# Lesson 2 Representations of Equal Groups of Fractions

• Let’s look at diagrams and expressions that can help us multiply a whole number and a fraction.

## Warm-up Number Talk: Three, Six, Nine, Twelve

Find the value of each expression mentally.

## Activity 1 Card Sort: Expressions and Diagrams

Your teacher will give you a set of cards with expressions and diagrams.

1. Match each expression with a diagram that represents the same quantity.

2. Record each expression without a match.

3. Han started drawing a diagram to represent and did not finish. Complete his diagram. Be prepared to explain your reasoning.

4. Choose one expression that you recorded earlier that didn’t have a match.

Draw a diagram that can be represented by the expression. What value do the shaded parts of your diagram represent?

## Problem 1

1. Write a multiplication expression that represents the shaded parts of the diagram. Then, find the value of the expression.

Diagram:

2. Draw a diagram that the expression  could represent. Then, find the value of the expression.

Diagram:

3. Draw a diagram and write an expression that gives the value .

Diagram:

## Problem 2

To represent , Diego drew this diagram:

Elena drew this diagram:

Are they representing the same expression and value? Explain or show how you know.

## Problem 1

Five friends go on a hike. They each bring cup of nuts.

1. If the shaded parts represent the amount of nuts the friends bring on their hike, which diagram matches the story? Explain your reasoning.

2. How many cups of nuts do the friends bring on the hike?