This lesson and the next one extend the “how many groups?” interpretation of division to situations where the “group” can be fractional. This builds on the work in earlier grades on dividing whole numbers by unit fractions.
Students use pattern blocks to answer questions about how many times a fraction goes into another number (e.g., how many \(\frac 23\)s are in 2?), and to represent multiplication and division equations involving fractions. In this lesson, they focus on situations where the quotient (the number of groups) is a whole number.
This lesson is the first in a group of six lessons that trace out a gradual progression of learning—from reasoning with specific quantities, to using a symbolic formula for division of fractions (MP8).
- Coordinate multiplication equations and pattern block diagrams in which the yellow hexagon represents one whole.
- Create a diagram to represent and solve a problem asking “How many groups?” in which the divisor is a unit fraction, and explain (orally) the solution method.
Let’s play with blocks and diagrams to think about division with fractions.
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).
- I can find how many groups there are when the amount in each group is not a whole number.
- I can use diagrams and multiplication and division equations to represent “how many groups?” questions.
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