Lesson 10
Fractional Side Lengths Less Than 1
Lesson Purpose
The purpose of this lesson is for students to find the area of rectangles with one nonunit fractional side length and one whole number side length.
Lesson Narrative
In the previous lesson, students extended their understanding of multiplication to find the area of rectangles with a side length that is a unit fraction. In this lesson, students will find the area of rectangles with a whole number side length and a nonunit fraction side length. Students will apply what they learned in earlier lessons to area representations and recognize that a side length of \(\frac{a}{b}\) is equivalent to a side length of \(a \times \frac{1}{b}\). This allows them to find areas by counting the number of pieces covering the area and then multiplying this by the unit fractional area of each piece. For example, in the image below, there are 8 shaded pieces and each piece has an area of \(\frac{1}{3}\) square unit.
 Representation
 MLR2
Learning Goals
Teacher Facing
 Find the area of a rectangle with one nonunit fractional side length.
 Represent the area of a rectangle with a multiplication expression.
Student Facing
 Let’s find the area of rectangles with a fractional side length.
Required Preparation
CCSS Standards
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
In the next lesson, students will find the area of a rectangle where one of the side lengths is a fraction greater than 1. Try finding the area of a rectangle that is \(\frac{5}{4}\) by 6. How do the understandings in today’s lesson support how you found the area of that rectangle?
Suggested Centers
 Target Measurements (2–5), Stage 5: Fractions of Angles (Addressing)
 How Close? (1–5), Stage 6: Multiply to 3,000 (Supporting)
Print Formatted Materials
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Additional Resources
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