I can still remember those nights when I would look at my pacing guide and realize my ratios unit was coming up next. My computer would have multiple tabs open, digging through old files, trying to remember what worked well and what left my students confused. I wanted my students to understand the relationships behind the numbers. I wanted them to see how everything connected. Over time, I realized I needed more than scattered resources. I needed a clear path from the introduction to the application. If you are preparing to teach ratios and rates, this blog post brings everything together so you don’t have to scramble. I am highlighting 6 ratio blog posts that will guide you through every part of your ratio unit. Each section gives you a snapshot of the strategy, along with links to where you’ll find the full breakdown and classroom examples.

Where to Start When Teaching Ratios

When you begin teaching ratios, start with my post, Teaching Ratios and Rates: Easy Strategies for 6th Grade Math. This is where I lay the groundwork. I walk through what a ratio actually is, the three ways to write a ratio, and how to distinguish between part-to-part and part-to-whole comparisons. You never want to assume your students remember these distinctions clearly, so I model them carefully.

The paired teaching videos within the post are especially helpful because they model the language and pacing you can use in your class. They include real-world examples and emphasize labeling units clearly.

Starting here gives the unit direction. When you teach ratios with a clear and intentional beginning, everything that follows feels smoother. The foundation becomes solid enough to support more complex reasoning later.

How to Confidently Teach Equivalent Ratios

Once your students understand what a ratio is, you move into equivalent ratios. This is where the real reasoning begins. In my post How to Confidently Teach Equivalent Ratios, you will learn practical and effective tips for teaching how to find equivalent ratios.

You will see how ratio tables and double number lines are used to make the relationships visible. Instead of memorizing a rule, your students see the numbers grow together. The examples are intentional and modeled step by step so you can mirror that instruction in your own classroom.

I also share my favorite resource that I used to teach equivalent ratios. The resource includes guided notes, structured practice problems, real-world scenarios, and an exit ticket. It’s everything you need to teach equivalent ratios.

Teach Ratios By Connecting to Proportions

As you continue through the unit, you want to help your students see that proportions are not a new concept. They are built directly on equivalent ratios. My post on Teaching Ratios and Proportions walks you through that connection clearly and intentionally.

In this post, we explore proportional reasoning using multiple representations. These include ratio tables, double number lines, and tape diagrams. Seeing the same relationship shown in different ways helps your students develop flexibility. When one method does not click right away, another often does.

The full Ratios and Proportions Unit that accompanies this post provides a consistent lesson routine. It includes guided notes, fold-it-up vocabulary tools, practice pages, exit tickets, and assessments. That structure makes planning easier for you and creates consistency for your students. When your lessons follow a predictable pattern, your students can focus more on understanding the math instead of trying to figure out what comes next.

Teach Ratios While Making Them Relevant

If you are teaching ratios and proportions, then you definitely don’t want to miss this blog post. It guides you through everything you need to know to implement my favorite hands-on Ratios and Proportions activity. The goldfish lesson simulates the capture-recapture method scientists use to estimate animal populations. Instead of working with real fish, your students use Goldfish crackers.

Check out this blog post for your step-by-step guide to completing the goldfish activity in your classroom.

Teach Ratios With the Math Wheel for Structure Notes

Do your students struggle with note-taking when you introduce a new skill or concept? If so, this blog post is for you! In this post you will learn about the Ratios and Rates Math Wheel. It provides a structured way to walk through definitions, writing ratios in multiple forms, equivalent ratios, and ratio tables, all in one place. Instead of scattered notes across several pages, everything lives on one interactive graphic organizer that your students build step by step with you.

As you complete the math wheel with your students, they are actively building a visual reference tool they can keep in their notebooks all year. The wheel includes the key topics students need to learn. The important definitions are included, as are step-by-step examples. Around the outer edge of the wheel, there are practice problems that allow your students to immediately apply what you just taught. It is one of the best note-taking tools I have ever used in the classroom. Check out the blog post to learn more about teaching ratios and rates with the doodle wheel.

Reinforce the Basics: Free Ratios, Equivalent Ratios, and Rates Fold It Up

If you’re looking for a simple reinforcement tool that requires little prep, this foldable is a great addition to your ratios unit. It’s the perfect way to review the difference between ratios and rates. And. . . the fact that the activity is a little different than normal notes gets students engaged. Head over to the Ratios, Equivalent Ratios, and Rates Fold It Up blog post to grab your copy.

