On the Concept of Balancing Equations

So often in the early grades kids become accustomed to seeing problems written out as below:

3 + 4 = ________

When the answer blank appears in different places in the equation, such as on the left-hand side, it can help, as can the creative use of manipulatives to represent the symmetry of equations. However, the connection between the equal sign and the demand for an answer may continue to confuse some students. Some students learn to think of the = sign as meaning "insert answer here" rather than as the fulcrum of the equation.

What do I mean by this?

Consider the term "balancing an equation".
If you envision an equation as a balance scale, you can put the = sign at the centre, or fulcrum of the scale. In this way, the equation is balanced when both sides are equal to each other. There is a symmetry in the weight on each side.

This can be used to demonstrate the mathematical meaning of the equal sign in a hands-on concrete way.

For students who have difficulty with the concept, consider having them use the balance with weight manipulatives. x might be the name of the 1 gram weights, y the two gram weights etc. Let them play around.

What if they put 2x on one side and y on the other? When the balance is level, the sides are equal.
What if you put 2y on one side and x on the other? When they balance is tilted one way or the other, the sides are unequal. Instead of an equation, you have an inequality ≠.

You can take this a step further if your scale is the kind that has an arrow on the fulcrum. Label the point of balance with an equal sign =, and the space on either side with an inequality sign ≠.

Encourage students to write the equations as they work with the balance to solve problems and also to make predictions of what expressions will be equations and which will be inequalities, as well as determine what is needed to turn an inequality into a balanced equation.

More of my math activities can be found here.