Comparing Fractions Game

The Game

This game is for two players. You will need a set of cards. Each card has two fractions on it.

Your job is to look at the two fractions and decide: Are they equal? Or is one bigger than the other?

Here is how to play:

1. Pick a card with your partner.
2. Each player decides alone: Are the fractions equal? If not, which one is bigger? Then show each other your answer.
3. If you both agree, take turns explaining how you know. If you disagree, talk about it until you agree.
4. Pick a new card and do it again.

Play 10 rounds. Then write down what ways you used to compare the fractions.

Why We Play This Game

This game helps you compare fractions and explain your thinking. Here are three ways to compare fractions:

Same top number (numerator): If two fractions have the same top number, look at the bottom number (denominator). The bottom number tells you how many equal pieces make one whole. More pieces means each piece is smaller. So thirds are bigger than fourths. That means two thirds is bigger than two fourths.

Same bottom number (denominator): If two fractions have the same bottom number, the pieces are the same size. Look at the top number to see how many pieces you have. One fifth is less than two fifths, because two fifths has one extra piece.

Comparing to one whole: Sometimes one fraction is less than a whole, and the other is more than a whole. For example, two thirds is less than one whole (three thirds). Five fourths is more than one whole (four fourths). So five fourths is bigger than two thirds.

A teacher might choose to take out cards that compare a fraction less than one whole with a fraction more than one whole, if that feels too tricky.

Some cards have pictures of the fractions. This helps you see the fractions and compare them. Some cards do not have pictures. A teacher might ask you to draw your own picture to show your thinking.

Some cards may show fractions that are equal, called equivalent fractions. That means the fractions look different but stand for the same amount.

After playing, talk with your class about what ways worked best for comparing fractions. Drawing pictures works for every card. But looking at the top and bottom numbers is an important way to compare fractions quickly, so be ready to talk about that too!

Examples

There are four kinds of fraction pairs you might compare:

1. Same top number (numerator).
Compare 2/3 and 2/5.
The whole is cut into more pieces for fifths than for thirds. More pieces means each piece is smaller. So fifths are smaller than thirds.
This means 2/5 is less than 2/3.

2. Same bottom number (denominator).
Compare 1/3 and 2/3.
Both fractions cut the whole into 3 equal pieces. But 2/3 has one more piece than 1/3.
So 1/3 is less than 2/3.

3. One fraction less than one whole, one fraction more than one whole.
Compare 2/3 and 3/2.
2/3 is a little less than one whole (which would be 3/3).
3/2 is more than one whole (one whole would be 2/2), plus a little extra.
So 2/3 is less than 3/2.

4. Equal fractions (equivalent fractions).
Compare 1/2 and 2/4.
Picture two same-size squares. Cut one into 2 equal parts and shade 1 part. Cut the other into 4 equal parts and shade 2 parts.
The same amount is shaded in both pictures!
So 1/2 and 2/4 are equal (equivalent).

What You Can Learn From This Game

• If you draw a picture of two fractions, the bigger fraction will have more shaded in. If the fractions are equal, the same amount will be shaded in both.
• The bottom number tells you how many pieces the whole is cut into. More pieces means smaller pieces. That is why 1/3 is smaller than 1/2.
• The top number tells you how many pieces you have. That is why 3/5 is more than 2/5 — you have one extra piece.
• All fractions are made of small building blocks called unit fractions (like 1/3 or 1/5). It helps to understand these first.
• When comparing pictures, make sure the wholes are the same size!
• Equivalent fractions can have different-sized pieces, but they show the same total amount.
• If the top number is bigger than the bottom number, the fraction is more than one whole.
• In math, we often see patterns. Patterns help us make good guesses, explain our thinking, and prove that we are right.