Putting Manipulatives to Work, Part 3: Developing Expressions & Equations in Grades 6–8 with Algebra Tiles & Algeblocks
Putting Manipulatives to Work is a three-part series of webinars designed to take advantage of manipulatives that are likely to be available in schools and in classrooms. Each session discusses several manipulatives that can be used to support a common topic: number sense (Part 1), geometric measurement (Part 2), and algebraic expressions/equations (Part 3).
The series came about from the questions of educators in the field regarding unused manipulatives they have accumulated in their classrooms. They could have been left behind by another teacher or part of a new program, but the common theme is that these materials are available and should be used. Teachers often aren’t sure how to use them. This series highlights a mix of manipulatives–some old friends like Cuisenaire® Rods, around for more than 80 years, and others newer to our classroom like Rekenreks. This webinar answers the question, how can we best use these manipulatives to enhance instruction?
What Are Expressions and Equations?
Middle grades students extend their knowledge of arithmetic to work with integers and with algebraic expressions. A key element of this work is understanding how operations with integers and operations with algebraic expressions are similar to the operations they already know with whole numbers. This webinar uses two manipulatives, Algeblocks and Algebra Tiles, to make these relationships visible.
Algeblocks are manipulatives that represent a unit, x and y with three-dimensional pieces and can represent terms up to the third power. Signs are indicated by position on a workmat. The pieces can be used to represent algebraic expressions of many types. Binomial multiplication is particularly familiar because it resembles what students already know about whole number multiplication with base ten blocks.
Algebra Tiles are manipulatives that use rectangles to represent a unit, an unknown (x) and the square of the unknown (x2). The pieces are typically colored red on one side and the red side represents a negative value (e.g., -1). Using the tiles, adding integers can be represented as joining two sets of integers, just as addition in kindergarten represents joining sets of objects. The concept of a zero pair allows this.