Create and Analyze Fractional Line Plots
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5th Grade Math › Create and Analyze Fractional Line Plots
A student measured the lengths of 10 pencils (in inches) to the nearest $\tfrac{1}{4}$ inch. The data can be represented and analyzed using line plots.
Line plot (inches):
Number line (inches): $5$ $5\tfrac{1}{4}$ $5\tfrac{1}{2}$ $5\tfrac{3}{4}$ $6$
Marks:
- $5$: XX
- $5\tfrac{1}{4}$: XXX
- $5\tfrac{1}{2}$: XX
- $5\tfrac{3}{4}$: X
- $6$: XX
Which claim about the measurements is incorrect?
Exactly 2 pencils are $5$ inches long.
Exactly 5 pencils are longer than $5\tfrac{1}{2}$ inches.
Exactly 3 pencils are $5\tfrac{1}{4}$ inches long.
Exactly 2 pencils are $6$ inches long.
Explanation
Line plots show measurement data by placing marks above a number line to represent the frequency of pencil lengths. Fractions are represented on the number line as quarters, such as 5 1/4 or 5 3/4, for lengths to the nearest quarter inch. To read the plot, count the X marks at each point; for lengths longer than 5 1/2, the total is three (one at 5 3/4 and two at 6). This pencil data connects to identifying incorrect claims, such as stating exactly five pencils longer than 5 1/2 when the plot shows only three. A common misconception is including the boundary value in 'longer than' counts, but 'longer than' excludes equals. Line plots help analyze data by allowing precise subgroup tallies and error detection. They support verifying statements through visual and numerical checks.