Shodor Education Foundation
Cross Section Flyer
Scholars see cross sections come to life using an app to investigate cross sections of three-dimensional solids. They look at prisms, pyramids, cylinders, cones, and double cones.
CK-12 Foundation
Volume by Cross Section: Volume of the Cone
Discover another way to find the volume of a cone. Pupils explore how the area of a cross section changes as it moves through a cone. The interactive uses that knowledge to develop the integral to use to find the volume of the cone....
EngageNY
General Prisms and Cylinders and Their Cross-Sections
So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the lesson develops the definition of a general cylinder. Scholars continue on to develop a graphical organizer for the...
Curated OER
Cross Sections
Young visual learners explore different cross sections of 3-dimensional objects. First, cross sections of cubes are explored by using an interactive flash activity. This is then extended by looking at cross sections of spheres,...
Mathematics Vision Project
Module 7: Modeling with Geometry
Model good modeling practices. Young mathematicians first learn about cross sections and solids of revolution. They then turn their attention to special right triangles and to the Laws of Sine and Cosine.
University of Utah
Geometry Part 2: Measurement in 2- and 3-Dimensions, Plane Sections of Solids
What kind of tree does a math teacher climb? A geometry! Here is a lesson that includes all the geometry resources you could ever wish for in one comprehensive workbook. Class members demonstrate what they have learned by determining the...
Curated OER
Tree Cookies!
"Tree Cookies!" is a delicious little presentation designed to introduce upper elementary or middle school botanists to the anatomy of a tree trunk. The cambium, phloem, xylem, and other vital structures are identified and defined. Two...
Illustrative Mathematics
Use Cavalieri’s Principle to Compare Aquarium Volumes
Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required. From calculating the volume of a composite shape through the abstract...
EngageNY
End-of-Module Assessment Task - Geometry (module 3)
It's test time! Determine your class's understanding of the topics of volume and cross sections with a thorough assessment on volume, area, and geometric shapes.
Mathematics Vision Project
Module 5: Modeling with Geometry
Solids come in many shapes and sizes. Using geometry, scholars create two-dimensional cross-sections of various three-dimensional objects. They develop the lesson further by finding the volume of solids. The module then shifts to finding...
EngageNY
How Do 3D Printers Work?
If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...
EngageNY
The Volume of Prisms and Cylinders and Cavalieri’s Principle
Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not...
Houston Area Calculus Teachers
Area and Volume
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...
Curated OER
Solids of Revolution - Disks
Young mathematicians solve the volume using the disk method in this calculus lesson. 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
Solid Rocket Boosters-II
For this solid rocket boosters worksheet, students 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...
Curated OER
Visualizing Solids of Revolution - Washers
Students solve the area of a cross section. In this calculus lesson plan, students solve areas rotated and bounded by two functions. They solve using the washer method.
Curated OER
Surface Area of Prism
Tenth graders are provided instructions, including a video, on calculating the surface area of a prism. The one-page interactive worksheet contains two worked questions. Answers are included.
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:...
Curated OER
Applications of Hyperbolas
In this hyperbola worksheet, 10th graders solve and complete 6 different problems. First, they determine the cross-section of a hyperbolic paraboloid curve. Then, students find where the cone intersects the ground in hyperbola as...
Curated OER
Planet Earth in Cross Section
Young scholars will examine the layers of the Earth. In this geology lesson, students create a scale model of the Earth's interior using cash register tape. They will determine the percentage of error in the scale compared to the actual...
CK-12 Foundation
Volume by Disks: The Vase Case
Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...
Curated OER
Poly-Mania
This hands-on lesson plan takes young geometers on a tour of 2D polygons and 3D polyhedrons. After exploring different web resources and discussing geometric shapes, small groups construct models of polyhedrons using bendable straws....
Texteam Geometry Institute
Geometry for the High School Classroom
What does it mean for apples to have chirality? This and other explorations in geometry, such as tiling the plane, boxing a tetrahedron, and investigating Euclid's Characteristic, are included in this resource on Euclidean geometry....
Curated OER
Solid Rocket Boosters
In this rocket worksheet, students calculate the burn rate for solid rocket boosters depending on exposed fuel area and burn depth. This worksheet has 2 problems to solve.