In this blog post, you will learn everything you need to know in order to use this free fold it up activity in your classroom.

This foldable is especially helpful at the beginning of your unit or after a pretest reveals gaps in understanding. If you notice your students leaving ratio questions blank or writing something that does not resemble a ratio at all, this gives you a structured way to reset and clarify expectations. It strengthens understanding without adding complexity to your prep time. You can introduce it in one class period and immediately give your students a reference tool they will continue using throughout the unit.

Extend the Unit to Cover Unit Rates

Once your students understand ratios and proportions, you are ready to extend the learning into unit rates. My post, Everything You Need to Know About Teaching Unit Rates, walks you through exactly how to introduce the concept in a way that feels practical and relatable.

By connecting unit rates to real-world examples, your students will see just how unit rates are used in a way that has meaning in real life. Head over to the unit rates blog post to learn more about connecting this concept to everyday life.

The Unit Rates blog post also shares a resource that includes everything you need to teach unit rates in your classroom. If you want your ratios unit to feel complete and connected, this final piece ties everything together.

A Clear Path to Teach Ratios From Start to Finish

When you look at all of these posts together, you see a complete instructional pathway. Instead of scrambling for disconnected resources, you have a clear progression. Each piece builds on the last, giving you confidence as you plan and teach. If you are preparing to teach ratios and rates (and proportions), everything you need is here. You can follow this path step by step and know that your instruction is intentional, organized, and designed to help your students truly understand the concept of ratios and rates.

Save for Later

If your ratios unit is coming up soon, don’t leave this until the night before. Pin this post so you have a clear plan ready when it’s time to start teaching. Future you will be so glad you did!

The post Everything You Need to Teach Ratios and Rates appeared first on Cognitive Cardio Math.

Whether you’re prepping for a new math teacher position or looking for a fresh approach to teaching equivalent ratios, this post has you covered. I’m sharing two helpful videos that walk you through key teaching strategies. I also include the Equivalent Ratios, Ratio Tables resource, which makes your next lesson simple to plan and effective to teach. Whether you’re a first-time math teacher or a seasoned educator looking to shake things up, this combination is a great way to boost your confidence and get your students thinking deeply about ratios.

Watch the Videos for A Step-by-Step Breakdown of Equivalent Ratios

Start by watching both videos. The first video introduces what equivalent ratios are using ratio tables and double number lines. These are visuals that make it easier for your students to see the relationship between quantities. You’ll hear familiar examples like batches of cookies and cups of flour. This helps to tie abstract math concepts to everyday thinking.

In the second video, you’ll see how to walk through a practice page from my Equivalent Ratios resource with your students. The pacing is intentional. Each problem is modeled step-by-step with explanations of why each move works. It’s a great tool whether you’re planning whole group instruction, prepping for a small group, or just reviewing the topic.

What The Equivalent Ratios Resource Covers

After introducing the concept in a whole-group lesson, I like to use the Equivalent Ratios Ratio Tables Lesson to keep the momentum going. The resource includes a clear, teacher-guided notes page that mirrors what I model in the video. Your students will follow along as they explore examples. Then, they move into a practice page with a variety of ratio table problems that require computation and reasoning.

From there, your students will encounter real-world scenarios that push them to apply what they’ve just learned. They will solve problems about eggs in cartons, minutes and hours, money earned per hour, and more. These problems aren’t just surface-level math. They help your students see the value of ratios in their daily lives. It also gives you multiple opportunities to reinforce how multiplicative relationships work.

There’s also an exit ticket included. The exit slip makes it easy to check for understanding at the end of the lesson or as a quick warm-up. Everything in the resource is scaffolded. It’s just enough to support your learners while still challenging them to think critically about the ratios they’re working with.

Bonus Tip: Emphasize the “Why”

As you work through this lesson, take time to highlight why we multiply or divide both parts of a ratio by the same number. It might seem like a small thing, but this step is where a lot of our students get tripped up. When our students understand the why, they can better transfer their knowledge to more complex problems later.

