Quick Look
Grade Level: 7 (79)
Time Required: 45 minutes
Expendable Cost/Group: US $1.20
Group Size: 2
Activity Dependency:
Subject Areas: Geometry, Problem Solving
Summary
Students learn how to create twodimensional representations of threedimensional objects by utilizing orthographic projection techniques. They build shapes using cube blocks and then draw orthographic and isometric views of those shapes—which are the side views, such as top, front, right—with no depth indicated. Then working in pairs, one blindfolded partner describes a shape by feel alone as the other partner draws what is described. A worksheet is provided. This activity is part of a multiactivity series towards improving spatial visualization skills.Engineering Connection
Orthographic projection is a technique used in spatial visualization, which is an essential skill for engineers in taking an idea that initially only exists in the mind, to something that can be communicated clearly to other engineers and eventually turned into a product. Orthographic views are especially helpful for detailing the product/structure designs for manufacturing and construction. Since orthographic drawings show multiple viewpoints, they are helpful to make sure that a product or object can be accurately created in accordance with an engineer’s requirements. While isometric drawings, which provide a threedimensional view of an object, can be a convenient means of providing a complete understanding of some objects from a single drawing, other objects require information from additional viewpoints; in these cases, engineers use orthographic drawings.
Learning Objectives
After this activity, students should be able to:
 Explain the concept of orthographic projection and why it is useful in engineering.
 Draw the three principle orthographic views of an object.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
Common Core State Standards  Math

Draw, construct, and describe geometrical figures and describe the relationships between them.
(Grade 7)
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Verify experimentally the properties of rotations, reflections, and translations:
(Grade 8)
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Apply geometric concepts in modeling situations
(Grades 9  12)
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Visualize relationships between twodimensional and threedimensional objects
(Grades 9  12)
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Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
(Grades 9  12)
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State Standards
Colorado  Math

Modeling geometric figures and relationships leads to informal spatial reasoning and proof.
(Grade
7)
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Verify experimentally the properties of rotations, reflections, and translations.
(Grade
8)
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Objects in the real world can be modeled using geometric concepts.
(Grades
9 
12)
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Visualize relationships between twodimensional and threedimensional objects.
(Grades
9 
12)
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Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
(Grades
9 
12)
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Materials List
Each group needs:
 8 snap cubes (interlocking cubes); available at https://www.amazon.com/LearningResourcesLER4285MathlinkCubes100/dp/B000URL296 or https://www.amazon.com/LearningResourcesLER7584SnapCubes/dp/B000G3LR9Y, ~$1013 for a set of 100)
 pencil with erasers, for each student
 Blank TriangleDot Paper, two sheets per student
 Orographic Drawings Worksheet, one per student
 blindfold
To share with the entire class:
 (optional) computer with projector to show examples as provided in the Spatial Visualization Presentation, a PowerPoint® file; alternatively, draw the examples for students
Worksheets and Attachments
Visit [www.teachengineering.org/activities/view/cub_spatviz_lesson01_activity2] to print or download.More Curriculum Like This
Students learn about isometric drawings and practice sketching on triangledot paper the shapes they make using multiple simple cubes. They also learn how to use coded plans to envision objects and draw them on triangledot paper.
In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided 12question quiz. Following the lesson, students complete the four associated spatial visualization activities and then retake the quiz to see how mu...
Students learn about twoaxis rotations, and specifically how to rotate objects both physically and mentally about two axes. Students practice drawing twoaxis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangledot paper the shapes from various x, ...
Students learn about oneaxis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing oneaxis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x, y and zaxis ro...
PreReq Knowledge
Before taking part in this spatial visualization activity, students should have taken the Spatial Visualization Practice Quiz and learned about spatial visualization in the associated lesson, Let’s Learn about Spatial Viz! They should know how to use triangledot (isometric) paper and how to make isometric drawings and coded plans, as can be learned in the associated activity, Connect the Dots: Isometric Drawing and Coded Plans. Students should also be familiar with the x, y and z axes.
Introduction/Motivation
Today, we are going to learn about orthographic views and why orthographic drawings are important in engineering. Orthographic views are twodimensional depictions used to describe threedimensional objects. This spatial visualization skill is different from our last activity, during which we worked on representing objects using 3D depictions. Typically, we only need three orthographic views—top, front and right—to describe an object. So, if you describe a skyscraper to someone, you might say, “The front of the building is all glass, but the top of the building is all steel.” That is an orthographic description. More complicated objects sometimes require more views, but for today we will just focus on the main three. The three orthographic views are defined by the three planes of an orthogonal coordinate system: the xy plane, the yz plane and the xz plane.
(Show students slides 1220, various depictions of isometric objects and their orthographic views, of which slide 13 is the same as Figure 1. The slides are animated, so a mouse or keyboard click brings up the next graphic or text.) Take a look at this graphic. On the left is a threedimensional object shown in isometric view. Recall that this is how we drew objects using coded plans and triangledot paper. The three side (orthographic) views of this object are shown to the right of the object. (Click to reveal.)
Notice that the top and front views are the same width, while the front and side views are the same height. We typically draw the views the way they are drawn in this figure, so that they are aligned. This helps us visualize the object.
