I’ll be the first to admit that when the concept of mean absolute deviation was added to our standards, I didn’t know what it was. Of course, I’ve worked with standard deviation and mean, but I was a newbie to this concept of MAD. As I’ve wrapped my head around it, I’ve learned it enhances other concepts students are learning, and it’s taught as part of helping students to understand variability. In this post I’m sharing with you 12 engaging activities for teaching mean absolute deviation (MAD) to help your students really get it.
There are a couple of prerequisite skills that are very important for students just getting the skill of finding the mean absolute deviation. They need to 1) know how to find the mean and 2) they need to understand what absolute value is. Finding the mean is a review concept from 6th grade, but my students always need a day or two to refresh their memories (you can read more about how I broke down MAD for my students here). Also, I work on the concept of absolute value for a day because it’s not intuitive for them. After reviewing finding the mean and absolute value, then we’re ready to move on to MAD.
The following is a list of activities that I use with my students to practice the prerequisite skills as well as find the mean absolute deviation (MAD). I work with a group of students who are not consistently working at grade level. However, this is a skill that they become very proficient at. I attribute that success to taking the time to build the foundational skills before we get into mean standard deviation.
The list of activities:
Finding Mean and Absolute Value:
- Absolute Value Discovery Lab
- Absolute Value Maze
- Find the Mean Card Game
- Paper Chain Activity
- Find the Mean On a Dot Plot Gallery Walk
Mean Absolute Deviation:
6. MAD Video
We started with a discovery lab for absolute value. This activity worked beautifully with my students. Instead of me just telling my students what absolute value is, they figured it out on their own. They own this concept now and I don’t have to keep telling them what it is. (you can read more about this discovery lab in action here). When we got to the absolute value part of MAD, they were very confident in absolute value. It was a great way to set them up for success with MAD.
The discovery lab doesn’t take very long and students get the chance to discuss distances between numbers. It is a great introduction to mean absolute deviation. (If you’re new to discovery labs, read this introductory post, or check out other posts on discovery labs.)
We use mazes in my class as warm-ups and for cyclical review. This maze is simple and easy to complete. It works as a reinforcement of the concept of absolute value. I used it for the three days after we completed the discovery lab.
The three mazes in this resource use fractions, whole numbers, and decimals. Students don’t just remember things (unfortunately!) and their brains needs repetition. Mazes are a great way to get that repetition and are a fun way to practice. I usually have students work on the maze and when they finish they come and get it checked with me. If it’s correct, they move on to the next activity. If they have mistakes they have to fix them. This gives me an opportunity to see what the misconceptions are and then we can work on them immediately.
I found this idea searching on the internet and it sounded really fun. We used it as an anticipatory set. The kids had so much fun and they were practicing finding the mean. They got a lot of repetitions in only a few minutes. I love playing games like this because I get to see my students in a less formal environment. They reacted to streaks of bad luck and it gave me a fun chance to build rapport with them.
We played the game by shuffling the cards and then each person randomly chose from 3 to 8 cards. They figured out the mean of their hand of cards and whoever had the highest mean won the round. They got to keep all of the cards as their points. We played for 10 minutes and each partnership finished a game. This game was a great way to brush up on finding the mean.
A paper chain activity is another way to quickly practice the skill of finding the mean. Students complete 12 mean problems. Then, the questions and answers make a paper chain. Putting the paper chain together only takes a couple of minutes. With my 7th graders we have been doing a lot of paper chain activities. When they finish solving the problems, every group puts their paper chains together.
Now we’re connecting all the paper chains we do into one mega chain when we’re done. My students have decided they want to make a chain that goes around the whole common area in our building. The kids came up with that idea and every time we do a new paper chain they get really excited. It’s like a cool trophy of all the work they’re doing. I used to think that every moment of every day had to be so focused on content, content, content. But over the years I’ve learned that you can get kids to buy into the work they need to more if you take a few minutes to add some fun and novelty.
Sometimes when I look at new standards and I see all the different things kids have to do to master the standard I get a little discouraged. I wish that my students could look at a dot plot graph and make sense of it with no help, but that is not reality. Dot plots are not super difficult, but for many kids they aren’t intuitive either. That’s why I love practicing finding the mean on a dot plot through a gallery walk activity. It get’s students moving and talking, and they get practice interpreting the same ideas of mean and MAD in a different format.
