In this unit, students extend their knowledge of multiplication and division to include fractional quantities. The unit builds on the understanding that a fraction is a number that can be operated on and represented on a number line. Using various representations, students demonstrate the ability to divide unit fractions and whole numbers. Students may struggle with applying this knowledge to create a story context.
Key Concepts:
 The meaning of division does not change when the dividend is a fraction.
 The relationship between multiplication and division holds for situations in which the divisor is a unit fraction; if \(ab=c\), and \(b\) is not 0, then \(c \over b\) must be \(a\).
 The relationship between multiplication and division does not change when working with fractions.
Prior Knowledge Needed:
 Understand the relationship between multiplication and division; (Grade 3, Unit 7; 3.OA.2, 3.OA.3)
 Multiply fractions by whole numbers (Grade 5, Unit 5; 5.NF.B.4a)
 Interpret multiplication as scaling (Grade 5, Unit 5; 5.NF.B.5a)
Units on the Horizon:
 Solving problems with fractional quantities (Grade 5, Unit 12)
 Dividing fractions (Grade 6, Unit 4)
 Unit rates associated with ratios of fractions (Grade 7, Unit 2)
 Rational number operations  multiplication and division (Grade 7, Unit 5)
Lessons

Lesson objective: Understand that the meaning of division does not change when dividing a unit fraction by a whole number, and that the name of the quotient is based on the whole. Students have worked with division for a few years, most recently in 5.NB...

Lesson objective: Divide unit fractions by whole numbers using number lines and tape diagrams. This lesson helps to build procedural skill with division including a unit fraction as the dividend and a whole number as the divisor. Number lines and tape d...

Lesson objective: Apply understanding of dividing unit fractions by whole numbers to solve problems. This lesson provides an opportunity for students to apply their knowledge and understanding of dividing unit fractions by whole numbers to a reallife s...

Lesson objective: Understand that the meaning of division does not change when the divisor is a fraction. Students bring prior knowledge of division of unit fraction by a whole number from 5.NBT.6. This prior knowledge is extended to fractions as studen...

Lesson objective: Practice dividing whole numbers by unit fractions using the question "How many (unit fractions) are in (this whole number)?" This lesson helps to build procedural skill with dividing whole numbers by unit fractions by thinking about ho...

Lesson objective: Understand that the relationship between multiplication and division does not change when unit fractions are included. Students bring prior knowledge of the relationship between multiplication and division of whole numbers from 3.OA.A....

Lesson objective: Use the relationship between multiplying and dividing to solve problems with fractions. This lesson helps to build procedural skill with writing equations that show the relationship between multiplication and division. Tape diagrams ar...