## The Nuts and Bolts of a Mathematical Expression

### Johnny WolfeSanta Rosa District Schools

#### Description

When an expression contains more than one operation, you can get different answers depending on the order in which you solve the expression. Mathematicians have agreed on a certain order for evaluating expressions, so we all arrive at the same answers.

#### Objectives

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

- Order of Operations Examples
- Order of Operations Worksheet
- Order of Operations Checklist
All three handouts from above are available in Associated File

#### Preparations

1. Prepare transparencies, if teacher uses overhead for examples.
2. Have ORDER OF OPERATIONS EXAMPLES prepared and ready to demonstrate to students. Available in Associated File.
3. Have enough copies of ORDER OF OPERATIONS WORKSHEET for each student. Available in Associated File.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, and decimals. This lesson addresses all areas of standard except inverse relationships.
1. Get students attention by making the statement “We are going to learn the nuts and bolts of mathematical expressions - what makes them work together and mold into a fine running machine.”
2. Ask the students if it matters how operations are performed in a mathematical expression. Then have two students work a problem on the board (example # 1 and example # 2 from the Order of Operations Examples in attached file would be good choices.) Have student # 1 work the example from left to right and student # 2 work the parenthesis first. Make sure the students understand that “Order” is important when working out a problem.
3. Make the following statement to the students, “When an expression contains more than one operation, you can get different answers depending on the order in which you solve the expression. Mathematicians have agreed on a certain order for evaluating expressions, so we all arrive at the same answers. We often use grouping symbols, like parentheses, to help us organize complicated expressions into simpler ones. Here's the order we use:
a. First, do all operations that lie inside parentheses.
b. Next, do any work with exponents or roots.
c. Working from left to right, do all multiplication and division.
d. Finally, working from left to right, do all addition and subtraction. “

4. Work the examples from the ORDER OF OPERATIONS EXAMPLES in the attached file. Have students indicate the order of operations as they occur. Then have the students evaluate the expressions.
5. Distribute the ORDER OF OPERATIONS WORKSHEET in associated file.
6. The student will state the operations that are needed to evaluate the expression and the order in which these operations occur.
7. The student will evaluate the expressions in the correct order using mental math and/or pencil-and-paper. These results are to be recorded on the worksheet.
8. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to the “checklist” (see attached file). These scores may be placed in the grade book if students have received enough practice and feedback to be successful. If they have not received enough practice and feedback, this lesson's work should be formatively assessed, ONLY.

#### Extensions

Ask students to pick 4 numbers and see how many different expressions they can come up with using the operation symbols (add, subtract, multiply, divide, exponents, and parenthesis.)