Fractions for kids start with one big idea: a fraction names equal parts of a whole. Begin by sharing snacks fairly, then fold paper into halves and fourths, cut a sandwich or pizza, and build fraction strips. Keep saying "equal parts," and wait to write numbers like 1/4 until the idea makes sense.
Here's what to teach, in what order, with simple activities and the mix-ups to watch for.
A fraction describes part of a whole that has been cut into equal parts. In 3/4:
The bottom number, 4, tells how many equal parts the whole is cut into. This is the denominator.
The top number, 3, tells how many of those parts we mean. This is the numerator.
The third grade Common Core State Standards describe it the same way: 1/4 is one part when a whole is split into 4 equal parts, and 3/4 is 3 parts of size 1/4.
The word that matters most is equal. If a sandwich is cut into one big piece and one small piece, neither piece is a half.
First grade: split circles and rectangles into two and four equal shares, and use the words halves, fourths and quarters. Children learn that more equal shares means smaller shares.
Second grade: split shapes into two, three or four equal shares, use words like thirds, and describe a whole as two halves, three thirds or four fourths. They also learn that equal shares of identical wholes don't need to be the same shape.
Third grade: treat fractions as numbers, place them on a number line, find simple equivalent fractions like 1/2 = 2/4, and compare fractions with the same top or bottom number. Third grade work uses halves, thirds, fourths, sixths and eighths.
A What Works Clearinghouse practice guide on teaching fractions recommends building on children's natural sense of fair sharing, then helping them see that fractions are numbers, using number lines. These steps follow that path.
The guide notes that sharing a set of objects, like 12 grapes among three children, tends to be easier for young children than sharing one object, like a candy bar. So start with sets:
Share 12 crackers between 2 plates, then among 3, then among 4. Does everyone get the same?
Then share one thing, like a pancake, between 2 people, then among 4.
The guide suggests starting with sharing among two, four or eight people, because children can keep cutting pieces in half.
Fold a square of paper in half and open it. Two equal parts make halves. Fold it in half again for fourths. Now fold a second square corner to corner. Those triangles are halves too, even though they look different from the rectangles. The second grade standards make exactly this point: equal shares of identical wholes need not have the same shape.
Cut a sandwich into halves, then into fourths.
Ask, "Would you rather have 1/2 or 1/4 of this sandwich?"
With a pizza, ask how the slices change if 3 people share it instead of 4.
The guide suggests helping children notice that as the number of people sharing goes up, each share gets smaller, then linking that to fraction names: 1/3 of something is more than 1/4 of it.
Cut several paper strips the same length. Keep one whole. Fold one in half, one in fourths and one in eighths, and label each part. Line them up:
Two 1/4 pieces line up with one 1/2 piece, so 2/4 = 1/2.
Four 1/8 pieces also match 1/2.
The fractions guide also describes measuring with strips. Measure a table with whole strips, then use a half strip for the leftover bit, like "3 strips and a half."
Draw a line from 0 to 1 and split it into equal parts. For fourths, mark 1/4, 2/4 and 3/4, and point out that 4/4 lands on 1. The third grade standards use number lines this way, and the fractions guide recommends number lines as a central tool from the early grades onward.
Once your child can say "one fourth" and show it, write 1/4. Connect the bottom number to "how many equal parts" every time.
Fair or not fair? Cut a slice of bread into two unequal parts and ask if they're halves. Then fix it together.
Measuring cup math: while baking, show that two 1/2 cups fill 1 cup, and so do four 1/4 cups.
Fold and color: fold paper into fourths and color 3 parts. "You colored 3/4."
Which is more? Hold up the 1/2 and 1/4 pieces of your fraction strips and compare them.
Snack plate fractions: put 4 crackers on a plate and eat 1. "You ate 1/4 of the crackers."
Calling every piece "a half." The fractions guide notes that some children think all fractional parts are called one-half. Use the right names early.
Ignoring equal size. Ask "Are the parts equal?" every time. When children draw, the guide says it's fine if parts aren't perfect, as long as they remember the parts should be treated as equal.
Thinking a bigger bottom number means a bigger fraction. A child may say 1/8 is more than 1/4 because 8 is more than 4. Fraction strips settle it quickly.
Counting pieces instead of amounts. The guide notes that young children may hand out equal numbers of pieces rather than equal amounts when the pieces differ in size.
Adding tops and bottoms. The guide says mistakes like adding the numerators and then the denominators come from not seeing fractions as numbers with sizes. For 1/2 + 1/4, use strips: the answer is 3/4, not 2/6.
Comparing different wholes. Half of a small pizza is less than half of a large one. The third grade standards point out that comparisons only work when both fractions refer to the same whole.
Say that a fraction is part of something that has been cut into equal parts. Show it with food or folded paper before writing any numbers.
Under the Common Core, first graders split shapes into halves and fourths, usually around age 6 to 7 in the US. Fractions as numbers on a number line come in third grade.
The bottom number tells how many equal parts the whole is cut into. Cutting the same whole into 4 parts makes smaller pieces than cutting it into 2.
One half. It's a familiar word, and halving again leads straight to fourths and then eighths.
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