Have you ever had the moment when your students could find the mean, but then everything after falls apart? You might be watching your students confidently calculate an average, only to freeze when asked what the data really showed. That is exactly where mean absolute deviation can start to feel overwhelming for them. Once I shifted how I introduced mean absolute deviation, everything clicked in a way it hadn’t before, and it can for you, too.

If you are teaching mean absolute deviation for the first time or looking for a refresher, you are not alone in wondering how to break it down. This concept can feel abstract at first, especially for your students who are still building number sense. The good news is that with the right structure and pacing, your students can absolutely understand it. I am going to walk you through exactly how to teach mean absolute deviation in a way that sticks.

Why Mean Absolute Deviation Matters for Your Students

Mean absolute deviation helps your students understand how spread out the data is around the mean. It gives meaning to numbers beyond just finding an average. When your students see how far values are from the mean, they start thinking more deeply about data. This is where real understanding begins to build.

In real life, mean absolute deviation is used more often than we realize. Think about sports statistics, where consistency matters just as much as performance. A player with consistent scores may be more valuable than one with unpredictable results. Mean absolute deviation clearly highlights that difference.

It is also used in fields like finance and science to measure variability. When people analyze trends or predict outcomes, they need to know how reliable the data is. Teaching mean absolute deviation gives your students a foundation for understanding those real-world applications. It moves them beyond basic calculations into true data analysis.

Steps for Teaching Mean Absolute Deviation Clearly

When teaching mean absolute deviation, be sure that your students are confident in finding the mean. Without that foundation, the rest of the process will feel confusing. I always recommend modeling this step slowly and checking for understanding before moving on. This keeps your students from getting lost later.

1. Find the Mean of the Data Set

I recommend writing out a small data set and thinking out loud while solving it. Show your students how to add each value carefully and then divide by the total number of values. On my Mean Absolute Deviation Wheel, this is the first section where your students record the data set and calculate the mean.

When using this math wheel, have your students complete this section with you, then turn and explain their steps to a partner. You can always stay here until most of your students can explain why we divide, not just how. A quick check I liked to use was asking, “What would happen if we forgot to divide?” That question quickly showed me who truly understood. Once they are solid here, the rest of the process becomes much smoother.

2. Find the Difference Between Each Number and the Mean

Next, guide your students to find the difference between each data value and the mean. This is where many of your students will need extra support, especially with subtraction. My Mean Absolute Deviation Wheel visually breaks this down step by step into a three-column chart. This is the point where you can slow things down again and model multiple examples. Write one value at a time and subtract the mean, showing every step. Your students may rush here and make small errors that throw everything off later, so have your students line up their subtraction vertically and show their work. You might allow them to use a calculator here since the focus isn’t on subtracting but on finding the MAD.

You might be wondering how to keep your students organized during this step. The wheel helps because each value has a clear space for recording its difference. Have your students circle their mean in the first section, so they consistently use the correct number. These small routines make a big difference in accuracy.

You’ll also need to introduce or review absolute value in a simple and approachable way. Your students need to understand that distance from the mean is always positive. I used to describe this as how far away a number is, not which direction. I would ask, “How far is this number from the mean?” rather than “What is the absolute value?” That small shift in language makes a big difference. On the Mean Absolute Deviation Wheel, this connects directly to the differences your students just found.

If you are wondering how to make this click, visuals help a lot. Draw a quick number line and show that distance is always counted positively. Some of your students may need to physically see that movement to understand it. Once they grasp this idea, you can connect it back to absolute value notation.

3. Find the Mean of the Differences

Finally, have your students find the mean of those absolute differences. This is the step that ties everything together and completes the process. Walk through one full example together before letting them practice with a partner or independently.

The last section of the Mean Absolute Deviation Wheel focuses on finding the mean of the differences. Be sure to remind your students that they are repeating a skill they already know. This helps reduce the feeling that this is a completely new concept. Add all the absolute differences together and divide by how many there are.

One thing to always clarify here is what the final answer actually represents. Mean absolute deviation tells your students the average distance each value is from the mean. This helps describe how spread out the data is.

To really lock this in, you can show two small data sets and have your students calculate the mean absolute deviation for both. Then compare the results and decide which data set is more consistent. This helps your students see that a smaller mean absolute deviation means the values are closer together, while a larger one signifies they are more spread out.

Quick Tips for Making Mean Absolute Deviation Stick

Once your students understand the steps for mean absolute deviation, give them a simple checklist to use during practice (or they can use the wheel). This helps them slow down and avoid skipping a step. You can have them check off finding the mean, subtracting each value, using absolute value, and finding the final average. That small routine builds accuracy and independence. Once your students have that routine, they can choose to keep using it or keep it nearby to pull out if needed.

Another helpful tip is to have your students label their work as they go. Instead of only writing numbers, encourage them to write words like mean, difference, absolute differences, and mean absolute deviation. You can even have your students color-code each part of the process. For example, they might write the mean in one color, differences in another, and absolute values in a third. This helps your students visually connect each step and makes their work easier to follow and check.

