In this unit, students extend their understanding of multiplication of a fraction by a whole number to include multiplication of a fraction by a fraction. This unit includes investigation of fair share situations to conceptualize a fraction as division of the numerator by the denominator, paying special attention to unit fractions as the building blocks of all fractions. In addition, students explore visual representations to help incorporate strategies for multiplying a fraction by a whole number, and multiplying fractions by fractions.
Content Standards: 5.NF.B.3, 5.NF.B.4, 5.NF.B.4a, 5.NF.B.4b
Practice Standards: MP1, MP4, MP5
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Unit at a Glance
Lessons 14 (4 days)
Key Concept 1: Fractions can be interpreted as the division of the numerator by the denominator; if the numerator is divided by the denominator, the quotient is located at the same place on the number line as the original fraction.

Lesson objective: Understand that fractions can be interpreted as the division of the numerator by the denominator, and that if the numerator is divided by the denominator, the quotient is located at the same place on the number line as the original fra...

Lesson objective: Understand that fractions can be interpreted as the division of the numerator by the denominator, and that a remainder can be partitioned to share items equally. Students bring prior knowledge of interpreting division and remainders fr...

Lesson objective: Practice determining an equal share in a situation where a remainder can be written as a fraction. This lesson helps to build procedural skill in working with fractional remainders. A tape diagram and a number line are used to help hig...

Lesson objective: Solve problems by reasoning about fractions as division. This lesson provides an opportunity for students to apply their knowledge and understanding of interpreting fractions as division and division results as fractions in a fair shar...
Lessons 56 (2 days)
Key Concept 2: We can interpret \(\frac ab \times q\) as \(a\) parts of a partition of \(q\) into \(b\) equal parts, or \(a \times\frac qb\).

Lesson objective: Interpret \(({a\over b})\times q\) as "a" parts of a partition of q into b equal parts. Students bring prior knowledge of multiplying fractions by whole numbers, in which they typically replicated a given fraction some whole number of ...

Lesson objective: Practice multiplying whole numbers by fractions by interpreting \(({a\over b}) \times q\) as a parts of a partition of q into b equal parts. This lesson helps to build fluency with multiplying whole numbers by fractions with whole numb...
Lessons 711 (5 days)
Key Concept 3: The area of a figure is invariant, regardless of the method used to find it.

Lesson objective: Practice multiplying whole numbers by fractions by interpreting \(({a\over b}) \times q\) as a parts of a partition of q into b equal parts, where the product is not a whole number. This lesson helps to build fluency of multiplying who...

Lesson objective: Extend understanding of multiplication with fractions and whole numbers to multiplying fractions by fractions. Students bring prior knowledge of whole numbers by fractions. This prior knowledge is extended to multiplying fractions by f...

Lesson objective: Find the area of a rectangle with fractional side lengths. This lesson helps to build fluency with multiplication of fractions. Area models are used here because they support students' conceptual understanding of multiplying fractions ...

Lesson objective: Find the area of a rectangle with side lengths that are mixed numbers. This lesson provides an opportunity for students to extend their understanding of multiplying fractions to multiplying mixed numbers. Area models are used to suppor...

Lesson objective: Apply skills and understanding of multiplying with mixed numbers to find area. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplying with mixed numbers. Students are asked to find th...