Wednesday, May 1, 2013

Now that I think about it, I can't remember why I chose ducks.

Here's a lesson that went better than it was supposed to.

Grab a whiteboard, and grab your partner. Draw Step 4 of this pattern. Then draw Steps 0, -1 and -2. If you finish that, find a rule for Step n. You finish that, graph the rule.

Here was my favorite:

Ah, who am I kidding, they were all my favorites:

  • Frank Noschese, whose posts convinced me to get a bunch of white boards even though I had no idea how to use them. 2 years later: they're for producing things that can easily be shared, and sharing actual work is crucial for the sort of things I'm trying to pull off in class. Starting conversations is just way easier with shareable work.
  • Paul Salomon, whose image I blatantly ripped off and made 1000% worse by using ducks instead of circles.
  • Fawn Nguyen, for rocking my world with
Thanks for making my "just OK" days a bit better, guys.

Speaking of which: any ideas for improvements, people? Drop a note in the comments with ideas.


  1. I love the negative steps and their graphics, Michael! Have to start adding these.

    Why ducks?? Ducks as in OREGON DUCKS are the best, that's why!!

    YOU rock!

  2. The negative steps are excellent. It's like analyzing fractals - you have to think about not just what you're looking at, but what it took to create what you're looking at - what it took to get there.

    I agree that the whiteboards are a nice way to share work - I think that knowing that the work will be erased soon takes away some pressure for students - and I love the duck inside the egg in step negative 2 in the first whiteboard. Students always 1-up our ideas!

    And rubber ducks must be in the air. I just spotted this giant rubber duck before visiting here:

  3. I do like the Steps 0, -1 and -2. And whiteboards are such a great way to encourage students to take risks when problem solving.
    A couple of Qs: 1) What grade was this with? 2) What would happen if you showed your students just one of the steps (e.g step 3) and then ask them to work out steps 2, 1, 0 (and -1, -2)? I ownder if you might see some creativity in the patterns they then create. You could then take these patterns and plot them all on one graph... and see where all the graphs intersect...and ask why this happens?

  4. I've seen these with pile patterns (example:

    The question was "What would step 100 look like?" and "What would step -1 look like?".

    What I like about saying "What would step 100 look like?" is that it creates the need for an explicit rule without saying "Create an explicit rule".