# How To Do Order Of Operations: An Extensive Guide For Teachers

As a math teacher, some concepts are easier to teach than others. Teaching students how to do order of operations is one of those concepts that falls under “than others.” But don’t worry, over the years I have developed a sequence of teaching and a variety of activities that helps my students understand this important math concept. I hope you can find some new ideas that you can implement in your classroom as you teach your students how to do the order of operations.

## Order of Operations Doodle Wheel Notes

Students today become easily overwhelmed when multiple steps come into play. I see it with multiplication, when we work on long division, and with fractions. And. . . I see it year after year when teaching the order of operations.

The first thing I do is reassure the students that they already know how to do all the math. I let them know that we aren’t going to be learning anything new – but instead, we are going to focus on the order we work through a problem. I want to break it down for them in this way to prove to them that they already have the knowledge they need. This tends to break down any walls and ease them into learning about the order of operations.

Before starting the notes, I write a couple of different math problems on the board to demonstrate the importance of the order of operations. For example, I may write on the board 3 + 4 x 7 = ?. I will ask the students to solve the problem. When it’s time to share out their answers, I may receive a range of answers varying from 31 to 49. The correct answer is 31, which usually elicits an uproar of shock from some students. They will argue that 3 + 4 = 7 and 7 x 7 = 49. They just cannot accept that 49 is not the correct answer. It’s this exact passion for being right that makes this the hook you need to open your lesson for the order of operations.

When choosing an opening equation for this topic, make sure to choose one that does not naturally follow the order of operations from left to right. For example, if I had used 3 x 4 + 7 most of the students would have gotten the correct answer of 19. And this . . . just reinforces the left to right misunderstanding. So carefully choose the equation.

Once they are curious about this new topic, I hand out our doodle wheel notes. At the beginning of the unit, we fill out the Order of Operations Notes Doodle Wheel as a whole class. It’s a low-pressure way to take notes, focus on a couple of examples for each step, and then add in the color to help remember each of the four steps.

## Helping Students Remember the Order of Operations with PEMDAS

PEMDAS (or GEMDAS) is an acronym commonly used to help people remember the correct order of operations. Teaching your students this acronym is a great mental tool to help them recall this important math skill. PEMDAS stands for Parentheses (or G for Grouping Symbols), Exponents, Multiplication / Division, and Addition / Subtraction.

Let’s dive into each step of PEMDAS and what students need to know.

### 1. Parentheses

The first step in PEMDAS is P – and that stands for parentheses. Parentheses, or other grouping symbols like brackets, are used to group a part of the mathematical expression together. If there are parentheses in the equation, that is what should be solved first. These symbols can be found at the beginning, middle, and end of the expression. No matter where they are, the students need to solve whatever is inside the parentheses first.

For example: 4 x (5 + 2)

Students will solve the parentheses first: (5 + 2) = 7

Then the students will multiply: 4 x 7 = 28

After we’ve gone through an example of an expression with parentheses on the board, we fill out our notes on our doodle wheel. Then we practice with a couple more examples using parentheses for them to refer to throughout their unit.

Throughout our practice on this step, you will hear me say this repeatedly: “What do we do first?” The students will remind me that we always do the math inside the parentheses first. When they start groaning their answer back to me, I know that I’ve said it enough to make it stick.

### 2. Exponents

The second step in PEMDAS, the E, stands for exponents. For this step, students will need to learn or already know how to work with exponents. If your students have not yet been introduced to exponents, then you can skip this step. I like to tell my students what the E stands for and then let them know that they will learn about it later in the year or next year. This allows me to teach the step and avoids any misunderstanding down the road.

If students have already been taught exponents, then now is the time to do them. This is also a great time for a little exponent review. While filling out the notes on the doodle wheel, we’ll refresh our minds on which number is the base and which number is the exponent. When solving with exponents, we multiply the base number by itself the number of times the exponent says. For example: 52 –> 5 x 5 = 25 and 54 –> 5 x 5 x 5 x 5 = 625.

