## IM Commentary

The purpose of this task is for students to add unit fractions with unlike denominators and solve addition and subtraction problems involving fractions that have more than one possible solution (5.NF.1). The reason that students are asked to record their results on a line plot is that they need a way to systematically record their sums and to help them reason about the possible sums they can make with the cards. While this task does not ask students to record measurement data (as described in 5.MD.2), it is a good introductory activity for working with line plots with non-whole numbers.

This activity would be best during the early months of 5th grade when students are gaining familiarity with adding and subtracting unlike fractions and strengthening their understanding of equivalency on the number line. The three fractions introduced can all be represented in eighths, thus making this task ideal to build fluency with fraction operations where one denominator is a factor of the other. If the teacher would like to add an extra level of challenge, he or she can label the number line with fractions as shown below, which would require students to find equivalent fractions for some of the sums.

The task also pushes students to engage in MP.3, Construct Viable Arguments and Critique the Reasoning of Others. Students will use their data and their reasoning to make conjectures about which values could not come up. Though their experimental data will likely point them in the right
direction, they will need to create an organized system to prove that
certain values cannot come up. If this task is discussed in a whole
group after individuals or pairs have had an opportunity to think about the
follow-up questions, there should be opportunities for students to show
different ways of constructing their arguments.

This task is designed to be used in class. If students become comfortable with this type of task, it could be used as a center in centers-based learning. Though the activity is for pairs, the questions posed after students create the line plot would be good to discuss as a whole group after students have had a chance to discuss them in pairs.

A printable copy of the cards is attached to this task.