The purpose of this activity is for students to place fractions greater than 1 on the number line, and to notice how fractions can be written as whole numbers. For example, students will see that for halves, every second half is located at a whole number because it takes two halves to make a whole.

Students work in groups. Each member will be assigned a different set of fractions to put on their number line so that the group can look for patterns across halves, thirds, and fourths. Through repeated reasoning, students may notice two types of regularity (MP8):

• It takes 2 halves, 3 thirds, or 4 fourths to make a whole.
• Whole numbers appear regularly (every 2 halves, every 3 thirds).

• Display 3 blank number lines from 0 to 5 to label as students share.
• Select previously identified students to share the patterns they noticed in the fractions that share the same locations as the whole numbers.
• Label the number line as students share, with the whole numbers written as , , , and so on, to highlight the idea that the number of equal parts (2, 3, or 4) in the fractions affects the number of parts needed to end up at a whole number.
• “Why might it make sense that the fractions show those patterns?” (It takes 2 halves, 3 thirds, or 4 fourths to make a whole. There are 2 halves in 1, so there are or 4 halves in 2, or 6 halves in 3, and so on.)

The purpose of this activity is for students to use the location of a unit fraction to locate 1 and 2 on a number line. It is likely that students will reason about repeating the size of the unit fraction to locate 1. They may continue to count unit-fraction-size parts to locate 2, or use the location of 1.

• “Tell me how you’ve tried to locate 1.”
• “How many halves (or thirds, fourths, or eighths) are in 1? How could we use that to locate 1?”

• Invite students to share a variety of strategies or representations of the number line for locating 1 when given the location of a unit fraction.
• Consider asking:
  • “Did anyone think about it in a similar way?”
  • “Does anyone want to add on to ____ 's reasoning?”
• “What did you notice about how different people located 1?” (They marked off the lengths of the unit fraction until reaching 1 whole. They used a multiple of a unit fraction and marked off that length as many times as needed to get 1 whole.)
• “What strategies did you have for locating 2 once you had located 1?”