You can also build in quick examples of error analysis. Show your students a worked problem with a common mistake, such as forgetting absolute value or dividing by the wrong number. Then have them find and fix the error with a partner. This gives them practice thinking critically rather than just following steps.

Using the Mean Absolute Deviation Wheel to Support Learning

One of the most helpful tools for teaching mean absolute deviation is a structured visual, such as a math wheel. Instead of feeling like a long list of steps, mean absolute deviation becomes something your students can actually see and follow. The wheel acts as a built-in roadmap that keeps everything organized in one place. Your students won’t be flipping between notes or trying to remember what comes next. That alone can reduce a lot of frustration, especially for your students who struggle with multi-step problems.

What really makes this tool impactful is that it functions as a differentiated graphic organizer, not just a worksheet. Your students are actively building their understanding as they complete each section. They are solving problems and organizing their thinking in a way that makes sense to them. Over time, this helps them internalize the process instead of relying on memorization.

Adding color and doodles takes that learning even further. When your students color-code sections or add simple visuals, they are creating mental connections that help with retention. It gives them something to anchor their thinking to when they revisit the concept later. Even your students who are hesitant with math tend to engage more when the work feels creative and less rigid.

This also turns the wheel into a year-long reference tool rather than a one-time activity. You can have your students add it to their notebooks and come back to it during review or test prep. Instead of asking, “What do we do again?” they have a clear example right in front of them. That independence is huge, especially as the year goes on and concepts start to build.

Take Mean Absolute Deviation Further with Ready-to-Use Support

Teaching mean absolute deviation does not have to feel complicated or overwhelming. When you break it into clear steps and support your students along the way, it becomes much more approachable. Your students will not only learn the process but also understand why it matters. The key is giving them structure, modeling your thinking, and connecting the concept to real situations. This is where structured notes and targeted practice make a huge difference. Instead of reteaching or creating new problems each day, you can give your students consistent opportunities to apply the process in different ways. That repeated exposure is what builds true confidence.

My Mean Absolute Deviation notes and practice pages walk your students through guided examples first, then gradually release them into independent practice. You will have access to guided notes, practice pages, and exit tickets, all in one resource. This makes it easy for you to plan an entire lesson without having to scramble for additional materials.

What makes this especially helpful is how the resource goes beyond just calculating mean absolute deviation. Your students are also asked to interpret what their answers mean and compare data sets. On the guided notes pages, your students explain how mean absolute deviation relates to how spread out the data is. That shift from solving to explaining is where deeper understanding occurs.

Looking for Even More Support?

If you are looking to build out your entire data unit, this is just one piece of a larger collection. Inside my TPT store, you will find additional math wheels, complete math units, review activities, and math centers for a wide variety of math concepts. Having access to those resources means you are not starting from scratch each time you teach a new concept. It allows you to stay consistent while giving your students the support they need.

Save for Later

If you are planning your data unit, this is one strategy you will want to come back to. Save this post so you have a clear roadmap for teaching mean absolute deviation when you need it. Having a plan in place makes all the difference during those lessons!

The post How to Teach Mean Absolute Deviation appeared first on Cognitive Cardio Math.

Throughout my years of teaching, especially in math, I’ve seen my share of students struggling. We want our students to be challenged but within reason. Sometimes this struggle is based on understanding the math concepts, but other times it is something completely different. It’s that “other times” that we’re going to talk about today. Specifically, how do poor executive function skills affect math performance? We’ll explore how these skills play a crucial role in mastering math and how tools like math wheels can come to the rescue!

What Are Executive Function Skills?

Think of executive function skills as the behind-the-scenes champions that help us navigate the complexities of daily life. At their core, executive function skills encompass a range of abilities that enable us to plan, organize, focus attention, regulate emotions, and tackle tasks with purpose and intentionality. Let’s take a closer look at the different components a bit more:

1. Planning and Organization: Have you ever mapped out your day, made to-do lists, and set goals? That’s your planning and organization skills at work! These skills help you break tasks into manageable steps, prioritize your time, and set yourself up for success.
2. Focus and Attention: Ah, the ability to concentrate amidst distractions. That’s a true superpower in this digital age with devices, apps, and TV screens! Focus and attention skills allow you to stay on task, filter out irrelevant information, and maintain concentration even when faced with tempting diversions (like that adorable cat video on YouTube).
3. Self-Regulation: Self-regulation skills help you manage your emotions, impulses, and behavior, allowing you to stay cool, calm, and collected in the face of challenges. It’s about hitting that pause button before reacting and making thoughtful, informed decisions.
4. Problem-Solving and Flexibility: Life’s full of curveballs, but with problem-solving and flexibility skills, you’re ready to conquer them! These skills enable you to adapt to new situations, think outside the box, and come up with solutions to overcome obstacles.

While some students have these executive function skills, others may need extra support and guidance to strengthen them. That’s where we, as educators, come in! When we are aware of these struggles with executive function skills in our students, we can incorporate strategies to develop these skills instead of assuming they’re just trying to avoid work.

