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Building Using the Front-Right-Top View

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Students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.

As a review from the previous lesson, discuss the role of isometric drawings as one way to represent a three dimensional figure. In this lesson, students will compare isometric drawings with another type of representation, namely the front-right-top (FRT) view.

For example, project the following images onto the overhead projector or television monitor:

Isometric Representation:

2017 frt1 

Front-Right-Top Representation:

2017 frt2 

The following PDF will allow you to print out the above images on an overhead transparency:

overhead Front-Right-Top Views (Images) 

Ask students to discuss, with a partner, what they notice about each of these representations. They may discuss the benefits of using each kind of representation. Some students may say they think it is easier to draw one representation over the other. Or they may discuss how they could use the isometric drawing tool to create each of these representations.

appicon Isometric Drawing Tool 

Using the View tool and the Rotation controls on the Isometric Drawing Tool, students should do the following:

  1. Create a three dimensional figure out of cubes. The figure should be somewhat complicated, such as the one students just saw.
  2. Use the View button to see a 3D view.
  3. Uncheck the 3D "box" to see a Front-Right-Top view.
  4. Check the 3D box to see the three-dimensional view once again.

As students are moving between views, they should observe how the views change and how they relate to the original three dimensional figure they created.

Going back to the original figure and view they created, students should delete one cube from their picture. Ask them to note what they observe about the Front-Top-Right view. Students should continue deleting cubes. Ask them to note the fewest number of cubes they can delete to make the front view look different, the right view look different, and the top view look different. If needed, students can try again using another figure they have created.

The next portion of the lesson will focus on students building the three dimensional figures when given the Front-Right-Top views.

Project the following images onto the overhead projector or television monitor for students to see:

2017 frtexpls

(These images are located on the same PDF as the images previously projected.)

Using the isometric drawing tool, students should construct isometric drawings that match each set of FRT views. Then, they should copy these drawings onto isometric dot paper. You may wish to encourage students to keep the FRT tool open while they draw.

As students finish their drawings, they can compare their results with their partners. Did they get the same drawings? Have students discuss any variations with their partners.

  • Computers or tablets with internet access
  • Isometric dot paper
  • Front-Right-Top Views (Images to be made into an overhead transparency)


Move on to the next lesson, Mat Plans

Questions for Students 

1. Do you think the front-right-top representation contains all the same information as an isometric view?

 [No, the three dimensional aspect is not necessarily present.]

2. In the previous activities you saw that sometimes two solids have the same FRT view but different isometric views. Do you think it is possible for two solids to have the same isometric drawing, but different FRT views? If so, create an example using the drawing tool. If not, convince a partner why.

 [Students solutions and drawings will vary.]

3. For what applications might a FRT view be more useful than an isometric view? For what applications might an isometric view be more useful? Explain your thinking in both cases.

[Student responses may vary.]

Unit Icon

Using Cubes and Isometric Drawings


Explore polyhedra using different representations and perspectives for three dimensional block figures. 

ExploringTheIsometricDrawingTool ICON

Exploring the Isometric Drawing Tool

Students explore using the isometric drawing tool and gain practice and experience in manipulating drawings.
FindingSurfaceAreaAndVolume ICON

Finding Surface Area and Volume

Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.
MatPlans ICON

Mat Plans

Students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan.
DoTheyMatch ICON

Do They Match?

Using three dimensional figures they have constructed, students determine when two isometric drawings can represent the same shape and explain their reasoning. Students will also determine what possible shapes might have the same isometric drawing and explain their reasoning.
AreTheyPossible ICON

Are They Possible?

Students examine some isometric drawings that seem to be impossible and investigate one way Escher used to create these "impossible" figures.

Learning Objectives

Students will:

  • Draw the Front-Right-Top view when given a three dimensional figure built from cubes.
  • Build a three dimensional figure when given the front-right-top view.

NCTM Standards and Expectations

  • Use visual tools such as networks to represent and solve problems.

Common Core State Standards – Mathematics

Grade 7, Geometry

  • CCSS.Math.Content.7.G.A.2
    Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.