This lesson is optional because it revisits grade 5 standards on division of multi-digit numbers. Students recall ways to divide two numbers using strategies based on place value, properties of operations, or the relationship between multiplication and division. Base-ten diagrams, the main representation used here, remind students that a base-ten unit can be decomposed into 10 of a smaller unit in order to divide. The insights from this lesson prepare students to reason more abstractly about division of decimals in upcoming lessons.

Students begin by interpreting base-ten diagrams that represent division of whole numbers in which the quotient is also a whole number. They recall that dividing 372 by 3, for instance, can mean finding the amount in one group if 372 is put into 3 equal-size groups.

Next, students analyze division of whole numbers that leave a whole-number remainder. To put the remainder into equal-size groups requires decomposing it into tenths or hundredths, giving a quotient that is no longer a whole number.

Finally, students use base-ten diagrams to represent division of a decimal by a whole number, which also yields a decimal quotient.

In all activities in the lesson, students may choose to represent decomposition and grouping of base-ten units visually. This can be done by drawing base-ten diagrams, using physical base-ten blocks (if available), or using paper cutouts of base-ten representations from the blackline master. Consider providing access to these tools as alternatives to drawing.