Order of Operations

In sixth-grade math we do quite a bit of work with order of operations. My students come with a working knowledge of the rules for order of operations however, there are some common mistakes that they make. The students can recite the famous saying, "Please Excuse My Dear Aunt Sally". They understand that the letters PEMDAS stand for parentheses, exponents, multiplication, division, addition, subtraction.

The problem with this saying is the students see the order in a linear manner and believe that multiplication is always performed before division and addition always before subtraction. To try and clear up this misconception I reteach my students the rules for order of operation using a stairs or steps method. I draw four stairs or steps and list the steps as follows.

I label the first step with a P and the second step with an E. The third step I label with a M and a D along with an arrow going left to right. The fourth and final step I label with an A and a S along with another arrow going left to right. This diagram helps students to remember that multiplication and division are the same step in the order of operations and should be completed left to right following the parentheses and exponents steps. It also shows the same concept for addition and subtraction being the same step.

This has had success in my classroom for my students to see the order of operations less linear and clear up some of the common mistakes being made.

If anybody has suggestions that have had success with teaching the order of operations please feel free to contribute.