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Lesson Plan
Mathematics Assessment Project

Representing 3-D Objects in 2-D

For Teachers 9th - 12th Standards
How  does the shape of the surface of water in a container change as water leaks out? After tackling this question, learners take part in a similar activity with more complex figures.
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Lesson Plan
EngageNY

Volume and Cavalieri’s Principle

For Teachers 11th - 12th Standards
Take a slice out of life. The ninth section in a series of 23 introduces classmates to Cavalieri's principle using cross sections of a cone and stacks of coins. Class members participate in a discussion using pyramids and how Cavalieri's...
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AP Test Prep
College Board

2011 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...
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AP Test Prep
College Board

2009 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
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...
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AP Test Prep
College Board

2008 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
This is integral to the test. Pupils realize that every question in the released free-response items from the 2008 AP® Calculus exam Form B requires integration. By reviewing the additional resources, scholars learn how important it is...
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AP Test Prep
College Board

2009 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Get a free peek into a calculus exam. Released free-response items from the AP® Calculus AB exam provide teachers and pupils examples of how topics may appear. The six questions cover topics such as growth rates, volumes of rotations,...
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Unit Plan
Arbor Day Foundation

Trees are Terrific...Inside and Out!

For Teachers 4th - 6th Standards
Trees are the star of a three-step unit celebrating Arbor Day. Step one takes an in-depth look into the structure of a tree, the process of photosynthesis, and the benefits of the leafy giants. Step two challenges scholars to create a...
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Assessment
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CCSS Math Activities

Smarter Balanced Sample Items: 7th Grade Math – Target E

For Teachers 7th Standards
How well do your classes understand scale? You'll certainly know after they answer the set of eight questions from an informative and helpful presentation. Questions include items from coordinate geometry, similar triangles, and scale...
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Unit Plan
Mathematics Vision Project

Module 7: Modeling with Geometry

For Teachers 9th - 12th Standards
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.
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Interactive
Shodor Education Foundation

Cross Section Flyer

For Students 9th - 12th Standards
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.
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Interactive
CK-12 Foundation

Volume by Cross Section: Volume of the Cone

For Students 11th - Higher Ed
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....
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Lesson Plan
Cornell University

Constructing and Visualizing Topographic Profiles

For Teachers 6th - 12th Standards
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...
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Assessment
EngageNY

End-of-Module Assessment Task: Grade 7 Mathematics Module 6

For Students 7th Standards
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,...
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Unit Plan
Mathematics Vision Project

Module 5: Modeling with Geometry

For Students 9th - 12th Standards
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...
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Lesson Plan
Teach Engineering

Designing Bridges

For Teachers 6th - 8th Standards
Introduces your class to the types of loads experienced by a bridge. Groups calculate the ultimate load combinations to determine the maximum load requirement. Using this information, builders then determine the amount of material they...
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Workbook
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University of Utah

Geometry Part 2: Measurement in 2- and 3-Dimensions, Plane Sections of Solids

For Students 7th Standards
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...
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Assessment
Mathematics Assessment Project

Fearless Frames

For Students 7th - 9th Standards
Show class members how to connect algebra to geometry. A high school assessment task has pupils determine volumes of two different containers given limitations on material for box frames. Pupils then write a paragraph on advice people...
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Lesson Plan
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NASA

Next Generation Spacecraft—Orion

For Teachers 9th - 12th Standards
What is the cross-sectional area of the Orion spacecraft? Groups work together to estimate the area of a cross section of the Orion spacecraft by first counting the number of grids a scale drawing covers. Pupils also employ a method...
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Assessment
EngageNY

End-of-Module Assessment Task - Geometry (module 3)

For Teachers 9th - 10th Standards
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.
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Lesson Plan
EngageNY

General Pyramids and Cones and Their Cross-Sections

For Teachers 9th - 10th Standards
Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...
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Lesson Plan
EngageNY

How Do 3D Printers Work?

For Teachers 9th - 10th Standards
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...
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Lesson Plan
EngageNY

General Prisms and Cylinders and Their Cross-Sections

For Teachers 9th - 10th Standards
So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the instructional activity develops the definition of a general cylinder. Scholars continue on to develop a graphical...
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Unit Plan
Texteam Geometry Institute

Geometry for the High School Classroom

For Teachers 9th - 12th
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....
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Activity
Houston Area Calculus Teachers

Area and Volume

For Students 11th - Higher Ed
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...