Researchers have found that students in the United States often view the equal sign as a “do something” signal.  What can we do to help students absorb the concept of balance that the equal sign represents?

The Common Core Standards for Grade 1 Mathematics provides us with a guide:

Understand the meaning of the equal sign, and determine if equations involving addition and   subtraction are true or false.  For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

In order for young children to appreciate the balance inherent in an equation, they need to see different forms of number sentences, where numbers and operations can appear on either side of the equal sign:

1 + 3 = 4, but also 4 = 1 + 3 (this is also an example of the Symmetric Property: If a = b, then b = a)

4 + 1 = 3 + 2, leading to 4 + 1 = __ + 2

In the second example above, many children will instinctively fill the blank with a 5, having become accustomed to the direction of “add 1 to 4” that they believe the equal sign represents.  This situation can be avoided by offering students a variety of number sentences and focusing on the relationship between the two sides of the equal sign, that is, that they represent the same quantity.

And how often have you seen a student do the following?

Question: Jill has some money for shopping. She buys two sweaters for \$24 each and a pair of shoes for \$32. If she has \$6 left after shopping, how much money did she have at first?

Solution: 6 + 32 = 38 + 24 = 62 + 24 = 86

Be sure to give feedback to students who show this kind of work so they can break the “equal sign as a do something” habit and learn to focus on the balance of equations.