Henri Picciotto's

# Lab Gear

A manipulative for algebra

The Lab Gear is a comprehensive manipulative environment I designed for the teaching and learning of algebra. I have written three books' worth of activities for it -- The Algebra Lab: High School, Algebra Lab Gear: Basic Algebra, and Algebra Lab Gear: Algebra 1. The first is available below. The other two, and the blocks, are now available from Didax. (Scroll down for more info on the books, or click here for info on how to get them.)

For a full training on the Lab Gear, see the video course I helped write for Dr. Ed Dickey of the University of South Carolina. (Where to get it.) Or hire me to run an in-service or pre-service workshop. I can introduce the Lab Gear in one or two days, or incorporate that into a more general course on teaching algebra, which can run from three to five days.

## On this site

An introduction to Base 10 blocks and the Lab Gear, followed by a general discussion of the uses and limitations of manipulatives. (Part of a longer article on "Early Mathematics".)

Short slide shows of Lab Gear basics, including cool animations.

Applets to explore and discuss multiplying binomials, squaring a binomial, and Completing the Square using the Lab Gear model.

A Microsoft Word file with Lab Gear graphics you can cut and paste into other documents. (The file is large: 46 MB.)

A gallery of three items for the SmartBoard and its Notebook software. Each will give you an unlimited supply of Lab Gear blocks to manipulate on the board and/or to copy/paste into a word processor.

A Lab Gear / graphing connection (from Algebra Lab Gear: Algebra 1) (PDF).

A worksheet: Factoring a Sum or Difference of Cubes

A rather technical comparison of the Lab Gear with other models of polynomials, including a history of algebra manipulatives.

## What to Get

### Blocks

I get much e-mail asking: "I would like to use the Lab Gear. What should I buy?" The answer is simple: get a "student pair" box for each pair of students. (Each box contains 24 ones, 8 fives, 2 twenty-fives, 18 x, four 5x, eight x^2, 4 xy, 8 y, two 5y, two y^2, one x^3, three x^2y, three xy^2, one y^3, and two corner pieces. This should be enough for each student to do almost all the problems in the new edition of the books.)

In addition, I recommend buying one or two extra boxes to help balance things out if pieces migrate between boxes.

### Algebra Lab Gear Books

Two books are available from Didax: Algebra Lab Gear: Basic Algebra, and Algebra Lab Gear: Algebra 1.

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.

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.

Both books have Common Core correlations, teacher notes, lesson plans, and answers. There is some overlap on the key concepts, but the two books are sequenced differently, and represent somewhat different pedagogic styles. If you can afford it, I recommend getting both so as to have more choices, and more activities on the most important topics.

### The Algebra Lab: High School

The Algebra Lab: High School (written in 1990, available below) has many great lessons, some of them available nowhere else, and offers a good introduction to the Lab Gear for teachers. Much of it is merged into the textbook Algebra: Themes, Tools, Concepts. However, it is not as easy to use with students as the other two. Still, it contains many activities I recommend for classroom use. In particular, check out the Explorations. (See pp. ix-x in the front matter for an overview and index of those.)