This activity allows students to integrate several concepts and skills on data analysis and fraction operations. Students plot fractional measurements on a line plot, interpret the data, and find sums or differences of fractions to solve problems in context (MP2).

To find the difference between the longest and shortest shoe lengths, students can reason in a number of ways, using visual representations or more abstract reasoning. For example, they may:

• Use the tick marks on the line plot and count up by eighths from to .
• Count up from to 8, and then from 8 to 9, and from 9 to .
• Subtract from in parts: first subtract , and then 7, and then another .
• Find by first decomposing the 9 into and then subtracting from it.

To complete the activity, students need to make sense of the data and the questions, identify relevant numbers or quantities, and persevere in solving problems (MP1).

• Invite students to share their completed line plot and their responses.
• Focus the discussion on the last two questions about the differences in the longest and shortest shoe lengths. Select previously identified students to share their reasoning strategies in the order shown in the Activity Narrative.
• As students explain, record and display their reasoning for all to see.
• “Did you use the same strategy to solve the last problem? How did you find out the shoe length of the student who made an error?” (Sample responses: I started at 9 on the number line and moved by eighths 7 times to the left to land at . I subtracted  from 9.)

In this activity, students analyze a line plot that is incomplete. They relate the list of given fractions to the data on the line plot and use their understanding of equivalence to determine the missing data points. Students also continue to interpret the data and add and subtract fractions to solve problems in context (MP2).

• Select students to display their completed line plot and to share how they decided which data points didn’t get plotted.
• Highlight that one missing point could be Jada’s, Diego’s, or Han's, as the fractions that represent their change in shoe length, , are equivalent.
• Select other students to share their responses to questions about Han’s and Priya's shoe lengths.
• Then focus the discussion on the last question about Tyler's error, his actual change in shoe length, and how the corrected value might affect the line plot.