When students in Grades 3 and up initially learn to add, subtract, multiply, divide, and work with basic numerical expressions, they begin by performing operations on two numbers. But what happens when an expression requires multiple operations? Do you add or multiply first, for example? What about multiply or divide? This article explains what order of operations is and gives you examples that you can also use with students. It also provides two lessons to help you introduce and develop the concept.
- Perform arithmetic operations involving addition, subtraction, multiplication, and division in the conventional order, whether there are parentheses or not. (Grade 3)
The order of operations is an example of mathematics that is very procedural. It's easy to mess up because it's less a concept you master and more a list of rules you have to memorize. But don't be fooled into thinking that procedural skills can't be deep! It can present difficult problems appropriate for older students and ripe for class discussions:
- Does the left to right rule change when the multiplication is implied rather than spelled out? (For example, \(3g\) or \(8(12)\) instead of \(3 \times g\) or \(8 \cdot 12\).)
- Where does factorial fall within the order of operations?
- What happens when you have an exponent raised to another exponent, but there are no parentheses? (Note that this lesson does not include exponents, although if students are ready, you can expand your lesson to include them.)
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