Executive Function Skills in Math

Let’s chat about the connection between executive function skills and math class. Math class is more than just crunching numbers and memorizing formulas. It’s a playground, or a battlefield depending on how you look at it, for executive function skills. I still remember learning long division as a student, and a problem taking up the whole page. I almost reached the end, only to discover a mistake four steps before. Math steps build on one another, so if there’s a mistake along the way, students have to start over, just like I did.

This is where executive function skills come in very handy. Let’s take another look at the four main ones, this time with a focus on math and how weak executive function skills can impact math performance!

Planning and Organization

Our students who need help with executive function skills may find it challenging to plan and organize their approach to math tasks. They might need help breaking down complex problems into manageable steps or mapping out a strategy for solving them. As a result, they may feel overwhelmed and need help figuring out where to start, leading to lower performance in math.

Focus and Attention

Math can be a bit of a brain workout. With strong focus and attention skills, your students can tackle the trickiest of math concepts. Whether deciphering word problems or working through a challenging proof, the ability to concentrate and block out distractions is key. They might need help staying on task, following along with lessons, or completing assignments without getting sidetracked. This can result in careless errors, incomplete work, and lower math performance.

Self-Regulation

Math can be a source of frustration and anxiety for many students, but those with weak executive function skills may have trouble regulating their emotions and impulses during challenging tasks. They might become easily frustrated when faced with difficult problems. This could lead to avoidance or giving up early on in the learning process. This lack of perseverance can hinder their ability to master math concepts, resulting in lower performance.

I feel for my students who have math anxiety, especially when they find they made a mistake after doing so much work. We talk a lot in my classroom about what to do in those situations and how it’s okay to make mistakes. We look at ways to manage frustration, bounce back from setbacks, and persevere.

Problem-Solving and Flexibility

Math is all about problem-solving, but students with weak executive function skills may need help to apply effective problem-solving strategies. They might need help identifying relevant information, formulating a plan of action, or evaluating their solutions for accuracy. As a result, they may make more errors, take longer to complete tasks, and achieve lower scores on math assessments.

By honing these skills, your students are on their way to mastering math and all areas of life. With a little practice and perseverance, they will become stronger math whizzes in no time!

How to Help Students Who Lack Executive Function Skills

Alright, fellow educators, it’s time to roll up our sleeves and dive into the nitty-gritty of supporting students who may be struggling with executive function skills. I’ve got a toolbox full of tried-and-true strategies to help us empower our students to succeed. Here are some direct examples of what we can do:

Provide Clear Instructions and Expectations

One of the best ways to support students with executive function challenges is to provide clear, step-by-step instructions for tasks and assignments. Break down complex tasks into manageable chunks and clearly outline the expectations for each step. For example, when assigning a math project, provide a detailed rubric outlining the requirements, deadlines, and grading criteria. When I am writing out directions for a project, I make sure to write them as steps so my students can check them off as they go.

Model and Scaffold Problem-Solving Strategies

You can help your students develop problem-solving skills by modeling the process step-by-step. Break down sample problems into smaller, more manageable steps and guide them through each stage of the problem-solving process. I encourage them to verbalize their thought process, use vocabulary, and explain their reasoning aloud. For instance, when solving a challenging math problem, demonstrate how to identify key information, formulate a plan, and check for errors.

Use Visual Supports and Organizational Tools

Visual supports and organizational tools can be invaluable for our students struggling with executive function skills. Provide visual aids, such as graphic organizers, flowcharts, and diagrams, to help students visualize concepts and organize information. Additionally, encourage the use of tools like planners, checklists, and digital apps to help students manage their time, prioritize tasks, and stay organized.

Offer Flexibility and Supportive Feedback

Recognize that students with executive function challenges may need additional support and flexibility to succeed. Be flexible with deadlines and allow students extra time to complete assignments when needed. Provide supportive feedback that focuses on effort, progress, and growth rather than solely on outcomes. Celebrate small victories and acknowledge students’ perseverance in the face of challenges.

Teach Self-Regulation and Coping Strategies

You can also help students develop self-regulation skills by teaching them coping strategies for managing stress, frustration, and anxiety. Teach relaxation techniques, such as deep breathing exercises and mindfulness practices, to help students calm their minds and bodies during challenging tasks. There are so many options for meditation or mindfulness practice that are only a few minutes, so no worries about taking away instruction time. A big must is to always encourage positive self-talk and self-reflection to help them build confidence in their abilities.

Math Wheels Can Help Students With Executive Function Skills

My math wheels are the perfect tool to help your students who may be struggling with their executive function skills. They are note-taking graphic organizers that break down your targeted math skill into simpler terms and steps. Remember how those bite-size chunks of instruction can help students with poor executive function skills? Well, that is exactly what Math Wheels do! And. . . they have proven an effective tool for all students. Explore Math Wheels Note-Taking Strategy to learn more about the benefits of math wheels!

Math wheels provide a structured framework for organizing information. With sections neatly divided and practice problems arranged in a pattern, your students can better manage complex math concepts and stay on track. Plus, they aren’t writing paragraphs of notes. They are writing short phrases or filling in the blanks and applying the step or direction immediately with examples.

