Math Core

Scientists measure tiny things, like beetles, raindrops and seeds, very carefully. Their measurements are often not whole numbers. A line plot marked in eighths lets you see a whole set of these small measurements at once, and then use fraction addition and subtraction to answer questions about them.

Measuring to the nearest eighth

A ruler has marks for halves and fourths of an inch. Many rulers also have smaller marks that split each inch into 8 equal parts. Each part is $\dfrac{1}{8}$ of an inch.

Some of these marks have other names. $\dfrac{4}{8}$ is the same as $\dfrac{1}{2}$ , and $\dfrac{2}{8}$ is the same as $\dfrac{1}{4}$ . Writing every mark in eighths makes it easy to add and subtract, because all the fractions have the same denominator.

Reading a line plot

Definition

Line plot

A line plot is a number line with an X above it for each measurement. Equal measurements stack up in a column.

Worked example: Beetle lengths

A class measured 12 beetles to the nearest eighth of an inch. Each X is one beetle.

Beetle lengths (inches)

Most common length: the tallest column is at $\dfrac{4}{8}$ inch, with 4 X's.
Longer than $\dfrac{1}{2}$ inch: $\dfrac{1}{2} = \dfrac{4}{8}$ , so look to the right of $\dfrac{4}{8}$ . There are 2 X's at $\dfrac{5}{8}$ and 2 at $\dfrac{7}{8}$ , so $2 + 2 = 4$ beetles.
Longest minus shortest: the longest beetle is $\dfrac{7}{8}$ inch and the shortest is $\dfrac{2}{8}$ inch. $\dfrac{7}{8} - \dfrac{2}{8} = \dfrac{5}{8}$ inch.

Making a line plot

Write every measurement with the same denominator (for example, change $\dfrac{1}{4}$ to $\dfrac{2}{8}$ ).
Draw a number line that covers the smallest and largest values, marked in eighths.
Draw one X for every measurement. Count the X's to be sure none are missing.

Worked example: Seed lengths

Omar measured 8 seeds, in inches: $\dfrac{3}{8}, \dfrac{1}{4}, \dfrac{5}{8}, \dfrac{3}{8}, \dfrac{1}{2}, \dfrac{3}{8}, \dfrac{2}{8}, \dfrac{5}{8}$ .

First rename: $\dfrac{1}{4} = \dfrac{2}{8}$ and $\dfrac{1}{2} = \dfrac{4}{8}$ .

Now count: $\dfrac{2}{8}$ appears 2 times, $\dfrac{3}{8}$ appears 3 times, $\dfrac{4}{8}$ appears 1 time and $\dfrac{5}{8}$ appears 2 times. That is $2 + 3 + 1 + 2 = 8$ X's. ✓

Seed lengths (inches)

Common mistake

Don't forget that one value can have more than one name. In Omar's list, $\dfrac{1}{4}$ and $\dfrac{2}{8}$ are the same length, so both X's go in the same column.

Finding totals

To find the total of several measurements, add them. When a column has several X's at the same value, you can multiply instead: 3 X's at $\dfrac{5}{8}$ make $3 \times \dfrac{5}{8} = \dfrac{15}{8}$ .

Worked example: Water in the rain gauge

Nia recorded how much rain fell each day for 7 days, in inches.

Daily rainfall (inches)

How much rain fell in all?

Add up each column:

\begin{aligned} 2 \times \tfrac{1}{8} &= \tfrac{2}{8} \\ 1 \times \tfrac{2}{8} &= \tfrac{2}{8} \\ 3 \times \tfrac{3}{8} &= \tfrac{9}{8} \\ 1 \times \tfrac{4}{8} &= \tfrac{4}{8} \end{aligned}

Total: $\dfrac{2}{8} + \dfrac{2}{8} + \dfrac{9}{8} + \dfrac{4}{8} = \dfrac{17}{8}$ .

Since $\dfrac{16}{8} = 2$ , that is $2\tfrac{1}{8}$ inches of rain.

Tip

Before adding, count the X's and check that you used every one. In Nia's plot there are 7 X's, and the multiplications use $2 + 1 + 3 + 1 = 7$ of them.

Practice

Practice 1

This line plot shows how much rain fell each day for 10 days.

Daily rainfall (inches)

On how many days did exactly $\dfrac{5}{8}$ inch of rain fall?

Type a number.

Practice 2

Use the same rainfall line plot.

Daily rainfall (inches)

What is the difference between the greatest and the least daily rainfall, in inches?

Type a number.

Practice 3

Use the same rainfall line plot.

Daily rainfall (inches)

On how many days did more than $\dfrac{1}{4}$ inch of rain fall?

Type a number.

Practice 4

Kim measured some leaves, in inches: $\dfrac{3}{8}, \dfrac{1}{4}, \dfrac{5}{8}, \dfrac{2}{8}, \dfrac{3}{8}, \dfrac{2}{8}$ . On her line plot, which value has the tallest column?

Practice 5

Use the same rainfall line plot.

Daily rainfall (inches)

How much rain fell in all on the days that had $\dfrac{5}{8}$ inch each? Write your answer as a mixed number.

Type a number.

Practice 6

This line plot shows the lengths of 9 pencil stubs.

Pencil stub lengths (inches)

How much longer is the longest stub than the shortest stub, in inches?

Type a number.

Practice 7

Use the rainfall line plot one more time.

Daily rainfall (inches)

How much rain fell in all 10 days together? Write your answer as a mixed number.

Type a number.