Previous Years‎ > ‎Visual Algebra‎ > ‎



All manipulatives for the workshop will be supplied by the host schools and the publishers.

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, and links to a book of activities from 1990 (Algebra Lab: High School), a SmartBoard "Gallery", and 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 they overlap 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 free 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 (20% off!)

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, at a 15% discount for workshop participants.

Online Manipulatives: For a free online 11 by 11 board, you should go to Didax


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, 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

...and much more!

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

Related lessons in ATTC:

Related lesson not in ATTC:

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)

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

In some versions of this workshop, we also explore:
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)

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 received at the Institute. You'll also find teacher notes, some answers / solutions, and pedagogical / philosophical comments there. Good places to start: 

Algebra links

Using Graphing Technology 


Make These Designs 

    (includes teacher notes for the activity, plus specific worksheets for TI calculators, or Desmos, or GeoGebra)

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

Also worth checking out: Teaching fractions.

There are many links about "Reaching the Full Range" on my Talks page. However note that my keynote address at Atrium only included part of my usual presentation, so the links address more topics.

For general articles about pedagogy, including "Reaching the Full Range", "The Assessment Trap", and a fun "Ignite" presentation, see my Teaching page.

My Blog

Lots of stuff there. Among other things, a couple of posts about story tables:
Story Tables in Middle School (co-authored with Shira Helft)
At Synapse, Shira mentioned the importance of "reading algebra", which I discussed at an Atrium workshop. Here is a post on that topic.