Students explore methods of dividing a fraction by a unit fraction.Key ConceptsIn this lesson and in Lesson 5, students explore dividing a fraction by a fraction.In this lesson, we focus on the case in which the divisor is a unit fraction. Understanding this case makes it easier to see why we can divide by a fraction by multiplying by its reciprocal. For example, finding 34÷15 means finding the number of fifths in 34. In this lesson, students will see that this is 34 × 5.Students learn and apply several methods for dividing a fraction by a unit fraction, such as 23÷14.Model 23. Change the model and the fractions in the problem to twelfths: 812÷312. Then find the number of groups of 3 twelfths in 8 twelfths. This is the same as finding 8 ÷ 3.Reason that since there are 4 fourths in 1, there must be 23 × 4 fourths in 23. This is the same as using the multiplicative inverse.Rewrite both fractions so they have a common denominator: 23÷14=812÷312. The answer is the quotient of the numerators. This is the numerical analog to modeling.Goals and Learning ObjectivesUse models and other methods to divide fractions by unit fractions

Students use models and the idea of dividing as making equal groups to divide a fraction by a whole number.SWD: Some students with disabilities will benefit from a preview of the goals in each lesson. Students can highlight the critical features or concepts in order to help them pay close attention to salient information.Key ConceptsWhen we divide a whole number by a whole number n, we can think of making n equal groups and finding the size of each group. We can think about dividing a fraction by a whole number in the same way.8 ÷ 4 = 2 When we make 4 equal groups, there are 2 wholes in each group.89÷4=29  When we make 4 equal groups, there are 2 ninths in each group.When the given fraction cannot be divided into equal groups of unit fractions, we can break each unit fraction part into smaller parts to form an equivalent fraction.34 ÷ 6 = ?     68 ÷ 6 = ?     68 ÷ 6 = 18  Students see that, in general, we can divide a fraction by a whole number by dividing the numerator by the whole number. Note that this is consistent with the “multiply by the reciprocal” method.ab÷n=a÷nb=anb=an×1b=an×b=ab×1nGoals and Learning ObjectivesUse models to divide a fraction by a whole number.Learn general methods for dividing a fraction by a whole number without using a model. 

Students explore methods of dividing a fraction by a fraction.Key ConceptsStudents extend what they learned in Lesson 4 to divide a fraction by any fraction. Students are presented with two general methods for dividing fractions:Rewrite the dividend and the divisor so they have a common denominator. The answer to the original division will be the quotient of the numerators.Multiply the dividend by the reciprocal of the divisor.These two methods will work for all cases, including cases in which one or both of the numbers in the division is a fraction or whole number.Goals and Learning ObjectivesUse models and other methods to divide fractions by fractions.

The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution.

The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number.

This task is from Tools for NC Teachers. Students compare the difference between a fraction times a whole number compared to a fraction divided by a whole number. This is remixable.

It is much easier to visualize division of fraction problems with contexts where the quantities involved are continuous. It makes sense to talk about a fraction of an hour. The context suggests a linear diagram, so this is a good opportunity for students to draw a number line or a double number line to solve the problem.

This task could be used in instructional activities designed to build understandings of fraction division. With teacher guidance, it could be used to develop knowledge of the common denominator approach and the underlying rationale.

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder or a mixed number.