EngageNY
The Volume Formula of a Sphere
What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...
Curated OER
Cross-Curricular Games
Learners participate in exploring and examining several cross-curricular, hands-on games that encourage active learning and exercise at the same time. They assess games like Freeze Tag, Parts of Speech games and a healthy heart game, etc.
College Board
2009 AP® Calculus BC Free-Response Questions Form B
Let 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...
Curated OER
Air Resistance and Friction
Physics learners experiment with three laboratory activities to learn about air resistance and friction. First, they use a hair dryer to move different sized spheres to determine the relationship between cross-sectional area and air...
Cornell University
Constructing and Visualizing Topographic Profiles
Militaries throughout history have used topography information to plan strategies, yet many pupils today don't understand it. Scholars use Legos and a contour gauge to understand how to construct and visualize topographic profiles. This...
Curated OER
Chopping Cubes
Middle schoolers work in small groups to make various geometric solids with Play-Doh. They use fishing line to make cuts and observe the shapes of the cross-sections. Pupils complete an assessment in which they answer questions such as:...
Teach Engineering
Load It Up!
See how a marshmallow can hold up a bridge load. Teams take a closer look at the design of bridge piers. They determine the types of loads that might affect a bridge, and, using that information, they calculate the needed cross-sectional...
Curated OER
Designing a Hiking Trail
Put your students' map skills to the test with this engaging cross-curricular project. Given the task of developing new hiking trails for their local community, young cartographers must map out beginner and intermediate...
Illustrative Mathematics
Distance across the channel
Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...
National Park Service
Leave it to Beavers
Many people know cats mark their territories by rubbing the back of their necks to leave a scent, but not many people know beavers also leave a scent to mark their territories. During the first activity of two, scholars use their noses...
Physics Classroom
Resistance Ranking Tasks
Resistance is not futile ... it is voltage divided by current. Scholars apply their knowledge to a series of ranking puzzles. First, they consider wires of varying lengths and then wires of varying cross-sectional areas. Finally, they...
EngageNY
End-of-Module Assessment Task: Grade 7 Mathematics Module 6
Determine the level of understanding within your classes using a summative assessment. As the final lesson in a 29-part module, the goal is to assess the topics addressed during the unit. Concepts range from linear angle relationships,...
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.
Curated OER
The Pyramid: Estimating Volumes
In this estimating volumes learning exercise, students determine the area and volume of pyramids. They draw a cross-section of the pyramid. This four-page learning exercise contains approximately 20 problems.
Concord Consortium
Maximum Volumes
It's great to have a large swimming pool. An interesting performance task asks learners to optimize the volume of pools for a given surface area. They consider four different shapes for pools and find the maximum volume for each pool.
Mathed Up!
Volume of Prism
The area is essential to volume. As part of the review for the General Certificate of Secondary Education math assessment, a helpful video covers how to find the volume of several common 3-D figures. Pupils use the general volume formula...
Curated OER
Splitting the Penstock
Students investigate the best way to calculate the measurements of an area. In this geometry lesson, students relate a large circle to a cylinder and its measurements. They use PVC pipes to gain hands on experience as they calculate the...
Curated OER
Cookie Topography
Learners construct a cross section diagram showing elevation changes on a "cookie island." Using a chocolate chip cookie for an island, they locate the highest point in centimeters on the cookie and create a scale in feet. After tracing...
Curated OER
Solids of Revolution - Disks
Young mathematicians solve the volume using the disk method in this calculus lesson plan. They revolve a graph around the x-axis and calculate the volume. They use the TI to see the revolving around the x-axis and create a virtual cross...
Curated OER
Hubble Spies Colliding Asteroids!
In this colliding asteroids instructional activity, students are given the equation to determine the collision time for asteroids. Students use this equation to solve 4 problems including finding the area of a cross-section through the...
Curated OER
Creating a Rock Sequence
In this rock sequence worksheet, students will sequence a list of 10 historical events according to the principle of superposition. Students will label these events on a cross-section diagram.
Curated OER
Solid Rocket Boosters-II
In this solid rocket boosters activity, learners solve 2 problems using a grid showing a cross section of a proposed solid rocket booster. Students complete the grid and shade the rings of combustion in 15-second step intervals. They...
Alabama Learning Exchange
How Old Is That Tree?
Fifth graders study environmental changes by examining the annual rings of a cross-section of a tree trunk. They access websites to complete a worksheet on the parts of a tree. They count the annual rings on a tree slice while observing...
Curated OER
Gettysburg Rocks Recycle to Win
Eighth graders use a geologic cross section to study the rock cycle of the Gettysburg battlefield. In this rock cycle activity, 8th graders connect the rock cycle and continental rifting.