Line Plots with Fractional Data

A line plot is a graph that displays data as points or check marks above a number line, showing how often each value occurs. In fourth grade, you will often see line plots where the data points are fractions, such as halves ($\frac{1}{2}$), quarters ($\frac{1}{4}$), or eighths ($\frac{1}{8}$).

How to Create a Line Plot with Fractions

Let's say you measured the lengths of several small objects in inches and got these results: $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{1}{4}$

Here is how you make a line plot for this data:

1. Draw a Number Line: Since your data includes quarters and halves, draw a number line from $0$ to $1$. Make tick marks for every quarter: $0$, $\frac{1}{4}$, $\frac{1}{2}$ (which is the same as $\frac{2}{4}$), $\frac{3}{4}$, and $1$.
2. Plot the Data: For every measurement in your list, draw an "X" above that fraction on the number line.
   • There are three $\frac{1}{4}$s, so draw three X's stacked above $\frac{1}{4}$.
   • There are two $\frac{1}{2}$s, so draw two X's stacked above $\frac{1}{2}$.
   • There are two $\frac{3}{4}$s, so draw two X's stacked above $\frac{3}{4}$.

Reading and Analyzing the Data

Once your line plot is created, you can use it to answer questions by counting, adding, or subtracting fractions.

Question 1: What is the total length of all objects that measured $\frac{1}{2}$ inch? Look at your line plot. There are two X's above $\frac{1}{2}$. To find the total length, add those fractions together: $\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1 \text{ inch}$

Question 2: How many measurements are greater than $\frac{1}{2}$ inch? Look at the fractions to the right of $\frac{1}{2}$ on the number line. The only data points we have greater than $\frac{1}{2}$ are at $\frac{3}{4}$. Count the X's above $\frac{3}{4}$. There are $2$ measurements greater than $\frac{1}{2}$ inch.

Question 3: What is the difference in length between the longest and shortest object? The longest measurement recorded on the plot is $\frac{3}{4}$ inch, and the shortest is $\frac{1}{4}$ inch. Subtract the shortest from the longest: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \text{ inch}$

By organizing fractional data onto a line plot, it becomes much easier to spot patterns, find totals, and compare measurements!