Unit 4, Lesson 4
How Many Groups? (Part 1) (Optional)
Grade 6
Preparation
Lesson Narrative
This lesson is optional because it revisits prior-grade work on multiplication and division of whole numbers by unit fractions. Students use a concrete reasoning tool—pattern blocks—to explore “How many groups?” questions where the size of a group is a fraction and the answer to the question (the number of groups) is a whole number.
Students begin by identifying the value of different pattern blocks if a hexagon represents 1 whole. They then use the blocks to represent multiplication of a whole number and a fraction (such as ) and interpret the situation in terms of equal-size groups (such as 3 groups of make ).
Then students use the blocks to reason in the other direction and find out how many times a fraction goes into another number (as in, “How many s are in 2?”). They relate such questions to multiplication equations (such as ).
- Coordinate multiplication equations and pattern block diagrams in which the yellow hexagon represents 1 whole.
- Create a diagram to represent and solve a problem asking “How many groups?” in which the size of a group is a fraction and the answer is a whole number, and explain (orally) the solution method.
Let’s play with blocks and diagrams to think about division with fractions.
Required Materials
Activity 2
Required Preparation
Prepare enough pattern blocks so that each group of 3–4 students has at least 2 hexagons and 6 of each of the other shapes (triangle, rhombus, and trapezoid).
Prepare enough pattern blocks so that each group of 3–4 students has at least 2 hexagons and 6 of each of the other shapes (triangle, rhombus, and trapezoid).
For the digital version of the activity, acquire devices that can run the applet.