The interactive nature of math wheels helps capture your students’ attention and keep them engaged. By incorporating elements like doodling and coloring, math wheels promote sustained focus and concentration. A win-win for mastering math skills.

As students tackle practice problems and apply key concepts, they engage in strategic planning and problem-solving. This approach helps develop critical thinking skills and enhances students’ ability to conquer math challenges with confidence. They also practice using a tool to assist them by using their notes.

Math wheels also encourage students to monitor their progress, identify areas of difficulty, and adjust their strategies. When I use math wheels, they help my students see where a sticky spot could be for them. This helps them self-advocate, leading our class discussions and practice problems. Instead of becoming overwhelmed by all the steps of a problem at once, they are able to focus on taking it one step at a time. They get to see how each step builds on the previous one to find the answer!

If you are looking for a tool to help your students become more successful in math class, take a look at Math Wheels. You can find math wheels for a variety of math skills and grade levels in my TPT store.

Continue to Build Students’ Executive Function Skills

As educators, it’s our mission to support our students in developing the executive function skills they need to succeed in math and beyond. By recognizing the importance of these skills and implementing strategies and tools like math wheels, we can help our students overcome obstacles and reach their full potential.

At the end of the day, it’s not just about mastering math concepts. We have a responsibility to equip our students with the skills they need to navigate the challenges of learning with confidence and resilience. Together, let’s continue to build a supportive and empowering learning environment where every student can thrive!

Save for Later

Remember to save this post to your favorite math Pinterest board to return to when you want to use math wheels to help with executive function skills!

The post How To Tell If Executive Function Skills Impact Math Performance appeared first on Cognitive Cardio Math.

TIPS TO DEVELOP PROBLEM SOLVING SKILLS AND MATH COMMUNICATION

Do your middle school math students need to improve their problem solving skills?

• Do they get to the end of a word problem and then guess at the operation they need to choose, maybe not realizing that there are multiple operations?

You may see something like this with some of your students, while other students have advanced math problem solving skills.

What methods have you found to help those who struggle? What methods can you use to help each student at his or her current level?

I’ve used many strategies over the years, to help students sort out how to make sense of word problems and how to approach them. These methods didn’t have a specific name at the time (like close reading or talking to the text), but some would fit into these categories.

Prompts to Help Focus
One of the methods I found to be most helpful for my math students to develop both their math problem solving skills AND their math communication skills was having them write responses to specific prompts before they attempted to solve a word problem. The prompts are general and applicable to any problem:

Select to download recording sheets

• “What I know…because,” from the problem
• “What I know…because,” from background information and
• “What I need to know….,” or what the problem is asking

We started using this framework many years ago, when writing in math/open-ended questions was new on the standardized test scene (new in my state any way:-). Every couple of days, we did sample problems that incorporated various strategies to solve problems – make a simpler problem, make a table, make an organized list, write an equation, etc. And as we practiced, the students became excellent at communicating what they understood about the information provided in the problem, as well as what they needed to figure out and how they did so.

For the “what I know…because” part, students identify the information from the problem that’s important for solving.

• We’d typically underline or highlight important information and cross out extra information.
• Instead of just highlighting/underlining, students also wrote the information, putting it into their own words as much as possible.
• Writing the information helps solidify it in their minds, and if they reword it or add detail to clarify the meaning, they understand it a bit better.

For “what I need to know,” students highlight/underline what the question is asking and then wrote it in their own words.

For example, with a problem like this:
Steve runs every other day and trains with weights every 3rd day. If he does both on Monday, how many times will he do both on the same day during the next 2 weeks?

Students might write:
What I know:

• Runs every 2 days. I know this because every other day means the same things as every 2 days.
• Weights every 3rd day – the problem states this information. 
• Runs and uses weights on Monday – the problem states that he does both activities on Monday.

What I need to know:

• I need to figure out how many times will Steve run and use weights on the same day, during the next 14 days – I know that 2 weeks is the same as 14 days. 

After students completed these written parts, we’d discuss what they identified as what they knew and what they needed to know,  before getting started with the solving. Then students would solve on their own and write a paragraph to explain exactly what they did to solve the problem.

Solution Explanation Example:
To solve this problem, I decided to make a table to find how many days Steve will do both activities.

• Since I want to know how many times this happened in 2 weeks, I made the table 2 rows of 7, and I labeled the days of the week at the top of the table, starting with Monday.
• In the first square of the table, I wrote an R and a W, since Steve did both on Monday.
• Then I wrote an R in every other square, and I wrote a W in every 3rd square.
• When I was finished, I counted how many squares had both R and W in them. There were 3 days total (including the Monday he started), so the answer is: Steve will do both activities on the same day 3 different times in 2 weeks.

Once students finished solving and writing their paragraphs, several of them would read their paragraphs to the class, giving students the opportunity to see if they could follow their peers’ explanations, compare the explanations to their own to see how similar they were, and learn/consider a new method if a student had solved a different way.

While this process did take a while, it was SO worth it. It really helped students break down the problems, become more in tune with how they were solving, and resulted in less “random” use of operations/solving methods. It also greatly improved their math communication abilities.

