Reason using Benchmarks to Compare Two Fractions on the Number Line

Examples, solutions, and videos to help Grade 4 students learn how to reason using benchmarks to compare two fractions on the number line.

Common Core Standards: 4.NF.2

New York State common Core Grade 4, Module 5, Lesson 12

Worksheets for Grade 4

Lesson 12 Concept Development
Problem 1: Reason about the size of a fraction compared to 1/2.
Problem 2: Plot points on a number line by thinking about fractions in relation to 0, 1/2, or 1. Compare the fractions.
Problem 3: Use the benchmarks 0, 1/2, and 1 to compare two fractions without using a number line.

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Lesson 12 Benchmarks
What is a “benchmark” in learning about fractions?

Lesson 12 Problem Set 1

1. a. Plot the following points on the number line without measuring.
   i. 1/3
   ii. 5/6
   iii. 7/12
   b. Use the number line in Part (a) to compare the fractions by writing <, > or = on the lines:
   i. 7/12 ____ 1/2
   ii. 7/12 ____ 5/6
2. a. Plot the following points on the number line without measuring.
   i. 11/12
   ii. 1/4
   iii. 3/8
   b. Select two fractions from Part (a), and use the given number line to compare them by writing <, > or =.
3. Compare the fractions given below by writing < or > on the lines.
   Give a brief explanation for each answer referring to benchmark fractions 0, 1/2, and 1.
   a. 1/2 ___ 3/4
   b. 1/2 ___ 7/8
   c. 2/3 ___ 2/5
   d. 9/10 ___ 3/5

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Lesson 12 Homework

1. a. Plot the following points on the number line without measuring.
   i. 2/3
   ii. 1/6
   iii. 4/10
   b. Use the number line in Part (a) to compare the fractions by writing >, < or = on the lines:
2. a. Plot the following points on the number line without measuring.
   i. 5/12
   ii. 3/4
   iii. 2/6
   b. Select two fractions from Part (a), and use the given number line to compare them by writing > ˂ or =.
   c. Explain how you plotted the points in Part (a).
3. Compare the fractions given below by writing > or < on the lines.
   Give a brief explanation for each answer referring to benchmark fractions of 0, 1/2, and 1.

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