Lesson 3
Patterns in Multiplication
Lesson Purpose
Lesson Narrative
In this lesson, students analyze two sets of multiplication expressions: one in which the number of groups is kept constant, and another in which the size of each group (a unit fraction) is kept constant. They look for regularity as they reason repeatedly about the expressions and their values (MP8). The patterns that emerge in the series of expressions formalize their prior observations about the value of \(a \times \frac{1}{b}\) as \(\frac{a}{b}\). They also enable students to see any fraction as a product of a whole number and unit fraction.
Note that students may write either \(a\times \frac{1}{b} = \frac{a}{b}\) or \(\frac{1}{b} \times a = \frac{a}{b}\) as long as they understand what each factor represents. Teachers can reinforce the meaning of each factor by consistently writing the multiplication in this order: \(\text{number of groups} \times \text {size of each group} = \text{total amount}\). This corresponds to how we tend to express situations with equal groups, which in the case of fractional amounts, is “_____ (whole number) groups of _____ (fraction).”
 Representation
 MLR8
Learning Goals
Teacher Facing
 Evaluate multiplication expressions and recognize that $n \times \frac{1}{b} = \frac{n}{b}$.
Student Facing
 Let’s look at patterns in multiplication of a fraction by a whole number.
Required Materials
Materials to Gather
Required Preparation
CCSS Standards
Addressing
Lesson Timeline
Warmup  10 min 
Activity 1  15 min 
Activity 2  20 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
Suggested Centers
 Rolling for Fractions (3–5), Stage 1: Equivalent Fractions (Supporting)
 Compare (1–5), Stage 5: Fractions (Supporting)
Print Formatted Materials
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Additional Resources
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