This is the first unit in sixth grade in which students encounter any operation with fractions. Multiplying fractions and dividing whole numbers and unit fractions were encountered in fifth grade. Students are first introduced to the conceptual idea of dividing a fraction by a fraction by connecting it to prior knowledge of multiplying fractions and dividing whole numbers and unit fractions, along with models, and situations in this unit. Students will use common denominators to divide fractions, and then use the multiplicative inverse, or reciprocal, to divide fractions. Students may struggle conceptually when the dividend is less than the divisor, as well as when the divisor does not divide evenly into the dividend. This is an essential standard for sixth grade, and may be addressed indirectly in the solving equations and inequalities unit, area unit, and volume unit, but will not be addressed directly until 7th grade.
Key Concepts:
 The connection between the operations of multiplication and division extend to situations in which it is necessary to divide fractions by fractions. (Lesson 1)
 Measurement division extends to division with fractions, and may be done with common denominators. The result names the number of groups. (Lesson 4)
 The relationship between multiplication and division (If ab=c, then c/b = a and c/a = b) holds for fractions. (Lesson 8)
Prior Knowledge Needed:
 Know the role of dividend, divisor and quotient in whole number division and understand the relationship between multiplication and division with whole numbers. (Grade 3, Unit 1; 3.OA.1, 3.OA.A.2)
 Understand the effects of multiplying a whole number by a scale factor greater than or less than one; (Grade 5, Unit 7; 5.NF.5, 5.NF.6)
 Understand that the relationship between multiplication and division do not change when working with fractions; (Grade 5, Unit 5; 5.NF.3, 5.NF.4)
 Divide whole numbers and unit fractions; (Grade 5 Unit 12; 5.NF.7)
Units on the Horizon:
 Understanding, writing, and solving equations and Inequalities (Grade 6, Unit 9)
 Proportional reasoning (Grade 7, Unit 1)
 Rational number operationsmultiplication and division (Grade 7, Unit 5)
Lessons

Lesson objective: Understand that the connection between multiplication and division extends to situations in which it is necessary to divide fractions by fractions. Students bring prior knowledge of the relationship between multiplication and division,...

Objective: Understand the relationship between the dividend, divisor, and quotient in a fraction division problem. This optional activity can be used after Unit 4 Lesson 1. Math concept addressed: In this Guided Collaborative Task, students will use the...

Lesson objective: Fluently connect fraction division with fraction multiplication and make sense of fraction division situations. This lesson helps to build fluency with making sense of fraction division. Number lines and area models are used here becau...

Lesson objective: Understand that measurement division extends to division of fractions, and may be done with common denominators. The result names the number of groups. Students bring prior knowledge of dividing with unit fractions from Grade 5 (5.NF.7...

Objective: Describe a comparison of two distances using "times as far as." This optional activity can be used instead of or in support of Unit 4 Lesson 3. Math concept addressed: In this Guided Collaborative Task, students will use their knowledge and u...

Lesson objective: Fluently use the common denominator strategy to divide fractions. Understand how the value of the dividend in relation to the divisor affects the value of the quotient. This lesson helps to build fluency with fraction division with lik...

Lesson objective: Fluently compute and interpret the quotient and remainder in a fraction division siutation. This lesson helps to build fluency with computing and interpreting the quotient in a fraction division situation. An area model is used here be...

Lesson objective: Connect fraction division to make equal portions of snack mix with and without left over. This lesson provides an opportunity for students to apply their knowledge and understanding of fraction division to a reallife situation. Studen...

Lesson objective: Understand that the relationship between multiplication and division can be extended to dividing whole numbers and nonunit fractions. Students bring prior knowledge of dividing whole numbers and unit fractions from 5.NF.7. This prior ...

Lesson objective: Extend understanding that the connection between division and multiplication can be extended to fraction division. Students bring prior knowledge of dividing unit fractions from Grade 5 (5.NF.7). This prior knowledge is extended to div...

Lesson objective: Fluently connect fraction division with multiplication by using multiplicative inverse. This lesson helps to build procedural skill with connecting fraction division with multiplication by using the multiplicative inverse. Multiplicati...

Lesson objective: Solve missing length area problems with fractional areas and side lengths using division. This lesson provides an opportunity for students to apply their knowledge and understanding of area and fraction division to a reallife situatio...