Previous Years‎ > ‎Visual Algebra‎ > ‎



All manipulatives for the workshop will be supplied by the host school.

The Lab Gear

Much of the work we will do involves the Lab Gear

There is a fair amount of info about the Lab Gear at the link above, plus a book of activities from 1990 (Algebra Lab: High School), a SmartBoard "Gallery", and links to the animations I used in the workshop.

Our worksheets (see Handouts) are from the two Algebra Lab Gear books, both available from Didax: Basic Algebra, and Algebra 1. Both include a Common Core correlation.

I recommend getting both books. While there is overlap between them on the main topics, they differ in what they cover, in their sequencing, and in their style. Having both will give you maximum flexibility. Either of them is a lot more user-friendly than the 1990 book, and moreover all their problems will work with the distribution of blocks offered by Didax. Note also that the online book does not include the 3D blocks. 

The blocks are also available from DidaxEach "student pair" 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.

A class set includes twelve student pair boxes and both books.

Workshop participants will be able to purchase those, and the Lab Gear books, at a discounted price.

Other Manipulatives

11 by 11 Geoboards and rubber bands — should be available from many sources. Many geoboard lessons are in my Geometry Labs book. (See below.) Other lessons (geometry, trig) in Geometry Labs involve a 10cm circle geoboard I designed. It is  on the back of a standard 11 by 11 board, and it is called the CircleTrig Geoboard. It is available from Nasco.

Pattern Blocks — should be available from many sources, in wood or plastic. However avoid the "foam" ones, because in my experience they are less accurately manufactured. There's a link to pattern blocks lessons on my Web site here.

Electronic Manipulatives: Heidi recommends a site with free apps: Math Learning Center

Unfortunately, their geoboard does not allow an 11 by 11 board, so you'd have to adapt some of the activities accordingly.

Their "pattern shapes" do include pattern blocks as the default.


Algebra: Themes, Tools, Concepts

Some of the work we will do is drawn from Algebra: Themes, Tools, Concepts (ATTC), an algebra textbook I co-authored with Anita Wah in the early 90's. It was groundbreaking in some ways, and includes many extraordinarily effective approaches to the teaching of algebra, and is very compatible with the Common Core State Standards. On the other hand, it is not particularly easy to use as a textbook, and never became a bestseller. It is available absolutely free on my Web site, along with its Teacher’s Edition and more.

More info and links, including these lessons:

Weight vs. Age

The Bicycle Trip

The McNuggets Problem

Constant Sums, Constant Products

...and much more!

Also: Stairs and Squares (includes Geoboard Diagonals, and Donna's Stairs)

The whole book, by lessons or chapters

ATTC is not easy to navigate. Here's a one-page index to selected topics and tools.

Geometry Labs

Some of the work we will do is based on my book Geometry Labs:
Polyomino Perimeter (Labs 8.1 to 8.3)
Geoboard Slope (Labs 10.1 and 10.2)
Oakland workshop only:
Area on the Geoboard (Lab 8.4 and 8.6))
Geoboard Squares (leading to the Pythagorean theorem) (Labs 8.5, 9.2)
Simplifying Radicals (Lab 9.3)
Distance from the Origin (Lab 9.4)

The book includes many more labs, plus answers and teacher notes.
It is available for free download on my Web site.

My Math Education Page

Some of the work will be based on material that is available elsewhere on my Web site. On some of those topics, there are more curriculum files available on the site than you have in your binder. You'll also find teacher notes, some answers / solutions, and pedagogical / philosophical comments there. Good places to start: 

Algebra links

Using Graphing Technology 


Stairs online, and links to downloads

Make These Designs (includes teacher notes for the  activity, plus specific worksheets for TI calculators)
Comparing Cell Phone Plans

Pattern Block Trains (SmartBoard Pattern Blocks)

Function Diagrams (includes animations, and a GeoGebra file to make your own diagrams)

Parabolas and Quadratics (includes a lot more than what we did!)

Using the Interactive Whiteboard 

On lagging homework: a guide, and a blog post. (Also follow the links at the end of the blog post for related articles.)