Order of Operations & Numerical Expressions

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

In today's opening we will discuss the importance of doing something that requires multiple steps in the proper order. To do this, I will ask my students the following questions:

• How do you make a sandwich?
• How do you clean your room?
• How do you vacuum the carpet?
• How do you wash the dishes?
• How do you clean the kitchen?

In asking these question, I want the students to realize that in each case there is a method to how they do each task to optimize the final result. When washing dishes, you wouldn't wipe the dishes off with a drying towel first and then put them in the soapy water. When making a sandwich, you wouldn't put the two slices of bread together before you put the ingredients that belong in between the slices on first. When vacuuming, you wouldn't pick up toys and other object not meant for the vacuum after you vacuum.

After having this discussion, I will inform my students that just like there is a method to making a sandwich, cleaning your room, vacuuming, washing dishes, or cleaning the kitchen, there is also a method to solving a mathematical expression with multiple operations.

Using today's opening discussion, I will segue into instruction that will demonstrate the importance of order of operation when it comes to mathematical expressions. During this instruction, I will also address the common misconceptions that multiplication always comes before division and addition always comes before subtraction. Most students coming to 6th grade have learned order of operations using the coin phrase "Please Excuse My Dear Aunt Sally," where the P in Please stands for Parenthesis, the E in excuse stands for exponents, the M in My for multiplication, the D for division, the A for addition and, the S for subtraction. While this phrase is useful in allowing students to remember the order in which expressions are to be solved, it is also misleading because multiplication doesn't always come before division and addition does not always come before subtraction. In reality, which ever of the two operations comes first in the problem when reading the expression from left to right is the operation that should be completed first. For example a problem such as 32/8 x 6, you should divide first and then multiply. If you multiply first, you will arrive at the wrong solution.

This misconception will be addressed as I demonstrate to my students how to evaluate a numerical expression using the order of operations. 

To do this, I will provide my students with a graphic organizer upon which they will take notes. The graphic organizer will allow students to take notes concerning the order of operations and how it is used to evaluate expressions. Furthermore, it will allow students to take note of the following three examples:

• 3 * (5 - 2)^2 +7
• 27/3 + 6 * 4 - 16
• (30 - 6)/3 * 3^2 - (2 + 5)

To practice I will have my students complete three practice problems involving order of operations. They will complete these problems individually. To get them really involved and motivated in the assignment,  I will have the students race to receive a prize as to who finishes first and all answers are correct. I will give a prize to the first 5 to finish first who also have all the correct answers.

The rules of the race are as follows:

1. When I say go, I will display the three problems on the projector. At this time students can begin avaluating the expressions.
2. Once they have completed all three, they are to turn thier paper over and raise thier hand.
3. I will write their names down in the order that their hand was raised.
4. This will continue until every student has raised their hand.
5. After all students have raised their hand, I will check to see which students were the first to get all three solution correct.

The PowerPoint that is attached to this section of this lesson contains the three problems that the students will need to solve properly to win the race.

To practice the concepts taught during this lesson, I will have my students do two things.

First, I will have my students solve 2 problems where all they have to do is follow the order of operations to arrive at the correct solution

Second, I will give my students 15 minutes to complete one real world situation problems that will involve writing an expression and then evaluating the expression using given data. Students will work with a partner on this assignment. Students will discus with partner ways to solve the problems. Together, they will create an ACTION PLAN to solving the problem and use that plan to actually solve the problem. Students will present their work on chart paper. They will write the problem, their action plan, their mathematical solution, and any problems that they came across when solving the problem.