The Colors of Algebra
Rigor and Resilience at a "Last Chance" School

Joanne da Luz, Life Learning Academy, San Francisco USD

Teaching Key Algebraic Concepts through Interdisciplinary Mathematics Teaching Students Who Have Failed in – and Been Failed By – Traditional Schooling

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What are my students learning?

Teaching Practice
What's my approach?

Student Work






This project demonstrates how I have used Henri Picciotto's Lab Gear manipulatives to motivate students at Life Learning Academy to become successful, "hands on," learners in an algebra class.  The project also describes the evolution of a collaborative interdisciplinary project based on the Lab Gear manipulatives. 

The Colors & Algebra Project provides students with an opportunity to create a unique representation of their own understanding of algebra through the use of color mixing and painting on canvas. Objectives and goals include the following:  Students will be able to a)accurately multiply algebraic expressions, factor quadratics, and combine like terms b) describe their understanding of multiplication and factoring by referring to geometric concepts of dimension and area and c)  describe their understanding of a variable by referring to their experiences with color, shapes, and materials.  Extensive assessment tools and journal prompts will provided to support implementation.

Expected Student Learning:



Students will know.....

Students will be able to .....

1. multiplication of algebraic expressions such as (x + 2) and (y + 3) means that you are given the dimensions of an area and you are looking for the area representation

1.accurately multiply algebraic expressions and combine like terms.

2. to factor a quadratic such as x²+ 2y + 3x + 6 means that you are given an area of a rectangle and you are looking for its dimensions

2. accurately factor a quadratic with the use of Lab Gear and/or a Generic Rectangle

3.  the properties of squares and rectangles

3.  use a T-square to draw parallel and  perpendicular lines

4. the properties of primary and secondary colors.

4.  create secondary colors by choosing appropriate paint to mix

5.  the difference between when variables are multiplied together to create squares and when they create rectangles. 

6.present their understanding of multiplication and factoring of algebraic expressions by referring to geometric concepts of dimension and area.

6.  The sense of a variable and its relation to the size of their variable shapes.

6.  Choose a size and make scale drawings to represent their variables. 

7.  The definition of commutative property.

7. Accurately provide examples of commutative property by referring to colors, variables, and constants.

Project Development History:

I have used Lab Gear during every year of LLA's existence. Most of our students arrive to the Academy without a successful career in mathematics.  The Lab Gear provides students with a fresh start and an opportunity to become "hands-on" learners.  For example, students handle actual squares that represent x² and y².  The geometric perspective of abstract concepts provides students with a new way into the math. 

interview: Justin Warren
In this clip, my colleage Justin, the art and photography teacher at Life Learning Academy, reflects on his own experience with algebra and explains how "space and dimension" help students to conceptualize the process of multiplication whether it be with numbers and/or variables.
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I had asked my colleague Justin to cover my class one day when he noticed the student produced posters hanging on the walls.   They represent factored quadratic equations of the form (Length) (Width) = Area where blue and yellow colors represent the x variables and the constants respectively.  Days later, as Justin was sitting across from me in our office he showed me some notes he had taken that were inspired by the posters.  He had carefully sketched another (L)(W) = Area representation but added his own idea of color mixing to further  explicate the multiplication of variables.  Those notes evolved into the Colors Project and Robin Havens collaborated with us to enhance the artistic methods and standards that could be addressed during the project. 

The history of the project continues to evolve.  During the second year of the project I will utilize more scaffolding techniques to support students' understanding of multiplication of variables.  Justin has plans for an extra credit art project that will address the sense of a variable in another medium.  Robin Havens has researched and provided some insight into the art standards and the connection to P. Mondrian’s work.


Site last updated July 5, 2006