In this lesson, students continue to work with division situations involving questions like “how many groups?” or “how many of this in that?” Unlike in the previous lesson, they encounter situations where the quotient is not a whole number, and they must attend to the whole when representing the answer as a fraction (MP6). They represent the situations with multiplication equations (e.g., “? groups of \(\frac12\) make 8” can be expressed as \(? \boldcdot \frac12 = 8\)) and division equations (\(8\div\frac12 = ?\)).
- Coordinate multiplication and division equations and pattern block diagrams in which the red trapezoid represents one whole.
- Create a diagram to represent and solve a problem asking “How many groups?” in which the divisor is a non-unit fraction, 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.
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).
- I can find how many groups there are when the number of groups and the amount in each group are not whole numbers.