# Lesson 4

Equal Groups of Non-Unit Fractions

### Lesson Purpose

The purpose of this lesson is to apply understandings from previous lessons to multiply a non-unit fraction by a whole number.

### Lesson Narrative

Previously, students learned that any unit fraction multiplied by a whole number results in multiples of that unit fraction. They also learned that any fraction can be written as a multiplication expression of a unit fraction by a whole number. In this lesson, students notice that they can multiply any fraction and a whole number by reasoning about the number of groups and amount in each group. They generalize that they can multiply the numerator by the whole number to find the number of parts. They also see that the denominator remains the same because the size of each part is the same. In other words: $$n \times \frac{a}{b} =\frac{n \ \times \ a}{b}$$.
• Representation
• MLR6

### Learning Goals

Teacher Facing

• Recognize that $n \times \frac{a}{b} =\frac{n \ \times \ a}{b}$
• Use diagrams to represent and evaluate the product of a whole number and a non-unit fraction.

### Student Facing

• Let’s multiply any fraction by a whole number.

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 20 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

What part of the lesson went really well today in terms of students’ learning? What did you do that made that part go well?

### Suggested Centers

• Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Addressing)
• Rolling for Fractions (3–5), Stage 1: Equivalent Fractions (Supporting)
• Compare (1–5), Stage 5: Fractions (Supporting)