Banapples aren't a thing!

How many times have we heard this:

“What have you been taught about fractions?”
“I know about the numerator and the denominator.”
“Great...can you tell me what they mean?”
“The numerator is in the top and the denominator is in the bottom.”

I sat down with my Goddaughter when she was 4.  She hadn’t yet started kindergarten.  I thought it was the perfect time to try something out.  I put an apple and a banana in front of her and asked her how many fruits she had.

“One apple and one banana.”
“How else can we count these?”
“Two fruits”.
“Why didn’t you count two banapples?”
“That’s silly!”

How right she was.  Kids know so much more than we give them credit for.  What she said was astute.  I learned from her that she naturally knows at a very young age that two unlike things can’t be added together.

We can make things so much easier, can’t we?  Before we get to the math “procedures”, we start with what the words mean:

“Numerator” comes from numerā(re) or to count.
“Denominator” comes from  dÄ“nōminā(re) or to give name to.

We explain fractions to our kids as being a counter (numerator) counting a thing (denominator).  My Goddaughter will never forget that adding two things with different names is silly … in other words, a banapple isn’t a thing!

Understanding why a rule exists ensures that the rule will never be broken.

-Carlo