Teaching algebra ideas in elementary school

Back in the 90's I offered to help at the local elementary school, and somebody took me up on it. They assigned me a half dozen 3rd grade TAG students and gave me a package called Hands-On Equations, in which students use marker and number manipulatives to get a feel for how to manipulate equations.

The theme of the system is a balance scale, and the balancing rules are made easy to visualize. Once you're set up, both sides of the scale always have to balance. You can add numbers to both sides, split into groups to show division, and get a feel for what it means to have a name for an unknown. The video shows a newer version, in which the cubes have actual numbers. I like the older approach better: if you want to represent 12, you count out 12 cubes onto the workpad. It makes numbers easier to visualize, and to separate into groups (divide), or to combine groups (multiply). Since you don't have to do the translations (a 10 cube is the same as a 5 and a 5), the lesson is simpler to visualize.

The kids learned the material quickly enough, and the last lesson had a sneaky problem or so that would trip up kids who were guessing their answers. I thought it was a clever approach. There was one more day than lessons, so I ended by giving them a little explanation of clock math and triangle math, not as parts of a field of study, but as examples of mathy things that didn't work like the usual counting numbers.