Order of Operations
- Why should I bother learning this?
Demonstrate what a big difference parentheses can make in the value of an expression. In the expression 4 + 2 x 7, order of operations requires you to multiply 2 x 7 first before adding the product to 4, giving a final sum of 18. If you put parentheses 4 + 2, then you find the sum of 4 + 2 (which is 6) and multiply that by 7 to get 42.
- Do parentheses have to go around only two numbers?
No! Many students think that parentheses are used only around two numbers. This does not have to be the case. For example, 6 x (3 + 2 x 5) 8 requires you to find the result of 3 + 2 x 5 first since it is in parentheses. When you have more than two numbers inside parentheses, you follow order of operations inside the parentheses as well. Therefore, you would find 2 x 5 first and add that to 3 which would yield 13. Then you would have 6 x 13 8. Since the parentheses have been removed, you now proceed with order of operations for the remainder of the problem.
- Can you use more than 2 parentheses in an expression?
Absolutely. Although your students may only encounter one set of parentheses at this level, you can show them that more than one set of parentheses can be used in a single expression. It will help to introduce the use of multiple parentheses by using two sets apart from each other such as (3 + 5) x (12 6). Show students that, just like with other operations, you start at the left. Depending on your students, you may also want to introduce the use of embedded parentheses such as 4 x (3 + (9 2) x 6) + 8. Be sure to calculate the value of the innermost set of parentheses first. Your students will see other ways to use embedded parentheses later in their mathematical development. Be sure not to overwhelm them at first. Students need to have a good understanding of using one set of parentheses before encountering multiple sets in one expression. These exercises can be fun and challenging for your more accelerated students.