Have you used concept sorts in your classroom?  If you have followed my blog for a while, you know that I use concept sorts regularly–and have posted a number of times about different ways I use them.  Click HERE and HERE for two of those posts!

Today I want to talk about a geometry sort I did the other day to “take the temperature” of my class after a few days of instruction about points, lines, segments, and rays and the terms “intersecting”, “parallel”, and “perpendicular”.  Although I wasn’t surprised at all the math misconceptions, I am ALWAYS surprised at how many NEW misconceptions I discover!  If you are looking for a way to get much deeper math talk going on in your classrooms, concept sorts are truly an amazing (and easy to prepare!) way to force students to share their thinking and have great mathematical discourse.  Check out some pics from this week’s sort!  I’d love to hear from any of you using sorts–and tell me if you think you’ve noticed an improvement in YOUR students’ mathematical thinking!

 My students can get their sorts cut in just a few minutes now…they divide and conquer by each taking a sheet, then cutting the 8 cards in half, stacking them, then cutting them apart.  Voila!

This is HUGE…you have to model (and if you have a group doing this well, try doing a fishbowl so the students can see this in action).  Students, by nature, want to just grab a stack of cards and put them into categories.  The assertive students take over, the passive ones sit back helplessly, and NO learning happens.  Show them how to take one card at a time to discuss it, interact with it–and make sure that all students are a part of it!  Watch for this as you teach. If you see students rushing, slow them down–even if they don’t get through the entire stack.

 As you walk around, listen for the dialogue and interject when needed…”Is it possible for two segments to be perpendicular if they don’t touch?” (YES!) or “Can two lines intersect if they don’t cross?” (YES!).  Try to ask questions that get them thinking without TELLING them!

 This is huge–and a piece of mathematics instruction we often overlook.  For this sort, I started off by NOT giving my students the category headers.  I wanted to see HOW they organized their cards on their own….and it allowed me to plan some instruction.  For example, one group made 14 categories–some of which only had one card!  We had a great talk about what makes good categories and then I handed out the four header cards.  Students then worked to reshuffle their groups to align to the new categories.  I also called groups over to look at this group’s work because they were keeping everything all lined up rather than in piles all over the floor.  It makes it much easier to compare cards when they are neatly arranged.

Some groups are pretty convinced that they have everything correct, and if I want the other groups to have a little more time, I ask them to use the blank cards to try to make more examples for each category that are NOT found on any of the other cards.  This asks them to really apply what they know and to work together to do so.

After my groups have their categories, we do a gallery walk. Students travel as a team to check out the other groups and have some math discussions about what they see.  They look for similarities and differences and work to use that specific math vocabulary as they explain their thinking.

 As they worked, I asked my students to put a yellow mark on the cards where they struggled to come to agreement.  As they did their gallery walks, they looked to see if other groups had the same struggles!  After the gallery walk, I collected these cards for our class discussion.  One by one, I put these tricky cards under the document camera and we had “debates” as a class. We look for ways to prove our thinking…from lining up rulers to check for intersections to revisiting definitions. (If lines go on forever, don’t they intersect even if the drawing doesn’t show it?  YEP!).  This was a great time for me to hit home some of the big concepts I needed them to have–and for them to hear the thinking of others.

So…there was a LOT of math thinking that took place during this 45 minute math concept sorts lesson!  Hope this gave you some ideas about what you could try in YOUR class!  Let me know how it goes!  Want to see a few of my concept sort resources?  Here are a few of them! (Check my store for the custom category “Concept Sorts” for more!)