These days, with shorter math classes:-(, and therefore less time to write, I’ve consolidated the “what I know” and “what I need to know” into ‘Find out,’ so it encompasses both the important info the question that needs to be answered. Where I used to have several students read their examples with the class, I now have students do a quick “pair-share” after the first stages, and then share a couple of the final explanations with the entire class. It still takes a good chunk of time, but I believe that time is made up with fewer struggles as we move through the year.

Tips When Reading Word Problems

A few tips to help students as they read the problem:

• Underline important information
• Cross out information that isn’t needed
• Read carefully to find numbers written as words and write the # above the word
• Underline or highlight words that indicate operations and add the operation symbol nearby
• When writing, write the information with fewer words, so key info doesn’t get “lost”

Select to see the bookmarks on TPT

I created some handy bookmarks that I give my students, to help them remember some of these ideas:-)

Another Example of Solving a Word Problem

Manny spent 64 minutes on 3 different subway trains. The first train ride was twice as long as the second. The third train ride was 10 minutes longer than the other two combined. He arrived at his destination at 4:00 in the afternoon. How long was each train ride?

What I know:

• 64 minutes
• 3 different trains
• Train 1 = 2 x as long as train 2
  (change words into numbers – sub words with symbols – x instead of times)
• Train 3  = 10 min longer than train 1 + train 2

What I need to know:

I need to find the length of each train ride.

Solution Explanation:
I decided to write an equation and use x as the variable to represent the shortest ride.

I know that all 3 rides add up to 64, so 64 is one side of the equation.

• I think Train 2 is the shortest time, because Train One is 2 times as long, so Train Two is x and Train One is 2x.
• Train Three is 10 more than the other trains combined, so Train Three is  x + 2x + 10.

This gives me the equation  x + 2x + (x + 2x + 10) = 64.

 

Solving:

1) I solve by combining all the like terms, which gives me
6x + 10 = 64. 

2) Then I subtract 10 from both sides to isolate the variable and that gives me 6x = 54.

3) Next I divide both sides by 6 and get x = 9.

I have to  figure out the other 2 trains based on Train Two = 9.
If Train Two = 9, then Train One (2 (9)) = 18 and Train Three (9 + 2(9) + 10 ) = 37.

• 9 + 18 + 37 = 64, which is the total number of minutes Manny spend on the trains

I hope this is helpful!!

What methods are most helpful for your students to continually develop their math problem solving skills?

The post Help Middle School Math Students Improve Problem Solving Skills appeared first on Cognitive Cardio Math.

The post Making Math Homework Work! appeared first on Cognitive Cardio Math.

How often have you gone to a conference and been super excited by what a speaker shared?

1. Going across the rows of the multiplication problem, “cast out” (just cross them out) any 9s or combinations of numbers that add up to 9.
2. Add the remaining digits across each row, until the result is a single digit.
3. Multiply the single digits, and if the result is a 2-digit number, add the digits to get a single digit.
4. Follow the same steps in the product, until you arrive at a single-digit number.
5. If the results match, the answer to the problem is most likely correct (not 100% certain, but most likely); if the results do not match, the product is not correct.Casting out nines can also be used with the other operations as well, but using it to check multiplication is my favorite.

Have you used casting out nines?

The post Casting Out Nines appeared first on Cognitive Cardio Math.

Having the perfectly-run, efficient and effective math class….that’s been my goal, year after year. Somehow, in middle school, it has consistently tried to evade me!

In other posts, I’ve shared  that I taught elementary math for years, and always had an hour for math class. That hour gave me the time I wanted to have good warm-ups every day (sometimes taking up half the class with one particular problem that led to additional discussion/extension!); the hour gave me the time to go over homework the way I wanted to. And it still gave me time for a new lesson and practice.

The post Making the Most of Your 40-Minute Math Class appeared first on Cognitive Cardio Math.

Making Math Stations Work in 40-Minute Class Periods

I taught elementary school for 12 years and I loved my math centers (or math stations, as you might call them)! They were great. They provided my students with focused practice time for the skills we had learned.  When I moved to middle school I wanted that same thing for my students.  But I found myself asking “Can I have math centers in middle school?” Keep reading to find out how I made it happen.

Math class was always an hour, and we had five computers in the classroom, so having a computer center was always an option.

Then I moved to middle school. Math class was 44 minutes (minus time for switching classes…..so more like 40 minutes). How could I fit more than two math station rotations in a 40-minute period?? 

I longed for block scheduling (our district has never had it)…that would make it so much easier to complete math center rotations!

For the first year or two of middle school, I kind of gave up on the idea of math centers…the activities I wanted students to complete took longer than 20 minutes. So, the class period would be enough time to finish two math station rotations, IF students started the second they walked in the door and then had no time to clean up/organize at the end of class.

But eventually I needed to get my math centers back, so I experimented with a few different set-ups. After a little trial and error I landed on a structure that works and makes math centers in middle school work.

Math Center Structure

I willingly admit that I have not found a perfect solution….40 minutes is just too short a time-period for math class!

