# Tips for Teaching Ratios and Rates in 6th, 7th and 8th Grade Math

Are your students hitting a bit of a roadblock when it comes to wrapping their heads around ratios and rates? Need a fun and colorful way to dive into these math essentials? Well, you’re in for a treat! In this blog post, I’m about to unveil how I teach Ratios and Rates using guided notes on a Math Wheel. It’s a lively, interactive graphic organizer that swoops in to make ratios and rates a walk in the park for your students.

So, if you’re on the lookout for a fresh and exciting way to tackle these fundamental math concepts, you’ve come to the right place. Plus, stick around to the end for some bonus resources ready to be used in your classroom today!

## How to Use the Guided Notes Math Wheel for Ratios and Rates

Liven up your lessons with these guided notes using the Ratios and Rates Math Wheel! This math wheel is perfect to use as you introduce and teach this topic or save and use as a review of the topic later in the unit. However you choose, this ratios and rates math wheel is sure to help your students understand this concept. It’s a graphic organizer and a handy study tool that students can stash in their notebooks for easy access. This specific math wheel is split into four parts!

### 1. What is a…

Let’s break down how I kick off the Ratios and Rates Math Wheel. First things first, I introduce students to our concept and we identify the topic found in the middle of the math wheel. Students love coloring in “Ratios and Rates” as they start to bring their math notes to life.

Next, we dive into the “What is a…” section, breaking down the definitions of ratios and rates.

We discuss how ratios compare two quantities, whether it’s part-to-part or part-to-whole, jotting down the definition in that section.

Then, we move on to add the definition of a rate. A rate, I explain, is essentially a ratio with a twist. It compares quantities with units of measure like inches, feet, or miles.

These definitions serve as the foundation, especially for students stepping into this concept for the first time.

### 2. Writing Ratios and Rates

Let’s dive into the next leg of our guided notes journey, which is the section titled Writing Ratios and Rates. In this section, I break down the process of expressing ratios and rates step by step.

First things first, we highlight the significance of the word “to” when jotting down these ratios. I then draw an arrow next to the line, and we work through an example. For example, 12 to 5. Next, we answer the question asking us to identify the ratio of stars to squares. On the math wheel, there are 3 stars and 2 squares, so we would write 3 to 2. I make sure to remind students that the item named first is always the first number in the ratio.

Building on that foundation, we step up our game by practicing how to express these ratios as fractions. Using our initial example of 12 to 5, we transform it into the fraction 12/5. Then we answer the next question of the ratio of squares to shapes. Again, I remind them that whichever item is named first in the sentence or question is first in the ratio. Since we have 2 squares and a total of 5 shapes, the fraction is 2/5.

We finish this section of the math wheel by exploring the third way to express ratios and rates by using a colon. Revisiting our first example, 12 to 5 becomes 12:5. If we’re pulling in units of measure, it might look something like 1 yard: 3 feet.

As we work through the math wheel, I maintain an ongoing check-in with my students to ensure we’re all on the same page and adjusting pacing as needed. We can always complete extra examples, revisit definitions or I can explain in a different way if needed.

### 3. Equivalent Fractions

In the third section of the Ratios and Rates Math Wheel, we dive into equivalent ratios. I break it down for my students, explaining that these ratios represent the same comparison of quantities. Since my students are already familiar with the concept of equivalent fractions I use that as a comparison.

I explain how we can find equivalent ratios by either multiplying or dividing both numbers in the ratio by the same number. We make sure to add this important information to the math wheel before working on the examples.

To practice, we return to familiar territory with our stars and squares. I remind my students that whatever is first in the list must be the first in the ratio. In this case, it’s the stars. With a total of 6 stars and 2 squares, we can write the ratio as 6:2. Once we have our starting ratio we set out to make some equivalent ratios. I generally do 2 or 3 examples with at least 1 using multiplication and 1 using division if that is possible. Here are some examples and how we do the math to find the equivalent ratios.

### Examples

1. Start with the ratio 6:2 and multiply each number by 2. It looks like this (6 x 2 = 12 and 2 x 2 = 4). That means 12:4 or 12 to 4 is an equivalent ratio of 6:2.

2. Start with the ratio 6:2 and multiply each number by 3. It looks like this (6 x 3 = 18 and 2 x 3 = 6). That means 18:6 or 18 to 6 is an equivalent ratio of 6:2.

3. Start with the ratio 6:2 and divide each number by 2. It looks like this (6 ➗ 2 = 3 and 2 ➗ 2 = 1). That means 3:1 or 3 to 1 is an equivalent ratio of 6:2.

Once we practice this step a few times, we move on to writing equivalent ratios for squares to shapes. We start with the ratio 2:8 because there are 2 squares and 8 total shapes.

Then, just as we did in the first example, we will find some equivalent ratios by multiplying and dividing both numbers by the same number. After we do these examples together, I have students practice what they have learned. There are ten practice problems around the wheel for us to practice the steps further.

### 4. Ratio Tables

In the final section of our guided notes math wheel, I dive into ratio tables to help organize equivalent ratios. We use the examples from the previous section to practice using tables in this section.

In the first example, we see that the first line is filled in and talks about where that information came from. The students are quick to share that there are 12 inches in 1 foot. We then use that to help us fill in the remaining sections of the table.

I make sure to model how I find the number we are multiplying by or dividing by in order to complete the table. In this example I ask the students this question: “What do I need to multiply 1 by in order to get the answer of 2?” When they tell me 2, then I remind them that they must do the same thing to the other number in the ratio. We then multiply 12 x 2 and add 24 to the table.

I continue this process for each row because I want them to begin asking themselves that question to work through ratio tables.

Next, we take on the challenge of creating a table for squares, stars, and the total number of shapes. The first column helps start because it is pre-filled with 2, 6, and 8. Multiply 2, 6, and 8 each by 2, and boom – the third column is completed, showcasing products: 4, 12, 16. Next, we multiply 2, 6, and 8 each by 3, and the fourth column becomes filled with 6, 18, and 24.

To wrap it up, we sprinkle in some division. Divide 2, 6, and 8 each by 2, and voila, the fifth column is completed with 1, 3, and 4.

## Teaching Ratios and Rates Has Never Been Easier

By working through the four sections of the Ratios and Rates Math Wheel your students will have a solid understanding of this concept, how to find equivalent ratios, and how to display ratios in a table.

When the math wheel is complete, students complete the practice problems found in the pattern around the circles. Depending on how students seem to be feeling about the concepts, we may do this as guided practice or independent practice. Then, students can color the background pattern if they’d like. After the wheels are finished, I have students keep them in their math notebooks. That way they can refer to them as needed or use them later in the year as a review. Whether deep into the unit, exploring equivalent ratios, or cruising through ratio tables, the math wheel provides structure and clarity. It becomes a reliable reference point for students, offering a visual aid and quick reminders whenever needed. Its condensed yet detailed format transforms complex concepts into an easily digestible visual aid!

## More Resources for Teaching Ratios and Rates

Looking for more easy to use resources to make teaching and learning ratios and rates a breeze? Make sure to check out the following resources to help as you teach these important math concepts.

## Ready for More Math Wheels?

Want to try out a math wheel for free? Grab this free Fraction Operations Math Wheel and give it a spin in your classroom.

## Save for Later

Remember to save this post to your favorite math Pinterest board for when you need guided notes or resources for ratios and rates!

## Ellie

### How to Use Math Small Groups 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!