Many students have a tough time visualizing algebra. One way to help students visualize math is to make a model. Modeling usually starts in the elementary grades.

Modeling can start simply by modeling a numerical value with pictures or manipulatives. For example, to model the number five, a student could draw 5 circles, 5 cubes, 5 whatever’s…

As students start learning about larger numbers, they begin to use arrays to model these values. For example, the number 12 might be modeled by an array with 3 rows and 4 columns. This is building the foundation for understanding multiplication. Eventually 3 rows by 4 columns turns into 3×4 =12.

The array modeling of 3×4=12 then leads to area models. A rectangular figure can be labeled with dimensions to represent the side lengths of an area.

You can then use an area model to help students model the distributive property. 5(10+2)

Eventually, we replace a value with x, but we can still use the idea of an area model to help conceptualize the distributive property. Let’s look at 5(x+2).

And finally more complex polynomials can be multiplied such as (x+2)(x+3). I hope that seeing these models helps you understand the importance of the mathematical progression of modeling a basic number like 5, because it helps students conceptualize the abstract later on in algebra.

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