I’ve found that modeling a few non-consecutive examples helps drive this point home. It discourages our students from simply adding down the column, and instead nudges them to focus on multiplicative reasoning. I also loved having my students create their own tables based on something they care about. Some might analyze the time playing video games compared to chores, or how long it takes to run a certain number of laps. These personal connections make the math feel more real.

Equivalent Ratios Made Simple

These videos and the equivalent ratios resource go hand in hand to help you teach with more clarity and confidence. You’ll have a toolkit of strategies that help your students reason through problems, represent their thinking visually, and apply their understanding in a meaningful way. If you’re ready to strengthen your ratios unit, this is the perfect place to start or refresh.

Save for Later

Ready to teach equivalent ratios with confidence but not quite there yet? Be sure to save this post to your favorite teaching Pinterest board so it’s easy to find when you’re planning your ratios unit. That way, when you’re ready to dive in, you’ll have everything—videos, explanations, and a complete, ready-to-go resource right at your fingertips.

The post How to Confidently Teach Equivalent Ratios appeared first on Cognitive Cardio Math.

Whether you’re prepping for a new school year or diving into some PD, this ratios and proportions professional development session is a goldmine for 6th grade math teachers. In just 25 minutes, you’ll get a refresher on the kinds of ratio reasoning skills your students need. Plus, you’ll discover ideas you can use right away when teaching ratios and proportions.

Start With the Ratios and Proportions Video

This PD session breaks down key concepts you’ll be teaching all year long. Concepts range from part-to-part and part-to-whole ratios to unit rates and percent applications. The video does a great job explaining why proportional reasoning is so important and where your students often struggle. It goes beyond just solving missing value proportions. You’ll get examples of different strategies like ratio tables, double number lines, and tape diagrams. They are all modeled clearly, so you can use them in your own classroom. There’s even a quick percent problem walkthrough and a look at the goldfish lesson that students love.

Don’t Skip the Goldfish Proportions Lesson

One of the most engaging parts of this training is the goldfish cracker proportions activity. It’s hands-on, it’s memorable, and best of all, it brings proportional reasoning to life in a way that clicks with your students. In this lesson, your students are presented with a real-world scenario. Scientists need to estimate the number of fish in a bay. How do they do that without counting every single one? Enter the tag-and-recapture method.

Your students start by tagging a sample of goldfish crackers, replacing them with pretzel goldfish to represent the marked fish. Then, they mix everything together and take additional samples, recording how many tagged fish appear each time. After several rounds, your students use proportions to estimate the total fish population in the bay.

This activity is so powerful because it connects classroom math to actual scientific practices. Your students aren’t just solving a made-up word problem. They’re simulating a method wildlife biologists use in the field. It naturally leads to rich discussions about ratios, sample sizes, and the accuracy of estimates. Plus, your students love the chance to be hands-on and collaborative. Grab the full activity breakdown.

Ratios and Proportions Resource

My Ratios and Proportions Unit includes everything you need to walk your students through the standards in a consistent, scaffolded way. The unit starts with guided notes and interactive fold-it-up activities that break down vocabulary. These materials give your students a reference to use throughout the unit. Each lesson follows a routine that keeps things predictable for your students: I Can statements, examples, a You Try It section, and practice problems.

The resource also includes exit tickets, a quiz, and a cumulative assessment to track how your students are doing. There’s even a printable word wall file that highlights key vocabulary like unit rate, equivalent ratios, and proportion. These visual supports can make a big difference for your students who need those reminders during practice and review.

Engage Your Students During Your Ratios and Proportions Lesson

This PD session and the paired classroom resource work hand-in-hand to help you teach ratios and proportions with more clarity and confidence. You’re building a toolkit of strategies that empowers your students to reason through problems, represent their thinking in multiple ways, and apply what they’ve learned to real-world scenarios.

You’ll have the tools to reach your learners at all levels, from hands-on exploration with manipulatives to visual models like tape diagrams and double number lines. The unit structure ensures that your instruction is consistent and scaffolded, so students grow their understanding day by day. You can feel confident that your students are mastering both the conceptual and procedural sides of ratios and proportions.

Save for Later

Remember to save this post to your favorite math Pinterest board for quick access to these resources to help with teaching ratios and proportions.

The post Teaching Ratios and Proportions in the Middle School Math Classroom appeared first on Cognitive Cardio Math.

