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.

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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.

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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?

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Slicing 3D Figures

One of the very first blog posts I came upon this summer when my blogging journey began was Julie’s Volume of 3D Shapes with Play-doh.  I have been so excited to do something like this since I read this post and since I found little tubs of play doh at the $1 spot at Target.

Instead of finding the volume, we used the play doh to do one of 7th grade’s new 7th grade stadards, slicing 3D figures.

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Each of the kids was given a container of play doh and a plastic knife.  We formed 3D shapes and then made parallel and perpendicular cuts and examined the cross sections.  This was one of my favorite things we have done this year, and I am pretty sure the kids agreed!  They really seemed to get what we were doing and had a little fun, too!

The other awesome part was the kids were over the top impressed with my amazing sculpting skills.  And I do not have amazing sculpting skills.  But every single class was in awe of my shapes and how quickly I made them.  Great ego booster.

Looking at Area the Old Way and the CCSS Way

Our school has designated next year as the yeard we are moving over to the new common core standards, but this year we are beginning the transition and are doing many things to start to get our kids prepared for this big change.  I am right in the middle of my unit on perimeter and area and wouldn’t you know it, we had a professional development session last week in which we talked about the old way of assessing area vs the new way of assessing area.  And while I already knew that the common core assessments will be different, and I have spent a lot of time looking at the smarter balanced example problems, the fact still remains that my teaching is going to have to change, as will my assessing.  These kids will just not be ready if we keep doing what has been ok in the past.  After our PD session, we had time to examine the new standards and work with them for a while.  I went back to the smarter balanced site and looked at the example problems they had again and found one that fit exactly with what I have been working on and assessing the kids on today. 

Old assessment-

Find the area and circumference of the circles. (Then I gave them several circles with the radius or diameter labeled.)

Skills needed:

          1. Knowledge of formulas for area and circumference

          2. Difference between radius and diameter and what to do if diameter is given.

          3. Ability to substitute a number into the correct formula

 

New assessment- (From the Smarter Balanced site)

An artist used silver wire to make a square that has a perimeter of 40 inches.  She then used copper wire to make the largest circle that could fit in the square, as shown.  How many more inches of silver wire did the artist used compared to copper wire?

Circle 2

Skills needed:

          1. Knowledge of the meaning of perimeter

          2. Knowledge that a square has 4 equal sides

          3. Ability/knowledge to divide the perimeter by the 4 sides to get the length of one side

          4. Knowledge that the length of one side would be the same as the diameter of the circle

          5. Knowledge that the “wire” in the problem would be circumference/perimeter not area

          6. Formula for the circumference of a circle

          7. How to find the radius after the diameter is found

          8. Ability/knowledge to subtract to find the difference between the numbers

 

Do the kids know all of those skills?  Absolutely!  And I showed them exactly this after I had them “take” the assessment.  We went through the entire problem and they all agreed they could do each of these skills individually.  The difference is that the common core wants them to all of this together. 

I refer to the students as “taking” the assessment because for most of them what they did was stare at the page for quite a long time, then picked their favorite formula for a circle- either area or circumference- and put the number 40 into the formula then solved it and turned it in.  Sigh.

Still, I am obsessed with this problem and I love what the kids have to do to solve the problem.  It will just take some hard work to get them there!  I think it is so much more valuable for the kids to do this kind of problem rather than being told exactly what to do.

What are you doing to get your kids ready for CCSS?