This is a level 5 geometry strand activity from the Figure It Out series.
draw different views of three dimensional shapes
interpret view drawings
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.
Answers to Activity
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 winnersÕ 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.