Placing fractions on a number line establishes that fractions are numbers with specific locations, not just shaded parts of shapes. The interval from 0 to 1 is divided into equal segments based on the denominator; the numerator tells how many segments to count from 0. This representation naturally extends beyond 1 (5/4 is one segment past 1 on a fourths number line), connects fractions to whole numbers (4/4 = 1), and supports comparing fractions by their relative positions. The number line is arguably the most important fraction model because it directly shows fractions as part of the number system.
Start with halves and fourths on a 0-to-1 number line, then extend to 0-to-2 and beyond. Have students physically partition and label. Progress to thirds, sixths, eighths. Overlay two number lines (halves and fourths) to reinforce equivalence. Ask "what fraction is here?" and "where does this fraction go?" in both directions.
You've worked with fractions as shaded parts of shapes — half a circle, three-fourths of a rectangle. Those pictures are useful, but they have a limitation: they show fractions as parts of a particular object, not as numbers in their own right. The number line fixes this. On a number line, a fraction is a location — it has a specific address, just like 0, 1, 2, or 3 do. This shift in perspective is one of the most important conceptual moves in all of elementary math.
Here's how to build a fractions number line. Take the segment from 0 to 1 and divide it into equal pieces. The denominator tells you how many equal pieces to make. For fourths, cut the segment into 4 equal parts — you get 4 intervals, with tick marks at 1/4, 2/4, 3/4, and 4/4. The numerator tells you how many of those intervals to count from 0. So 3/4 is the point 3 intervals from 0. It lives 3/4 of the way between 0 and 1.
The most common error is counting tick marks instead of intervals. If you put 4 tick marks between 0 and 1 (plus the 0 and 1 themselves), you've created 5 sections, not 4. The fraction 3/4 is the third interval endpoint — the fourth object you encounter (after 0) — not the third mark you make. A cleaner way to think about it: mark 0 and 1 first, then divide the *space* between them into equal parts. Count spaces, not lines.
The number line also escapes the "fractions only go between 0 and 1" trap. Once you know that 4/4 = 1, you can keep counting: 5/4 is one more fourth beyond 1, landing between 1 and 2. This naturally introduces improper fractions as numbers greater than 1, and it makes their size immediately visible — 5/4 is clearly bigger than 1 but smaller than 2. Two number lines laid side by side (one divided into halves, one into fourths) also let you see equivalence at a glance: 1/2 and 2/4 land at exactly the same point. Same address, different names — that's what equivalent fractions mean.