Reason using Benchmarks to Compare Two Fractions on the Number Line


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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

Grade 4, Module 5, Lesson 12 Worksheets

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.

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

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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