Our first activity as new third graders is called Two Squares. The rules are:
- Use a square template, a pen or a sharp pencil. Anything square can be traced, say, 3 x 3 sticky notes!
- Trace the square once. Slide and/or turn the template and trace the square a second time.
- Some part of the two tracings must overlap. Draw sharp corners!
- Count the number of sides around the perimeter. Do NOT count any inside sides, or corners. Write this number inside your drawing.
Careful drawing and counting give good results. Less careful work means mistakes are made: non-square “squares,” counting internal sides.
Students discovered that the minimum number of sides is 4, the maximum number of perimeter sides is 16.
It is interesting to see how many different possibilities an individual student might be able to generate successfully. Rarely, a student will get all the possible answers. A whole class of students usually obtains all the possible answers together. If a class does miss one of them, the whole grade level will certainly be able to find any missing one by combining their results, and continuing to experiment. They may come to decide that certain solutions are impossible, or just not discovered, yet. So far, we have NOT found solutions with sides numbering 5, 11, 12, 14, or 15. Can you find one of these?
Science and math work like this; there is strength in numbers. Individuals do research, combine forces with other researchers, and become surer and surer about the results of their experiments. They know what they know. Sometimes, they know what they don’t know.