Order of Operations
Before your students use parentheses in math, they need to be clear about the order of operations without parentheses. Start by reviewing the rules for order of operations, and then show students how parentheses can affect that order.
Materials: Overhead projector or front board
Prerequisite Skills and Concepts: Students should have a working knowledge of order of operations for addition, subtraction, multiplication, and division. Students should also have mastered the basic facts for all four operations.
- Ask: What operation do I perform first in the expression 5 7 + 3? Why?
Write the expression on the front board or overhead projector. If students don't remember the rules for order of operations, remind them that multiplication and division come before addition and subtraction.
- Ask: What is the value of this expression?
Walk students through evaluating the expression. 5 7 = 35, so the expression becomes 35 + 3, which equals 38.
- Ask: What happens if I switch the addition and multiplication symbols? What value would I get?
Rewrite the expression as 5 + 7 3, and work through the evaluation. 7 3 = 21, so the expression becomes 5 + 21, which equals 26.
- Ask: Did we get different answers when we changed the operations?
This result will probably not surprise your students too much. They most likely know that performing different operations on the same numbers will give different answers.
- Ask: What if I wanted to keep the multiplication and addition symbols in the same place but get a different answer? How do you think I could do that?
Discuss the question for a short time, then write 5 (7 + 3) on the board.
- Point to the parentheses.
- Say: We call these symbols parentheses. If there are parentheses in an expression, do whatever is inside the parentheses first.
- Ask: What is inside the parentheses in the expression 5 (7 + 3)?
Make sure that students can identify the parts of the expression before continuing.
- Say: Now, let's find the value of the expression with parentheses. (The value is 5 10, or 50.)
Is that the same value we got before?
Help students notice that the answer isn't the same as either the original expression or the expression with the operation symbols switched.
Give students a few more examples, showing an expression with and without parentheses. Have student volunteers evaluate the expressions and compare the answers.