Box-and-whisker plots are a brand new concept for my 6th-graders, and when students are first introduced to them, they seem a little scary. However, with some structured directions, students catch on very quickly.
Teaching Box-and-Whisker Plots
I break down 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 remember that if there is 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 is 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 are ok with circling the halves on either side of the median and then finding the median of each half, as in figure 1.
However, 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 that 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 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.
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.
I created two versions - a blank one for students and a completed one for me:-) 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).
When students miss the instruction due to absence, I give them a copy of the completed version on their return.