Hands on activity- check!
Partner work- check!
NO TEACHER PREP- BIGGEST CHECK!
This activity is a great way to practice multiplying binomials, or you can even use this for factoring quadratic trinomials! I like these activities because they are challenging, but not intimidating. They could work with a partner, and move their pieces around. If they got stuck, they could move on to something else and use process of elimination to fit their puzzle together.
A few notes- if this is the first time that your students are working with a Tarsia puzzle (or the first time you're using one), I suggest to start with the two triangles that have problems/answers on all three sides. Those are the middle ones. Match those ones first, then move out from there. If your students don't need that scaffolding, then just let them start wherever! I found that my students had a lot of matches, but didn't necessarily have any idea how they all went together. If you want to show them the general shape, that might help too. Mine took about half of the period, 25-30 minutes. They got a lot out of it!
The first three pages are what they cut out (they're scrambled, so no need to cut 30 sets out for your kids...no prep!) and the football shaped thing is the answer key.