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  • CCSS.Math.Content.HSG-GMD.A.3
2D Representations of 3D Objects
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This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Floaters and Sinkers
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Educational Use
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Students are introduced to the important concept of density with a focus is on the more easily understood densities of solids. Students use different methods to determine the densities of solid objects, including water displacement to determine volumes of irregularly-shaped objects. By comparing densities of various solids to the density of water, and by considering the behavior of different solids when placed in water, students conclude that ordinarily, objects with densities greater than water sink, while those with densities less than water float. Then they explore the principle of buoyancy, and through further experimentation arrive at Archimedes' principle that a floating object displaces a mass of water equal to its own mass. Students may be surprised to discover that a floating object displaces more water than a sinking object of the same volume.

Subject:
Engineering
Physics
Material Type:
Full Course
Unit of Study
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
Date Added:
09/18/2014
Doctor's Appointment
Unrestricted Use
CC BY
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The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Evaluating Statements About Enlargements (2D and 3D)
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This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Floaters and Sinkers: Lesson
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Educational Use
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This lesson introduces students to the important concept of density. The focus is on the more easily understood densities of solids, but students can also explore the densities of liquids and gases. Students devise methods to determine the densities of solid objects, including the method of water displacement to determine volumes of irregularly-shaped objects. By comparing densities of various solids to the density of water, and by considering the behavior of different solids when placed in water, students conclude that ordinarily, objects with densities greater than water will sink, while those with densities less than water will float. Density is an important material property for engineers to understand.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
Date Added:
09/18/2014
Geometry Module 3:  Extending to Three Dimensions
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CC BY-NC-SA
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Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume formulas for solids. The student materials consist of the student pages for each lesson in Module 3. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/03/2014
Who are the Northern Arapaho?
Conditional Remix & Share Permitted
CC BY-NC-SA
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Students will gain an understanding of the Northern Arapaho people located on the Wind River Reservation in Wyoming. In the accompanying lessons plans (found in the Support Materials), students will learn how the Northern Arapaho come to Wyoming, what are the Arapaho values, and why were Arapaho tribal names changed?

LEARNING OBJECTIVES:

Students will be able to evaluate what geographical places were used by the Arapaho people and understand how historical events changed the future for the Arapaho people.
Students will compare and contrast between their social and ceremonial structures.
Students will understand the hierarchy of the Arapaho Tribe.
Students will analyze how their social and ceremonial structures contribute to their cultural identity.

Subject:
English Language Arts
U.S. History
Material Type:
Activity/Lab
Lesson
Provider:
Wyoming PBS
Date Added:
09/17/2019
Determining Densities
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Educational Use
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Students use two different methods to determine the densities of a variety of materials and objects. The first method involves direct measurement of the volumes of objects that have simple geometric shapes. The second is the water displacement method, used to determine the volumes of irregularly shaped objects. After the densities are determined, students create x-y scatter graphs of mass versus volume, which reveal that objects with densities less than water (floaters) lie above the graph's diagonal (representing the density of water), and those with densities greater than water (sinkers) lie below the diagonal.

Subject:
Education
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
Date Added:
10/14/2015
G-GMD Volume Estimation
Unrestricted Use
CC BY
Rating

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Charles and Olivia are trying to estimate the volume of water that could be held by the figure shown below, which is 10 feet high and has a circular to...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
02/17/2014
Calculating Volumes of Compound Objects
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CC BY-NC-ND
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This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Advanced Calculus
Conditional Remix & Share Permitted
CC BY-NC-SA
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Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.

Note: this is a 57 MB PDF Document.

Subject:
Calculus
Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Individual Authors
Author:
Sternberg Shlomo and Lynn Loomis
Date Added:
02/16/2011
Scale Model Project
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Educational Use
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Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Subject:
Mathematics
Geometry
Measurement and Data
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Aaron Lamplugh
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
02/07/2017
Surface area and volume of Cube
Conditional Remix & Share Permitted
CC BY-NC-SA
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Here they learn Total Surface area, Lateral SUrface ARea and volume of Cube

Subject:
Mathematics
Material Type:
Lesson
Author:
K S Gireesh
Suchetha S S
Date Added:
01/15/2020
Modeling: Rolling Cups
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

Subject:
Functions
Geometry
Measurement and Data
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
G-GMD  The Great Egyptian Pyramids
Unrestricted Use
CC BY
Rating

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Subject:
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/06/2015
Above-Ground Storage Tank Design Project
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Educational Use
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At this point in the unit, students have learned about Pascal's law, Archimedes' principle, Bernoulli's principle, and why above-ground storage tanks are of major concern in the Houston Ship Channel and other coastal areas. In this culminating activity, student groups act as engineering design teams to derive equations to determine the stability of specific above-ground storage tank scenarios with given tank specifications and liquid contents. With their floatation analyses completed and the stability determined, students analyze the tank stability in specific storm conditions. Then, teams are challenged to come up with improved storage tank designs to make them less vulnerable to uplift, displacement and buckling in storm conditions. Teams present their analyses and design ideas in short class presentations.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Emily Sappington
Mila Taylor
Date Added:
09/18/2014
Surface Tension Lab
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Educational Use
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Students extend their understanding of surface tension by exploring the real-world engineering problem of deciding what makes a "good" soap bubble. Student teams first measure this property, and then use this measurement to determine the best soap solution for making bubbles. They experiment with additives to their best soap and water "recipes" to increase the strength or longevity of the bubbles. In a math homework, students perform calculations that explain why soap bubbles form spheres.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Chuan-Hua Chen
Date Added:
09/18/2014