Most said 'one-sixth' apart from one student who was adamant it was a fourth. Initially, I thought she had miscounted the parts but upon further questioning it was apparent that this student also thought that the following were also fourths: can you see why?
Basically she is describing the fractions using ordinal or positional language. What was neat about this is that before I had a chance to challenge her thinking, her partner did it for me (referring to the first diagram above):
"Well if that's the case, you could count from the right side and it would be called a third and it can't be a fourth and a third!"
The original student was pretty adamant that she was correct though which got me wondering what experiences she might need to understand how we name fractions. Perhaps she never had an opportunity (or not enough opportunities) to split a shape into equal parts like this as shown in this previous post . After the lesson I realised that I could also have challenged her fractional thinking by bringing in spatial reasoning and asked her if each of the following are fourths:
Or by asking her to name each of these fractions (will she name them 'firsts', 'seconds', 'thirds' and 'fourths'?)
It got me thinking how important spatial reasoning is in helping students understand fractions.
There are some other great ideas for thinking about how we can teach fractions in the Ontario Ministry of Education's latest document Paying Attention to Fractions. One of the ideas coming out of this is to avoid solely teaching fraction as a unit but rather to incorporate it as much as possible throughout other strands and subjects all year long.
Or to put it another way, Fraction Immersion.