Grade 3 Representing a/b on a Number Line

Visual Model 1

Question: On a number line, the distance from \(0\) to \(4\) is divided into fourths. Which mark shows \(\frac{3}{4}\) of the distance from \(0\) to \(4\)?

• A. \(3.5\)
• B. \(2\)
• C. \(4\)
• D. \(3\)

Why it works: \(\frac{3}{4}\) of the distance from \(0\) to \(4\) means \(\frac{3}{4} \times 4 = 3\). This lands at the \(3\) mark.

Answer: \(3\)

Visual Model 2

Question: The number line above is divided into equal parts. What fraction of the way from \(0\) to \(4\) is the point marked \(?\)

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{3}{4}\)
• D. \(\frac{2}{3}\)

Why it works: The point is at \(3\) on a distance from \(0\) to \(4\). Since \(3\) out of \(4\) equal units are covered, the point is \(\frac{3}{4}\) of the way from \(0\) to \(4\).

Answer: \(\frac{3}{4}\)

Example 1

Question: The tick marks divide a number line from \(0\) to \(4\) into halves. Where is point \(S\)?

• A. \(\frac{3}{2}\)
• B. \(\frac{5}{2}\)
• C. \(\frac{7}{2}\)
• D. \(\frac{9}{2}\)

1. Counting from \(0\): each small tick mark is \(\frac{1}{2}\).
2. Point \(S\) is at the 5th tick (at position \(2.5\)), so it is \(5 \times \frac{1}{2} = \frac{5}{2}\).

Answer: \(\frac{5}{2}\)

Example 2

Question: The number line shows tick marks dividing the distance from \(0\) to \(3\) into thirds. Which fraction labels point \(T\)?

• A. \(\frac{1}{3}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{4}{3}\)
• D. \(\frac{3}{2}\)

1. Point \(T\) is at the second tick of three equal parts from \(0\).
2. That is \(\frac{2}{3}\).

Answer: \(\frac{2}{3}\)

Example 3

Question: Two points \(M\) and \(N\) are marked on a number line from \(0\) to \(4\). Point \(M\) is at \(1\) and point \(N\) is at \(3\). What fraction of the whole distance from \(0\) to \(4\) is point \(N\)?

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{3}{4}\)
• D. \(\frac{3}{3}\)

1. Point \(N\) is at \(3\) on a number line from \(0\) to \(4\).
2. The fraction is \(\frac{3}{4}\).

Answer: \(\frac{3}{4}\)

Problem 1

Question: A number line from \(0\) to \(1\) is divided into \(6\) equal parts. Which point is at \(\frac{4}{6}\)?

• A. The \(2\)nd tick
• B. The \(3\)rd tick
• C. The \(4\)th tick
• D. The \(6\)th tick

Why it works: \(\frac{4}{6}\) means count \(4\) copies of unit \(\frac{1}{6}\) starting at \(0\). The 4th tick mark is \(\frac{4}{6}\).

Answer: The \(4\)th tick

Problem 2

Question: Ben marks the location of \(\frac{5}{6}\) on a number line from \(0\) to \(1\) divided into \(6\) equal parts. Which statement is TRUE?

• A. \(\frac{5}{6}\) is \(1\) tick away from \(1\)
• B. \(\frac{5}{6}\) is \(5\) ticks away from \(0\)
• C. \(\frac{5}{6}\) is closer to \(0\) than to \(1\)
• D. \(\frac{5}{6}\) is at the \(6\)th tick

Why it works: \(\frac{5}{6}\) means \(5 \times \frac{1}{6}\), so there are \(5\) equal steps from \(0\). Distractor A: distance to \(1\) is \(\frac{1}{6}\), which is \(1\) part, not \(1\) tick per se (ambiguous). Distractor C: false; \(\frac{5}{6}\) is much closer to \(1\). Distractor D: false; it is at the 5th tick.

Answer: \(\frac{5}{6}\) is \(5\) ticks away from \(0\)