# Variability

In the past, my data standards always consisted of teaching the students how to make graphs.  While there were a few graphs they weren’t familiar with, many of them seemed very repetitive.  These kids have been making line and bar graphs since first grade.  The new common core standards change things drastically.  It is all about sampling and variability now.

On Tuesday I started with an AIMS activity from the Statistics and Probability book.  The activity had the students comparing synonyms for blue, yellow, and red to see the different lengths of the words.  I added a component where the students would have to find the interquartile range and mean absolute deviation, two things that they weren’t familiar with at all until now.

Then today, we did another activity, Counting Characters, from the same book.  For this one, the students had to find a random sample by throwing squares of paper at a sheet of newspaper, then they counted the characters in each of these squares.  Students used that data to estimate how many characters would be on the entire page.  From there, I had the students find the mean absolute deviation of their data and we compared these numbers to the rest of the groups to see which group had data with the highest variability.

I think both of these activities went pretty well.  I was quite shocked at a few of the things that happened during the random sampling for the counting characters activity.  First of all, I had the students cut out squares to throw on the newspaper.  I had a few groups that didn’t cut on the lines for the squares.  They simply cut between the lines on the paper.  Really???  I really just didn’t think this would be something I would have to say specifically.  I also had students toss the squares at the newspaper, lean down and straighten the square so it was nice and neat on the paper, then throw the next one.  Not a random sample then, guys!  And then, again, the cutting out of the squares from the newspaper was appalling.  How do you get jagged edges?  How do you have pieces that are drastically different sizes?  All I kept thinking of was the common core standard for mathematical practice “Attend to Precision”.  While I don’t think that cutting newspaper squares was exactly what they were thinking of when they wrote this standard, it certainly fits the bill.  How can we expect our kids to do higher level precision when cutting carefully isn’t even on their radar?