## Thursday, September 17, 2015

### Rotations Card Sort

If you have read my blog for some time, you may know that I love a good card sort.  Here's one I did on multiple representations of linear functions last year.  One on piecewise functions from two years ago led to a journaling opportunity.

So last week, when a teacher mentioned needing something engaging for rotations, I got to work building a card sort.  The rotations card sort is available here, along with a notes sheet and exit ticket.  There is also a version for reflections.  I'll be working on a translation version and dilation version as time allows and I'll add them to the same folder.

The teacher who originally asked for it used it.  Two other geometry teachers were intrigued and I co-taught/modeled the lesson for them.  The lesson is designed to be an introduction to the rules and notation associated with rotations.  Students should have a foundational understanding of a rotation as a turn and some understanding of multiples of 90 degrees.

The lesson basically goes like this:
1. Have students sort the cards into any number of piles they want as long as they can explain the reason for the grouping.  (2 min)
2. Have students share out their sorting strategy.  ALL strategies are valid.  We're basically getting comfortable with the information that is on the cards and maybe refining the vocabulary students use to describe the different representations of the transformations. (3 min)
3. Say, "For you to meet today's learning target of correctly representing rotations, you will need to sort the cards into exactly 3 group."  (If you do reflections, it's 4 groups)  You can decide at this point whether or not you are ready to tell students that the groups must be equal in size.  I'd definitely give that hint if you want to give extra support or if any groups originally had 3 groups.
4. Walk around, question groups, and coach as needed.  (Figure perhaps as little as 15 minutes for a class with lots of background knowledge to as much as 45 minutes for a class that is fresh into this.)  I find that handing out a small stack of 1.5x2" post-its or some scratch paper will help because students can note coordinates or try out rules without juggling so many numbers in their heads.
5. Inevitably there are some groups that put 90 degrees clockwise and 90 degrees counterclockwise in the same group.  Take a moment to do a kinesthetic intervention with them- "Stand up and face the front of the room.  This is your preimage.  Rotate your body 90 degrees clockwise.  What are you facing?  Right, the door.  This direction is your image.  Now turn back to your preimage.  Please turn 90 degrees counterclockwise.  What are you facing?  Right, the teacher's desk.  This is the image.  What do you notice about the two images?"  The students will say the images are different.  "So what does that tell you about the cards?"  The two 90s can't go together, they soon realize.  "Last time we turned, we ended up facing the teacher's desk.  Can you return to your preimage and come up with a different way we could rotate to face the teacher's desk?  270 clockwise?  Show me.  Great!"
6. When students have sorted the cards and you've spot checked them for accuracy, give them the notes sheet to record their findings on.  It's important that they still have the cards at this point so they can record from what they put together.  You will also most likely need to tell them that counterclockwise is the default direction for rotations unless the directions specify differently.
7. Go over any trouble spots on the notes.  I like to use the large box to record multiples of 90 (when talking about how many quadrants the figure would move) and a diagram of the 4 quadrants numbered for students who may have forgotten.
8.  Use the exit ticket.  It shows 4 "cards" and asks students if they belong together or if not to correct the mistakes.

The first class, where I co-taught, was OK.  Most students were engaged, but I think groups of 3 would have been better than groups of 4; it was easy to find one student trying to take it easy with a group of 4.  I found the students less willing to say what they were thinking, which meant that the whole process felt a bit slow.  Overall, it was still a solid lesson.

The second class, where I modeled the lesson, went better. (I don't think it's because I led; I think it's a class dynamic issue.) I only saw one student who I felt was trying to check out.  The discussions were more open, which meant it was easier for students to make progress because they knew what their teammates were thinking.  A quick spot check of the exit passes revealed that most students were able to identify the card with the mistake (though not all of them were able to correct the mistake).  The classroom teacher was so pleased with this lesson that she had the kids give me a round of applause.  It was just an average lesson to me, but I'm glad it energized her.  She's eager to try more lessons like this one, so if you have any great geometry lessons on triangles or triangle congruence, please leave me a note; they'll be starting triangles soon.