Missing anything!
This is a level 5 geometry activity from the Figure It Out series. It is focused on drawing different views of three-dimensional shapes and interpreting view drawings. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Draw different views of three-dimensional shapes.
- Interpret view drawings.
Missing anything!
Achievement objectives
GM5-6: Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.
Required materials
- Figure It Out, Level 4+, Geometry, Book Two, "Missing anything", page 6
- square dot paper
- multilink cubes
See Materials that come with this resource to download:
- Missing anything activity (.pdf)
Activity
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 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.
1.
The two possible top views are:
2.
Possible front views are:
3.
Possible left-side views are:
4.
Possible rear views are:
The quality of the images on this page may vary depending on the device you are using.