In Module 2, Topic A, students extend their previous understanding of multiplication and division to divide fractions by fractions. They construct division stories and solve word problems involving the division of fractions (6.NS.1). Through the context of word problems, students understand and use partitive division of fractions to determine how much is in each group. They explore real-life situations that require them to ask, “How much is one share?” and “What part of the unit is that share?” Students use measurement to determine the quotients of fractions. They are presented with conceptual problems where they determine that the quotient represents how many of the divisor is in the dividend. For example, students understand that 6 cm/2 cm derives a quotient of 3 because 2 cm divides into 6 centimeters three times. They apply this method to quotients of fractions, understanding 6/7 divided by 2/7 = 6 sevenths/2 sevenths = 3 because, again, two-sevenths divides into six-sevenths three times. Students look for and uncover patterns while modeling quotients of fractions to ultimately discover the relationship between multiplication and division. Using this relationship, students create equations and formulas to represent and solve problems. Later in the module, students learn to and apply the direct correlation of division of fractions to the division of decimals.
