I'll write more when I have a chance to do the full activity sequence with kids (including building the 1-through 4-ominoes with unifix cubes) but, as always, one thing leads to another and I started wondering if I could make something similar using pattern blocks.
Turns out I can. And, it turns out it was an enjoyable challenge for my daughter, who is somewhat of a skeptic when it comes to trying out my new ideas. Here's what I did:
I made an isometric dot grid.
I created some closed figures, some very open and balanced, some less regular. The goal of these puzzles is to fill in the entire shape using as few pieces as possible. My daughter did it by herself, but I could see it being an enjoyable, conversation-inducing project for a team of two.
I tried it out myself and thought, "This is too easy." Then I had the thought to ask my eight year old help me figure out if this was something that might work with kids in her class. Lucky for me, she consented.
To initiate a second try I wondered if she could fill in the space using less pieces. As she looked at her first solution I wondered aloud if there were any places where a larger shape could take the place of the smaller ones. This time she reduced the number of shapes to eleven!
Again I wondered if she could use less shapes, and on her third try she brought it down to nine!
I wondered how she would do with a less balanced, less regular shape. Here's the first try, eleven pieces. In the process she observed that using a trapezoid and a triangle together covers the same area as two rhombi and uses the same number of pieces.
"This is a fun puzzle...and challenging!" she gushed. Second try, eleven pieces.
In the end, this may be a system with a short shelf life -- once you 'get it' you get it, but I love that it's very open ended and allows for multiple right answers (11 pieces, three ways, for example). It's also a really friendly way to encourage perseverance in problem solving, spark discussions about composition and decomposition of units, and, heavy on my mind these days, a great way to ease into fractions.
I know this looks somewhat like a traditional pattern block activity but hopefully you can see that it has a different focus. At the very least it's telling that my kid (who has never been into 'solving' the already designed pattern block images) was really into this puzzle format. The only structure here is the outline of the puzzle shape. No need to give any hints by subdividing it in any way. That would ruin the fun!
If you make puzzles of your own, I'd love to see them. I'm going to keep working on a few more outlines and if I come up with some good ones, I'll be sure to share them.