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Compare Fractions using the Number Line


Videos to help Grade 3 students learn how to understand distance and position on the number line as strategies for comparing fractions.

Common Core Standards: 3.NF.2a, 3.NF.2b, 3.NF.3c, 3.NF.3d, 3.MD.4

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Common Core For Grade 3

New York State Common Core Math Module 5, Grade 3, Lesson 19
Application Problem

Thomas has 2 sheets of paper. He wants to punch 4 equally spaced holes along the edge of each sheet.
Draw Thomas’ 2 sheets of paper next to each other so the ends meet.

Label a number line from 0 at the start of his first paper to 2 at the end of his second paper.
Show Thomas where to hole-punch his papers and label the unit fractions.

What unit fraction is labeled on the eighth hole?

Concept Development

Draw 2 same-sized rectangles on your board and partition both into 4 equal parts.
Shade your top rectangle to show 1 fourth and shade the bottom to show 3 copies of 1 fourth.
Compare the models. Which shaded fraction is larger? The 3 fourths is larger because 3 parts is greater than just 1 part of the same size.

Use your rectangles to measure and draw a number line from 0 to 1. Partition it into 4 equal size segments. Label all parts of your number line.

Compare 1 fourth to 3 fourths using the number line. How do you know which is the larger fraction? 1 fourth is less distance from 0, so it is the smaller fraction. 3 fourths is a greater distance away from 0, so it is the larger fraction.

We can compare the fractions by seeing their distance from 0.
1 unit is a smaller distance from 0 than 3 units.

If we know where 0 is on the number line, how can it help us to find the smaller or larger fraction? The smaller fraction will always be to the left of the larger fraction. Because the further you go to the right on the number line, the further the distance from 0.
That means the fraction to the left is always smaller. It’s closer to 0.

Lesson 19 Homework

1. Divide each number line into the given unit fractions. Then place the fractions. Write each whole as a fraction.
a. thirds
b. sixths
c. fifths
2. Use the number lines above to compare the following fractions using >, <, or =.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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