Teaching ratios and rates in 6th grade math doesn’t have to be intimidating. If you’re just getting started, this post has everything you need to break it down with clarity and confidence. These two short videos offer simple explanations and real-world examples. I’ve paired them with a ready-to-go resource that makes your lesson planning easier than ever.

Start With the Ratios and Rates Videos

The first video walks you through the basics of ratios. A ratio is a comparison between two quantities. It also breaks down the three ways to write a ratio (fraction, colon, and the word “to”). It also gives real-world examples to show the difference between part-to-part, part-to-whole, and whole-to-part ratios. Using phrases like “for every” helps your students visualize these comparisons more clearly.

The second video focuses on rates and unit rates. You’ll learn how a rate is a type of ratio that compares two different units, like miles per hour. It also explains how to find the unit rate by dividing and offers tape diagrams and real-life examples to make it click. If your students are confused about how rates differ from ratios, this video helps you clear that up fast.

Extra Tips

One especially helpful tip is encouraging your students to label every part of a ratio or rate. Writing units clearly, like 6 books to 3 students instead of just 6 to 3, helps them see what each number represents and prevents confusion down the line.

Also, look for this common mistake. Students will mix up part-to-part and part-to-whole ratios. Have them draw quick visuals or use color-coding to clarify which parts they’re comparing.

When teaching unit rates, use real-life scenarios like shopping or travel. It helps your students see how these concepts apply to their own lives and keeps engagement high.

Ratios and Rates Resource Overview

To reinforce the skills from both videos, the Ratios and Rates lesson provides print and digital materials that make it super simple to introduce and practice these skills. The first day covers ratios with a guided notes page and foldable vocabulary organizer. Your students get multiple opportunities to identify, write, and classify ratios as part-to-part or part-to-whole. Practice pages follow the same structure with real-world examples, making them easy to complete independently.

On the second day, the focus shifts to rates. Your students review how to compare two quantities with different units, calculate unit rates, and write them in multiple forms. The included practice activities range from straightforward to slightly more complex, allowing for differentiation. The exit ticket makes it a breeze to check understanding at the end of the lesson.

Teach Ratios and Rates Lesson With Confidence

These videos and the resource work beautifully together to take the stress out of teaching ratios and rates. With clear definitions, helpful visuals, and scaffolded practice, you can feel confident helping your students master these foundational 6th grade math skills!

What makes this combo so effective is the balance of guided instruction and hands-on learning. The videos give you the teaching language and strategies to explain tough concepts clearly. The resource offers your students multiple ways to practice and build understanding at their own pace. Whether you’re introducing these ideas for the first time or reviewing them mid-year, this set-up helps ensure your students don’t just memorize terms but understand how to use them.

Save for Later

Remember to save this post to your favorite math Pinterest board to access these resources for ratios and rates quickly.

The post Teaching Ratios and Rates: Easy Strategies for 6th Grade Math appeared first on Cognitive Cardio Math.

I’m a huge fan of giving our students the right tools they need to succeed. I believe they’re never too old to use them! When I discover tools that help my students with math, I feel like I’m setting them up for success, both mentally and academically. It’s amazing to see how much more confident they become when they have resources to guide them. One tool that’s always available in my classroom is number lines. Yes, even in middle school! Today, I’m excited to show you just how beneficial using number lines can be for our middle schoolers!

How Number Lines Help Middle Schoolers

Using number lines in middle school math is a game-changer! When we first think about number lines, we automatically think about our younger learners. While we traditionally think of number lines as a tool for elementary students, I want to challenge you to get the idea of a 0 to 10 number line out of your head and instead think of number lines in relation to the skills and concepts you teach. They’re incredibly valuable for our older students, too. When we introduce them to middle schoolers, we give them a visual tool that helps make abstract concepts more concrete. They are fantastic for introducing new concepts, reviewing previously taught ones, or as part of intervention.

Number lines boost confidence and comprehension in middle school math. When our students see math problems visually laid out, it reduces anxiety and makes learning more interactive and engaging. I’ve seen firsthand how my students light up when they “get it” after using a number line. It’s a tool that truly supports their mathematical journey and helps them thrive!

