Lesson 6

Equivalent Fractions on Number Lines

Est. Class Sessions: 2–3
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Mathematical Standards

5.NF.A
Use equivalent fractions as a strategy to add and subtract fractions. (5.NF.A.1)
5.NF.B
Apply and extend previous understandings of multiplication and division. (5.NF.B.3)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP5.
Use appropriate tools strategically.

Students use number lines to find equivalent fractions when they locate fractions that are the same distance from zero. They play the Fraction Trails Games to develop flexibility with adding fractions, breaking fractions into sums of smaller fractions, and recognizing equivalent fractions.

Content in this Lesson

  • Representing and identifying fractions using number lines and number sentences (e.g., 1/2 = 3/6 and 1/2 = 1/3 + 1/6) [E1].
  • Finding equivalent fractions using area models, number lines, and multiplication and division strategies [E4].
  • Decomposing fractions into the sums of smaller fractions (e.g., 3/4 = 1/2 + 1/4) [E5].
  • Adding fractions including those with unlike denominators [E7].
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Books

 Student Guide
Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Students

  • ruler or piece of paper

Supplies for Student Pairs

  • 6 small game markers such as beans or centimeter cubes
  • clear plastic spinner or a paper clip and pencil

Materials for the Teacher

Materials Preparation

Gather Materials for Spinners. Students can either overlay clear spinners or use a pencil and a paper clip.

Figure 1
Figure 1: Using a paper clip and a pencil as a spinner

Prepare Optional Targeted Practice. Make copies of the Fraction Games Spinners and Fraction Trails Games pages from the Student Activity Book. Place the copies along with small game markers and clear plastic spinners or paper clips and pencils in a center.

TIMS Tip

At the end of the lesson, ask students to save their Fraction Trails Games and Fraction Games Spinners from the Student Activity Book pages. They will revisit the games in the workshop in Lesson 7.

Assessment in this Lesson

Assessment Expectation Assessed Math Practice Assessed

Equivalent Fractions on Number Lines
Check-In: Questions 7–9
Student Guide
Pages 78–79
E4.
Find equivalent fractions using tools (e.g., area models, number lines) and multiplication and division strategies.

Miguel's Fraction Trails Moves
Student Activity Book
Pages 59–60
E4.
Find equivalent fractions using tools (e.g., area models, number lines) and multiplication and division strategies.
E5.
Decompose fractions into the sums of smaller fractions (e.g., 3/4 = 1/2 + 1/4).

Show Equivalent Fractions
Teacher Guide - digital
E1.
Represent and identify fractions (e.g., proper, improper, mixed number) using area models, drawings, number lines, words, symbols, and number sentences.
E4.
Find equivalent fractions using tools (e.g., area models, number lines) and multiplication and division strategies.
MPE5.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.

DPP Item S
Fact Families
Teacher Guide - digital
E10.
Demonstrate fluency with the multiplication and division facts for the 5s and 10s.

Vocabulary in this Lesson