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Students in Jolene Collier’s class worked with manipulatives to practice visualizing mathematical expressions during a recent lesson.
Manipulatives are physical objects that engage students in the hands-on learning of mathematics and are used to introduce and practice concepts. For the lesson, students were first introduced to the concept of a variable -- a letter that represents an unknown number.

“We then build a solid foundation of what an expression is, and that they are made up of variables, numbers and math operations,” explains Mrs. Collier. Students practiced writing expressions from real-world situations and sentences. An expression cannot be solved, unless the value of the variable is given, but expressions can be simplified.

The manipulatives include number cubes to represent the numeric value and pawns to represent the unknown variable. There are different colored pawns to represent different variables (ex. yellow = X and blue = Y). Recognizing that students would need time to grasp the concepts, Mrs. Collier encouraged them to “have rich mathematical discourse and keep going.”

Once students “got it” they could lend their expertise to other math learners, fostering collaboration among peers. “At this stage, the process is more important than getting the answer right,” said Mrs. Collier. “We’ll have lots and lots of practice with this lesson.”

Once students have a solid understanding of expressions they will move onto solving equations. “We will use the analogy of a scale to represent the two sides of the equation and we will use the same manipulatives,” she added.