Let's get students excited about statistics for 6th grade!
It’s nearing the end of the school year and students are growing weary with state testing right around the corner and the idea of summer vacation being dangled in front of them just slightly out of arm’s reach. You can’t help but think your students are starting to grow tired of the normal day to day routines of school. So it’s time to treat them to something different! However, you know you still have a very important topic to cover; statistics for 6th grade. You know any old 6th grade statistics worksheet won’t work, so you’re seeking those impressive, engaging 6th grade statistics activities students will get excited about. Luckily, you’re in the right place for some awesome ideas!
6th grade statistics unit: The Hook
Data and statistics can be a daunting unit with the excessive calculations, plotting of points and interpreting of graphs. In fact, many students see no point in even learning about it until you provide them with the perfect motive. To decide once and for all: Which is the superior gender when it comes to physical fitness? Students use measures of center and variability to formulate an argument to explain why they are the overall winners of the competition. All of this is determined with a good old fashioned fitness test. Spoiler alert, the boys talk a big game, but in my class, the ladies usually come out on top.
*Please be aware of gender preferences prior to placing students into groups. To ensure inclusion of all students, consider splitting the students into two groups other than male and female. Do what is best for your students.
The Competition
This head to head competition goes on in my class for five days straight. It’s a grueling battle between the sexes and things get heated! Students make claims like “Look how much higher our mean is than yours!” “The only reason you won is because John is an outlier!” “Twenty-five percent of the girls did better than half of the boys.” Yes, the students actually talk about math, just to prove they are better or won that day’s competition.
Each day, we ask a statistical question such as “how many pull-ups can the students in my block two math class perform?” We set the mood with some high energy music, collect data, write it down in a chart and solve the math to decide who wins.
Mean, Median, Mode and Outlier - Push-Ups
Here’s how I break down the exercises to ensure the students are learning the appropriate concepts based on the data provided. I have personally been using and perfecting which exercise is best for each lesson for over seven years. Mean, median, mode and outlier is our first lesson and we hold a push-up competition to collect data. Check out the free lesson here! The reason I use this exercise to collect data for this concept is due to the spread of the data. Normally, my students do anywhere from zero to fifty consecutive push-ups. At the bottom of the list, the students see my name and tell me I still need to perform the exercise (or in your case, your name or a “celebrity” such as the gym teacher or a YouTube star).
My Turn
It’s time to go to work! Once all the students have completed their push-ups, I take off my lanyard, empty my pockets, blast some inspiring fitness music and get busy. It’s time to teach them what an outlier is! My goal is to shoot for one hundred push-ups. When students start to question my form, I throw in a few perfect form clap push-ups to quiet the grumbles.
Now for the Data
Once completed, we compare the scores using the mean, median and mode (including my score for the boys). The girls claim “it’s not fair, you helped them”. I respond a little too enthusiastically, “You’re right! That’s what is called an outlier, a number that does not fit with the rest of the data. Let’s see how much I helped them.” We then find the mean, median and mode without my push-ups included.
This leads to a rich discussion as to how outliers affect each of the measures of center. We relate this concept to scoring very low or very high on a test or quiz. The students are able to communicate how a single grade could drastically pull their grade down or up. With the first competition over and the foundation of the days to come laid out, the students are ready for more. The battle was won, but the war is far from over.
Mean Absolute Deviation - Jump Rope
During the second day, we complete as many jumps with a rope as possible in thirty seconds. This competition usually has a good amount of spread between data points. In fact, our focus for this day is to find the mean absolute deviation. This competition is a way for students to review their foundational learning from the push-up competition and extend their understanding by finding the mean absolute deviation.
This measure of variability is difficult for students to grasp or understand its purpose. Having two sets of data tremendously helps to explain this concept. With the data for the boys and girls, it is easier for students to understand what a higher or lower mean absolute deviation means.
