Which Polynomial is Represented by Algebra Tiles? 

If you’ve been using algebra tiles in your math class, you probably have at least a vague idea of what they do. They represent different variables, simplify expressions, and even model algebraic processes. However, it is not uncommon for students to question whether algebra tiles are really the best way to do certain calculations. 

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One way to answer that question is to use the area model. This is a method for multiplication in which a rectangle with dimensions of two factors is formed. The product is represented as a series of values for the variables in the rectangle’s dimensions. For example, the area model is used to solve linear equations. 

Using the area model, students can understand how to multiply a polynomial. In the process, they’ll be introduced to the concepts of exponents, exponents, and factoring. These concepts will be crucial when they begin to apply algebraic equations in their everyday lives. As a result, algebra tiles will become an indispensable tool in their learning. 

During the elementary years, students usually work with concrete manipulatives. However, as students progress through middle school and high school, they will increasingly be exposed to virtual and abstract algebraic manipulatives. With these tools, students can perform mental calculations and problem solving with consistency and ease. Moreover, this type of tool can help them build number properties. 

To make the most of the area model, you need to know how to represent the variables in your rectangle in a meaningful way. You’ll also need to determine the degree of the polynomial that you’re trying to multiply. That degree equates to the degree of the highest degree monomial you have. 

Once you’ve determined how to represent the variable in your rectangle, you can start to solve the equation. To do so, you’ll need to figure out which algebra tiles fill in the rectangle. For example, you might want to use tiles with the values 1, 2, or 3. Doing so will demonstrate that a combination of those tiles will fill the rectangle. 

In addition to the area model, you may want to check out algebra tiles that illustrate the concept of substitution. For example, if you are solving a linear equation, you might want to use a pair of tiles to show that x + y = 2. Or, you might want to use the tiles to show that x + y is the same as x. 

Another way to represent the equation is by utilizing segments. A segment is a small square that represents one of the terms in the equation. A red square and a -x square are examples of this. Similarly, a yellow square and a -1 square represent the other two terms. By combining these symbols, you can create a larger graph. 

Finally, you can use algebra tiles to demonstrate the inverse operation of multiplying. For example, you might want to use the algebra tiles to help you factor x2 into x.