I love using math manipulatives. For some kids, using visual logic, or a hands-on approach can help to remove barriers to understanding, and can take some of the intimidation and fear out of learning about difficult concepts. Using Algebra tiles to teach polynomial multiplication and factoring quadratics help to reinforce an area model of multiplication, and completing the square – well it does make more sense if you actually complete a square. (And if you get the lab gear designed by Picciotto, you can complete the cube too!) I’ll post about my experience with these sometime soon. For today, here are some ways that we have used Geoboards in my Algebra classes.

My Algebra students had a blast using geoboards to find triangles and squares. The Math Forum has put together a set of very rich ideas for using geoboards, and we worked over a few days to discover line segments, triangle area, and practice with the pythagorean theorem. I asked students to use the geoboards to find solutions, and then to translate their ideas into pictures on dot paper by drawing all of their solutions.

I had some challenges handy for some students who were ready. Here are some extensions to the challenges posed by the Math Forum, which my students grappled with.

- How many different squares can you find in a 5 pin x 5 pin board?
- How many different triangles can you find in a 5 pin x 5 pin board?
- How many total squares can you find in in a 1 x 1? …2 x 2? …3 x 3? How about
*n*x*n?* - How many total rectangles?

There was some beautiful and deep thinking going on, and this is a highly differentiable activity. Students who are at the concrete level could physically count squares, while students who were ready to generalize could find the cubic (I guess that’s not too much of hint), which describes the number of squares in an *n * x * n * area. Teachers, feel free to drop me a note or tweet at me for my solutions. In an effort to keep the problems from being Google-able, I haven’t included them here.

Geoboards are excellent to physically see how slope works as well. For next year, I’ve ordered the 11 x 11 pin versions. Stay tuned! How have you used Geoboards in Algebra class?