Winning ways
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.
Winning ways
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, "Winning ways", page 5
- multilink cubes
- isometric dot paper (Isometric paper CM)
See Materials that come with this resource to download:
- Winning ways activity (.pdf)
- Isometric paper CM (.pdf)
Activity
Like the previous activity, this one asks the students to visualise 3-D objects from 2-D drawings and to create isometric drawings. This time, they work within a practical context.
In question 1, the numbers on the diagrams make it clear how many layers of cubes there are in each part of the structure.
When doing question 2, the students should remember that where two or more adjoining cubes are part of the same unbroken plane (flat surface), the join in the blocks is not shown. See the previous activity for more guidance on isometric drawing.
Questions 3 and 4 pose a technology-type challenge, in which the students have to find the best outcome given the constraints of accessibility and resource minimisation and then justify their decision.
As an extension, the students could create some winners' stands (see the example to the right) using a 3-D drawing program. If your school doesn't have such a program, there are a number available on the Internet as downloadable freeware.
Find them using keywords such as "3-D graphics freeware".
Once one cube has been created by constructing a square and clicking on an appropriate 3-D shape, it can be copied and dragged as many times as necessary to form the winners' stand. The students may find that they need to use the Control and/or Alt keys to position the cubes precisely.
1.
a. 6 cubes
b. 14 cubes
c. 10 cubes
2.
Drawings should look like this:
3.
Practical activity. Results will vary.
4.
Drawings and comments will vary. Three possible solutions, each using 9 cubes, are:
Isometric views of the three stands above are:
Designs i and iii are mirror images, so they are not really different. They provide a good solution because each person can get into position without anyone else blocking their way, the extra steps are hidden tidily behind the three winners steps, and a minimum number of cubes is needed. Design ii is fine as long as the 2nd- and 3rd-place getters stand back and allow the winner to get into position before moving forward.
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