Curated OER
Area of Curve
In this calculus activity, students calculate the area of a curve bounded between two regions. There are 2 questions asking for the area and length of a curve.
Curated OER
The Region Between Two Curves
Learners find the area of a region between two curves. They integrate functions such as sin(x) and cos(x) on a given interval and find the area bounded by the two functions. Pupils use their TI-89 to aid them in finding the bounded...
Curated OER
Area Under A Curve
Young scholars investigate the concept of finding the areas under curves while examining the graphing for inscribed and circumscribed rectangles. Finally, students compute the area under the curve by using the left-hand endpoints. The...
Curated OER
Lesson #94 Exact Area Under A Curve
Students examine diagrams to determine the exact area under a curve. Using given formulas, they identify the area of the curve using the x and y-axis, as well as rectangles. As a class, students sing a song called "Failing My Calculus"...
Curated OER
Area Between Two Curves
Students investigate the concept area that is found between two curves. They find the area in the top and bottom curve and then examine the differences. The examples can be used for direct instruction and to provide a guide for helping...
Shodor Education Foundation
Overlapping Gaussians
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...
Curated OER
Matrices
In this calculus learning exercise, learners practice solving equations of area and integrals. There are 14 multi-step problems.
Curated OER
Area Under A Curve
Calculus young scholars 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...
Curated OER
Processing Satellite Images
Young scholars comprehend the meaning of "pixel." They recognize patterns using pixels. Students observe how land use can be determined from a pixel. They measure off a 30 x 30-meter area to show the size of the surface area of one...
Curated OER
Ice Cream Lab
I scream, you scream, we all scream for ice cream! Even high schoolers enjoy making ice cream. This laboratory exercise has them record the temperature changes throughout the process of liquid becoming solid, graph the results, and...
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
Curve Ball
Learners explore the concept of parabolas by collecting quadratic data on a bouncing ball as it is falling using a motion detector. They plot the data and determine the equation of the quadratic in vertex form, then determine the values...
Curated OER
Shapes and Their Insides
Learners follow a series of instructions for drawing and coloring different shapes in order to learn the difference between the perimeter and area of a polygon. Then they are asked to find the perimeter and area of a 3x4 rectangular...
Flipped Math
Calculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area
Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...
Curated OER
Area Between Two Curves
Students engage in a instructional activity that is concerned with the concept of computing the area between 2 curves with respect to the x and y axis. They concentrate on using positive and negative intervals and find the curve while...
Curated OER
Areas Between the Curves
In this algebra worksheet, students solve and complete 12 problems involving sine, cosine, area and function.
Curated OER
The Bell Curve
Learners are introduced to the concepts of the normal curve, skewness and the standard deviation. They discuss how the normal distribution has been used and misused to support conclusions.
Illustrative Mathematics
Designs
A resource that makes for excellent group work as students explore the area and perimeter of different complex designs made up of squares and circles. The commentary gives a clear definition of perimeter, but suggests that group members...
College Board
2007 AP® Calculus BC Free-Response Questions
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...
College Board
2009 AP® Calculus AB Free-Response Questions
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...
Curated OER
AP Calculus Practice Exam BC Version: Part B
In this calculus worksheet, students solve 17 multiple choice problems. Students find limits, summations, and derivatives of functions. Students find the area of an enclosed region between two curves.
Houghton Mifflin Harcourt
Unit 7 Math Vocabulary Cards (Grade 6)
Thirty-eight flashcards make up a set designed to reinforce math vocabulary. Two types of cards can be found here; a word card in bold lettering, and a corresponding definition card that offers a labeled example. Terms include area,...
Mathematics Assessment Project
Sports Bag
Why not give surface area of cylinders a sporting chance in your classroom? A strategic problem-solving task requires pupils to consider the net of a cylinder. Individuals must determine the sizes of the pieces needed to make a sports...
Curated OER
The Definite integral and Area Under a Curve
Students define integrals and explore how they relate to the areas under a curve. In this calculus lesson, students solve word problems relating curves and integrals. They sing a song to help them remember the formula for the area under...