# How to Teach Exponents in Middle School with Math Wheels

Teaching exponents is a personal highlight for me. However, I noticed that my middle school students struggled to grasp the concept. I turned to my trusty math doodle wheels to enhance our note-taking process. My hope was to simplify the various steps involved in working with exponents. I’m excited to share with you how to teach exponents using the Exponents Math Wheel. It’s the best way I’ve found to teach exponents while engaging my students as they apply the concepts immediately.

## What is a Math Doodle Wheel?

Before fully diving into how to teach exponents, I want to give you more background on the doodle wheel mentioned earlier. Say goodbye to the era of conventional fill-in-the-blank notes and the hurried transcribing of information from the board. Doodle wheels are a form of note-taking that uses one side of a page to efficiently organize and condense class notes on specific subjects. Throughout the year, both you and your students can consistently refer to these note pages for easy access to definitions, reminders, and examples of the concepts your students have been learning.

Doodle wheels aid students in note-taking and memory retention. These study tools become invaluable resources for organizational skills, encouraging independent learning and reinforcing key concepts. Positioned at the wheel’s center, your students can doodle and color in the central concept, essentially designating it as the “title” of the math wheel.

The remaining sections of the wheel are dedicated to essential vocabulary, as well as the sequential steps and strategies for the focused math skill or other subject area concept. In each section, students jot down definitions or steps, which are then followed by opportunities to practice the step with a few practice problems independently, in pairs, or as a whole class.

After the note-taking process, students revisit their notes and add color to each section, whether through background shading, font styles, or doodles. These visual cues assist students as they apply their skills throughout the unit or later in the academic year. It’s an engaging method to cement understanding and retention of math concepts!

Want to give Doodle Wheels a try? Grab the free Fraction Operations Doodle Wheel and try it out in your classroom.

## How to Teach Exponents with the Math Doodle Wheel

Now that we know what Doodle Wheels are, let’s jump right into how I use them to teach exponents.

I start out by passing out the Exponents Math Doodle Wheel to each of my students. As they wait for notes to start, they can doodle in the word “exponents” in the center of their wheels. This wheel is divided into four sections that review exponents and bases, what exponential form is, square and cubed powers, and special exponent rules. We’ll dive into how to teach exponents and additional rules with the next wheel.

### 1. Exponents and Bases

I always start with this section first because it starts with the foundation for exponents. Our kiddos have to know what they’re looking at, right? We write out the definition for base, which is a number that is multiplied by itself. I go up to the large five in the center of this section, and we immediately label it with the word “base.” This way, my students have heard the definition, written it down, and now can see an example of a base number.

We move on to the next definition, which is for exponent. The definition we use is “a number that indicates how many times the base is multiplied by itself”. We head back to where the five is, but this time, we zero in on the three to label it “exponent.” I point out how the three is smaller than our base number and appears to be floating off the line. That is also a good clue to know that number is an exponent.

### 2. Exponential and Expanded Form

Moving on to our next section, we look at the part of the definition that mentions how the exponent tells us how many times the base is multiplied. Very often, my students want to take that exponent and the base number and multiply them against each other like a regular multiplication problem. This is where we work through exponential form and expanded form.

We first start with the definition of exponential form. I explain how it’s a numerical expression written as a base and an exponent, like our example in the first section, 53. Then we take a look at expanded form, which is taking the same expression and writing it out as multiplication.

For example, 53 would become 5 x 5 x 5 (= 125). The exponent, 3, tells us we need to multiply our base number, 5, three times. That’s why we have three fives. We add a different example of expanded form to our Doodle Wheel to help students remember this important form. This time I start with the multiplication problem (expanded form) and have students figure out the exponential form. I write 6 x 6 x 6 x 6 and let students determine that this is the same as 64 (= 1296). Even though it’s not shown on this wheel sample, you could add the expanded form of 53 near the term ‘expanded form’. AND, you could add 64 up near ‘exponential form’ if you want. Since there’s a little bit of white space in this section, you could have students add additional examples of these forms.

You may also want to add the solutions to 53 and 64 so students quickly begin to understand that the products here are NOT 15 and 24. However, the point of this section is to understand the difference between exponential and expanded forms.

### 3. Squared, Cubed Powers

In our third section, I guide my students through a series of key vocabulary and a couple of examples. The first vocabulary word we look at is “squared”. I explain that squared means raised to the 2nd power. An example of this would be 92 = 9 x 9 = 81. We start with a base number of 9 and an exponent of 2. The exponent tells us to multiply 9 two times. When we multiply 9 x 9, we find the product of 81.

The next term is cubed, which means raised to the 3rd power. An example would be 83 = 8 x 8 x 8 = 512. Our base in this example is 8, and our exponent is 3, which tells us to multiply 8 three times. I tell my students to start from left to write and multiply two numbers at a time. So, 8 x 8 = 64 and 64 x 8 = 512.

The last two terms in this section are power and 24. I explain to them that the term “power” is a synonym for exponents. An example would be 24. We would read that as “2 to the 4th power” since our exponent is 4. And if you want students to practice with expanded form, they can write out 2 x 2 x 2 x 2. And then find the product of 16. Again, there’s a little bit of space here if you want to practice having students write different expressions using ‘power.’ For example, ask students to write 4 to the 5th power or 3 to the 6th power.

### 4. Special Exponent Rules

Our last section shows how to teach exponents in special cases. In the middle of this section, there is a x0 and x1.

I start with the x0 and write on the left side of this section that when we see a base number with a 0 for an exponent it will always equal 1. So, x0 = 1. We add a couple more examples in the section, such as 190 = 1 and 1000 = 1.

On the right side of the section, I explain what x1 means. I write that any base number to the 1st power equals that number. For example, x1 = x. We also write down 21 = 2 and 161 = 16 for additional examples.

## Engaging Activities After Note-Taking

After working through each of the definitions and rules, I allow my students to add color to help them remember the information. They revisit their notes, adding color, drawing doodles, and extra symbols. The use of colors and doodles proves effective in reinforcing our lessons on exponents.

Once we have established a strong foundation for exponents, I pull out games and activities to continue reinforcing the skills. Read Playing Exponent War: An Exponent Activity for 6th Grade Math to learn a well-loved game amongst my students. In this activity, students play in pairs with half a deck of cards, each representing a base and an exponent. They calculate the value of their exponential expressions, and the student with the higher expression wins the cards. I do suggest using calculators for large numbers and introducing scientific notation if needed. There is a free recording sheet available for download in the post.

## How to Teach Exponents Made Easy

Teaching exponents has become a rewarding experience for me. When I saw my middle schoolers struggling to grasp this math concept, I knew I needed to figure out how to teach exponents in an approachable way.

The math wheel proved to be a game-changing tool in simplifying the complex steps involved in working with exponents. By infusing color, doodles, and engaging activities, I created an accessible learning experience for my students. Teaching exponents has indeed become a more manageable task, thanks to these effective and visually appealing instructional tools.

## Save for Later

Remember to save this post to your favorite math Pinterest board for when you are looking for guidance on how to teach exponents.

## Ellie

### New Middle School Teacher Guide to the First Days of 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!