Lesson 7

What Fraction of a Group?

Lesson Narrative

In the previous three lessons, students explored the “how many groups?” interpretation of division. Their explorations included situations where the number of groups was a whole number or a mixed number. In this lesson, they extend the work to include cases where the number of groups is a fraction less than 1, that is, situations in which the total amount is smaller than the size of 1 group. In such situations, the question becomes “what fraction of a group?”.

Students notice that they can use the same reasoning strategies as in situations with a whole number of groups, because the structure \(\displaystyle \text{(number of groups)} \boldcdot \text{(size of a group)} = \text{(total amount)}\) is the same as before (MP7). They write multiplication equations of this form and for the corresponding division equations.

Throughout the lesson, students practice attending to details (in diagrams, descriptions, or equations) about how the given quantities relate to the size of 1 group.

Learning Goals

Teacher Facing

  • Comprehend the phrase “What fraction of a group?” (in spoken and written language) as a variation of the question “How many groups?” that is used when the quotient is less than 1.
  • Create a tape diagram to represent and solve a problem asking “How many groups?” in which the quotient is a fraction less than 1.
  • Write multiplication and division equations to represent a problem asking “How many times as long?”

Student Facing

Let’s think about dividing things into groups when we can’t even make one whole group.

Required Materials

Learning Targets

Student Facing

  • I can tell when a question is asking for the number of groups and that number is less than 1.
  • I can use diagrams and multiplication and division equations to represent and answer “what fraction of a group?” questions.

CCSS Standards

Building On

Addressing