CK-12 Foundation
Trapezoidal and Midpoint Approximations: Area of a Skirt
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...
Flipped Math
Calculus AB/BC - Approximating Areas with Riemann Sums
There 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,...
Curated OER
Exploring the Area Under a Curve
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...
Curated OER
Area Under A Curve
Calculus 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 Trapezoidal rules...
Shodor Education Foundation
InteGreat
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...
Curated OER
Roller Coaster Robot
Learners calculate the area under a curve. In this calculus lesson, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
EngageNY
What Is Area?
What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and upper...
Curated OER
A.P. Calculus Integration Test
In this A.P. Calculus worksheet, learners complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are...
EngageNY
Normal Distributions (part 2)
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.
CK-12 Foundation
Method of Cylindrical Shells
Approximate the volume of a solid of revolution. Using a method similar to approximating the area under a curve, pupils investigate the volume of a solid of revolution. The learners use a given definite integral to find the volume of...
Curated OER
Estimating Pi as a Length
In this pi learning exercise, students evaluate the curve of a quarter of a circle. They analyze the length of the curve, and explain that if the area under the curve is equal to pi, the length of the curve above is also equal to pi....
EngageNY
Using a Curve to Model a Data Distribution
Show scholars the importance of recognizing a normal curve within a set of data. Learners analyze normal curves and calculate mean and standard deviation.
Curated OER
Errors in Riemann Sums
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.
Teach Engineering
Exploring Acceleration with an Android
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.
Shodor Education Foundation
InteGreat!
Take a great look at integration! Young scholars use an interactive to learn how to integrate a function. Learners input a function and view the integral as well as see a graphical representation.
Curated OER
Z-Scores
Learners solve problems by identifying the percent of area under the curve. For this statistics lesson, students discuss z-scores as they calculate the different percentages under the bell curve. They calculate the standard deviation.
Curated OER
Trapezoid and Midpoint Rule
Students solve problems of area using the trapezoid and midpoint rule. In this calculus lesson, students take the derivative of the functions as they approximate the area under a curve. They calculate the exact area using the area formula.
Curated OER
Using Riemann Sums
In 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...
Curated OER
Numerical Methods of Integration
Learners review Riemann Sums with rectangles, used to approximate the area under a curve. They listen as the teacher introduces the Trapezoidal Rule to approximate the area under a curve. Students use Simpson's Rule to find the area...
Curated OER
Continuous Probability Distributions
In this continuous probability distribution worksheet, students identify discrete and continuous distributions. They calculate the linear combination of the independent normal random variable and determine probabilities using exponential...
EngageNY
Modeling Riverbeds with Polynomials (part 2)
Examine the power of technology while modeling with polynomial functions. Using the website wolfram alpha, learners develop a polynomial function to model the shape of a riverbed. Ultimately, they determine the flow rate through the river.
Curated OER
Calculating Total Radiation Dosages at Mars
In this Mars radiation worksheet, students use data from the Mars Radiation Environment Experiment to solve 4 problems. They determine the total radiation dosage during a specific period of time, they determine the dosage during the...
Curated OER
Worksheet 4
For this math worksheet, students define the details of a definite integral and how it is used. They also apply math to physics to compute how work for lift is calculated.
Curated OER
Integration Unit: Riemann Sum
Students investigate Riemann Sums. In this calculus lesson, students solve problems involving Riemann sums and Right Riemann Sums.