this idea was used in research by G Noelting (in 1980)
'the development of proportional reasoning and the ratio concept'
the powerpoint is here
students should be given the opportunity (i.e. time) to debate
with the teacher remaining silent or encouraging other views to be aired, "I wonder if that is right?"
at some stage techniques will need to be considered though...
my preference (now) is to remain with ratio ideas (i.e. equivalences) rather than moving to fractions,
using lcm to do one of the following:
- get the number of orange portions the same
- get the number of water portions the same
- get the total portions per container the same
reversing the question could include:
can students devise proportions where
- the concentrations are the same?
- where A is slightly more concentrated than B?
- where A is twice as concentrated as B?