Students extend their understanding of multiplication and division to divide fractions by fractions, and develop fluency with whole number and decimal operations.
In Unit 3, sixth grade students focus on the number system, extending their understanding of multiplication and division to include fraction division, and developing fluency with whole number and decimal operations. Throughout the unit, students work toward developing and understanding efficient algorithms. By examining the structure of concrete models and patterns that emerge from these structures, students make sense of concepts such as multiplying by a reciprocal of a fraction when dividing or using long division as a shorthand to partial quotients (MP.8). With these efficient computation algorithms, students solve and interpret realworld problems, including rate applications from Unit 2. Throughout this unit, students will develop, practice, and demonstrate fluency with decimal operations; however, practice and demonstration opportunities should continue throughout the year with the goal of fluency by the end of the year. Several opportunities are already built into future units, such as the unit on Expressions and the unit on Equations, but additional opportunities need to be planned for and included. See our Procedural Skill and Fluency Guide for additional information and strategy and activity suggestions.
Throughout elementary grades, students developed their understanding of the baseten system. They found sums and products and quotients by using concrete models, place value, properties of operations, and the relationships between operations. Intentionally, students did not learn a standard algorithm until they had the conceptual understanding to back it up. Some of these strategies are revisited in this unit in order to ensure that students firmly understand the reasoning behind an algorithm, rather than using it without understanding.
Once students have mastered the positive number system of fractions, decimals, and whole numbers, sixthgrade students will investigate the numbers to the left of 0 on the number line, or negative rational numbers, in Unit 4. In seventh grade, students will learn how to compute with all rational numbers, including negatives, and in eighth grade and high school, students learn about irrational numbers, rounding out their study of the real number system.
Please note that in the Massachusetts Framework for Math, standard 6.NS.4 varies slightly from the CCSSM; it specifies the use of prime factorization to find the greatest common factor and least common multiple of pairs of numbers. The lessons in this unit include this strategy, among others, as one of the ways to approach such problems.
Pacing: 20 instructional days (17 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 20202021 school year due to school closures, see our 6th Grade Scope and Sequence Recommended Adjustments.
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quotient
dividend
divisor
long division/ standard algorithm for division
prime number
composite number
prime factorization
greatest common factor (GCF)
least common multiple (LCM)
reciprocal
relatively prime
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Partial products 
Example: Multiply 12.6 and 4.8 using partial products.

Partial quotients 
Example: Divide 67,764 by 12 using partial quotients. 
Venn diagram 
Example: Use a Venn diagram to find the GCF of 12 and 18. 
This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
6.NS.A.1
Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.
6.NS.A.1
Divide a fraction by a whole number using visual models and related multiplication problems.
6.NS.A.1
Divide a whole number by a fraction using visual models.
6.NS.A.1
Use visual models and patterns to develop a general rule to divide with fractions.
6.NS.A.1
Solve and write story problems involving division with fractions.
6.NS.A.1
Solve problems involving division with fractions.
6.NS.B.3
Add and subtract decimals using the standard algorithm.
6.NS.B.3
Multiply decimals using strategies, and develop an understanding of the standard algorithm.
6.NS.B.3
Multiply decimals using the standard algorithm.
6.NS.B.2
Divide multidigit whole numbers using the standard algorithm.
6.NS.B.2
6.NS.B.3
Divide numbers with decimal quotients. Divide decimals by whole numbers.
6.NS.B.3
Divide decimals by decimals using the standard algorithm.
6.NS.B.3
Solve problems involving decimals using all four operations.
6.NS.B.4
Use prime factorization to represent numbers as products of prime factors.
6.NS.B.4
Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.
6.NS.B.4
Find the least common multiple of two numbers. Solve application problems using the least common multiple.
6.NS.B.4
Solve mathematical and realworld problems using the greatest common factor and least common multiple.
Key: Major Cluster Supporting Cluster Additional Cluster
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