I use a foldable to show them how to work with a dot plot and then we complete this activity. It gives them a variety of situations and numbers for finding the mean. And there’s a great bonus! This can be used later with mean absolute deviation. It can have a dual purpose. I used these posters from the gallery walk again as situations for us to do together when we got to MAD.
Songs can really help students remember how to do something. Some of the math songs can come across as a little cheesy. To this I say- embrace the cheese! When I find myself getting too serious about it, then the students balk at it. But when I let them know up front that I’m fully aware that the song is silly, it’s a whole different experience. I like to listen to a song a couple of times. Before too long I will start to see a few kids singing it under their breath. Usually, it is a class clown kind of kid and you can see that they appreciate it.
This particular video goes through all of the steps in finding the MAD. It has a visual representation of it as well. I would recommend watching it on a couple of different occasions and use it as cyclical review, too.
This mean absolute deviation graphic organizer is a freebie from Amazing Mathematics on TPT. As you will notice in the graphic organizer there are three tables for you to complete problems on. The graphic organizer can also be shrunk down and used in an interactive notebook. Also, you could use it in a SmartPal dry erase sleeve and have a copy of it to use all day in your class. I just love that you don’t have to prep anything with this graphic organizer.
If you are looking for a real life example of people who use MAD then look no further. This video shows how scientists used mean absolute deviation in their efforts to clean-up Boston Harbor. It was a great conversation starter with my students and they seemed fascinated with seeing math in real life. They asked some questions about what was going on in the video and it acted as a great anticipatory set for the lesson.
This basketball worksheet gives students practice finding the mean absolute deviation in a meaningful situation. It has a dot plot graph and students have to figure out the variability in a kid’s basketball scoring. There is a whole blog post that goes along with the worksheet. I like that it has more than one question. Students can get so caught up in finding the right answer and not thinking about what they are doing. This activity gives them a chance to really think about variability and draw some conclusions.
The scavenger hunt that I have created for mean absolute deviation consists of 12 multiple choice problems that are hung around the room. Students go around in partners and answer the questions. The question have a symbol assigned to each one. Students come and check their answers with the teacher to win the symbol.
I usually play this as a competition for which team as the most symbols collected in the allotted time. Kids really like this activity. Just the other day a student told me about how much he likes that type of activity (unsolicited no less!). Also, they get to practice with a partner and they get a chance to move around the room.
Some of the problems have dot plots and some have written scenarios. If you are looking to add a little spice to your class, this is a great activity.
When it comes time to review we often use a knockout game in my class. The whole class can review at the same time and by using SmartPal dry-erase sleeves I can see what students don’t understand.
The format of the knockout game goes like this:
- A student chooses a picture and a question is revealed.
- Students work independently to answer the question.
- The answer is revealed.
- The teacher models when necessary and goes over the problem.
- Students who got the right answer get points. There are some good and bad bonuses along the way.
This knockout game reviews mean, absolute value, and mean absolute deviation. There are tables and graphs. Actually, there is a wide variety of questions so that you can identify what you students need more work on.
There are two different calculators that will find MAD for you. I use this to help students check their answers. Some teachers don’t feel comfortable with this sort of help. They are afraid that students will cheat. But I find that it’s possible to get out in front of that- you just have to teach them not to cheat. Instead, by shifting the focus away from completing answers and getting them right, it opens up a different way to talk about tools like this to check their reasoning and get instant feedback. One of the best ways is to not put so much pressure on grades or on finishing every problem. In my experience, when you take some of that pressure away, most students won’t cheat.
Try one thing…
I know it can be overwhelming when you see a lot of new ideas. Some people can implement a lot of new ideas at one time, but most people work better by trying one new thing at a time. My challenge to you is to just try one new thing. Then, take your success and confidence at that one thing and then you can add one more thing.
Maybe you have been wanting to get your students up and moving around. If that’s you, then you might want to try a gallery walk or scavenger hunt. Or maybe you want to get better hooks for your lesson. If that’s what’s on your mind, then try out the mean card game or a video. You might also be looking for a fun way to review with the class. The knockout game would fit the bill for a review game that gets all students involved. Try one thing to increase engagement in your class and let us know how it went by leaving a comment below. Thanks so much for reading. Until next time.
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