3rd Grade Understanding Fractions Lesson (Free PDF)

3rd Grade math lesson: Understanding Fractions – Maths PDF

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

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.

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

Key facts in this fractions lesson

Key facts

A fraction describes equal parts of one whole.
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.
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
\(\frac{1}{3}\)	one third	3
\(\frac{1}{4}\)	one fourth	4
\(\frac{1}{6}\)	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.

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.

How to use this fractions lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

Download the fractions lesson as a PDF with the button below and keep it with your notes.

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