ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] (6) 4 :

4. Interpret and compute quotients of fractions using visual models and equations to represent problems.

a. Use quotients of fractions to analyze and solve problems.

[MA2019] REG-7 (7) 4 :

4. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

a. Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

b. Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

c. Explain subtraction of rational numbers as addition of additive inverses.

d. Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

e. Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

f. Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

g. Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

This video focuses on modeling division of a whole number by fractions using fraction strips.

   View Standards     Standard(s): [MA2019] (6) 4 :

4. Interpret and compute quotients of fractions using visual models and equations to represent problems.

a. Use quotients of fractions to analyze and solve problems.

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.