# 5.7 - Order of Operations

The student will

• simplify whole number numerical expressions using the order of operations.*

*On the state assessment, items measuring this objective are assessed without the use of a calculator.

### BIG IDEAS

• So that I can correctly solve multistep problems with different operations.
• So that when I am shopping I can make the proper calculations to find the tax and/or discount on an item.  For example, you buy four items and go to the cashier.  The cashier will enter the four prices, then find the total and finally apply the discount to the total.
• So that I can also use order of operations in everyday life  (i.e ordering food for multiple people or collecting money for multiple family members for an event).
• So that I understand that I do things in a certain order to get the correct outcome. When are you getting ready for the day you do things in a certain order.  For example you would not put your pants on and then your underwear.  Math is the same way.  You have to do certain operations first.

### UNDERSTANDING THE STANDARD

• An expression is a representation of a quantity. It is made up of numbers, variables, computational symbols, and grouping symbols. It does not have an equal symbol (e.g., 15 × 12).
•  Expressions containing more than one operation are simplified by using the order of operations.
•  The order of operations is a convention that defines the computation order to follow in simplifying an expression. It ensures that there is only one correct value.
• The order of operations is as follows:
• First, complete all operations within grouping symbols. If there are grouping symbols within other grouping symbols, do the innermost operation first. (Students in grade five are not expected to simplify expressions having parentheses within other grouping symbols.)
• If there are multiple operations within the parentheses, apply the order of operations.
• Second, evaluate all exponential expressions. (Students in grade five are not expected to simplify expressions with exponents.)
• Third, multiply and/or divide in order from left to right.
• Fourth, add and/or subtract in order from left to right

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Use the order of operations to simplify whole number numerical expressions, limited to addition, subtraction, multiplication, and division. Expressions may contain parentheses.
• Given a whole number numerical expression involving more than one operation, describe which operation is completed first, which is second, etc

### KEY VOCABULARY

Updated: May 29, 2019