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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
Connect the Dots: Isometric Drawing and Coded Plans
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Educational Use
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Students learn about isometric drawings and practice sketching on triangle-dot paper the shapes they make using multiple simple cubes. They also learn how to use coded plans to envision objects and draw them on triangle-dot paper. A PowerPoint® presentation, worksheet and triangle-dot (isometric) paper printout are provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Emily Breidt
Jacob Segil
Date Added:
02/07/2017
Drawing Designs in Detail
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Students practice creating rudimentary detail drawings. They learn how engineers communicate the technical information about their designs using the basic components of detail drawings. They practice creating their own drawings of a three-dimensional block and a special LEGO piece, and then make 3D sketches of an unknown object using only the information provided in its detail drawing.

Subject:
Engineering
Education
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Benjamin S. Terry
Brandi Briggs
Denise W. Carlson
Stephanie Rivale
Date Added:
09/18/2014
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
Exploring Tessellations (Grades K-2)
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In this activity, learners repeat patterns in two and three dimensions to create tessellations. This activity combines the creativity of an art project with the challenge of solving a puzzle. This lesson features three investigations that are appropriate for varying grades and levels.

Subject:
Geometry
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010
Help Bill! Bioprinting Skin, Muscle and Bone
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Students operate mock 3D bioprinters in order to print tissue constructs of bone, muscle and skin for a fictitious trauma patient, Bill. The model bioprinters are made from ordinary materials— cardboard, dowels, wood, spools, duct tape, zip ties and glue (constructed by the teacher or the students)—and use squeeze bags of icing to lay down tissue layers. Student groups apply what they learned about biological tissue composition and tissue engineering in the associated lesson to design and fabricate model replacement tissues. They tangibly learn about the technical aspects and challenges of 3D bioprinting technology, as well as great detail about the complex cellular composition of tissues. At activity end, teams present their prototype designs to the class.

Subject:
Engineering
Life Science
Biology
Measurement and Data
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
A. L. Peirce Starling
Angela Sickels
Hunter Sheldon
Nicholas Asby
Ryan Tasker-Benson
Shayn M. Peirce
Timothy Allen
Date Added:
06/20/2017
The Hole in the Pole Gang
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CC BY-SA
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This article is about the latest remake of Jules Verne's popular 144-year-old novel Journey to the Center of the Earth that also provides links to the American Geologic Institute's (AIG) Educator Guide for using the movie (Journey to the Center of the Earth 3D) to interest students in geology and earth science.

Subject:
Environmental Science
Material Type:
Reading
Provider:
Ohio State University College of Education and Human Ecology
Provider Set:
Beyond Penguins and Polar Bears: An Online Magazine for K-5 Teachers
Author:
Carol Minton Morris
Date Added:
10/17/2014
Intro to 3D Bioprinting: Design, Applications and Limitations
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Students learn about the current applications and limitations of 3D bioprinting, as well as its amazing future potential. This lesson, and its fun associated activity, provides a unique way to review and explore concepts such as differing cell functions, multicellular organism complexity, and engineering design steps. As introduced through a PowerPoint® presentation, students learn about three different types of bioprinters, with a focus on the extrusion model. Then they learn the basics of tissue engineering and the steps to design printed tissues. This background information prepares students to conduct the associated activity in which they use mock-3D bioprinters composed of a desktop setup that uses bags of icing to “bioprint” replacement skin, bone and muscle for a fictitious trauma patient, Bill. A pre/post-quiz is also provided.

Subject:
Engineering
Life Science
Biology
Material Type:
Lesson
Provider:
TeachEngineering
Provider Set:
Lessons
Author:
A. L. Peirce Starling
Angela Sickels
Hunter Sheldon
Nicholas Asby
Ryan Tasker-Benson
Shayn M. Peirce
Timothy Allen
Date Added:
06/20/2017
Learn 3D Design Using Tinkercad
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This series of lessons will teach all of the key features in Tinkercad, a free, web-based 3D design platform. When you have finished the lessons you will have a comprehensive knowledge of how to design/draw in 3D. After that all you need is practice to improve your skills.

