Order of Operations
As you continue teaching your students about parentheses, be sure to demonstrate that parentheses do not always change the value of an expression though they often do.
Materials: Overhead projector or front board; student parentheses activity sheet
Preparation: Make one copy of the student parentheses activity sheet for each student.
- Ask: What operation do I perform first in the expression 3 + 5 8 and why?
Write the expression on the front board or overhead projector. Make sure students remember that the order of operations requires you to do multiplication before addition.
- Ask: What happens if I want to add 3 and 5 before I multiply by 8?
Allow students to discuss ideas of how to override the order of operations. If they don't mention parentheses, remind them of what you did in the first lesson.
- Say: By putting parentheses around 3 + 5, we are saying that you must add three and five first, then multiply by 8. Today we're going to practice finding the value of expressions with and without parentheses and see what difference the parentheses make.
- Pass out the student parentheses activity sheet to each child.
- Say: Do exercises 1, 2, and 3.
Allow time for students to finish the exercises. Then have student volunteers report their answers.
- Ask: Did you get the same answer for all three exercises? Why do you think that is?
Students should notice that problems 1 and 3 yield the same answer while problem 2 is different. Discuss that problem 2 requires you to add before you multiply while problems 1 and 3 have you multiply before you add. The goal is for students to see that the use of parentheses sometimes changes the outcome of the problem. Then have students complete exercises 4 and 5.
- Ask: Are the answers to problems 4 and 5 the same? Why are the values different?
Once again, students should see the significance of the use of parentheses.
- Put students in pairs. Have students complete problems 6, 7, 8, and 9 on the activity sheet. Have students compare answers for 6 and 7 with each other as well as problems 8 and 9.
- Ask: Are the values for problems 6 and 7 the same or different? Why?
The answers are different because the parentheses cause you to perform addition and subtraction before the multiplication. You want students to see that parentheses can sometimes alter the order of operations.
- Ask: What about problems 8 and 9? Are the answers the same or different? Why?
The answers to these two exercises are the same. It is important that students see that parentheses do not always change the order of operations.
Wrap-Up and Assessment Hints
Make sure that you provide exercises that include parentheses and some that don't. It is important for children to have exposure to and be familiar with both types of problems. Make sure students can remember the rules for order of operations both with and without parentheses.