How do you teach data distribution to 11 year olds??
by Bridget Adam
The 6th grade Common Core Standard, 6.SP.5, is incredibly daunting (see below). It is the first time students are asked to analyze data using measures of center and measures of variability. I have been skeptical if 6th graders are truly ready to access this standard to the intended depth. Asking students to compute the interquartile range is a big task, but requiring them to understand and summarize this measure seems a monumental task.
Summarize numerical data sets in relation to their context, such as by:
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
What makes this standard so hard to teach?
While this is not an exhaustive list, these are some of the major challenges I see when planning to teach this standard:

Students do not always have a connection to the data

Data is abstract if they have not collected it themselves

It is the first time they are asked to summarize or make conclusions from data

Having students verbalize in the math classroom is always a struggle

Although it is only an “additional” cluster, this standard requires exposing students to various data sets and allowing them time to grapple with verbalizing and writing what they see

Understanding that one number or one value can represent an entire data set
Implementation 2013
Last year, aware of the difficulties mentioned above, I introduced the interquartile range with a focus on procedure. My strength as a teacher is breaking down concepts into clear, manageable steps for my students, so this seemed like the easiest way to implement 6.SP.5 for the first time (see below). At the end of the Statistics Unit, students were able to compute the interquartile range, identify the median, upper and lower quartiles as well as the minimum and maximum of a data set, but had NO idea what this value indicated or how it related to the data. It was obvious that students did not conceptually understand the interquartile range when they were asked to explain how this value reflected a data set.
Making Improvements in 2014

Analyzing Data Starting with Visuals
Having encountered the obstacles above, I decided to focus this year on the conceptual understanding of the interquartile range. I pushed computation to the side for a week. What did I want? I wanted students to interact with data, visualize and informally describe data. I thought by introducing this “beast” of a concept with visuals, I could ease my students into the world of data. Initially, I gave students magnets or Postit Notes to represent a piece of data that reflected them personally (i.e. Number of Siblings, Number of Hours Slept, etc.). Each student placed their piece of data on a line plot on the front board. Students were then given time to observe and write using the following prompts:
 What stands out to you?
 Is this what you had expected?
 Is your eye drawn to something in particular? Why?
 What descriptive words can you use to reflect how the data looks?
Over the course of the week, students were given data displayed in various ways and were continually asked to verbalize and write about their observations.
These activities gave students the opportunity to “talk data” and build their confidence in mathematical discourse. Using visuals allowed for a smooth transition from the use of words to describe data to the use of numbers to describe data, specifically variability.

Exaggerating Data
Having mastered measures of center (mean, median and mode), it was time for students to dig deeper with measures of variability. Using students as data points was engaging, and allowed for them to “feel” how close, or how spread out the data was. Students were asked to line up at the front of the room in height order. As a class, we determined the range of the data.
We then began to play the “What Happens If…” game. I played the part of Kevin Garnett (standing on top of a desk). We then found the range of the data with the additional height. Students verbalized how the range changed and why. Then we added my daughter’s height, age 2, and discussed the differences between the ranges calculated.
The more we analyzed the data visually and verbally, the more students wanted to know about how we could represent these specifics with the use of numbers. This was the perfect time to move into the calculation of the interquartile range. We continued the verbalization and visualization, but added on the steps to calculate the IQR. They were now able to see that by breaking up the data into quarters, we could focus on various parts of the data, and we could begin to see the spread between these landmarks.
Lessons Learned
In order to improve my students’ understanding of measures of variability, I must:

Introduce data with visuals
 Introduce students to data by using values that were personal and tangible

Use exaggerated data and ask “What Happens If…”

Question students informally about data and their findings

Expect students to verbalize and write about various data sets before and after mastering the computation of numerical values
I have learned that students must, before anything, learn to step back and look at data. They have to slow down and ask themselves questions. Analyzing data takes a different type of thinking, and I must model this for them. Before any complex task is mastered, students must be exposed to a variety of data sets, in various forms, and be comfortable with verbalization and statistical terms. The focus on language and visual observation serves as an access point for all of my students. Having now taught 6.SP.5 for two years, in two very different ways, I am now confident that students CAN analyze data, specifically measures of variability.
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