Teaching algebraic expressions to middle schoolers has been a journey. One thing that stood out was the jungle of vocabulary words. It’s easy for students to see them as just mandatory terms to jot down, but I wanted to flip the script.
Gone are the days of monotonous two-column notes with definitions that rival the length of a novel. Instead, I’ve embraced bite-size definitions. Now, my students immediately see the words in action, accompanied by examples.
The tool that helped me make this shift is the Algebraic Expressions Guided Notes Doodle Wheel, which I am walking you through today! This resource informs my students about each relevant term. Coefficients? Check! Variables? Double-check! If you stay with me until the end, I have even gathered some bonus activities to help make introducing and reviewing algebraic expressions a breeze!
How to Use the Algebraic Expressions Math Wheel
Elevate your algebraic expressions lessons with the Algebraic Expressions Doodle Math Wheel! I love using this tool in my math classes because it injects life and energy into them. It’s a learning aid that creates vibrant visuals and hands-on engagement. And. . . it really breaks down the key concepts and helps students understand algebraic expressions better than anything else I’ve used over the years.
This wheel invites students to dive into algebraic expressions with enthusiasm. Carefully placed practice problems around the wheel add some reinforcement of key concepts. Plus, I have my students keep it in their notebooks for easy reference all year long.
With thoughtful sectioning, this graphic organizer provides a clear roadmap to mastering algebraic expressions. This math wheel is divided into six parts and we are going to take a look at each section.
1. Center of the Algebraic Expressions Math Wheel
Before diving into the different sections with my students, I ensure they clearly understand what expressions mean. In the center of the wheel, we write two key pieces of information that will help them.
I discuss and write how expressions are statements that use #s (yes, the hashtags on social media, but they are also called the pound sign and number sign!), variables, and operations. Depending on your students, you may want to review those two terms. Variables represent numbers, and operations are adding, subtracting, multiplying, and dividing.
The other statement I have my students write down is that these expressions can be numerical (4+5) or algebraic (x +2). I underline that x while explaining it to them because that is an example of a variable.
Once my students are feeling confident with what expressions mean and are, we move to the first section of the wheel. In this section, we look at terms and like terms with some examples. I use two different colors of markers because I write one definition and set of examples in one color and the other definition and its examples in another.
First, we talk about how a term is part of an expression that is usually separated from other terms with an addition sign (+) or a subtraction sign (-). An algebraic expression can have multiple terms in one expression. For example, 3z + 4 has two terms, while 7y – 6b + 8 has three terms. To help my students see these terms, I draw a box around each term.
I pick up my second color and explain that there can be ‘like terms’. Like terms are terms with the same variable and exponent. For example 7x + 5 – 2x. There are three total terms, but only 7x and 2x are like terms because they have the same variable, x.
In the next example I do with my students, they are exposed to exponents: 3x2 + 4y – x2. There are once again three terms, but 3x2 and x2 are the like terms because they both have an exponent of 2. As we go through these two examples, I draw a box around the like terms to help my students zero in on them.
As you work through the wheel, take as much time as you need to make sure that your students understand terms. It will help them with the remaining sections of the wheel.
The next term we look at together is coefficient. I explain how a coefficient is a number that’s multiplied by a variable. Sounds simple, but I still provide a series of examples to show my students.
While we write down the examples, we box the number that is being multiplied. One example that I use is 7y – 6b + 8. We draw a box around the 7 and the 6 because those are the numbers next to the variables that will be multiplied.
We work through the other examples to make sure that the students can see the setup of the algebraic expressions. As we do this I will even throw in some review. “7x – term or coefficient?” Once they tell me it is a term, then I will ask “Does this term have a coefficient? What is it?” We work through all of the examples and box all of the coefficients.
Now that my students and I have talked about the role of coefficients, some, at this point, will wonder about the numbers that aren’t paired with a variable. I explain that a constant is a number in an algebraic expression that is not multiplied by a variable. It stands by itself in the expressions.
Once we have the definition written down, we write down examples for them to see which numbers we’re talking about. I start off with an algebraic expression that has only 2. We take a look at 3z + 4. Right away, we see that 3 has a partner, the z, but 4 has no partner. So, we draw a box around the 4 because it is the constant with no variable.
Another example is 7y – 6b + 8. We immediately move past 7y and 6b because they have variables. We draw a box around 8 because it stands alone without a variable.
In the next example, I take a minute to explain that not every algebraic expression will have a constant. We jot down 3x2 + 4y – x2 as an example of this. Each term is a variable or paired up with a variable, resulting in no constant.
The last example is 7x + 5 – 2x. Since this is the fourth example, I let my students guide me with their thinking. They ignore the 7x and 2x because they have variables. The 5 is identified as the constant and we box it!
If students are struggling with this concept then I will continue to provide examples and questioning to help clear up the concept.
The variable section is the last section of the wheel focused on vocabulary. This section also tends to amp the math nerves. This section isn’t one to rush through, and I typically have the most questions during this section.
