Fraction Equivalence Using a Tape Diagram and the Number Line

Examples, solutions, and videos to help Grade 4 students learn how to explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division.

Common Core Standards: 4.NF.1, 4.NF.3b

New York State Common Core Grade 4, Module 5, Lesson 11

Worksheets for Grade 4

The following diagram shows how to use tape diagrams to show fraction equivalence. Scroll down the page for more examples and solutions.
 

Lesson 11 Concept Development
Problem 1: Use a tape diagram and a number line to find equivalent fractions for halves, fourths, and eighths.
Problem 2: Use a number line, multiplication, and division to decompose and compose fractions.
Problem 3: Decompose a non-unit fraction using a number line and division.

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Lesson 11 Problem Set 1

1. Label each number line with the fractions shown on the tape diagram. Circle the fraction that labels the point on the number line that also names the selected part of the tape diagram.
2. Write number sentences using multiplication to show
   a. the fraction represented in 1(a) is equivalent to the fraction represented in 1(b).
   b. the fraction represented in 1(a) is equivalent to the fraction represented in 1(c).
3. Use each shaded tape diagram below as a ruler to draw a number line. Mark each number line with the unit fractions shown on the tape diagram, and circle the fraction that labels the point on the number line that also names the selected part of the tape diagram.
4. Write number sentences using division to show
   a. the fraction represented in 3(a) is equivalent to the fraction represented in 3(b).
   b. the fraction represented in 3(a) is equivalent to the fraction represented in 3(c).
5. a. Partition a number line from 0 to 1 into fifths. Decompose 2/5 into 4 equal lengths.
   b. Write a number sentence using multiplication to show what fraction represented on the number line is equivalent to 2/5.
   c. Write a number sentence using division to show what fraction represented on the number line is equivalent to 2/5.

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Lesson 11 Homework

1. Label each number line with the fractions shown on the tape diagram. Circle the fraction that labels the point on the number line that also names the selected part of the tape diagram.
2. Write number sentences using multiplication to show
   a. the fraction represented in 1(a) is equivalent to the fraction represented in 1(b).
   b. the fraction represented in 1(a) is equivalent to the fraction represented in 1(c).
3. Use each shaded tape diagram below as a ruler to draw a number line. Mark each number line with the unit fractions shown on the tape diagram, and circle the fraction that labels the point on the number line that also names the selected part of the tape diagram.
4. Write number sentences using division to show
   a. the fraction represented in 3(a) is equivalent to the fraction represented in 3(b).
   b. the fraction represented in 3(a) is equivalent to the fraction represented in 3(b).
5. a. Partition a number line from 0 to 1 into fourths. Decompose 3/4 into 6 equal lengths.
   b. Write a number sentence using multiplication to show what fraction represented on the number line is equivalent to 3/4.
   c. Write a number sentence using division to show what fraction represented on the number line is equivalent to 3/4.

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