We will do some warm-up problems as well to get back into the swing of solving with exponents if it has been a while. Once I feel like they are confident, I will introduce the exponents in an order of operations problem. Generally, I like to include an example problem that also includes parentheses so that we can review that step too. This also allows students to see the steps in order.

### An Exponents Example

An example problem is below:

43 + (6 / 2) + 3

Students will first look for parentheses and solve what is inside. 6 / 2 = 3

This makes our problem 43 + 3 + 3

Next, they will calculate the exponents: 4 x 4 x 4 = 64

Now the problem looks like 64 + 3 + 3

Last, students will add all 3 numbers together: 64 + 3 + 3 = 70

As we are working through our problems I will continue to reinforce the steps with a little chant. It might sound like this:

Teacher: First comes. . .

Students: Parentheses

Teacher: Next comes. . .

Students: Exponents

### 3. Multiplication / Division

The third step in PEMDAS focuses on the 3rd and 4th letters – M and D. This step is when we do all multiplication and division in order from left to right. It’s important for students to understand that the M and D are on the same level in this step. They do NOT do all the multiplication first and then all the division. Students will need to look through the expression, starting at the beginning (left side), and complete all the remaining multiplication and division in the problem. Sometimes these operations will already be completed because they were in parentheses.

An example problem may look like this:

3 + 5 x 6 + (3 x 2)

First, students will look for and solve what is in parentheses: (3 x 2) = 6

Then, students will look for exponents, which this example does not have.

Next, students will look for additional multiplication or division symbols. They will solve: 5 x 6 = 30

Lastly, students will add all 3 numbers: 3 + 30 + 6 = 39

I find that my students have higher confidence in approaching multiplication and division due to how frequently they use these operations. Once these operations have been introduced on the board, we fill out our note section on the doodle wheel and work through additional examples.

You should not be surprised to find out that I continue with interactive questioning to help reinforce the steps in the order of operations. For this step, I will likely add something like “Then comes. . .” to the same chant we used during step 2. I’ll also follow up with some questions like “Do you do all the multiplication first?” just to help reinforce this important aspect of the step.

### 4. Addition / Subtraction

The last step in PEMDAS focuses on the last two letters – A and S. Similar to step 3, students will do two operations in the final step. This time the focus will be on addition and subtraction. By this step, my students are feeling like seasoned pros because, just like with multiplication and division, they can move from left to right and are familiar with how to do these operations.

Again, students need to understand that addition and subtraction are both done as they appear from left to right. The addition parts do not get done first just because the A comes before the S in PEMDAS.

An example problem may look like this:

10 – (2 x 4) + 8

First, students need to see if there are parentheses and solve what is inside them: (2 x 4) = 8

Then, students need to work from left to right: 10 – 8 + 8

Subtraction comes first: 10 – 8 = 2

Then, addition comes next: 2 + 8 = 10

By this point, my students are having lightbulb moments and are itching to jump into more practice. So, we finish up our doodle wheels by completing the note section on addition and subtraction along with a couple of examples.

### Finish with Review of the Steps

At this point in class, I give the rest of the time to read over our notes on their own, color in the wheel, and work on some of the practice problems on the outside of the wheel. While they do so, I walk around and answer questions or do an information check for understanding.

I highly encourage you to check out the Math Doodle Wheel because the colorful and creative design helps students to remember the order of operations and each of the rules. It also is versatile, allowing it to fit into your classroom and to meet your students where they are! As a teacher, you can use this resource as a way to introduce or review the order of operations with your students. This resource is an excellent addition to any math teacher’s toolkit, helping to make the order of operations more accessible and enjoyable for students.

## Order of Operations Practice Activities

Now that I’ve laid the foundation with notes, examples, and visuals, I look for hands-on activities to engage my students while they apply what they’ve learned. I have 3 go-to order of operation activities that my students have loved year after year!

### 1. Order of Operations Color by Number Pages

My students are obsessed with working on these pages during independent work time and center rotations. They also don’t seem to mind homework as much when it’s one of these pages. I am personally obsessed with them because they are easy to prep, my students are repeatedly practicing the order of operations, they are self-checking, AND coloring can be calming to my students.

