void of context. The items range from...\n
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AP Test Prep
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\n\"2008\n\n
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\nCollege Board\n
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\n2008 AP® Calculus AB Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nHow would those items score? The resource provides pupils an opportunity to answer actual free-response questions and determine their scores. Items from the AP® Calculus AB exam from the 2008 administration demonstrate how topics appear...\n
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AP Test Prep
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\n\"2007\n\n
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\nCollege Board\n
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\n2007 AP® Calculus AB Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nWhat do the questions look like? Six free-response questions provide pupils with knowledge of how calculus topics appear on the AP® Calculus exam. The questions involve calculator and non-calculator problems by providing mathematical and...\n
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\n\nGet Free Access\n\nSee Review\n
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AP Test Prep
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\n\"2007\n\n
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\nCollege Board\n
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\n2007 AP® Calculus BC Free-Response Questions Form B\n

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\n\nFor Students\n\n10th - 12th\n
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\nThere is just a single real-world problem. Released free-response items from the 2007 AP® Calculus BC Form B contains only one real-world question. The question involves rate of change of wind chill scenario. The mathematical problems...\n
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AP Test Prep
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\n\"1998\n\n
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\n1998 AP® Calculus AB Free-Response Questions\n

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\n\nFor Students\n\n10th - 12th\n
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\nTake a peek into the exam. Released items from the Calculus AB exam provide pupils insight into how questions appear on the exam. The six questions range from finding the area under a curve and the volume of the revolution to working...\n
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