This is a level 5 geometry strand activity from the Figure It Out series.
draw different views of three dimensional shapes
interpret view drawings
This activity illustrates the fact that we often assume something is true based on incomplete information. It should be done after the two preceding activities, X-ray Vision and Winning Ways, because these activities explore the conventions of isometric drawing and give students practice at visualising 3-D objects. Students
will find it much easier to answer the questions if they first make the objects using cubes.
In question 1a, students may assume that there is no cube in the far (hidden) corner of the object because there is no cube in the three corners that they can see. There is, however, no reason why this should be so, and the Answers show the two possibilities.
In question 2, the students consider the front views of each object. There is only 1 possible front view of object a, but object b may have from 1 to 3 cubes on the right wing, and if there are 2 cubes, these can be placed in 2 different configurations. So there are 4 possible views from this angle. In the case of c, the bottom right-hand (middle row) position is obscured. This means that there are 3 possible front views
depending on whether there is a cube in the far right bottom row, and if there is, whether it is in the nearer or farther position. Similar thinking is needed to produce the different possible views in question 3.
Question 4 is not easy, but the alternative views all require the same considerations that the students have met in questions 1-3. For example, in a, is there is a cube in the far corner? One view will show a cube in that position; another won't. There are 8 possible views for b and 8 for c. You could challenge your students
to find them all.
Answers to Activity
1. The two possible top views are:
2. Possible front views are:
3. Possible left-side views are:
4. Possible rear views are: