“Daddy, I’m full. I had 1 and a half…no, one and a quarter slices of pizza which is the same as five quarters of pizza,” said my son at dinner tonight.
“Okay,” I said, “you can go play if you like.”
“You know you can do that right, have five quarters of pizza, or even 10 quarters of pizza,” he continued.
“How many slices of pizza is 10 quarters of pizza?” I asked.
“Hrmmm…,” My son thought for about 10 seconds, and then said, “Two and a half slices of pizza,” and then he went off to play.
My son can do this kind of manipulation with wholes, halves, and quarters of pizza because the idea of dividing food into smaller fractions is familiar to him, and because he has seen halves and quarters used in many different contexts quite a bit during his life. Simple fractions are familiar to him, and so he can manipulate them as needed. Note that I have never once taught my son how to convert between an improper fraction to a mixed fraction, or even what those words mean. I’ve just slowly and deliberately introduced him to the ideas of fractions as they naturally fit our daily lives.