I met with the Kindergarten team yesterday, and they were looking for new ideas for comparing numbers to 20. I suggested starting with concrete materials--teddy bear counters, linking cubes, or two-color counters. I like showing groups of ten, even with manipulatives. So if the students were building 13, I would like to see them use 10 bears of one color and 3 bears of another color. The same thing with the linking cubes or two-color counters. It builds the concept of 10 and also makes the comparison much easier for them. It's much quicker to count a ten and 3 more, instead of having to count 13 one by one.
Another great tool for comparing numbers is ten-frames, so I made a little recording sheet the teachers can use with their kiddos. Click on the picture to grab your own copy.