Lesson 4: Thinking about space; 1, 2 and 3 dimensions
Grades: all, depending on the leading questions
| Possible Questions
What meanings can the word “dimensions” have? What are words which mean something similar?
What are examples of objects with 0, or 1, or 2 ,or 3 dimensions
Can you make a table (classify) these objects?
How does Rickey use ideas of dimensions in his sculptures?
Does the wind act differently for sculptures with different dimensions?
The questions can be very grade-dependent on the geometry skills of the class:
their understanding of ideas of point, line, area and volume can provide the focus for the lesson
- the lower grades can be qualitative and object-oriented; the higher grades can be quantitative.
Besides Rickey sculpture illustrations, you might need some simple example objects for them to begin the discussions.
At the end of the discussion, you need to get the class to realize how the wind will not affect a simple line, but the second and third dimensions of a Rickey sculpture are important so that the wind can “grab” the sculpture.
Hands-on group work - the groups should decide to build Rickey-like models with 1, 2, or 3 dimensions.
Summing up the experience: Whole class discussions
Comparing the different models - the different dimensional types should be compared -
e.g. which ones move most easily? And do the movements depend on the number of dimensions?
Why do old windmills and new “windfarms” look very different?
Extensions: What other things make the models move faster/slower?
How do the shapes of the different models determine the motion?
At the higher grades you can start to discuss the center of mass, and the mass distributions