# 3. Divide a fraction by a fraction using common denominators (C)

teaches Common Core State Standards CCSS.Math.Content.6.NS.A.1 http://corestandards.org/Math/Content/6/NS/A/1
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3

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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). This prior knowledge is extended to dividing non-unit fractions as students use common denominators to divide fractions. A conceptual challenge students may encounter is making sense of the remainder.

The concept is developed through work with a double number line, which allows students to use common denominators to create same size pieces, then see how many of the divisor are in the dividend.

This work helps students deepen their understanding of operations because the remainder is not simply the left over portion, but is expressed in comparison to the divisor as the whole.

Students engage in Mathematical Practice 3 (construct and critique arguements) as they compare Diego and Susan's interpretation of the problem and solution.

Key vocabulary:

• common denominator
• dividend
• divisor
• quotient
• remainder

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