Unit 4, Lesson 5
How Many Groups? (Part 2)
Grade 6
Preparation
Lesson Narrative
In this lesson, students continue to use visual tools to reason about “How many groups?” questions and representing them with equations. The number of groups is not always a whole number, prompting students to quantify a partial group. The connection between “How many groups?” questions and division is also made explicit.
Students begin by using fraction strips—a familiar representation from earlier grades—to determine how many whole-number groups of a fraction are in a given number. The fraction strips allow students to count groups of unit and non-unit fractions.
Next, students use pattern blocks to find an unknown number of groups and encounter a case in which the answer is not a whole number. They consider how to express a fraction of a group and the multiplication and division equations that can represent the situation.
The last activity, which is optional, gives students an opportunity to practice reasoning about situations with equal groups of fractions, writing equations, and creating their own diagrams to answer the questions.
- Coordinate multiplication and division equations and pattern block diagrams in which the red trapezoid represents 1 whole.
- Create a diagram to represent and solve a problem asking “How many groups?” in which the size of a group and the number of groups are fractions, and explain (orally) the solution method.
- Identify or generate a multiplication or division equation that represents a given situation involving a fractional divisor.
Let’s use blocks and diagrams to understand more about division with fractions.
Required Materials
Activity 2
Required Preparation
Prepare enough pattern blocks such that each group of 3–4 students has at least 1 hexagon and 4 of each of the other shapes (triangle, rhombus, and trapezoid).
Prepare enough pattern blocks such that each group of 3–4 students has at least 1 hexagon and 4 of each of the other shapes (triangle, rhombus, and trapezoid).
For the digital version of the activity, acquire devices that can run the applet.