## Tuesday, April 19, 2011

### Sets and Grouping, Part II

Today we will be using elementary math (as taught in Excel Math curriculum) to group items by common characteristics. Yesterday I showed you my collection of data about t-shirts from Duluth Trading Company.

I looked at my spreadsheet to see if I could see how to organize the shirts. I decided to draw a Venn diagram to illustrate a few sets of items that share common features:

I organized the t-shirts into 4 sets. I counted the number of shirts in each set and put those numbers into yellow circles  (2 different ones), a green circle and a blue circle based on the type of fabric used to make the shirt.

Within those 4 fabric sets, I separated the shirts with pockets (beige small circles) from those with no pockets (grey small circles). Since shirts either have pockets or they don't, all shirts in a fabric set fit into either the pocket set or no-pocket set.

Now I have added ovals. The pale yellow one indicates that there's a larger set which includes shirts made of pure cotton (yellow) and shirts of blended cotton-polyester. Similarly, there's a pale green oval to include shirts made of pure polyester (green) set and the cotton-polyester blend shirts.

Notice that there are two sets of circles in the cotton oval, and two in the polyester oval. But there are only 3 fabrics included in these two ovals, not 4, because one fabric (the cotton-polyester blend) belongs to both.

The nylon fabric (blue) is by itself. No shirts are made in a cotton/nylon-spandex blend or a polyester/nylon-spandex blend.

How can we include the blue circle in a larger set? Let's try grouping by pockets or no pockets, instead of fabrics.

The dark blue lines show the set of shirts with pockets. The red lines show the set of shirts with no pockets. These two sets transcend the fabric choice sets. They include the nylon-spandex shirts.

Set relationships take a lot of thinking. It's fairly straightforward to draw these groupings and to shade the diagrams appropriately, once you see the relationships.We give kids opportunities to do this in class.

It's harder when you are using Adobe Illustrator, various degrees of transparency, and trying to get all the layers in the proper order from top to bottom so you can turn them off and on!

Come back to see more sets tomorrow.