The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction.

 Students will be given a division model, mathematical sentence, or practical problem to solve. After solving a problem, they will enter their answer into the Google Form and it will tell them if they got the correct solution.  If they answered incorrectly, they will need to try again to move on.  If they answer correctly, they choose which problem they want to solve next.  This activity is designed so that students will complete 5 problems.

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one.

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and to use this understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

This task gives students word problems with a given a set of a specified size and a specified number of subsets. The questions ask the student to find out the size of each of the subsets.

One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.

The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division.

This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.

This task builds on a fifth grade fraction multiplication task and uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem.

This task builds on a fifth grade fraction multiplication task and uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem.

In Grade 5 Unit 5, students continue their exploration with fraction operations, deepening their understanding of fraction multiplication from Grade 4 and introducing them to fraction division.

Students began learning about fractions very early, as described in the Unit 4 Unit Summary. However, students’ exposure to fraction multiplication only began in Grade 4, when they learned to multiply a fraction by a whole number, interpreting this as repeated addition. For example, 4×2/3 is thought of as 4 copies of 2 thirds. This understanding is reliant on an understanding of multiplication as equal groups (3.OA.1). In Grade 4, however, students also developed an understanding of multiplicative comparison (4.OA.1), which will be of particular importance to the new ways in which students will interpret fraction multiplication in this unit.

The unit begins with students developing a new understanding of fractions as division. In the past, they’ve thought of fractions as equal-sized partitions of wholes, but here they develop an understanding of a fraction as an operation itself and represent division problems as fractions (5.NF.3). Students now see that remainders can be interpreted in yet another way, namely divided by the divisor to result in a mixed-number quotient. Then, students develop a new understanding of fraction multiplication as fractional parts of a set of a certain size (5.NF.4), which is a new interpretation of multiplicative comparison. Students use this understanding to develop general methods to multiply fractions by whole numbers and fractions, including mixed numbers. Throughout this work, students develop an understanding of multiplication as scaling (5.NF.5), “an important opportunity for students to reason abstractly” (MP.2) as the Progressions notes (Progressions for the Common Core State Standards in Mathematics, Number and Operations - Fractions, 3-5, p. 14). Then, students explore division of a unit fraction by a whole number and a whole number by a unit fraction (5.NF.7), preparing students to divide with fractions in all cases in Grade 6 (6.NS.1). Then, students also solve myriad word problems, seeing the strategies they used to solve word problems with whole numbers still apply but that special attention should be paid to the whole being discussed (5.NF.6, MP.4), as well as write and solve expressions involving fractions as a way to support the major work (5.OA.1, 5.OA.2). Finally, students make line plots to display a data set of measurements in fractions of a unit and solve problems involving information presented in line plots (5.MD.2), a supporting cluster standard that supports the major work of this and the past unit of using all four operations with fractions (5.NF).

These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.

The purpose of this task is to help students see the connection between aÖb and ab in a particular concrete example. The relationship between the division problem 3Ö8 and the fraction 3/8 is actually very subtle.

These problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.

This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division.