 # Compare Fractions on the Number Line

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Lesson Plans and Worksheets for Grade 3
Lesson Plans and Worksheets for all Grades

Videos, examples, and solutions to help Grade 3 students learn how to compare fractions and whole numbers on the number line by reasoning about their distance from 0.

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

New York State Common Core Math Grade 3, Module 5, Lesson 18

Application Problem

Third grade students are growing peppers for their Earth Day gardening project. The student with the longest pepper wins the “Green Thumb” award. Jackson’s pepper measured 3 inches long. Drew’s measured 10/4 inches long.

Who won the award? Draw a number line to help prove your answer.

Concept Development

Create a number line that shows the interval from 0 to 1
Make each unit show a third. Mark 1/3 and 2/3 on the number line.

Where would you put 1/6 on this number line? 1/6 is in the middle of the first third.
Looking at the number line, which value is the furthest from 0? 1?
Notice that the distance from 0 as an important feature of the comparison.

Lesson 18 Problem Set

Directions: Place the 2 fractions on the number line. Circle the fraction with the distance closest to 0. Then compare using >, <, or =. The first problem is done for you.

6. JoAnn and Lupe live straight down the street from their school. JoAnn walks 5/6 mile and Lupe walks 7/8 mile home from school every day. Draw a number line to model how far each girl walks. Who walks the least? Explain using pictures, numbers, and words.

7. Cheryl cuts 2 pieces of thread. The blue thread is 5/4 meters long. The red thread is 4/5 meters long. Draw a number line to model the length of each piece of thread. Which piece of thread is shorter? Explain how you know using pictures, numbers, and words.

8. Brandon makes homemade spaghetti. He measures 3 noodles. One measures 7/8 feet, the second is 7/4 feet, and the third is 4/2 feet long. Draw a number line to model the length of each piece of spaghetti. Write a number sentence using <, >, or = to compare the pieces. Explain using pictures, numbers, and words.

Lesson 18 Homework

Directions: Place the two fractions on the number line. Circle the fraction with the distance closest to 0. Then compare using >, <, or =.

6. Liz and Jay each have a piece of string. Liz's string is 4/6 yard long, and Jay's string is 5/7 yard long. Whose string is longer? Draw a number line to model the length of both strings. Explain the comparison using pictures, numbers, and words.

7. In a long jump competition, Wendy jumped 9/10 meter and Judy jumped 10/9 meters. Draw a number line to model the distance of each girl’s long jump. Who jumped the shorter distance? Explain how you know using pictures, numbers, and words.

8. Nikki has 3 pieces of yarn. The first piece is 5/6 feet long, the second piece is 5/3 feet long, and the third piece is 3/2 feet long. She wants to arrange them from the shortest to the longest. Draw a number line to model the length of each piece of yarn. Write a number sentence using <,>, or = to compare the pieces. Explain using pictures, numbers, and words.

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