Math Building Blocks
Some learners may need or prefer to use a grid that does not rely on colors. The principal is the same as before. Each symbol is matched with a particular number.
Introduce the Math Building Blocks by guiding students to build natural numbers consecutively beginning at 2. Whenever possible, students use blocks that they have already 'created' to build each new number. Otherwise, they invent a new block. The link takes you to a page on the National Council of Teachers of Mathematics website where NCTM members can download an article I wrote on the subject in the October 2009 issue of Mathematics Teaching in the Middle School.
Sieve of Eratosthenes animations
Download and play these movies showing a way to build prime factorizations using a modified form of the Sieve of Eratosthenes based on the Math Building Blocks.
Prime Out is a prime factorization game that I wrote for the Math Building Blocks at around the same time that I wrote the article above (back in about 2009). It's a bit dated now in terms of both appearance and functionality, but it still works—so I thought I'd share it with you anyway. My students enjoyed playing it, and it develops both computation and reasoning skills.
I thought it would be cool to have a picture of all prime factorizations for numbers through 1000. (You can decide if this is crazy or not!) I created a 32 by 32 grid. The file is a pdf document, and you will need to zoom in quite a bit to see what it really looks like. A print shop should be able to take the pdf and make a large copy of it if you want something physical to look at (or hang up). 3 ft by 3 ft works well for me.