Middle School Concepts & Number Lines

Number lines are fantastic for helping our students understand positive and negative numbers. They can see the relationship between these numbers and grasp the idea of moving left or right on the line to add or subtract. This visual representation makes a world of difference, especially for our students who struggle with traditional methods. It’s a great way to differentiate learning for your students as well.

These tools also simplify the process of finding common denominators and understanding fractions. By seeing fractions on a number line, our students can easily compare sizes and understand equivalences. This visual approach takes the mystery out of fractions and makes them much more approachable.

Number lines are also great for reinforcing the concept of absolute value. Students can quickly see the distance between numbers and zero, which solidifies their understanding. It’s one thing to memorize a rule, but it’s entirely different (and more effective) to visualize it on a number line.

Three Ways to Use Number Lines in Your Classroom

I want to share three specific ways you can use number lines in the classroom to help students excel in math. These methods have been impactful for my students, making math more interactive and easier to understand and I know they can help your students too. Let’s check out these three strategies and see how we can bring number lines to life in our lessons!

1. Classroom Decor

One of my favorite ways to use number lines in the classroom is by making them an integral part of classroom decor that stays up all year round. This is a perfect way to make decorating functional and useful! I like to refer to them as tools that my students can reference all year long.

In my classroom, I have a fraction, decimal, and percent number line displayed above the whiteboard at the front. It shows the most common fractions and their decimal and percent equivalents. This visual aid is incredibly helpful for my students, as they frequently refer to it to learn and remember these common equivalences. It’s like having a cheat sheet right there in front of them every day!

I also have a positive and negative integers number line displayed at the top of another wall. When we start exploring negative numbers, this huge visual helps us discuss moving in the positive or negative direction when combining numbers. It’s also super handy when we dive into absolute value. Seeing that both -5 and 5 are the same distance from zero makes it clear why they have the same absolute value.

2. Double Number Lines

I love finding different ways to use this tool in my classroom. One of my favorite methods is using double number lines (or two number lines side by side) to explore the relationship between different amounts. It’s an easy way for students to see how numbers in different formats relate to each other. This is especially useful when we’re working with percentages or ratios.

For instance, when finding the percent of a number, I place the number we’re working with on one number line and the percentages from 1% to 100% on another. This makes it easy for my students to visually grasp how percentages relate to the original number. It’s a great way to make abstract concepts more tangible!

Teaching ratios are made easy with these tools. My students can see the relationship between two quantities side by side. This visual representation helps them understand how ratios work and how to find equivalent ratios. It’s a powerful way to make the concept of ratios more concrete and less intimidating.

3. Vertical Number Lines

I also like to use vertical number lines, similar to thermometers, to visualize patterns in numbers. These are particularly helpful when we’re looking at the increasing tens and ones in two-digit numbers. My students can clearly see the sequence and repetition of digits. This makes it easier for them to understand the value of numbers. They quickly get the hang of counting up and counting down when adding or subtracting, seeing how sums increase and differences decrease in value.

A key benefit of number lines is how they help students connect the concepts of rounding up and rounding down. When they see numbers on the line, it becomes much clearer why we round up or down to the nearest five or ten. The visual representation really solidifies their understanding.

Helpful Resources for Middle School Math

I love using the Fraction, Decimal, and Percent Number Line to help my students keep their conversions straight! This resource is a one-page number line that’s packed with useful information. It includes common decimals placed right on the number line, along with their equivalent fractions in their lowest terms and the corresponding percentages.

I have my students place this number line in their math notebooks. It becomes their go-to reference for quick conversions. Having this tool in their toolbox helps make math problems a lot less daunting.

I also post a larger version of this number line as part of my classroom decor. This way, my students can easily glance up and find the information they need. It’s amazing how much this visual tool can boost their confidence and understanding of fractions, decimals, and percentages!

If you want to ensure that your students have this resource at their fingertips, I also have a Fraction, Decimal, Percent Number Line Bookmark. Have your students place them in their book they are reading or even their math textbook!

To read more about number lines, check out my post on Fraction, Decimal, and Percent Conversions. You can also check out the Using Number Lines in the Math Classroom episode on The Teaching Toolbox podcast. It is filled with examples and ideas on how you can use number lines in your math classroom.

