The Lab Gear is a comprehensive manipulative environment I created for the teaching and learning of algebra. I devote a fair amount of space to it on my Web site, so if you’re not familiar with it, start on the Lab Gear home page and follow the links. Those will take you to a general introduction about the role of manipulatives, to some Lab Gear animations and applets, and to a comparison with other hands-on models for algebra such as algebra tiles. (The one thing that comparison fails to mention, by the way, is that the Lab Gear is a lot more fun than the competition! This is in part because kids like blocks a lot better than tiles, but also because of the many puzzle-like challenges included in the books.)
Algebra Lab Gear: Basic Algebra is intended for grades 6-9, and features activities on integer arithmetic, equivalent expressions, perimeter and surface area, the distributive property, and equivalent equations, as well as some “from blocks to symbols” pages. Those provide teachers with some strategies to help move students in that direction. (One of my students put it well when she said “I want to be free of the blocks!”) I also added a chapter on functions, and one on proportional relationships, to reflect some of the changes in what we expect basic algebra to include in the era of the Common Core.
Algebra Lab Gear: Algebra 1 is intended for grades 7-10. It focuses on polynomial arithmetic, equations and identities, quadratics, factoring, and connections with graphing. It includes some lessons that I’ve used successfully in Algebra 2.
Some teachers, never having used such materials themselves, do not trust that anything good can come from introducing them into their classes. All I can say is that many teachers have found the Lab Gear to be helpful in improving students’ relationship to algebra. Stanford prof Jo Boaler’s research about “Railside School” identified the Lab Gear as one key ingredient in the success of that program.
The Lab Gear helps at a basic level. (As one of my struggling students once put it: “The Lab Gear saved my butt”.) But it also helps with more sophisticated ideas, such as completing the square. Having experience with the Lab Gear model of multiplication, and some familiarity with trinomial squares, students enter into completing the square with confidence and understanding. (See these related applets: Squaring a Binomial and Completing the Square.)
Or take a look at this activity, which makes connections between the Lab Gear representations of trinomials, and the graphs of parabolas.