What is this skill?
Naming fractions means looking at a shape divided into equal parts and writing the fraction that is shaded. A circle cut into 4 equal parts with 3 parts shaded shows 3/4, read as three-fourths. The bottom number, the denominator, tells how many equal parts the whole is split into. The top number, the numerator, tells how many of those parts are being counted.
In third grade, children work with halves, thirds, fourths, sixths and eighths. They learn that a unit fraction like 1/4 is one equal part of the whole, and that 3/4 is three of those parts. The parts must be equal for the fraction to make sense: a circle cut into four unequal slices does not show fourths.
Why it matters
Fractions are one of the most important topics in elementary math, and third grade is where they really begin. Everything that follows, including comparing fractions, equivalent fractions, adding and multiplying fractions, decimals and ratios, builds on understanding what a fraction is.
Fractions are also everywhere in daily life: half a sandwich, a quarter of an hour, three-fourths of a cup of flour. Children who connect the written fraction to a picture of equal parts are much less likely to treat fractions as two unrelated numbers stacked on top of each other, which is the root of many later fraction mistakes.
Common mistakes
- Counting the unshaded parts instead of the shaded ones, so 3/4 becomes 1/4. Ask "How many parts are shaded? How many parts are there in all?"
- Writing the shaded parts over the unshaded parts, such as 3/1 instead of 3/4. Remind your child that the bottom number is all the parts in the whole.
- Not noticing that parts must be equal. Showing a shape with unequal parts and asking whether it shows fourths makes a good conversation.
- Thinking a bigger denominator means bigger pieces. One-eighth of a pizza is smaller than one-fourth, because the pizza is cut into more pieces.
How to help at home
- Use food: cut a sandwich, a pizza or a fruit bar into equal pieces, eat some, and ask what fraction is left.
- Fold paper into halves, fourths and eighths, color some parts, and name the fraction.
- Point out fractions in daily language: half past the hour, a quarter of a cup, half a tank of gas.
- Draw shapes divided into equal and unequal parts, and ask your child to find the ones that show real fractions.
- Turn it around: name a fraction, like 2/3, and ask your child to draw a shape and shade it to match.
Worked examples
These are real questions from the Tutorsaurus naming fractions practice, with the answers worked out.
Example 1
What fraction is shaded?
Choices: 2/5, 3/4, 4/2, 2/4
Answer: 2/4. 2 out of 4 equal parts are shaded, so the fraction is 2/4. The bottom number is the total parts.
Example 2
What fraction is shaded?
Choices: 2/6, 6/4, 5/6, 4/6
Answer: 4/6. 4 out of 6 equal parts are shaded, so the fraction is 4/6. The bottom number is the total parts.
Example 3
What fraction is shaded?
Choices: 6/8, 5/9, 5/8, 3/8
Answer: 5/8. 5 out of 8 equal parts are shaded, so the fraction is 5/8. The bottom number is the total parts.