Lesson 8
Addition of Fractions
Lesson Purpose
Lesson Narrative
Previously, students decomposed nonunit fractions into smaller unit and nonunit fractions. Here they continue to think about decomposing fractions, but they now use number line diagrams to support their reasoning.
A number line can illustrate the number of unit fractions that make a whole number. This in turn allows students to see that a fraction greater than 1 can be decomposed into a whole number and a fraction less than 1, preparing them to work with mixed numbers. For instance, on a number line partitioned into fifths, the fraction \(\frac{7}{5}\) is 7 fifths away from 0 and 2 fifths away from 1, so we can express \(\frac{7}{5}\) as 1 and \(\frac{2}{5}\). One way to illustrate that sum is by drawing “jumps” on the number line.
Note that in grade 3, students came across mixed numbers in the context of measurement. For instance, they use inch rulers to measure lengths greater than 1 inch to the nearest halves and fourths, express them using numbers such as \(2\frac{1}{4}\) and \(5\frac{1}{2}\). They did not, however, reason about mixed numbers as sums of smaller fractions or sums of a fraction and a whole number.
 Action and Expression
 MLR8
Learning Goals
Teacher Facing
 Decompose fractions greater than 1 into a sum of a whole number and a fraction less than 1.
 Reason about addition of fractions with the same denominator using a number line.
Student Facing
 Let’s explore sums of fractions on a number line.
Required Materials
Materials to Copy
 Make Two Jumps
Required Preparation
Activity 3:
 Create a set of cards from the blackline master for each group of 2.
CCSS Standards
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Activity 3  20 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
Suggested Centers
 Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Addressing)
 Estimate and Measure (1–4), Stage 3: Quarter Inches (Supporting)
 Target Measurements (2–5), Stage 2: Quarter Inches (Supporting)
Print Formatted Materials
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Additional Resources
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