I start off by explaining how all algebraic expressions have variables, which we write to the side of the section. I then explain that a variable is a quantity that can change or vary. This quantity is usually represented by a letter. Once we know the definition it is time to put it into practice.
We move to examples but follow the same pattern of just writing down algebraic expressions and drawing squares around the terms we are focusing on. In this case, we are drawing squares around all the variables.
We start off simple with an algebraic expression that has two terms, which is 3z + 4. I explain in this section we can ignore any constant, a term without a variable. We also don’t need to include the coefficient because I want them to practice identifying the variable. In this example, we draw a square around the z.
The next example we work through is 7y – 6b + 8. We have two variables in this example, so we draw a square around the y and b. To get in the habit of math talk, I have my students tell me why we can’t draw a square around 8 (because it’s a constant).
We move on to another similar example, which is 7x + 5 – 2x. At this point, if they are feeling confident, I have my students guide me through this example. The five stands alone, so it is a constant. There are two like terms, 7x and 2x, but the variable for both is x. We draw a square around each x.
The last example for this section includes exponents, which is 3x2 + 4y – x2. I point out how this algebraic expression does not have any constants because all three terms have variables. We then draw a square around each x and the y.
Time for the action! We have identified and defined each of the essential parts that make up an algebraic expression. Now, we combine all of that knowledge to actually evaluate or simplify the algebraic expression.
Before jumping right into the simplifying, I first take time to define what “evaluate” means. We write down that evaluate means to find the value of the expression. We substitute a value in place of the variable and then we simplify. The big question, and we write this down, is how?
I have found that the best way is to show with an example because otherwise, those whirling brains begin to shut down faster than I can say evaluate.
I walk them through step by step on how to evaluate the algebraic expression of 7y – 6b + 8. We then look at our variables’ values, which include y = 3 and b = 2. So, 7y – 6b + 8 becomes 7(3) – 6(2) + 8. I remind my students that we want to multiply first to follow the order of operations. We multiply 7 x 3, which equals 21, and we multiply 6 x 2, which equals 12. About this time, that look of panic starts to fade and students begin seeing how focusing on one step at a time makes something that looks confusing or complicated quite simple.
Now our expression looks like 21 – 12 + 8. From here, we can subtract 21 – 12, which equals 9. We then add 9 and 8 making our final answer 17.
7. Examples of Algebraic Expressions in Action
For the last section, we practice two more examples together to help stabilize their understanding of how to evaluate algebraic expressions.
The first example in this section is an algebraic expression that has two terms 3x + 4 with x = 7. We insert the 7 for the x to make our expression look like 3(7) + 4. After multiplying the 3 and 7, we have 21 + 4. Adding those two numbers together we solve for the final answer, which is 25.
Our next example we work through has like terms 7x + 5 – 2x with x = 6. We plug 6 in for every x: 7(6) + 5 – 2(6). After multiplying 7 x 6 and 2 x 6, our expression becomes 42 + 5 – 12. We add 42 and 5, which is 47, and we subtract 12 from it, which equals 35.
Algebraic Expressions Made Easy!
The Algebraic Expressions Doodle Math Wheel is your ticket to unraveling the web of algebraic expressions. With 6 unique sections, this math wheel leads students through the different parts of expressions and evaluating expressions.
Once the wheel is completed, have your students practice problems scattered around the wheel. Depending on how my students are feeling, we might tackle these together for some guided practice or I let them venture into independent practice mode. Adding a burst of color to the background pattern is the finishing touch on their guided math notes.
After completing the math wheel, I have my students place them in their math notebooks. This math wheel becomes a reliable reference point that stays with them throughout the unit and beyond. Whether navigating the many parts of expressions or breezing through the evaluation problems, this math wheel offers structure and clarity. It’s a visual aid that transforms complex concepts into bite-sized, easily digestible bits of information making math approachable.
Ready to teach your middle schoolers algebraic expressions? Head over to the Cognitive Cardio Math TPT store, and discover the Algebraic Expressions Doodle Math Wheel that is ready to be downloaded, printed, and used in your classroom!
Oh, and if your students need more support with this topic, be sure to check out this post all about translating words into algebraic expressions. This exercise is a helpful first step in understanding each term and wrapping your brain around this concept.
More Resources for Teaching Algebraic Expressions
Looking for more easy-to-use resources to make teaching and learning algebraic expressions approachable for your students? Make sure to check out the following resources to help as you teach these important math concepts.
- Algebraic Expressions Math Game | Math Activity | Truth or Dare
- Algebraic Expressions Math Game Truth or Dare Math Activity Digital Resource
- Algebraic Expressions 2 Digital Resource Math Task Cards and Quiz
- Algebraic Expressions Math Task Cards and Quiz Digital Resource
- Algebraic Expressions Footloose Math Task Cards, Quiz Print and Digital Resource
Save for Later
Remember to save this post to your favorite math Pinterest board for when you need guided notes and resouces for algebraic expressions.