However, I’ve figured out what works for me, and maybe it can work for you too, if you also have short math classes.  It might not be perfect but there are so many benefits to having math centers in middle school math classes.  So here’s the solution I use.

My math centers are:

• One center per day
• 30 minutes a day
• For 3-4 days, depending on the topic

Assigning Math Center Groups and Tasks

There are many ways to group students and assign tasks, but these are the grouping/activity options I normally stick to:
1) When we only do three days, I create six groups and prepare two sets of materials for some tasks.

• Students will all complete three tasks over the course of the three days, but they might not all complete the same three…it depends on the topic, their needs, and my goals.
• The image below has two different examples of how I might assign the tasks.

2) When we do four days, I create four to six groups (if my class size is the usual 27-30).

• If I have only four groups, I usually assign them each a different task and then rotate through those tasks over the four days.
• If I have five or six groups, then I’ll have two groups complete the same task on the same day, similar to the three-day example.

Fast Finishers During Math Centers

My math students are not ability-grouped, so they finish activities at various times.

• I decided that I have to be ok with some students/groups finishing early and others not finishing (or finishing during a free, non-math period).
• Doing one math center a day, for about 30 minutes allows for some flexibility here.

If group members finish early, they can do the following:

1) Finish another center activity, if they had something unfinished.  

2) Complete a math color by number from our “finished early” resource bin.

3) Answer the math trivia cards – a set that isn’t one of the center activities. (click here to grab this free resource!)

4) Use the pentominoes that we use on the first day of math class – there are always students who want to complete this challenge!

5) Use a technology source for additional math practice, if extra computers are available.

Before Using Math Centers in Middle School

Just like when I was in an elementary classroom, before we start using math centers in middle school, I make sure students have a complete understanding of expected behavior AND of the activities they’ll be completing.

• We complete the different activities together with different concepts at the beginning of the year, and then I use those activities in the centers, using some of the same ones each time.

Six Activities for Math Centers in Middle School

The math center activities I typically use are:

1) Footloose task cards:
Students are up and around the room for this, so I typically assign only one or two groups per day. (I’ve added a bunch of Google Slides versions of these for more options:-) Read more about Footloose activities here.

2) Math Truth or Dare Game
(with paper and pencil):
This version is a group game, so I only assign one group per day, for less “noise” in the room. They have to talk, and they definitely have fun with this one! 

OR Google Truth or Dare:
I created digital versions of these math games. This allows two different groups to complete the same activity, but one group can use whatever technology we have available.

• This version could be played by group members independently or in teams.
• Learn more about Truth or Dare math games here.

I have these on a website now too = more options!

3) Color by Number:
This is a quiet activity that provides some self-checking practice. Students can also check answers with their group members if they’d like.

• (Students often don’t finish the coloring during the center time, so I have them complete all the problems first and then color….they can come back to the coloring if they finish an activity early on another day.)

• I’ve added digital versions of these….great for students who are absent and easy to use the activity with two different center groups.

4) Math Doodle Wheels:
I use this as a teacher-guided center sometimes, but I can also use the wheels as an independent center for review – students can copy the notes and complete the practice on their own.

• Coloring is similar to color by number – that part is last and they can return to it later.

• These math wheels get added to students’ binders to keep for the year, so they can finish coloring any time they finish something early.
• Learn more about this note-taking method in this post.

5) Problem Solving: 
I make this a collaborative center (I love when students have math conversations!), but it could also be independent work. 

6) Math Trivia Cards:
This is a fun activity to practice more general knowledge, with less calculation involved.

• Students can just quiz each other and share correct answers, or they can record their answers to be checked later. 
• There are three sets: Numbers and Operations, Geometry, and Algebraic Concepts (link to download them is below.)

As you can see, some of the center rotations require students to work together, while others allow them to work independently.

• I like to have this mix, so students can share ideas and solving methods but also have time to work with the concepts and skills on their own. 
• I also like to compare the work they did alone with the work they completed with others:-)

What to Do With Finished Math Center Work

When students complete a center assignment, I have them put that assignment into a specific tray in my classroom.

• I go through the trays at the end of each day and use my checklist to record who has handed in their work.
• I do grade all of the math center activities….sometimes it takes me quite a while!!

Activity Sets for Math Centers in Middle School

I have sets of 4-5 math center activities for each of the topics below, so these are the ones I use/have used. However, I don’t use all of them every year…because, time! 

I pick and choose based on student needs, time of year, etc. 

To check out the center activities, click the images below.

(I have 2-3 activities for many other topics, but won’t bundle those until I have 4-5.)

Have fun with your math centers in middle school!  They can change the look and feel of your classroom AND change how your students feel about math.

Access the Math Trivia Cards

The post Math Centers in Middle School appeared first on Cognitive Cardio Math.

Problem solving in math, or tackling word problems in math can be challenging for students, whether they’re in early elementary, upper elementary, middle school, or even high school! 

Especially if they don’t have any type of strategies to help them know where to start.

I’m not necessarily a fan of using ‘tricks’ or a specific approach every time students approach a problem.

But, there are times when students will feel very ‘stuck’ as to where to start, especially if they have trouble understanding or breaking down the actual text of the problem. They may also have difficulty in middle school if they don’t have a strong problem solving foundation.

