In module 3, students use various strategies to multiply and divide with fractions. They multiply fractions by whole numbers and by fractions, divide whole numbers by unit fractions and unit fractions by whole numbers, and convert customary measurements.
Students extend their understanding of fractions from parts of a whole (e.g., 1 third of a shape) to parts of a set or a number (e.g., 1 third of a group of 12 items). They find fractions of a set and then transition to finding a fraction of a whole number. Students learn that finding a fraction of a whole number means they are finding the product of a fraction and a whole number. They apply this learning to converting customary measurement units.
Students use area models and number lines to multiply fractions by unit fractions and then fractions by fractions. Throughout the topic, they reason about the value of products by considering whether the factors involved are greater than 1 or less than 1.
Students use tape diagrams and number lines to divide a whole number by a unit fraction and to divide a unit fraction by a whole number. They solve word problems that involve multiplication of fractions and division of whole numbers and fractions, and students explain the relationship between multiplication and division.
Students apply their previous learning about all operations with fractions to compare and evaluate expressions that contain grouping symbols. They create and solve word problems involving fractions, and they write equations with parentheses for word problems that require multiple steps to solve.