In This Unit of Study…

Students multiply a fraction by a fraction, including mixed numbers and fractions greater than 1. When multiplying a given number by a fraction less than 1 or a fraction greater than 1, students predict and explain the relative size of the product to the given number without calculating. They accomplish this by connecting their knowledge of the relationship between fractions and decimals and by using estimation strategies to assess the reasonableness of an answer. They apply their understanding of multiplying fractions to solve real-world problems involving the multiplication of fractions. Problem solving includes using visual models and formulas to determine the perimeter and area of a rectangle with fractional side lengths. Instruction includes the use of manipulatives, drawings, and the properties of operations. Denominators are limited to whole numbers up to 20.

B.E.S.T. Benchmarks:

• MA.5.FR.2.2 Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
• MA.5.FR.2.3 When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
• MA.5.AR.1.2 Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.
• MA.5.GR.2.1 Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.

Key Concepts:

• I can use area models, tape diagrams, and number lines to make sense of the process for multiplying two fractions or for multiplying a fraction by a whole number.
• I can reason about how numbers change when they are multiplied by fractions.
• I can recognize that when multiplying by a fraction greater than one, the number increases, and when multiplying by a number less than one, the number decreases.
• I can use visual fraction models or equations to represent and solve problems that involve multiplying any combination of fractions, whole numbers, and mixed numbers.
• I can find the perimeter and area of a rectangle with fractional side lengths using models.
• I can find the perimeter and area of a rectangle with fractional side lengths using formulas.
• I can solve real-world problems involving multiplication of fractions, mixed numbers, and fractions greater than 1.