We often see students in middle school who can understand what to do mathematically when presented with a problem situation. But some of those same students kind of freeze when that problem is presented in several sentences…. especially if there’s some extra information in there.

So, I created two different math wheels to help students with:

• Deciphering word problems 
• Problem solving strategies

Problem Solving Math Wheel #1

The first problem solving math wheel includes eight ideas students can use when breaking down a word problem and then solving:

1) Carefully read the problem

2) Identify the question, to be sure about what is being asked

3) Reread. Once students know what the problem is asking, they can reread to find pertinent information.

4) Circle key numbers. By circling key numbers students are taking the time to identify numbers they’ll use in their calculations.

This is helpful:

• for identifying numbers that may be in word form
• for identifying numbers that are NOT needed for the problem. These would not be circled and could even be crossed out.

5) Locate and box important words

• These words don’t necessarily need to be ‘operation’ words, but rather any words that help students understand what is happening in the problem

6) Evaluate, or solve the problem

7) Interpret and label

• The mathematical answer may not be the answer to the question (like when interpreting the quotient results in the answer being rounded up or down)
• Adding the unit label to the answer

8) Take time to check

• Is the answer reasonable? Does it make sense as an answer to the question?

This wheel has a word problem that you can work through with students when discussing these ideas.

Problem Solving Math Wheel #2

The second problem solving math wheel includes some of the well-known problem solving strategies and can be used as a simple reference to remind students that these strategies exist.

These problem solving strategies include:

1. Organized List
2. Guess and Check
3. Work Backwards
4. Make a Table
5. Draw a Diagram
6. Write an Equation
7. Look for a Pattern
8. Use Logical Reasoning

This wheel would be great for a center or finished early activity, because it doesn’t require direct instruction.

• Students can color this problem solving math wheel and then add it to their binders/notebooks and use as a reference throughout the year.
• This wheel could also be used in conjunction with the Problem Solving Doodle Notes, which can be used to teach each individual strategy, as explained in this problem solving strategies blog post.

Find the Problem Solving Math Wheels here

I know your students will love this engaging way to talk about and reinforce math problem solving strategies.

The opportunity to color and add some of their own creative touches will help make the strategies more memorable. 

Keeping these finished notes in their math notebooks will give students a reference for the entire school year!

The post Problem Solving Math Wheels appeared first on Cognitive Cardio Math.

Teaching Box-and-Whisker Plots in 6th Grade Math

Box-and-whisker plots are a brand new concept for my 6th-grade math students, and when 6th graders are first introduced to them, they seem a little scary. 

However, with some structured directions, students catch on very quickly.

As with all math concepts, there are different approaches to teaching this one. 

See Box and Whisker Plot Resources

What has worked in my classes is this: 

I break the creation of the box-and-whisker plot into 5 steps, in order to plot the 5 points needed to create the box and whiskers:

1) Order the data set from least to greatest.

2) Identify the smallest and largest values; place those points on the number line (above the number line).

3) Identify the median and place that point on the number line.

• Students need to understand and remember that if there’s an even number of numbers in the data set, the median will be the mean of the two middle numbers. Even though they’ve found median in the past, many students tend to need this reminder.

4) Find the first and third quartiles and place those points on the number line.

This step can be tricky for students…I’ve found it to be the step that most often throws off their box.

• Here’s what I’ve noticed: when there’s an odd number of numbers in the data set, it’s a little easier for students – the median is not included in the upper and lower halves of the data, so they have no trouble with circling the halves on either side of the median and then finding the median of each half, as in figure 1.

• When the data set has an even number of numbers, students need to remember that the median is between numbers and that exactly half of the numbers are in the upper half of the data and half are in the lower, as shown in figure 2.

The common mistake students make is to assume that since the two middle numbers (in this case 6 and 7) were used to find the median, they aren’t part of the upper and lower halves. 

This throws off their 1st and 3rd quartiles. I’ve found it’s important to spend extra time on the different scenarios possible in this step. I’ve also found that drawing that middle line to represent the median is a very helpful visual.

5) Draw the box and whiskers:
a) Draw a box, with the (vertical) end lines going through the points of the first and third quartiles.
b) Draw a vertical line through the median.
c) Draw lines from the box to the least and greatest values.

Box-and-Whisker Plot Fold It Up

I created this notes/fold-it-up a couple years ago, to help guide my students as they began creating box-and-whisker plots on their own. 

There are two versions: a blank one for students and a completed one for me:-) 

(If students miss the instruction due to absence, I give them a copy of my completed version when they return.)

Using the blank version, I walk the students through their creation of the box-and-whisker plot. And when we’re done, they have the notes for their independent work.

The only folding part of this fold-it-up is the section at the very bottom that has the definitions of the vocabulary. 

Students will need to cut the vertical lines along the bottom, fold them up, and then write the vocabulary words on the outside of the flaps

• quartiles
• first quartile
• third quartile
• variation
• interquartile range

Download the Fold it Up Here

Box-and-Whisker Plots Notes and Practice

I recently created a box-and-whisker math wheel. 

