Today we started by reviewing last lesson, and then I invited the children to draw a (number) line of length 30cm on a piece of A3 paper, marking the ends 0 and 1. I asked them if they could find as many fraction names as possible for each centimetre mark, using Cuisenaire rods or otherwise. I demonstrated this using the orange rod (length 10cm), which fits into 30cm three times, allowing me to mark 1/3, 2/3 and 3/3 on the number line.
Following this, I invited them to reflect on (a) how they worked out the fractions, and (b) what they found out. Here are their responses, along with comments based on conversations I had with each child.
If the therapist disapproves of resistances, he might as well give up.
I'll start the next lesson with a couple of questions like "Which marks had three fraction names?" and then draw attention to the relationship between the numerators and denominators.