Applications

Applications of using the Order of Operations

Order of operations is an important mathematics topic typically introduced in grades 5 through 8. It is taught in the middle grades because understanding it is essential for many topics taught in Algebra I (Glidden,2008).

The Number and Operations Standard in the National Math Standards and Expectations from National Council of Teachers of Mathematics states:

Instructional programs from pre-kindergarten through grade 12 should enable all students to:

Understand numbers, ways of representing numbers, relationships among numbers, and number systems;
Understand meanings of operations and how they relate to one another;
Compute fluently and make reasonable estimates.

The following are suggestions for teaching Order of Operations:

Have students create narrative stories out of order of operation problems. For instance, ask them to describe a real-life situation that could be represented by the expression 5 + 8 x 6. Students might come up with stories about money, party planning or cooking, and their stories may reveal misunderstandings that are easy to correct. There are many opportunities for rich extension and discussion here: For instance, ask students how their story for that expression would differ from a story for the expression (5 + 8) x 6.
Use functions and patterns to have students derive the order of operations. For instance, an output pattern of 1, 3, 5, 7 could have a rule of 2 x N - 3, but that function will only give the correct outputs if the order of operations if followed properly.
Have students do comparison activities, evaluating the same expression in different ways. For example, students could try doing the problem 3 x 4 - 8 / 2 on their own and then with a calculator, or they could try doing the problem by putting parenthesis in different places. The variety of answers provides the opportunity for strong discussions about the why behind order of operations.
If you do use PEMDAS, list the letters in rows, to avoid the misunderstanding that multiplication comes before division or addition before subtraction.