In previous lessons students solved equal sharing problems involving division of whole numbers with answers in the form of mixed numbers and fractions using diagrams. They noticed patterns and made generalizations about the relationship between the expression and the fraction for specific values of and . Students have observed that the numerator of the fraction is the number of objects being shared, while the denominator is the number of equal shares. This lesson brings all of these ideas together through contexts, equations, and diagrams. Students continue to notice patterns across these contexts and build flexibility with interpreting fractions in terms of division by creating their own situations. Fluently moving between representations gives students the ability to choose an appropriate representation to solve a problem (MP1).

Consider what division situations students or their families might be familiar with. Measurement contexts often present situations when division results in a fraction or mixed number. For example, making something with fabric, dividing large amounts of food into smaller containers, or measuring and cutting wood for a project.

What strategies are students using to divide numbers that result in a fraction or mixed number quotient? What questions have you asked that encourage students to see the relationship between the dividend and the numerator and the divisor and the denominator?