I like this, from Segar Rogers, a lot!
From the man himself:
“I think both the grid and the vertical approaches have their merits; I did a straw poll with a class a couple of years ago (which type they preferred) but the results were inconclusive. Mine is based on the Hackenberg/Norton/Wright (‘Developing Fractions Knowledge’) schema:
– unit fraction of a unit fraction
– non-unit fraction of a unit fraction
– unit fraction of a non-unit fraction
– non-unit fraction of a non-unit fraction
… although looking at it now I see that page 2 doesn’t adhere to this as strictly as I remember.
… and of course for Hackenberg it’s firmly in the realm of part-whole relationships and the word ‘multiplication’ isn’t even mentioned!
The only other thing to say is that I’m not convinced that page 1 should necessarily precede page 2; for some people it might work better in reverse order.”