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.

*rod,*which she

*then*used to write down fraction names for each mark!

*two*methods allowed her to think more deeply about what was happening.

*very*interesting fraction names, for example 2/3.75 (two brown rods)! She used the black rod to write fraction names such as 1/4.2857142 = 7/30.

*why*the blue rod didn't "work" (fit into the whole), conjecturing that it was because it was "odd".

*must*be 1/15."

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.