For this standard, it is important for students to understand why it is important to follow an order of operations. In mathematics, it is so important that readers understand expressions exactly the way the writer intended that mathematics establishes conventions, agreed-upon rules, for interpreting mathematical expressions. The basic principle: “more powerful” operations have priority over “less powerful” ones. The standard calls for students to evaluate expressions with parentheses ( ), brackets [ ] or braces { }.

Summary of the rules:

Parentheses first. Referring to these as “packages” often helps students remember their purpose and role. Exponents next. Multiplication and division next. (Neither takes priority and when there is a consecutive string of them, they are performed left to right).  Addition and subtraction last. (Again, neither takes priority and a consecutive string of them are performed left to right.)

Students will be given opportunities to explore and evaluate numerical expressions with mixed operations, including real-world contexts. Before students can tackle complex word problems, they will need to know how to translate simple problems into algebra. Generally, they will do this by replacing the words with operators that mean the same thing. Students will also need to understand how to write and analyze the expression based on the order of operation's basic principle and rules. This standard calls for students to verbally describe the relationship between expressions without actually calculating them. This standard calls for students to apply their reasoning of the four operations as well as place value while describing the relationship between numbers.