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?

Activity 2 Different Representations

Problem 1

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


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


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


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.

Practice Problem

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.

    4 diagrams of equal length. 5 equal parts. 1 part shaded. Total length, 1 cup.
    5 diagrams of equal length. 4 equal parts. 1 part shaded. Total length, 1 cup.
  2. How many cups of nuts do the friends bring on the hike?