More Venn Diagrams

Just as we sorted objects, then people, then names into "not boxes," we moved from sorting objects to sorting people and then names into Venn Diagrams.  Today I made a giant Venn Diagram on the floor with masking tape and we sorted children into it, followed by sorting of name cards, and finally created a Venn Diagram together on chart paper.  Then each child came up with their own question and surveyed their peers, asking their friends to sign their Venn Diagrams in the appropriate spot.  We used the same procedures as when students created their own "Not Box" surveys.  Afterwards students took turns sitting in the Mathematician's Chair and describing their data using the words "greatest," "least," "most," "more," and "less."  For homework everyone surveyed their family members using a Venn Diagram.   

Venn Diagrams

Our work with sorting into "Not Boxes" last week involved sorting by one attribute at a time.  We sorted buttons that had holes from buttons that did not have holes, lids with stickers from lids without stickers, etc.  Today we began sorting using two attributes and introduced Venn Diagrams to accommodate this more complex sorting. 

I modelled using sorting hoops on the floor-- trying to put lids with stickers in one hoop ad lids with writing in another hoop, only to bump up against the reality that some lids had both stickers and writing and therefore belonged in both hoops, leading then to the creation of a Venn Diagram with overlapping hoops. 

Then with the kids' help, we sorted green lids and lids with screw tops.  This time we recorded the sorting on chart paper.  Then they worked independently on sorting lids and recording their own work on paper.  As with the "not box" work, the sorting is done on Venn Diagrams copied onto yellow paper which I refer to as "mats" and recorded on Venn Diagrams copied on white paper which I call "recording sheets."  The "recording sheets" have lines for writing on a name and date as well as a label for each circle. 

Sorting People

We began our sorting and graphing work by sorting manipulable objects--buttons and lids.  Then we moved onto recording those sortings on paper, stepping from the concrete to the abstract.  Our next step today was to sort people and their preferences. 

Again, we used "Not Boxes," and moved from the concrete to the abstract.  I outlined large sorting boxes on the floor of our meeting area in masking tape.  Then sorted four or five children at a time into the boxes, first by looking at obvious physical traits (long pants/not long pants, wearing blue/not wearing blue), then by personal preferences (Do you like spaghetti/not like spaghetti?  Do you like swimming/do you not like swimming?)  After everyone had a turn, we repeated this process in a slightly more abstract manner by sorting name cards into the giant boxes.  Another step towards abstraction was writing children's names onto a set of boxes drawn on chart paper.  For homework tonight, children will sort the names of their family members into boxes after asking the question "Do you like pizza?" 

Was this lesson differentiated?  Not at first glance.  It was a whole group lesson without being particularly open-ended.  Tomorrow, as students do some of their own surveying, there will be more opportunity for students to modify the lesson to suit their own needs.  I'll have to think more about this one.  Perhaps there is something more that I could do with questioning throughout-- planning out questions ahead of time tiered for different levels.  Let me know if you have ideas!

NOT Box Recording

Graphing is all about taking the concrete--some actual things, actual events, actual people--and rendering a more abstract representation of a situation.  Children in the primary grades (and perhaps learners of any age) must work first with the concrete--the actual buttons, or lids, or blocks, or what-have-you-- before attempting the more abstract--the recording on paper.  Yesterday we just sorted the objects.  Some created very obvious sorts, some made the task more challenging by attending to unusual details.  Today we took the next step, recording these sortings on paper. 

Again, I began by modeling a sort and this time modelled recording my work on chart paper with pictures and words.  Then I created a sort and asked students to help me label my sorting rule.  Again, we had an open-ended workshop period with students creating as many sorts as they had time for, trading zipper baggies of buttons and lids for new ones when they were ready. 

NOT box sorting

Today as we launched our next math unit (sorting and graphing), I found myself wondering again about the validity of spending instructional time on what seem like simple skills.  The new common core standards  ask kindergarteners to "classify objects in categories," while first graders are supposed to "organize data in up to three categories" and second graders are supposed to create graphs.  I feel like these are fair goals for each grade level, but I also know that while classifying objects sounds simple, it can actually be incredibly complex.  When given a handful of buttons to sort, many first graders will create two piles:  the thin buttons and the buttons with holes.  When faced with thin buttons that also have holes, they may be completely stymied. 

Sorting buttons is an open-ended task that I find to be appropriate for both my first- and second-graders.  Up until now, sorting has been considered a preliminary skill for graphing work and again, is a task that will undoubtedly help them meet more complex goals.  I have decided to carry on with this work, even though the new standards would suggest it is more appropriate for younger students. 

Earlier this week, Organized Chaos posted about the complexity of counting to 100-- a seemingly simple task, but one that is not easy for kindergarteners to master.  She expresses frustration that more and more standards are being added to the list of kindegarten responsibilities, some of which are less than developmentally appropriate.  My frustration as we work with the new common core is that fewer standards sounds great, but cutting out simpler precursor skills only makes the learning more difficult.  Mastering fewer standards does not mean teaching fewer lessons.

Today's lesson is based on an Investigations lesson with sorting boxes called "Not Boxes."  Students need to identify an attribute and sort items into those that have the attribute and those that don't.  Any objects could be used for sorting, but today we used buttons and lids.  I began by modelling this sorting, then sorting again and challenging the class to figure out the rule I used for sorting.  Then I gave each child a paper sorting mat and asked them to sort a baggie full of buttons into a "Not Box" in any way that they saw fit.  As students sorted, I circulated around the room and tried to guess the sorting rules they were using.  Could I always guess?  Sometimes, yes, and sometimes, no.  Many times I needed to coach a re-sort, even for second graders.