Mean absolute deviation can sound very intimidating. I remember being in a master’s class and we had to find the standard deviation of some data. Most people in the class had no clue what to do. Most 7th grade math teachers have been teaching math since before the Common Core came on the scene, so this makes mean absolute deviation a new topic for many of us. If you’re like me, you get worried when there’s a new topic. You want to teach it right, but you’re not confident with how to teach it. At least, not yet. It’s taken me a bit of time to feel comfortable with it, but this year I had so much fun teaching this concept. Let me show you step by step how I broke down and taught my 7th grade students about mean absolute deviation.
Mean absolute deviation has thrown many of us for a loop. As I was planning for it this year, I wrote down some I Can statements to help me think through the way to teach it. I do this with all of my topics and I find it especially helpful with this topic because I’m not as familiar with it as most. In my class we use interactive notebooks and at the beginning of each unit we put a list of I Can statements in our notebook to keep us on track. We refer back to this list on a daily basis to check our class and individual progress (read more about how we use I Can statements here).
I Can statements for mean absolute deviation
Here’s the list of I Can statements that I used this year for teaching mean absolute deviation:
- I can determine the absolute value of rational numbers.
- I can find the mean of a set of data.
- I can find the mean on a dot plot graph.
- I can find the mean absolute deviation using a set of data.
- I can draw conclusions about the mean absolute deviation.
You can download your own print and go copy of these I Can statements (including a blank template) here. This is not the only list of I Can statements that would work for this topic. But it’s the one that I used this year. If you want to use it, you may need to change things or add something. I’ve found that getting the perfect list is not the most important part, but rather having a list as road map really helps students understand what they are learning.
I can determine the absolute value of rational numbers
In my early days as a teacher I may have made the mistake of thinking that if I tell the kids what something is, then they will understand and remember it. (And by “may have”, I mean definitely did, over and over again. Heck, I still fall into this trap sometimes even though I think I’ve already learned this lesson!) I suppose if it worked that way then kids would learn everything on their own through books and YouTube. I made this mistake last year with teaching students MAD with absolute value. Absolute value seems so simple, but students still need to learn what it is and attach it to something in their schema or background knowledge.
I now use a discovery lab on absolute value as an introduction to this topic. Instead of me telling students what absolute value is, they discover it. It’s very easy for them to get, and it helps to build their confidence. I will never go back to just telling them what it is for this topic. Once students understand absolute value, it naturally weaves into our learning when we get to mean absolute deviation.
I can find the mean of a set of data
Next, we delve into mean. Students should have some background in finding the mean because it falls into the 6th grade standards. I work with students who struggle with math and many of them have had their memories wiped clean of this concept, or so it seems. We start back at the beginning and only focus on finding the mean. We don’t do median and mode at this time because it can confuse them.
Basically, we spend two days doing a lot of practice finding the mean. We write notes in our interactive notebook for about 10 minutes and then we are off to the races. We play games and complete partner activities to get a lot of practice. I have written another blog post that has some of the activities that we use for finding the mean. When we are done with the two days, my students are super proficient at finding the mean. This skill is essential for finding the mean absolute deviation.
I can find the mean on a dot plot graph
Dot plot graphs seem so straight forward, but just like anything else, students have to practice with them to understand them. We complete a gallery walk activity that’s great for introducing and working with dot plot graphs. It helps to show me what the common misconceptions are with dot plots. Some kids get confused about which value has the most data points and what is the highest value on the graph.
Practicing with dot plots also gives students a little more practice with finding the mean. It’s in a different format so they can extend their understanding of it. There are also some other questions that I have them answer like:
- What is the range?
- Which value has the most points of data?
- What is the highest value?
- What question could someone be asking when they created this dot plot?
These questions help students to understand more about the purpose and data on a dot plot graph. We also look at the graph and talk about variability from the center. This activity lays a foundation for dot plot graphs and mean absolute deviation.
I can find the mean absolute deviation from a set of data
Now, it’s time to put it all together. All the groundwork has been laid and we move to finding the mean absolute deviation. We go through an example in our notebooks for finding the MAD. It can be done in 3 easy steps. First, find the mean. Next, find the absolute value from the mean for each value. Last, find the mean of the absolute values. This process is fairly straightforward and I didn’t find that my students struggles with this part. They came into this lesson with so much background on the required skills that this part came very, very easy.
Many people use a graphic organizer to keep the information organized. You can find one from Amazing Mathematics here. I found that making my students use the graphic organizer was a little time consuming and it made the process seem more complicated than it is. I have been toying with the idea lately that maybe students don’t need to show all of their work unless they are not being successful. There are certain that they need to write down and other things that they should be able to do in their heads.
This is what it looks like when we do a mean absolute deviation problem:
If I find that a student is messing up a lot, then I will introduce the graphic organizer to them. Otherwise, they solve as shown in the examples above. I don’t make them write down every step. They keep track of what they are doing on the calculator.
I can draw conclusions using mean absolute deviation
Ultimately, we want students to being about to do stuff with data and not just manipulate it. There are MAD calculators out there that do the work for you. This part of the standard, drawing conclusions using mean absolute deviation, is my favorite because they get to show if they understand it or not. Sometimes, with how quickly our calendar moves us through the curriculum, we don’t get a chance to let kids make sense of what they are doing.
When students look at data, find the MAD, and then draw conclusions they are being mathematicians. They get to do the same things that mathematicians do. There’s a video that we watch that shows using MAD in a real world situation. It helps to get students to see that what they’re learning is relevant. You can read about more activities and resources to help students practice making sense of data with MAD in the post “12 Engaging Activities for Mean Absolute Deviation.”
Try using I Can statements to chunk learning for kids in your class
Using I Can statements to chunk learning can really change how students learn. It helps them to be accountable and to know what they are trying to learn. Sometimes, as teachers we feel like we don’t have enough time to do things like review learning objectives. But taking a few minutes to preview what students will learn and then reflect on their learning will make all of your hard work go farther. Students remember things better when they know what they are doing. So, try using some I can statements for the next topic that you teach. Have the students write them in their notebooks and refer to them through the unit. Let us know how it goes by leaving a comment below. Thanks for reading. Until next time!
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