The Order of Operations Color by Number activity has a variety of levels in it. This makes differentiating for your current grade level or the needs of your students so easy. Two versions have the same 20 questions, but with a different color scheme. The questions are in a different order on the question pages, so students can’t easily check out their neighbor’s answers (if they aren’t working together). A third version has only 15 problems that are different from the other versions and has a less complex coloring page. There are also digital versions of these!

As your students start mastering the order of operations, they could create their own color-by-number page using the blank coloring page! This is awesome for early finishers, extension projects, or just to demonstrate mastery of the math concept instead of a test.

### 2. Order of Operations Truth or Dare Game

Truth or Dare – three words I can say in class and instantly have everyone’s attention. I love using Truth or Dare Games with my students! They always cheer or at least perk up a bit more when this is on the schedule for the class. And. . . playing Truth or Dare when we are practicing the Order of Operations is no different.

When I pull out the Order of Operations Truth or Dare game, I’ll place my class into partners or groups 3. This way, I know that each of my students is receiving ample practice with how to do order of operations.

The cards will be stacked in a truth pile and a dare pile. The truth pile has cards with a true or false question on it about the rules of the order of operations or a simple order of operations problem. The dare pile will have more challenging order of operations problems for the students to solve.

While the students work through the cards, they record their answers on the recording page and keep track of the points they earn. You can make this a game where the person with the most points wins – or use the points as the goal for the assignment (i.e. you must earn 15 points or more).

This game is not just fun, but also challenging and engaging for my students. I usually walk around checking in with students, and my favorite part is hearing the conversations that the groups enter into. You’re not typically going to hear students willingly talk about math, but with this game, they do!

### 3. Order of Operations Footloose Math Task Cards

The third resource that my students love is the Order of Operations Footloose Math task cards. This resource checks so many boxes that we as educators always look for. This activity gets our students up and moving around the classroom, all while practicing the order of operations. Students love any opportunity where they can leave their seats. It creates buy-in and encourages the students to be more willing to participate actively in the activity.

The setup is also really simple. Before class, I will tape the cards around the perimeter of the room. After the directions are given, students will grab a clipboard and recording page and begin visiting each of the cards. You can make this as structured as you want – allowing students to move at their own pace or having them move in a set rotation after a certain amount of time.

These 30 Footloose task cards have different ‘difficulty’ levels, so you can choose the cards that best meet the current level of your students.

I like to use these free Footloose Order of Operations Task Cards as a practice activity. But I will also pull out these task cards at the end of our unit or before our end of the year test to review for our upcoming assessments.

## Have Fun with the Order of Operations

Teaching the order of operations can sometimes be frustrating. There are lots of steps and rules that students must remember. For the best results, use a variety of different activities that gets them thinking about and practicing the order of operations in different ways. Just like other skills, some years the class grasps the concept faster than other years. Having a variety of resources at your fingertips will help you guide your students to mastery on this topic.

Once they get it, order of operation problems can be a lot of fun! Sometimes I will even share a social media math problem that I came across on my feed. My students love figuring out the answer and when they find out they solved the problem better than many adults they get super excited.

## An Order of Operations Freebie

To help you get started with teaching the order of operations, I am sharing this Order of Operations Sequencing Activity that I created for my students. I’ve written a blog post that walks you through step-by-step how to prepare and use this activity in your classroom! It is another fun and engaging way to get your students to practice the order of operations.

## Save for Later!

Remember to save this post to your favorite math Pinterest board! The included examples and activities will come in handy when you are working with your students on how to do order of operations!

## Ellie

### 7 Ways to Practice Multiplication Facts in Middle School

Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

• All subject areas in 4th and 5th grades
• Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

If you’re looking for ideas and resources to help you teach math (and a little ELA), I can help you out!

## LET'S CONNECT

##### Archives

Select the image above to learn more!

Engage students in taking math notes with this FREE Fraction Operations wheel and 3 wheel templates!