Lesson 3

Compose and Decompose Mixed Numbers

Est. Class Sessions: 2
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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.A.2)
5.NF.B
Apply and extend previous understandings of multiplication and division. (5.NF.B.4, 5.NF.B.7)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP4.
Model with mathematics.
MP5.
Use appropriate tools strategically.
MP6.
Attend to precision.
MP7.
Look for and make use of structure.
MP8.
Look for and express regularity in repeated reasoning.

Students play a game using fraction circle pieces to compose and add mixed number fractions. The Circle Duets game emphasizes the use of manipulatives rather than procedures to add mixed numbers so that students develop fraction number sense. Students use fraction circle pieces to decompose and rename numbers greater than one as mixed numbers and improper fractions.

Content in this Lesson

  • Finding equivalent fractions for mixed numbers [E1].
  • Adding mixed numbers using fraction circle pieces [E8].
  • Naming and representing fractions greater than one as mixed numbers and improper fractions with area models and number sentences [E3].
  • Representing and identifying the simplest form of a fraction using tools (e.g., area models) and multiplication and division strategies [E2].
  • Estimating sums of fractions [E9].
  • Finding strategies for adding mixed numbers [MPE2].
  • Estimating to check for reasonableness [MPE3].
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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

  • all of the red, pink, orange, yellow, aqua, and black pieces from a set of fraction circle pieces

Supplies for Student Groups

  • clear plastic spinner or paper clip and pencil. See Materials Preparation.

Materials for the Teacher

Materials Preparation

Prepare Spinners. Each group will need one spinner for the game. If clear plastic spinners are not available, students can use an opened paper clip and a pencil as shown in Figure 1.

Figure 1: Using a paper clip as a spinner

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed

Compose and Decompose Mixed Numbers
Check-In: Questions 10–15
Student Guide
Page 469
E1.
Identify and find equivalent fractions using tools (e.g., area models, number lines) and multiplication and division strategies.
E2.
Represent and identify the simplest form of a fraction using tools (e.g., area models) and multiplication and division strategies.
E3.
Represent addition, subtraction, multiplication, and division of fractions with area models, number lines, number sentences, drawings, and stories.
E8.
Add and subtract fractions including those with unlike denominators using area models and paper-and-pencil methods.
MPE2.
Find a strategy. I choose good tools and an efficient strategy for solving the problem.
MPE5.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.

Vocabulary in this Lesson