Teaching Fractions

Fractions don't have to be painful. Teaching fractions is one of my favorite math subjects to teach, probably because it can be so hands on, it makes so much sense, and kids seem to get it rather easily.

You don't have to introduce the idea of fractions with numbers and lines. That is too abstract for "living math," and one of your goals in teaching math is to show them math that they will use every day.
My two favorite ways of introducing fractions are first through felt or paper cut outs, and then through cooking. I found that my children understood the measuring cup concept after they played with laying colored cut outs on top of each other, and learned to name the fractions.
For some kids, the pie fractions are easier than the measuring cup volume fractions.

Get some different colored felts from the craft store. Cut, out of the same sized but different colored circles: one whole, halves, thirds, quarters, sixths and eighths.

You can also do this with pieces of paper, which you can let your children color different ways -- blue for blueberry pie, red for cherry, or even pizza-colored!

Then, just play with the cut outs, naming the fractions. First, have your child identify the pieces. Say to her, " Show me one whole pie," Then take the two halves and say, "One pie cut in two parts for me and for you. Let's cut it in half," and pretend to cut it in half. Have the child serve you 1/2 of the pie. You play around with this a variety of ways, giving her fun quizzes, such as, "How many quarters can you fit into a half?"
You can also see which fractions don't fit. Ask her to show you how many thirds she can fit into a half and see what she does.
The goal here is to be casual, fun, and light-hearted.

You can also draw up several same-sized rectangles with lines for the half mark, quarter marks, third marks, sixth marks, and eighth marks. Let the child color, then cut the rectangles on the lines, and play that way.

If you order or make a pizza, have your child help you cut the pizza into halves, fourths, then quarters. Play games with this too, saying "I'm so hungry I could eat HALF of this pizza. Show me half of the pizza. Can you eat half of that pizza? Really?! Wow. I think I might only be able to eat a quarter of it..." and so on.

Cooking is another fun way to "play" with fractions. Simply include your child in baking and cooking projects, letting him wield the measuring cup. Help him measure the ingredients, naming the fractions when you come to them. Things WILL spill, so expect a mess and don't worry about it.
Take time to play with measuring cups at the sink, or with water in a bowl. Let your child explore the concepts through play.

Then later, when fractions turn into numbers and lines on paper, your child will already be able to visualize what 1/3, 1/4, or 3/4 looks like and will understand their values.