

1. Interpret the relationship between multiplication and division by recognizing that a quotient is also a factor
Big Ideas: Multiplication can be used to check division. The operations “undo” each other. The quotient of a division problem is the same as a missing factor in a multiplication problem. This lesson builds on students’ understanding of dividing unit fractions by whole numbers and whole numbers by unit fractions. This task gives students a chance to develop a deeper understanding of the meaning of division and its relation to multiplication. Students will look at a scenario and determine whether the operation used is multiplication or division and reason about the relationship between the two operations. Vocabulary: dividend, divisor, quotient, inverse operation
 6.NS.A.1
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2. Interpret the quotient by considering the context of the problem
Big Ideas: The quotient of a division problem can be interpreted by considering the context of the problem. The quotient represents how many or how much of the divisor fits in the dividend. The quotient may be greater than or less than the dividend or divisor. Dividing a whole number by a fraction results in a quotient greater than the divisor because the whole number is being split into many more pieces. This lesson builds on students’ work in fifth grade dividing whole numbers by fractions. This lesson is intended as both a review and a segue into division of fractions by fractions. Students are working on developing a deeper understanding of the concept of division, as well as interpreting the quotient in the context of a real world scenario. The task in this lesson gives students a chance to use a visual model to interpret the difference between the remainder and the fractional part of a mixed number answer. The mathematical concepts in this lesson build toward students’ future work with dividing fractions by fractions using visual models and connecting the relationship between multiplication and division of fractions. Vocabulary: dividend, divisor, quotient
 6.NS.A.1
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3. Interpret the meaning of division by using the context of the problem
Big Ideas: Two interpretations of division are partitive (the number of parts) and measurement (the size of one part). The quotient of a division problem can be interpreted by considering the context of the problem. Dividing a fraction by a whole number results in a quotient smaller than the divisor or dividend. A part is being separated into smaller, equal portions. This lesson builds on students’ work in fifth grade dividing whole numbers by fractions. This lesson is intended as both a review and a segue into division of fractions by fractions. Students are working on developing a deeper understanding of the concept of division, as well as interpreting a quotient in the context of a real world scenario. The task in this lesson gives students a chance to use a visual model to divide a fraction by a whole number, as well as interpret the difference between a partitive model and measurement model. The mathematical concepts in this lesson build toward students’ future work with dividing fractions by fractions using visual models and connecting the relationship between multiplication and division of fractions. Vocabulary: dividend divisor quotient

6.NS.1 Interpret and compute quotients of fractions
Posted: August 24, 2014 in Advance, Periods 1&2, Periods 3&40
Interpret and compute quotients of fractions
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
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