Examples, videos, and solutions 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
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?
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
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.