3rd Grade Understanding Fractions Lesson: Notes and Examples (Free PDF)

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This 3rd grade fractions lesson covers understanding fractions (Common Core 3.NF.A.1, 3.NF.A.2), with a free PDF to print.

Key takeaway: This lesson helps Grade 3 students understand fractions as equal parts of a whole and as points on a number line.

Topic: Understanding Fractions (3rd grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 3.NF.A.1, 3.NF.A.2
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

A fraction names equal parts of a whole. The denominator is the number of equal parts in the whole, and the numerator is the number of parts we count. A unit fraction such as 1/4 is one part, and 3/4 is three copies of it. You can also place a fraction on a number line from 0 to 1.

This lesson helps Grade 3 students understand fractions as equal parts of a whole and as points on a number line. First, children learn that the denominator counts the equal parts in the whole. Then they learn that the numerator counts the parts named.

Next, the lesson introduces unit fractions and shows that a fraction like 3/4 is three copies of 1/4. Also, it explains how to place a fraction on a number line from 0 to 1 by hopping. Finally, it shows how to write fractions from words and pictures. Plan about 20 minutes, with paper strips and a number line.

Grade 3 · Common Core State Standards: 3.NF.A.1, 3.NF.A.2

Key facts in this 3rd grade fractions lesson

Key facts

A fraction describes equal parts of one whole.
Next, the denominator (bottom) counts the equal parts in the whole; the numerator (top) counts the parts named.
A unit fraction has numerator 1 and shows one equal part, such as 1/8.
Then, the fraction a/b is a copies of the unit fraction 1/b.
On a number line from 0 to 1, a/b is the point reached after a hops of length 1/b.

What is a fraction?

Think about sharing a pizza. A fraction tells how much of one whole you have when the whole is cut into equal parts.

Numerator and denominator

The denominator (bottom number) tells how many equal parts make the whole. The numerator (top number) tells how many of those parts are counted. The parts must always be equal in size.

A pizza cut into 4 equal slices. Three slices have peppers, so 3/4 of the pizza has peppers.

The pizza has 4 equal slices, so the denominator is 4. Three slices have peppers, so the numerator is 3. The fraction is $\frac{3}{4}$.

What is a unit fraction?

A unit fraction has 1 on top. It names exactly one equal part of the whole. $\frac{1}{6}$ is one sixth of a bar cut into 6 equal parts.

The unit fraction 1/6 is one part. Five copies of 1/6 make 5/6.

Every other fraction is built from unit fractions. The fraction $\frac{5}{6}$ means 5 copies of $\frac{1}{6}$.

Fraction	How to say it	Equal parts in the whole
$\frac{1}{2}$	one half	2
$\frac{1}{3}$	Also, one third	3
$\frac{1}{4}$	one fourth	4
$\frac{1}{6}$	Also, one sixth	6
$\frac{1}{8}$	one eighth	8

How do you show a fraction on a number line?

Draw a number line from 0 to 1. Cut that space into equal lengths. If there are 4 lengths, each one is $\frac{1}{4}$ long. To find $\frac{3}{4}$, start at 0 and hop three lengths of $\frac{1}{4}$. The point where you stop is $\frac{3}{4}$.

Start at 0 and take 3 hops of size 1/4. You land on 3/4.

How do you name a fraction step by step?

Check that all the parts are the same size.
Count all the equal parts in the whole. This is the denominator.
Count the parts you are naming. This is the numerator.
Write the numerator over the denominator.

Example. Jamal paints a ribbon that is cut into 8 equal pieces. He paints 5 pieces.

The ribbon has 8 equal pieces and 5 are painted, so 5/8 of the ribbon is painted.

There are 8 equal pieces, so the denominator is 8. Five are painted, so the numerator is 5. Jamal painted $\frac{5}{8}$ of the ribbon. The 3 pieces left are $\frac{3}{8}$ of the ribbon.

3rd grade fractions lesson: questions and answers

What is a fraction in third grade?

A fraction is a number that names equal parts of a whole, such as 3 of 4 equal pizza slices. It is written as a numerator over a denominator.

What does the denominator tell you?

The denominator tells how many equal parts the whole is cut into. In 5/8 the whole has 8 equal parts.

What is a unit fraction?

A unit fraction has 1 as the numerator and names one equal part, like 1/2, 1/3, 1/4, 1/6, or 1/8. Other fractions are copies of a unit fraction.

How do you find a fraction on a number line?

Split the space from 0 to 1 into equal lengths, one for each part of the whole. Then hop the number of lengths shown by the numerator, starting at 0.

Why do the parts have to be equal?

A fraction compares one part to the whole, so every part must be the same size. If the parts are different sizes, the fraction name does not fit.

Common mistakes with this 3rd grade fractions lesson

Students count the parts of a shape that are not equal. For example, a rectangle cut into three unequal pieces does not show thirds. Check that every part is the same size first.
Children swap the numerator and the denominator. As a result, 3 out of 4 parts becomes 4/3. Say the fraction in words, such as three out of four equal parts.
On a number line, students count the tick marks instead of the spaces. For example, to find 2/6, hop two spaces from zero, not two marks.

How to study this chapter

First, fold paper strips into equal parts. Then shade some parts and write the fraction for each strip. Also, saying the steps aloud helps you spot a slip.
Say the numerator and denominator aloud for every fraction. Also, point to the part of the picture that each number describes.
Parents can cut food into equal pieces. For example, cut a pizza into 8 slices and ask what fraction is left after dinner.

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