The Using Grouping Symbols Lesson shows when to use parentheses, brackets, and braces in expressions. Those grouping symbols are the first step in the rules developed by mathematicians long ago.
Having a standard order for solving math problems allows everyone to get the same result. In this lesson, you will be learning and practicing the rest of the order of operation rules.
By the end of this lesson, your children will be able to follow the order of operation rules to correctly evaluate math expressions and equations.
If you have not already done so, review the Using Grouping Symbols in Expressions lesson with your children. It covers the grouping symbols: parentheses, brackets, and braces, that are used in expressions and equations.
When there are no special grouping symbols, math problems are solved from left to right. The order of operations rules tell you the order in which you should do the operations (addition/subtraction/multiplication/division) in a math expression (math sentences that do not include an equal sign) or equation (math sentences that do include an equal sign). The Using Grouping Symbols in Expressions lesson covered the grouping symbols: parentheses, brackets, and braces. You know that math enclosed in one of these grouping symbols is done before math that is not inside a pair of grouping symbols. You also know that parentheses are the grouping symbols used most often.
As you begin to learn and practice applying the order of operation rules, you need to be able to quickly identify grouping symbols and operation signs. Take the pre-test that follows to see if you are ready for this lesson.Pre-assessment worksheet
Have your children take the Pre-Test that follows to see if they are ready for this lesson. If they get 5 or less correct, review the introduction with them or go back to the lesson on grouping symbols before continuing on to the lesson.
– Order of Operations in Expressions – Pre-assessment
Main Lesson: Order of OperationsSome people use PEMDAS or “Please Excuse My Dear Aunt Sally” to remember the order of operations.
P=parentheses (and other grouping symbols)
E=exponents (introduced in 6th grade)
When mathematicians from around the world met long ago to decide on a standard order for doing mathematical operations, this is the order they agreed upon:
- Do any math inside grouping symbols first: Parentheses, brackets & braces.
- Evaluate numbers with exponents: Whole number exponents will be explained as part of 6th grade lessons. They are not included in this lesson, except to know the correct order.
- Multiplication or Division: Multiplying and dividing have the same priority. When you are reading from left to right, do whichever one you come to first. Skip adding and subtracting until after all multiplication and division has been done.
- Addition or Subtraction: Adding and subtracting have the same priority. When you are reading from left to right, do whichever one you come to first.
Have your children work through these problems to practice applying the order of operation rules. After these model problems, there some more practice problems for your children to try on their own.
Practice Using Order of Operations
|14 – ( 7 + 6)|
Parentheses come first, so 7 + 6 = 13.
Plug in the 13 where (7 + 6) was, so: 14 – 13
There are no exponents in this lesson, so go on to operations.This problem contains only subtraction, so subtract.
14 – 13 = 1
|(8 – 4) + 5 x 8|
Parentheses come first, so 8 – 4 = 4.
Plug in the 4 where (8 – 4) was, so: 4 + 5 x 8.
There are no exponents in this lesson, so go on to operations.
This problem contains addition and multiplication. Multiplication comes before addition, so 5 x 8 = 40.
That leaves 4 + 40. Finally, add 4 + 40 = 44.
Children are often overwhelmed by a complicated math expression or equation. Remind them to focus on just one step at a time. Big tasks become easier to think about and accomplish when broken down into small steps.
Try evaluating these expressions by following the order of operations rules and then check your answers by clicking on the “Show/ Hide Answer” link.
|4 + (3 – 1) x 6|
|Click to Show/ Hide Answer
Parentheses come first, so 3 – 1 = 2.
4 + 2 x 6
Multiplication comes before addition, so 2 x 6 = 12
4 + 12
Addition is all that is left, so 4 + 12 = 16.
|(11 + 9) – 5 x 2|
|Click to Show/ Hide Answer
Parentheses come first, so 11 + 9 = 20
20 – 5 x 2
Multiplication comes before subtraction, so 5 x 2 =10
20 – 10
Subtraction is all that is left, so 20 – 10 = 10
|[17 – (2 + 8) + 2] ÷ 3|
|Click to Show/ Hide Answer
Grouping symbols come first, and parentheses before brackets, so 2 + 8 = 10.
That leaves: [17-10+2] in brackets. 17-10 = 7,
7 + 2 = 9.
The total value inside the brackets is 9.
That leaves just division: 9 ÷ 3 = 3
- Mathematicians agreed upon certain rules for solving math, called the order of operations.
- Grouping symbols come first. If there is more than one grouping symbol they go in this order: parentheses, brackets, braces.
- Exponents come next. You will use these in future lessons. For this lesson, you just need to know that they come after grouping symbols in the order.
- Multiplication or Division comes next. They have the same priority, so whichever is first left to right goes first.
- Addition or Subtraction comes next. They have the same priority, so whichever is first left to right goes first.
- Don’t feel overwhelmed by complicated problems. Take them step by step, one piece at a time, and you’ll be able to solve them!
Review the recap points above with your children and then print out the Assessment Worksheet below.
- Evaluating Expressions – Post-assessment (10 questions)
At least 7 out of 10 correct will show that your children are ready to go on to the next lesson: Writing Simple Expressions.