# The Equal Sign Means Relationship, Not Action

Blog post #1 in the series, Lies We Tell Our Students

The Story

A while back, I was working in a fifth-grade classroom, and as a warm-up, I put the following equation on the board:

8 + 4 = 1 + 11

I then asked the students, “Is this statement true or false?” After waiting several seconds, I asked them to raise their hands to indicate their votes. At that point, two students voted for true, and the other 22 students voted that the statement was false.

Being the good teacher that I am, I asked the students to discuss their thinking, believing that those two students who said it was true would quickly convince the others. However, when I brought the class back together and once again asked my questions, 24 hands went up stating that the answer was false.

“Yikes!” I said, “What’s going on here? This statement is actually true. Can you tell me what you’re thinking?”

“Mrs. Rimbey,” started one of those original two students, ”8 + 4 does not equal 1.”

The Lie

I’ve since come to learn that this is not an isolated case. Many students across the grade levels believe that the equal sign is a symbol that indicates the action of finding the answer, when, in fact, it actually signals a relationship between the expressions on each side. In the vast majority of classrooms, students develop this misconception because virtually every equation they see in the early grades follows the same format: 3 + 3 = 6; 4 x 4 = 16; 20 – 13 = 7; and so forth. The “answer” appears last.

The Truth

So, what do we do about this? We can be sure to provide students with multiple daily opportunities to see equations written in different formats, pointing out that the equal sign indicates an equal relationship, not the action of finding the answer. Provide examples with the “answer first” (e.g., 6 = 2 + 4), with “nothing to do” (e.g., 1000 = 1000), or with “no answer” (e.g., 32 + 42 = 20 + 5).

The Series

This blog post is the first of a series that addresses the lies we tell our students. It’s important to note that these lies are not deliberate untruths. Rather, they are rules, procedures, mnemonics, and tricks we teach kids in an effort to make math easier for them. Sometimes the lies come in the form of omission, such as the example of the equal sign, shared above, where we don’t provide enough varied examples. Sometimes they come in the form of half-truths, such as addition and multiplication always make bigger, which is only true with natural numbers (not including 0).

In Summary

To sum up this week’s Lies We Tell Our Students: