Algebra demystified at the Middle School

Teachers in the Churchville-Chili Central School District are always searching for new and better tools to help students learn. Math, and in particular algebra, with its abstract concepts of equations and solving for variables like X, can be daunting for many students. The district recently introduced a system of learning that uses manipulatives to help students grasp complex mathematical problems more quickly.

Manipulatives (concrete objects, that can be touched and moved, that aid in counting, equations, fractions, multiplication and other math tasks) help students visualize complex math concepts. Middle School teacher Brittany Fitzgerald is using manipulatives to introduce her seventh-grade class to algebra.

“Equations are like balances,” she explains to her class. “Each side must be equal to the other.” She demonstrates by moving red cubes, representing positive integers, to both sides of a scale. “If I replace the cubes on one side with this single unmarked blue figure, which represents a variable called X, then we know that X is equal to the total number represented on the cubes sitting on the other side.”

The math progresses from simple to challenging as the lesson proceeds. Students become more proficient. Green cubes are added to represent negative integers; yellow figures represent (-X). One by one, little mental light bulbs go off in the classroom as students grasp the processes they are using. They will soon easily be solving equations like 2(2x+3) = x+12.

After this introduction, students gradually use the manipulatives less frequently. They will be able to solve equations using only paper and pencil. Manipulatives can help them master the abstracts of algebraic concepts more quickly and be better prepared to win at math.

Churchville-Chili teachers are now using manipulative math tools like these in the Middle School and the Ninth Grade Academy. The approach, Hands-On Equations ( has been well-validated by extensive research and testing, and the district has already seen great success at the ninth-grade level. 

Students have been enthusiastic and quick to adopt the method. Comments include: “This is much easier. Very hands on, more visual.” “I can actually see the answers with this.” “I can solve harder, more complicated equations than I could solve before.” 

Fitzgerald said, “Many students find that the visual representation makes algebra simpler to understand. It is an easier way for them to solve problems and to check their answers. It is already making a noticeable difference for students in my classes.”

Photo: Middle School students employ manipulatives to understand the complex mathematical concepts they will soon be learning in algebra.
This page: Teacher Brittany Fitzgerald uses a balance scale and manipulatives to demonstrate algebraic equations.

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