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# Comparing Fractions: Bubble Gum Blowing Contest

Media Type:
Interactive

Size: 1.3 MB

or

Source: Teaching Math Grades 3-5: "Equivalent Fractions"

This asset is adapted from an activity from Annenberg Learner's Teaching Math Grades 3-5, a professional development course for teachers.

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This interactive activity adapted from Annenberg Learner’s Teaching Math Grades 3–5 invites students to be the judge of three bubble gum blowing contests. To determine the winner of the contests—Class A or Class B—students have to create and then compare fractions based on how many students blew bubbles and the size of each class. These numbers vary from contest to contest. Students use the activity to plot the fractions on number lines, which provides them with the comparison. The winning class will have a larger part of the number line filled in.

Background Essay

This activity builds on the understanding that students have of fractions as numbers and how they can use a number line to represent and compare fractions. Using the backdrop of two classes holding a bubble gum blowing contest, students create a fraction, represent that fraction on a number line, and compare fractions to determine which one of a pair of fractions is the larger one. They can then declare the winner of the contest.

For example, in a class of six students, if four blow a bubble, the fraction that represents the class’s score for the contest is four-sixths (4 out of 6, or 4/6). To represent this fraction in the activity, students would start by subdividing the number line according to the denominator. In this example, this means dividing the line, which defines the whole, into six parts, equally spaced between the 0 and 1. They would then locate the numerator’s correct position along the number line by clicking on each student who blew a bubble (four). They would now see a plot on a number line they can compare against a similar plot for another class.

Students should know that they can readily compare two fractions when both fractions refer to the same whole (the denominator), without needing a number line to assist them. In such cases, the larger fraction is the one with the larger numerator. By presenting students with different class sizes within each contest, this activity asks them to compare two fractions with different wholes—for example, four-sixths and five-eighths. When plotting these fractions on number lines of equal length and aligning the two number lines, students can compare their plots. Smaller fractions will fill in less of the number line and remain closer to the 0. Larger fractions fill in more of the number line and move closer to 1.

Working with number lines in this way can add meaning to fractions for students. As they work with and discuss the number line, they see that fractions can be represented and compared on a number line, even if they do not share the same denominator.

Connections

Connections to the Common Core State Standards

Numbers and Operations—Fractions

• Extend understanding of fraction equivalence and ordering.
• 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction, such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, and <, and justify the conclusions, e.g., by using a visual fraction model.

Teaching Tips

Before the activity
Students should understand that fractions can describe part of a set, such as a class. They should also have some familiarity with the basics of number lines, such as knowing that larger numbers are to the right, that equal intervals must be used, and that number lines can be used not just to represent whole numbers, but fractions as well.

During the activity
Ask students to begin each contest by making a prediction in their heads as to which class won.

After the activity
Here are some discussion questions you might wish to use to check for understanding:

• What does the numerator tell you?
• What does the denominator tell you?
• How does the size of the denominator influence the size of the fraction?
• How does the size of the numerator influence the size of the fraction?
• How does the relationship between the numerator and denominator influence the size of the fraction?

Extension
When your students become more competent in comparing fractions on number lines, introduce the idea of identifying common denominators between fractions. This will prepare them to add and subtract fractions with like and unlike denominators.

Standards

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