For several years now, I have used this pentomino activity on the first day of math class. I've written a few posts about it, because each year I find more benefits to using the activity.
It's a seemingly simple activity, and when I first explain it, students think it'll be a piece of cake. BUT, they find it to be quite challenging. And I find it to be an excellent way for students to start working cooperatively at the very beginning of the year. Students work in small groups of 3 or 4 to create a rectangle using all 12 of the pentominoes. That's it - make a rectangle, with no gaps or overlaps. Students are given a frame to work within (as shown in the photo). As I said, it sounds pretty simple, but if you've attempted it yourself, you know that it's not as easy as it sounds.
It takes the groups quite a while (and some never finish if I don't give some hints), which is great, because they are really thinking, talking to each other, sharing ideas, speaking their thought processes, working together, and being persistent. In the years that I've been doing this, I have yet to find a student who wasn't engaged. This is the type of activity that allows all students to persevere, regardless of their background knowledge in math. All students can manipulate the pentomino pieces and offer suggestions, and while some students are strong in certain areas of math, others are stronger spatially; this introduction activity allows them all to have success.
While this activity is great for the students, it's also great for me! It gives me the opportunity to observe the students and start learning about them - how they approach tasks, how they interact with others, who will try to take charge, who will sit back and watch/listen. It's a fantastic learning time for me.
In my classroom, I only had 12 by 5 inch frames, which I inherited from someone along the way. I decided, though, that I wanted to make frames with different dimensions (10 by 6 and 15 by 4), so I made those on the computer (on 8.5 x 11 pages).
So that the pentominoes would fit into these frames, I had to make the pentominoes smaller. So, now I have 3 different sizes of pentominoes (once I cut them out and laminate them!)
Having the different sizes and different frames allows me to give groups slightly different tasks, if I choose, or will give the groups who finish a new configuration to figure out.
If you'd like to try using these pentominoes, click on the Pentomino Exploration picture below to download.