Modeling Equations

A math expression is a math sentence that contains numbers, symbols, and operators. An algebraic expression is a math expression with variables. Variables are symbols that represent an unknown number. The algebraic equation shows that two expressions are equal. One or both expressions can have variables.

The equal sign works much like a balance beam in which both sides of the equation (on opposite sides of the equal sign) are the same value.

Algebra Tiles

algebra tiles

Algebra tiles are manipulatives often used to model algebraic equations. Usually, algebra tiles consist of one yellow square, one red square, one green rectangle, and one red rectangle. The yellow square equals 1. The red square equals -1, The green rectangle equals “X” and the red rectangle equals “-X”.

Equations are set up using a line or some type of graphic such as a balance to stand for the equal sign. The yellow and red squares are used to create numbers. A yellow and red square put together equals zero (zero pair). The green and red rectangles are used to create coefficients ( the variable portion of the equation).


Zero Pairs

zero pair

Zero pairs are when the sum of two values that equal zero. For example, -2 + 2 equals zero, so the two numbers combined form a zero pair. With algebra tiles, a yellow square placed with a red square equals zero, this forms a zero pair. A green rectangle placed with a red rectangle equals zero, this also forms a zero pair.

Modeling Expressions and Equations

Here is an example of using algebra tiles to model an equation.

equation model


Steps for Solving Equations

The goal of solving an equation is to isolate a variable. In the case of algebra tiles, you are trying to get one green rectangle on side of the equal sign and squares of either yellow or red color on the other side. Whatever is done on one side of the equal sign, you must do the same thing on the other side. You can remove the square by using zero pairs.

Steps to follow:

1. All numbers and variables must be represented by tiles. You can use a line or symbol to represent the equal sign.

2. You must have one green rectangle on one side of the equal sign when you are done solving.

3. Eliminate squares on one side of the equal sign using zero pairs. You have to use tiles of the other color to eliminate the tiles you started within the model.

4. Once you have created zero pairs, remove all zero pairs.

5. You are done when you have one green rectangle on one side of the equal sign and squares of the same color on the other side.

Here is an example:

Check out the video


Solving Equations


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