+
Interactive
CK-12 Foundation

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...
+
AP Test Prep28:02
1
1
Flipped Math

Calculus AB/BC - Approximating Areas with Riemann Sums

For Students 10th - 12th
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,...
+
Lesson Plan
Curated OER

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...
+
Lesson Plan
Curated OER

Area Under A Curve

For Teachers 9th - 11th
Calculus learners 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...
+
Lesson Plan
Shodor Education Foundation

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...
+
Lesson Plan
Curated OER

Roller Coaster Robot

For Teachers 10th - 12th
Students 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.
+
Lesson Plan
EngageNY

What Is Area?

For Teachers 9th - 10th Standards
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...
+
Worksheet
Curated OER

A.P. Calculus Integration Test

For Students 12th - Higher Ed
In this A.P. Calculus learning exercise, students 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...
+
Lesson Plan
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.
+
Interactive
CK-12 Foundation

Method of Cylindrical Shells

For Students 11th - Higher Ed
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...
+
Worksheet
Curated OER

Estimating Pi as a Length

For Students Higher Ed
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....
+
Lesson Plan
EngageNY

Using a Curve to Model a Data Distribution

For Teachers 9th - 12th Standards
Show scholars the importance of recognizing a normal curve within a set of data. Learners analyze normal curves and calculate mean and standard deviation.
+
Worksheet
Curated OER

Errors in Riemann Sums

For Students Higher Ed
For this Riemann Sums worksheet, students use the Riemann Sums method to approximate the area under the curves. This two-page worksheet contains three problems.
+
Activity
1
1
Teach Engineering

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. 
+
Interactive
Shodor Education Foundation

InteGreat!

For Students 11th - Higher Ed
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.
+
Lesson Plan
Curated OER

Z-Scores

For Teachers 9th - 11th
Students solve problems by identifying the percent of area under the curve. In this statistics lesson, students discuss z-scores as they calculate the different percentages under the bell curve. They calculate the standard deviation.
+
Lesson Plan
Curated OER

Trapezoid and Midpoint Rule

For Teachers 9th - 11th
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.
+
Worksheet
Curated OER

Using Riemann Sums

For Students Higher Ed
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...
+
Lesson Plan
Curated OER

Numerical Methods of Integration

For Teachers 11th - 12th
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...
+
Worksheet
Curated OER

Continuous Probability Distributions

For Students 10th - 12th
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...
+
Lesson Plan
EngageNY

Modeling Riverbeds with Polynomials (part 2)

For Students 10th - 12th Standards
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.
+
Worksheet
Curated OER

Calculating Total Radiation Dosages at Mars

For Students 9th - 12th
In this Mars radiation learning exercise, 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...
+
Worksheet
Curated OER

Worksheet 4

For Students 11th - Higher Ed
In this math learning exercise, 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.
+
Lesson Plan
Curated OER

Integration Unit: Riemann Sum

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