Math Core

Your class measures some earthworms, and not one of them is exactly a whole number of inches long. One is $1\tfrac{1}{2}$ inches, another is 2 inches, another is $2\tfrac{1}{2}$ inches. A line plot puts all of those measurements on one number line so you can see the whole group at once.

A number line marked in halves and fourths

When you measure with a ruler, you can measure to the nearest half inch or the nearest quarter inch (fourth of an inch). To show those lengths, you need a number line with marks between the whole numbers.

This number line is marked in fourths. There are 4 equal spaces between each pair of whole numbers:

A mark like $1\tfrac{1}{4}$ means "1 whole inch and one fourth more." Notice that $\tfrac{2}{4}$ sits at the same spot as $\tfrac{1}{2}$ , so we label it $\tfrac{1}{2}$ .

What is a line plot?

Definition

Line plot

A line plot is a number line with an X above it for every measurement. If two measurements are the same, their X's stack up in a column above that number.

The taller a column, the more times that measurement happened. Numbers with no X's still stay on the line, so the spaces stay equal.

Worked example: Reading a line plot

Kids measured 12 earthworms to the nearest half inch. Each X is one worm.

Worm lengths (inches)

Which length was most common? The tallest column is above $1\tfrac{1}{2}$ , with 4 X's. So $1\tfrac{1}{2}$ inches was most common.
How many worms were exactly 2 inches long? Count the X's above 2: 3 worms.
How many worms were longer than 2 inches? Look to the right of 2. There is 1 X above $2\tfrac{1}{2}$ and 2 X's above 3. $1 + 2 = 3$ worms.

Making a line plot

How to make a line plot

Find the smallest and largest measurements.
Draw a number line that covers them. Mark it in wholes, halves or fourths, to match how you measured.
Draw one X above the number for every measurement. Cross each measurement off your list as you go.
Count the X's. The total should match the number of measurements.

Worked example: Leaf lengths

Lena measured 10 leaves to the nearest quarter inch. Here are her lengths, in inches:

$1\tfrac{1}{4}, \ 1\tfrac{1}{2}, \ 1\tfrac{1}{4}, \ 2, \ 1\tfrac{3}{4}, \ 1\tfrac{1}{2}, \ 1\tfrac{1}{4}, \ 1\tfrac{3}{4}, \ 1\tfrac{1}{2}, \ 1\tfrac{1}{4}$

The smallest is $1\tfrac{1}{4}$ and the largest is 2. She draws a number line from 1 to 2 marked in fourths:

Now count each length: $1\tfrac{1}{4}$ appears 4 times, $1\tfrac{1}{2}$ appears 3 times, $1\tfrac{3}{4}$ appears 2 times and 2 appears 1 time. Draw that many X's:

Leaf lengths (inches)

Check: $4 + 3 + 2 + 1 = 10$ X's, and she measured 10 leaves. ✓

How many more leaves were $1\tfrac{1}{4}$ inches than 2 inches? $4 - 1 = 3$ more leaves.

Common mistake

Don't draw just one X for each length. If $1\tfrac{1}{4}$ shows up 4 times in the list, it needs 4 X's. Every measurement gets its own X.

Tip

Keep the marks evenly spaced, even where there are no X's. In the leaf plot, 1 has no X's, but it still gets its own spot on the line.

Practice

Practice 1

Kids measured ribbons to the nearest half inch.

Ribbon lengths (inches)

How many ribbons are $1\tfrac{1}{2}$ inches long?

Type a number.

Practice 2

This line plot shows the lengths of crayons in a box.

Crayon lengths (inches)

How many crayons were measured in all?

Type a number.

Practice 3

This line plot shows how tall some bean sprouts are.

Sprout heights (inches)

Which height is the most common? (You can type a mixed number like 2 1/4.)

Type a number.

Practice 4

Sam measured bugs to the nearest quarter inch. His lengths, in inches, are:

$\tfrac{1}{2}, \ \tfrac{3}{4}, \ \tfrac{1}{2}, \ \tfrac{1}{4}, \ \tfrac{1}{2}, \ \tfrac{3}{4}, \ 1$

He makes a line plot. How many X's go above $\tfrac{1}{2}$ ?

Type a number.

Practice 5

A line plot is marked in fourths. The labels are $2$ , $2\tfrac{1}{4}$ , $2\tfrac{1}{2}$ , ___, $3$ . Which label is missing?

Practice 6

This line plot shows the lengths of paper clips.

Paper clip lengths (inches)

How many paper clips are longer than 1 inch?

Type a number.

Practice 7

This line plot shows the heights of plants in a class garden.

Plant heights (inches)

How many more plants are $5\tfrac{1}{2}$ inches tall than $6\tfrac{1}{2}$ and 7 inches tall together?

Type a number.