The following fraction talk is under the my favorite problems tab at the top of this blog. The quest is what fraction is yellow, and how do you see it?
As you can see, students came up with 1/3, 2/3. 1/6, 1 1/6, and 1/4.
The biggest misconception I can see with those answers is that the students aren't including the yellow part in their denominator. Also, most were not willing to share why they came up with those answers.
Miguel was able to explain that 2 red's make a yellow. So, I drew a diagram of his thinking as he explained it. He kept moving the red blocks up to make yellows. Therefore, he had a total of 4 yellow blocks. so, 1 yellow out of 4 yellow blocks is 1/4. Another student converted the yellow into 2 red, so he had 2 red out of 8 total red. I also showed them that since there's a line of symmetry, just like the one going down the middle of your face, you can see how much yellow there is of half of it, which is 1/4.
We also started Clapper, but didn't have time to finish it, so I'll write that one up later.