Line Plots - Pull-ups
The next topic I teach during this unit is how to create and analyze a line plot. We start with the creation and naturally, start by collecting real data. I choose to do pull-ups for this lesson. From my experience, many of the students cannot do any or can only do a minimal amount of pull-ups (under twelve). This keeps our line plot from being too long, but more importantly, provides the students with an excellent example of a graph that is skewed to the right (right tailed) and has a cluster around zero and one. Also, the data often lends itself to talk about gaps in the data which is also an important concept for students to understand and be able to identify.
This is where making friends with the gym teacher comes in handy. He or she will most likely be willing to allow use of the pull-up bar(s) to help out with this lesson. Otherwise, if a playground is available, this is also a great place to collect data on pull-ups. The monkey bars work perfectly.
Frequency Tables and Histograms – Chair Pose
Frequency tables and histograms are my favorite! Well, let me rephrase that, collecting data for the frequency tables and histograms is my favorite. My reasoning, the face my students make when I introduce it. It’s priceless! After three days of exercise, some of the less physically active students start to grow a little weary of all the activities. So, I tell them I have decided to give them a break. The only thing they have to do today is hold both hands overhead and hold them there for as long as they can while seated.
As I explain the action to the kids, I demonstrate from a chair. I get moderate student buy-in from the more gullible students as they show signs of relief that I am giving them a break. However, those who know my sarcastic side all too well, know there must be a catch. Those uneasy students are true to think there must be more. I continue to tell the students there is a slight catch… “there is no chair” I declare as I kick the chair out from underneath me while maintaining perfect chair pose form. The look on their faces…priceless, trust me or try it yourself!
The Data
The data being collected in this particular example is how much time each student is able to hold the chair pose. Since this exercise takes minimal space, all the students compete at once and simply record their time as they give up. Normally, I place a stopwatch on the Smart Board so students can easily track the time. Since everyone has very different data values, we begin to discuss the value of using intervals over exact numbers. We then use this data to create frequency tables and histograms. When I’m lucky, the graphs are fairly symmetrical and we can discuss the peak and shape of the graphs. After creating the graphs and viewing a few more examples, we discuss some of the pros and cons to this type of data depiction.
Box Plot - Burpees
The final component to my exercise unit is the box plot. This graph can be daunting and confusing for students upon the first exposure. In contrast, having the ability to physically show the four sections as equal parts by having students stand or raise her hand for each quartile helps tremendously. Collecting actual data for this topic is a must! In fact, it may be beneficial to have the students write the amount on a piece of paper and hold it up to provide students with a human visual aid that clearly shows the same number of people in each group.
For the data collection, I use burpees which provide a great deal of variety in the data. This variety provides an uneven looking box plot which allows for deep conversation about why some sections of the box plot are longer or shorter than others. Comparing the two box plots even allows for students to make statements such as “Our median is higher than your first quartile. We crushed you!” In fact, depending on the minimum and maximum, students will spend a lot of time coming up with creative ways to determine the winner for the burpee competition.
6th Grade Statistics Unit: Conclusion
Overall, exercise is a fun and exciting way to get students involved in collecting and understanding data. The competition provides a necessity to do the math, so they have a way to prove they are better than the opposing team. Not only does this make the math more fun, it makes it more meaningful. My students always perform well when it comes to data and statistics and I can’t help but think the main reason is they are completely engaged in the data collection and analysis. Even the students who aren’t the most physically active enjoy getting up and moving around. For more ideas on how to get students up and moving, check out this post.
6th Grade Statistics Unit: Recap
A Word of Caution
Some classes may be gender sensitive. If this is the case, consider splitting the class into two teams in a different way. However, it is important to keep the teams the same from day to day to make it feel more like an ongoing competition. Furthermore, remind students not to make fun of any students who are not able to do a push-up or pull-up or are not coordinated enough to jump rope. I always remind my students they must remember everyone may not be good at the same things you are good at. I also take time to show students how to modify some of the exercises so in the future, if they want to get better at the exercise, they know where to start.
6th Grade Statistics Project - Assessing Learning
To extend or assess student learning, I have the students create a game or activity. You can check out my blog post about the statistics project here.
