The purpose of this activity is for students to further develop the idea that fractions can be represented on a number line. Students sort a given set of cards showing number lines. They first sort in a way of their choice, which might include the number of parts or the length of the number line. Look for different ways groups choose to categorize the number lines, especially for categories that distinguish between number lines with whole-number partitions and fractional partitions.

When students identify common properties of the number lines for their sorts, such as the numbers listed on the tick marks or the total number of tick marks, they look for and make use of structure (MP7).

• “How did you know if a number line had tick marks that represent fractions?” (If there is one or more tick marks between two back-to-back whole numbers, like 0 and 1, or 1 and 2, then the tick marks between them represent fractions.)
• Attend to the language that students use to describe their number lines, and give students opportunities to describe the number lines more precisely.
• Highlight the use of phrases, such as “parts less than 1” or “partitioning one part into smaller parts less than 1.”
• Consider displaying a number line with fractions that are less obvious, such as Number Line I. Ask students to help identify the fractions on that number line, and label 1 and 3 so that the tick marks between the whole numbers are clear.

The purpose of this activity is to transition students from thinking about fractional lengths on fraction strips to thinking about fractions as numbers on the number line. Students build on their experience of folding fraction strips to fold number lines into halves, thirds, fourths, sixths, and eighths, and then they label unit fractions.

Students begin by considering how the fraction can be labeled on the number line. They learn that each part of the number line has a length of one-half, but the endpoint of the first one-half part is the location of the number on the number line. This distinction is important for understanding fractions as numbers that can be represented as points on the number line and for using the number line precisely (MP6).

When folding the number lines, students also need to attend to the fact that it is the interval between 0 and 1 that needs to be partitioned, rather than the length of the entire strip of paper that contains each number line.

• Display a number line folded into fourths and a fraction strip of fourths.
• “How was partitioning these number lines similar to partitioning our fraction strips?” (The number lines were folded, like the strips, but instead of a rectangle it’s just a line. We labeled the location of a unit fraction at the end of the first part on a number line, instead of the space in between.)