It has the same steps outlined above, just in a different format, which is a little more colorful and fun! Both of these resources are great for interactive notebooks!

See the Wheel on TPT

Box and Whisker Plot Practice

If you need some additional, engaging practice for box-and-whisker plots, check out this color by number activity!

The problems in this activity require students to identify:

• First quartile
• Median
• Third quartile
• Interquartile range

Check out the color by number

• Range
• Minimum
• Maximum
• Number that would be in each quartile, based on a number of students surveyed
• Data in terms of percent (25%, 50%, 75%)

Box-and-Whisker Plots Lesson ~ Reading and Creating

If you’d like a full lesson, which includes the fold-it-up and additional guided and independent pages plus exit tickets, check out the lesson using the button below.

See the Full Lesson Here

Interested in more Fold It Ups? Check out these blog posts:

• Integers Fold it Up Freebie
• Fraction, Decimal, Percent Fold it Up for Middle School Math
• Using the Ladder Method in Middle School Math, for GCF, LCM, Factoring

The post Teaching Box-and-Whisker Plots appeared first on Cognitive Cardio Math.

Why Ping Pong?

Ping Pong and Math Facts

• When the score is 5-0, 4-1, or 3-2, serving switches.
• To switch servers at 10 points, players need to know that the score would be: 10-0, 9-1, 8-2, 7-3, 6-4, or 5-5.
• When serving switches at a total of 15 points, the score possibilities are: 15-0, 14-1, 13-2, 12-3, 11-4, 10-5, 9-6, 8-7.
• At 20 points, the score would be: 20-0, 19-1, 18-2, 17-3, 16-4, 15-5, 14-6, 13-7, 12-8, 11-9, 10-10.

Engaging Kids with Games

• Math Games for Teachers: Activities for an Epic Start to the Year
• Engaging Fraction Games and Activities
• 7 Amazing Homeschool Math Games
• Math Review Games for Parents to Empower Their Learners
  ​

The post Practice Math Facts with Ping Pong! appeared first on Cognitive Cardio Math.

Lots of teachers use beach balls for fun math in middle school and elementary classrooms, but I haven’t used them in such a long time that I thought I’d share my excitement about finally getting some new ones!

I often used beach balls for basic math fact practice when I taught 4th and 5th grades in the elementary school

Our math classes aren’t that long, but I figure I can squeeze in 5 minutes of extra math review at the end of class once or twice a week. We can toss the beach balls around for some quick math practice:-)

The post Beach Ball Math Activities in Middle School appeared first on Cognitive Cardio Math.

Today, as my 6th grade students were working on a color by number in math class (which I thought was a fun, different way to practice math), one of them asked, “How does coloring help with math?” The question was asked with a “there’s no reason I should have to do this” attitude.

I explained that:

1. Coloring helps with motor skills.
2. Coloring helps us to use the brain in a different way.
3. Exercising the brain in different ways could help in all things that require thinking (not just math).

I don’t think he really appreciated my answer:-)

So, I decided to do a little research, to see what I could find.

Most of what I found (I didn’t spend a super-long time searching, because I didn’t have that much time!) was related to:

1. Benefits of coloring for young children (and did relate to math skills)
2. Benefits for adults

Here are a few benefits I found, as coloring relates to adults:

Benefits of Coloring

According to the Huffington Post (10/13/14), coloring benefits adults (and I would assume children as well) because it”…generates wellness, quietness and also stimulates brain areas related to motor skills, the senses and creativity.” In addition, psychologist Gloria Martinez Ayala states that when we color, we activate different areas of our two cerebral hemispheres.”

The action involves both logic, by which we color forms, and creativity, when mixing and matching colors. This incorporates the areas of the cerebral cortex involved in vision and fine motor skills [coordination necessary to make small, precise movements]. The relaxation that it provides lowers the activity of the amygdala, a basic part of our brain involved in controlling emotion that is affected by stress.”According to PenCentral (their link is no longer active), coloring benefits adults in helping them to maintain fine motor skills – this requires extra work by your brain to coordinate your actions and muscle control in your hands and arms.

Coloring can help delay the loss of fine motor skills as people age. Coloring may also help fight cognitive loss, especially if challenging pieces are completed every so often.

Click to download this FREE color by number!

Incorporating Coloring in Math Class

I didn’t necessarily find research to answer my student’s exact question. But I did find was quite interesting and can certainly be applicable to middle school math students!

Anecdotally, I’d add that when I spend time coloring, my mind wanders a bit….thinking, exploring ideas, brainstorming. While my hand is coloring and my brain is being stimulated, I’ve often thought of solutions to problems and stumbled upon excellent new ideas:-)

If you know of other articles or published research to support the role of coloring in improving math skills, please let us know in the comments! This post was originally written in 2015, so there may be new research by the time you read this!

In a few more recent blog posts, I wrote about:

1.  Why it’s important to include coloring in math even if your students are virtual.
2. What types of coloring you can include!

The post How Does Coloring in Math Class Help Improve Math Skills? appeared first on Cognitive Cardio Math.