Friends with fractions

I know lots of kids who can tell you that the top number in a fraction is called the numerator and the bottom number is called the denominator. But they don’t understand how the two numbers function or relate to each other.  The words numerator and denominator do technically describe the functions of each number, but only if you happen to recognize all the Latin roots.  So in the absence of Latin fluency, this might help.

Try giving each number a nickname that describes its function.  Nickname the denominator something like the “How big?-er,” and the numerator something like the “How many?-er.”  For each fraction, the bottom number tells you what size the pieces are (thirds, sixths, etc.) and then the top number tells you how many of those pieces.

If you have 2/3, the 3 is the How big?-er and the 2 is the How many?-er.  Out of three equal pieces, two.

The sillier and more creative you’re willing to be about naming and explaining things this way (I do a similar thing with the distributive property in algebra), the more success you’re likely to have with conveying the concepts.  And it’s not just because kids receive things better when the learning conditions are less… solemn.  It’s also because thinking up new ways to talk about things, new names and labels and explanations for things, means you have to get to the bottom of how the things work.  It’s possible/likely that no one ever told you, so it takes something to do this.  It can be VERY scary if you had a lousy time with math (in particular) yourself, but that experience actually makes you better qualified to work with kids who are struggling with concepts.  To just tell kids how to do things from a place of omniscience is not actually all that helpful.  To get in there with them and fumble around with it and find a way to befriend it… that’s what’ll make it accessible, and even appealing.  It’ll take courage, but it’ll be worth it.

*I don’t recommend trying what I’ve described here or any other fraction work without the support of some type of hands-on illustration of the concept in question.  My favorite fraction tool is rainbow fraction tiles, because the tiles are visually and tactilely excellent, but if you don’t have those, you can use or make something similar.  What matters is that whatever you’re using shows the size of the pieces relative to the whole.

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