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85 resources with the concept area under a curve

14:56
Lesson Planet

Area under a Graph

For Students 8th - 12th Standards
What? 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...
Lesson Planet

Integral Calculus

For Teachers 10th - Higher Ed
From derivatives to antiderivatives and back again. Building on the second instructional activity of the three-part series covering functions, learners explore the concept of an antiderivative. They connect the concept to the graph of...
7:42
Lesson Planet

Calculus, What Is It Good For?

For Students 11th - Higher Ed
Explore the meaning of differentiation and integration. A video lesson describes in detail what differentiating and integrating an equation means using the momentum and kinetic energy formulas. Progressing from a linear to a quadratic...
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Normal Distribution

For Students 6th - 12th Standards
Does the size of the bin matter? The resource allows pupils to explore the relationship between the normal curve and histograms. Learners view histograms compared to a normal curve with a set standard deviation. Using the interactive,...
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Overlapping Gaussians

For Students 9th - 12th Standards
Adjust the overlap to compare probabilities. Using sliders, learners adjust the shape of two Gaussian curves. The interactive calculates the area of the left tail for one curve and the right tail for the other. Pupils set the interactive...
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Trapezoidal and Midpoint Approximations: Area of a Skirt

For Students 11th - Higher Ed
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
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Properties of Definite Integrals

For Students 11th - Higher Ed
Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....
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Area Sums: Estimation with Rectangles

For Students 11th - Higher Ed
The 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.
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Properties of a Normal Distribution: Uniform Distributions

For Students 9th - 12th Standards
There's nothing normal about an extraordinary resource. Scholars change the dimensions of a normal distribution using a slider interactive. Determining the area under the graph gives probabilities for different situations.
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Interactive Calculus Tool

For Students 9th - 12th
It's almost like a graphing calculator, but it's completely free. An interactive allows users to graph a polynomial function on a coordinate plane. Additionally, the program can draw tangent lines, draw derivative curves, and calculate...
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Probability of Your Next Texting Thread

For Students 9th - 12th Standards
Are 13 texts in a thread normal? Given the mean and standard deviation of the number of texts in a person's text threads, pupils create a normal curve and label the mean and standard deviations. Class members then use their knowledge of...
20:45
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Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8

For Students 11th - Higher Ed
Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance helps...
12:38
Lesson Planet

What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9

For Students 11th - Higher Ed
It 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.
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Area Under the Normal Curve

For Students 9th - 12th Standards
Use more than one method to find the area under the normal curve. Given a data set with normal distribution, pupils calculate the proportion of scores between values two different ways—once by using a standard normal distribution table...
EngageNY

Normal Distributions (part 2)

For Students 10th - 12th Standards
From z-scores to probability. Learners put together the concepts from the previous lessons to determine the probability of a given range of outcomes. They make predictions and interpret them in the context of the problem.
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Exploring Acceleration with an Android

For Teachers 9th - 12th Standards
Small groups use rubber bands to accelerate an Android device along a track of books. They collect the acceleration data and analyze it in order to determine the device's velocity. 
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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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Are Kitchen Cabinets at the Correct Height? Lessons 1-5

For Teachers 9th - 12th Standards
Here's a not-so-normal unit on normal heights. Future statisticians anonymously collect class data on female heights, weights, and shoe sizes. They then analyze the data using normal distributions, z-scores, percentiles, and the...
Lesson Planet

Area and Volume

For Students 11th - Higher Ed
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created from the...
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Filling The Urn

For Teachers 9th - 12th Standards
Students calculate the area under a curve. In this calculus instructional activity,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.
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Definite Integrals and Area Under a Curve

For Teachers 11th - Higher Ed
Students explore the concept of definite integrals.  In this definite integrals lesson, students find the area between two curves.  Students use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.
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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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2007 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Provide a review for the exam so individuals don't tank. AP® provides the free-response questions for teachers to use to help their pupils prepare for the exam. The six BC questions from 2007 include regions bounded by functions, water...
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2009 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...