Note: to give credit where it is due, my introduction came via Mike Lawler's blog that linked with Dan Meyer's blog.
Our first loops-de-loop
To start us out, I drew one example, then gave two different sequences to J1 and J2 to draw: (3, 7, 6) and (3, 1, 4).
As you can see from the picture, that led quickly to their own questions:
- What if we did (3, 4, 1) instead of (3, 1, 4)?
- What if we had four numbers in our sequence instead of 3? Their first test was (1, 1, 2, 2)
- How can we figure out where we should start drawing? This was a pressing problem, since we had fairly course graph paper (the grid was hand made!)
Ahead of introducing this to the J's, I had made a short pencilcode program to automate drawing the loops-de-loop: Draw a rectangular loop-de-loop with your choice of step lengths
This let us easily try many different combinations of step lengths and build up our menagerie very quickly. As usual, the kids came up with ideas that wouldn't have occurred to me. These are behind some of the challenges below.
For each of the following, what sequence of numbers defines the loop-de-loop pattern we created?
|Challenge 1: a basic l-d-l|
|Challenge 2: test your assumptions about loops-de-loop|
|Challenge 3: Where's my 4-fold symmetry?!|
|Challenge 4: Whoa! Do we turn clockwise sometimes?|