Exploring Fractions: Thirds, Fifths, Eighths

Lesson Plan - Get It!

Audio:

• What is a fraction?

Fractions are commonly used to name parts of a whole or a group.

If the circle below represents a whole, the shaded parts represent the parts of the whole. The most commonly-used fractions that are a little easier to understand are ½ and ¼.

• Have you ever had to share something with someone and each of you took half?

You were using fractions!

A whole can be divided up into any number of parts.

Before you begin exploring thirds, fifths, and eighths, watch a short video about fractions. As you watch Let's Learn Fractions - Understanding Math for Kids (Kids Learning Videos) below, answer these questions on a piece of paper:

• How do we measure a "part of a whole," like a donut or pizza?
• What are the two numbers that make up a fraction? What does each represent?
• If a pizza were divided into 12 slices and you ate 3 slices, what would the fraction be to show how much you ate?

For this lesson, it will be helpful to have fraction pieces or manipulatives. You will need fractions that represent thirds, fifths, eighths, fourths, and halves.

To use pie charts to explore fractions, download and print Pie Chart Templates from the Downloadable Resources in the right-hand sidebar.

If you create your own, you will need to make perfect circles by tracing a circular object. Be sure to use straight lines and divide the circles into equal parts.

A fraction describes part of a whole. The whole can be a single thing or a group of things, such as part of a whole pizza or part of a group of people. A fraction is made up of two parts, a numerator and a denominator.

• The numerator is the top number that tells the number of equal parts being counted.
• The denominator is the bottom number that tells the number of equal parts in the whole.

Many fraction problems talk about equal groups. The number of equal groups is shown by the denominator. Divide the total by the denominator to find the number in each group.

Example 1 Write a fraction that represents the shaded part of the circle below:

The circle is divided into 3 equal parts, so the denominator is 3.

There is one shaded part, so the numerator is 1.

The fraction that represents the shaded part of the circle is ¹⁄₃.

Example 2 Write a fraction that represents the unshaded part of the circle below:

The circle is divided into 5 equal parts, so the denominator is 5.

There are 2 shaded parts and 3 unshaded parts, so the numerator is 3.

The fraction that represents the unshaded part of the circle is ³⁄₅.

Example 3 At the beginning of the lesson, you were asked this question:

One-third of the kids at the park were boys. There were 15 kids at the park. How many of the kids were boys?

This is an equal groups question. There were 15 kids total and one-third of them were boys. The word “third” means to divide the total number of kids, 15, into 3 equal groups. There are 5 kids in each group. If one-third of the total was boys, then 5 kids were boys:

Example 4 Look at the circle below:

• What fraction of the circle is shaded?
• What fraction of the circle is unshaded?
• What do you notice about the two fractions that represent shaded and unshaded?

The fraction of the circle that is shaded is ⁴⁄₈. The fraction of the circle that is unshaded is ⁴⁄₈. Some fractions may look different, but they are really the same. If the shaded parts were side-by-side, ¹⁄₂ of the circle would be shaded.

Answer the following:

• What does the numerator represent in a fraction?
• What does the denominator represent in a fraction?
• Describe what a fraction means in your own words.

In the Got It? section, you will practice solving interactive problems involving fractions.