The neat part about being in math classes right now as I pursue my Elementary Ed. degree is thinking about how I will apply what I'm learning to my future classroom one day. How do I take this information and prepare to present it to my students in ways that they can understand and actually use in their real lives? How will I break these large mathematical concepts down into smaller bite-sized chunks for them? For example, how do we teach young children about fractions?
Even children of very young ages can understand the idea of "half." "Give half of those animal crackers to your brother..." "Here, we'll split the pile of Legos in half so that you can both build with them..." Half is pretty understandable, but what about more complicated fractions? For example, which is bigger, 1/8 or 1/4?
I guess I have a bit of a theme here lately with references to food. I didn't intentionally do that, but here I go again. In the classrooms that I work in as a Para Educator, I find that food can be very helpful when discussing fractions. A Kit-Kat bar works nicely to show fourths since it is conveniently packaged as one chunk of chocolate that can be broken apart quickly and easily into four separate but equal parts.
We can show our students that one of the four smaller bars is one fourth of the whole candy bar. Simple enough. The fun part is to lay another Kit-Kat bar under the overhead projector so that the children can watch each "fourth" being cut in half. Now the candy bar is divided into eighths. This makes it easy to see that you would rather have one fourth of the candy bar than one eighth. Children tend to think that the bigger denominator must be a bigger number. This visual helps them to understand what fractions mean. Would they rather have 4/8 of a candy bar or 4/4?
Another idea that makes learning about fractions easier is the use of pizza. We can cut one pizza into eight equal pieces and another into sixteen equal pieces. Then let the fun begin. Which is more? 4/16 or 2/8? There are some surprises for children when working with fractions. Even those children who are not typically visual learners benefit from visuals when it comes to fractions.
I found an interesting article from the U of M titled, "Teaching About Fractions: What, When, and How." The article states that we need to let our students use manipulatives and give them many opportunities to explore fractions in hands-on ways. It doesn't always have to be food. It can be blocks or coins or paper cut into equal parts. (Kids do get excited about getting to eat an 1/8 of a Kit-Kat during math, though.)
Here is one example of a neat manipulative for learning about fractions:
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