Solid lines are drawn to represent an edge, while dashed lines show components of the object that are hidden from a particular view. (Next show students slides 1417 for other graphics that depict orthographic drawings and views. Then show students slide 18—drawings of a bench and a church.) Here are two realworld examples.
Procedure
Before the Activity
 Gather materials and make copies of the Blank TriangleDot Paper and Orographic Drawings Worksheet.
 Prepare to project the Spatial Visualization Presentation, a PowerPoint® file, and use its content to aid in your instruction, as makes sense for your class. Slides 1220 support this activity. The slides are animated so a mouse or keyboard click brings up the next graphic or text.
With the Students
 Present to the class the Introduction/Motivation content. Also ask the preassessment question, as described in the Assessment section.
 Divide the class into student pairs. Hand out two pieces of triangle dot paper and four cubes to each student.
 Explain to students that they will use two methods to draw cube shapes.
 Method 1: BlocknDraw Relay
 Each pair joins up with another pair to form a group of four. Have students bring their blocks and paper with them when merging groups.
 Each of the four group members builds an object.
 Each student’s object is passed to the person on his/her right. That person then produces on his/her triangledot paper orthographic and isometric views of the object.
 After two minutes, each student passes the object to the next student on the right. Repeat step C.
 Repeat step D until all objects have been drawn by each student in the group.
 After all objects are drawn by all students, the group compares results and discusses the correct solutions for each object.
 As makes sense, show students the drawing tips on slide 19.
 Method 2: The NoLook Pass
 Working in pairs, one student wears a blindfold. The other student builds an object using up to four blocks.
 Holding the object, the blindfolded student describes to the partner the front, side and top views of the object.
 The partner draws ONLY what the blindfolded student describes, make note of missing or problematic features.
 Switch roles and repeat steps AC.
 Repeat steps AD with five blocks.
 Repeat steps AD with six blocks.
 If students are struggling with their drawings, show them slide 20 (same as Figure 2).
 Have students complete the worksheet. Observe and assist as necessary.
Vocabulary/Definitions
orthographic views: A way to draw an object that shows three views of an object from the three planes in an orthogonal (right angle) coordinate system. The views represent the exact shape of an object as seen from one side at a time as you are looking perpendicularly to it. Depth is not shown. An orthographic drawing is also called a multiview drawing.
spatial visualization: The ability to mentally manipulate two and threedimensional objects. It is typically measured with cognitive tests and is a predictor of success in STEM fields. Also referred to as visualspatial ability.
triangledot paper: A grid of dots arranged equidistant from one another. Used in making isometric sketches. Also called isometric paper.
Assessment
PreActivity Assessment
Question/Answer: Ask students:
 Why are orthographic drawings important to engineers? How do orthographic views help engineers to visualize something? (Point to make: Orthographic views show the exact shapes and details of an object or structure seen from one side at a time as you are looking perpendicularly to it. That’s helpful to engineers who are communicating their designs to other people for accurate manufacturing or construction.)
 Challenge question: When might an engineer choose to use orthographic drawings instead of—or in addition to—a single isometric drawing? (Point to make: Sometimes a single isometric drawing can provide a complete understanding an object, such as a simple cube. In other cases, orthographic drawings of additional viewpoints are needed in order to accurately communicate all of an object’s details. Going back to the example of a cube, if each side of the cube has different details, engineers would use orthographic drawings in order to fully and accurately describe each cube side.)
Activity Embedded Assessment
Worksheet: After completing the classroom instructions and group exercises, have students complete the Orthographic Drawings Worksheet. Observe whether students are able to draw the objects or if they are struggling. Assist them as necessary. Review their answers to gauge their depth of understanding.
PostActivity Assessment
Discussion: Ask students to explain and describe their drawings with specific focus on orthographic views. What strategies did they use to draw their cube shapes? What were the limitations they experienced, if any? How did students solve any drawing challenges? Since everyone has worked through the same exercises, group sharing of their challenges and approaches informs the teacher of students’ depth of understanding and provides their peers with relevant ideas and tips.
Activity Scaling
 For lower grades, spend more time introducing the concept by having the entire class make the same object, giving students time to draw the three orthographic views, and then drawing them on an overhead projector as a class. This provides more time to fully practice and grasp the topic before branching off in pairs. Also, provide students with a longer time on the BlocknDraw Relay.
 For higher grades, have students use more blocks to make more complicated objects. Also, during the BlocknDraw Relay, have each student draw all four isometric views of the object before passing the object to the next person. Adjust the time allotment as needed.
Contributors
Emily C. Gill; Jacob Segil; Emily BreidtCopyright
© 2011 by Regents of the University of ColoradoSupporting Program
Engineering Plus Degree Program, University of Colorado BoulderAcknowledgements
This activity was developed by the Engineering Plus degree program in the College of Engineering and Applied Science at the University of Colorado Boulder.
This lesson plan and its associated activities were derived from a summer workshop taught by Jacob Segil for undergraduate engineers at the University of Colorado Boulder. The activities have been adapted to suit the skill level of middle school students, with suggestions on how to adapt activities to elementary or, in some instances, high school level.
Last modified: November 21, 2019
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