Embrace Number Lines in the Middle School Math Classroom

Bringing number lines into our middle school math classroom will change how your students approach math. From helping them understand complex concepts to serving as a constant visual aid, number lines are invaluable tools. Whether we’re using them for fractions, decimals, percents, or even decorating the classroom with them, they make math more accessible and less intimidating for our students. By providing these resources, we’re not only boosting their confidence but also paving the way for their academic success.

Save for Later

Remember to save this post to your favorite math Pinterest board for ideas on how to use number lines!

The post Using Number Lines in Math Class with Middle Schoolers appeared first on Cognitive Cardio 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!

If you are ready to add the Ratios and Rates Math Wheel to your instruction on this topic, head over to the Cognitive Cardio Math store on TPT. This resource is ready to download, print, and use in your classroom.

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.

• 6th Grade Math Ratios, Rates, Proportions Curriculum Unit, Editable
• Ratios and Proportions Math Activities Math Centers
• Ratios & Proportions Equivalent Ratios Unit Rates Color by Number 6th Grade Math
• Ratios and Proportions Activity for Middle School Math

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!

The post Tips for Teaching Ratios and Rates in 6th, 7th and 8th Grade Math appeared first on Cognitive Cardio Math.

Ratios, Equivalent Ratios, and Rates Fold it Up

Select to Download Fold It Up

This Fold It Up is now part of my Grade 6 Ratios Unit. Select to see the Ratios Unit on TPT

The post Free Ratios, Equivalent Ratios, and Rates Fold it Up appeared first on Cognitive Cardio Math.

Ratios and Proportions Activity for the Middle School Math Classroom...Plus Goldfish!

Food can make a ratios and proportions activity in a middle school math class more fun, right?

“Something Fishy” is a great hands-on lesson to help students understand a real-life application of ratios and proportions. It also gives them the chance to munch on a few Goldfish 🙂

This is a lesson I found through the Mathline Middle School Math Project, sponsored by PBS (I mentioned this program in the “Remove One” post also).

 

About the Ratios and Proportions Activity

This ratios and proportions lesson presents the students with an environmental problem:
“Scientists have determined that the number of fish in the Chesapeake Bay has decreased. Assuming this is true, scientists must have counted the number of fish and noted the change. How did they count the fish?”

After introducing the problem, the students brainstorm ways that the scientists could count the fish. I have four math classes, and in each class, there was a student who said that scientists could tag the fish. So we discussed how tagging the fish would work, and talked about the capture-recapture method. Using a sample ratio, we talked about how we could create a proportion to figure out an estimate of the population.

Ratios and Proportions Lesson Materials

For this lesson, we used:

• regular Goldfish crackers
• pretzel Goldfish crackers
• 2 paper bowls per group (any container that they can scoop from will work…we used the 2nd bowl to put the “captured” fish into)
• a spoon to scoop with

I didn’t count the number of fish that I gave each group…I simply poured fish into the bowl…but they all ended up having 70-90 fish.

 

Ratios and Proportions Lesson Procedure:

Teacher Demo
I demonstrated ALL of the following steps for the students, so they understood what to do, and then I gave them a recording sheet (found below) that also included the directions.

Student steps for the lesson:
1. Students “capture” a sample of regular goldfish from the container. This sample should be tagged by replacing them with pretzel goldfish, and the “captured” goldfish should be set aside and no longer counted in the population.

2. Students put the tagged fish back into the container and mix up the fish so  the tagged fish are evenly distributed.

Move on to the recapturing:
3. Capture a new sample and record both the total number of fish in the sample and the number of tagged fish in the sample. Return all fish to the container.
4. Recapture 6 times (or whatever you have time for…we were able to do 6 times, and we have a 40-min math period).
5. Guide the students to create and solve the proportion for their “bay.”

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6. Have students count their fish and then compare their estimated total with the actual number of fish. Some of my groups got fairly close…I believe the closest was an estimate of 68 and an actual count of 74. It seemed that the groups with larger sample sizes ended up with closer estimates than those with smaller sample sizes.

 7. Allow students to eat the goldfish (if they don’t have allergies)!

 

To see the PBS Mathline lesson, click HERE.

Download the recording sheet

What ratio and proportions lessons are your favorites?

For some engaging ratios and proportions notes, check out the Ratios Fold it Up post!

Resources to Teach and Practice Ratios and Proportions

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