Subject:
Architecture and Design
Computer Science
Graphic Arts
Visual Arts
Electronic Technology
Graphic Design
Educational Technology
Elementary Education
Geometry
Material Type:
Activity/Lab
Diagram/Illustration
Interactive
Lesson
Lesson Plan
Teaching/Learning Strategy
Unit of Study
Author:
Tom Guellich
Date Added:
09/25/2018
Let’s Learn about Spatial Viz!
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Spatial visualization is the study of two- and three-dimensional objects and the practice of mental manipulation of objects. Spatial visualization skills are important in a range of subjects and activities like mathematics, physics, engineering, art and sports! In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided 12-question quiz. Following the lesson, students complete the four associated spatial visualization activities and then re-take the quiz to see how much their spatial visualization skills have improved.

Subject:
Mathematics
Material Type:
Lesson
Provider:
TeachEngineering
Author:
Emily C. Gill
Jacob Segil
Date Added:
02/07/2017
Let’s Take a Spin: One-Axis Rotation
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Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis rotation perspectives on triangle-dot paper (isometric paper). They learn the right-hand rule to explore rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Emily Breidt
Jacob Segil
Date Added:
02/07/2017
Mashups
Conditional Remix & Share Permitted
CC BY-NC-SA
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Locating restaurants in an unfamiliar place, reporting potholes to the local DOT, obtaining real-time traffic conditions... All of these are examples of geospatial web apps that are revolutionizing how people obtain and share information about the world. In GEOG 863, you will learn how to build apps like these. You'll start with a quick look at the fundamentals of web programming (HTML and CSS) before diving in to using JavaScript and a mapping application programming interface (API) developed by Esri. Using this API, you'll create both 2D and 3D visualizations of your own data and learn how to develop a user interface to enable users to interact with your map.

Subject:
Computer Science
Information Science
Material Type:
Full Course
Provider:
Penn State's College of Earth and Mineral Sciences
Author:
Jim Detwiler
Date Added:
10/07/2019
Math, Grade 6, Surface Area and Volume
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Surface Area and Volume

Type of Unit: Conceptual

Prior Knowledge

Students should be able to:

Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights.
Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices.
Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units.
Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.

Lesson Flow

The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.

Subject:
Mathematics
Geometry
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7
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CC BY-NC
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Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
Date Added:
10/06/2016
Math, Grade 7, Zooming In On Figures
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Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Subject:
Mathematics
Geometry
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Zooming In On Figures, Methods Of Calculating The Surface Area
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Students will continue to explore surface area, looking at more complex solids made up of cubes. Students will look at the 2-D views of these solids to see all of the surfaces and to find a shorter method to calculate the surface area.Key ConceptsThe 2-D views of 3-D figures (front top and side) show all of the surfaces of the figure (the area of the three views is doubled or the back, bottom, and other side) and so can be used to calculate surface area. The only exception is when surfaces are hidden or blocked and must be accounted for.GoalsExplore the relationship between 2-D views of figures and their surface area.Find the surface area of different solids.

Subject:
Geometry
Material Type:
Lesson Plan
Provider:
Pearson
Date Added:
09/21/2015
New Perspectives: Two-Axis Rotations
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Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. A two-axis rotation is a rotation of an object about a combination of x, y or z-axes, as opposed to a single-axis rotation, which is about a single x, y or z-axis. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, y- and z-axis rotation perspectives. They use the right-hand rule to explore the rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills. At activity end, students re-take the 12-question quiz they took in the associated lesson (before conducting four associated activities) to measure how their spatial visualizations skills improved.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Emily Breidt
Jacob Segil
Date Added:
02/07/2017
A Place in Space
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Educational Use
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Student groups use a "real" 3D coordinate system to plot points in space. Made from balsa wood or wooden dowels, the system has three axes at right angles and a plane (the XY plane) that can slide up and down the Z axis. Students are given several coordinates and asked to find these points in space. Then they find the coordinates of the eight corners of a box/cube with given dimensions.

Subject:
Engineering
Mathematics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Ben Burnham
Date Added:
09/18/2014
Scaling Cubes
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In this activity, learners explore scale by using building cubes to see how changing the length, width, and height of a three-dimensional object affects its surface area and its volume. Learners build bigger and bigger cubes to understand these scaling relationships.

Subject:
Geometry
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
Date Added:
12/07/2010