In previous lessons, students saw that isometric drawings were not always what they appeared to be. A Dutch artist, M.C. Escher
(1898-1972), is famous for his use of unusual perspectives to trick the
viewer into seeing "Impossible Figures." In this lesson, students will
examine some isometric drawings that seem to be impossible, and they
will investigate one way Escher used to create these "impossible
Project the following images for the students to see:
As in previous lessons, you may print out the following PDF to create an overhead transparency:
Are They Possible?
Students should attempt to mentally construct each figure before using the isometric drawing tool.
Isometric Drawing Tool
Now, using the Isometric Drawing Tool, students should build each figure. Next, they should use the Inspect mode
to look at the figure from different perspectives. Students can open
several windows so they can have access to all three drawings.
Now students can try and create their own impossible figures. If students wish, they can print out their constructions using the Print function on the applet. As students work, circulate the room and use the Questions for Students section to engage students in math talk.
To wrap up the class, have students create one final construction. Have students print out their constructions and close their windows. This will prevent them from using the interactive to find the answers to the questions you will ask them. Ask students to:
- Find the surface area and volume.
- Sketch the front, right, and top (FRT) view.
- Sketch the mat plan.
- Discover if it is possible to have another figure that has the same isometric drawing.
You can either have students share their results or collect this as a form of assessment.