Line Plots of Fraction Measurements | Grade 5 Math | LevelKite

A line plot shows data as marks above a number line. It is a good way to show measurements, even when they are fractions.

Your class grew 10 bean plants. After one week, you measured how much each plant grew. You used a ruler marked in fourths of an inch. The line plot below shows the results.

Line plot

How much each of 10 bean plants grew in one week, in inches. Each mark stands for one plant.

Read the scale first. The scale is the row of numbers along the number line. Each number sits at a short line called a tick. The ticks are evenly spaced, so each step from one tick to the next is the same size.

On this plot, each step is $\frac{1}{4}$ inch. So you count by fourths from 0: $\frac{1}{4}$ , $\frac{2}{4}$ , $\frac{3}{4}$ , $\frac{4}{4}$ , $\frac{5}{4}$ , $\frac{6}{4}$ . Some of these have simpler names: $\frac{2}{4} = \frac{1}{2}$ , $\frac{4}{4} = 1$ , $\frac{5}{4} = 1\frac{1}{4}$ and $\frac{6}{4} = 1\frac{1}{2}$ . The scale runs from 0 to $1\frac{1}{2}$ inches.

Other line plots may step by halves or by eighths. You read them the same way: find the size of one step, then count by that step along the line.

Key concept

Every mark is one measurement

Each mark on a line plot stands for one measurement. It sits above that measurement's value on the scale. The marks above one value form a stack. The number of marks in a stack tells how many measurements have that value.

In the bean plant plot, the stack above $\frac{3}{4}$ has 3 marks, so 3 plants each grew $\frac{3}{4}$ inch. No plant grew 0 inches, so no mark sits above 0. All the stacks together hold $1 + 2 + 3 + 2 + 1 + 1 = 10$ marks, one for each plant.

Worked example

Read the line plot

Use the bean plant line plot. How many plants grew more than $\frac{3}{4}$ inch?

Find the values greater than three fourths of an inch. Values get larger as you move right on a number line, so these are the ticks to the right of three fourths: one, one and one fourth, and one and one half inches. Leave out the stack above three fourths itself, because those plants grew exactly three fourths of an inch, not more.
$1 > \frac{3}{4}, \quad 1\frac{1}{4} > \frac{3}{4}, \quad 1\frac{1}{2} > \frac{3}{4}$
Count the marks in those stacks, because each mark is one plant. The stack above 1 inch has 2 marks. The stack above one and one fourth inches has 1 mark, and so does the stack above one and one half inches.
$2 + 1 + 1 = 4$

Answer

Four plants grew more than $\frac{3}{4}$ inch.

To make a line plot from a list, start by choosing the scale. Every measurement needs a tick to land on. Every step between ticks must also be the same size. If a value falls between two ticks, its mark has nowhere to go. Moving it to a nearby tick would change the data.

Worked example

Make a line plot

You measured how much rain fell on each of 10 rainy days. Here are the amounts, in inches: $\frac{1}{2}, \frac{1}{4}, \frac{3}{8}, \frac{1}{8}, \frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{7}{8}, \frac{3}{8}, \frac{1}{2}$ . Make a line plot of the data.

Choose the scale. The list includes one eighth, three eighths and seven eighths. A scale in fourths has no tick for these, because each one falls halfway between two ticks. A scale in eighths works for every value, because each half and each fourth can be renamed in eighths.
$\frac{1}{2} = \frac{4}{8}, \quad \frac{1}{4} = \frac{2}{8}, \quad \frac{3}{4} = \frac{6}{8}$
Draw the number line. Start at 0 and step by one eighth of an inch. End at 1 inch, a whole number just past the largest value, seven eighths. Keep the tick for five eighths even though no day had that much rain. Skipping it would make the step from four eighths to six eighths twice as big as the others.
$0, \frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{6}{8}, \frac{7}{8}, 1$
Place the marks. Go through the list in order and draw one mark above each value. Cross off each value as you go, so you skip none. One half goes at four eighths, one fourth at two eighths, and three fourths at six eighths, because they name the same amounts. When a value comes up again, stack its mark on top of the earlier one.
Check the count. The list has 10 values, so the plot needs 10 marks. Add the number of marks in each stack, from left to right.
$1 + 2 + 2 + 3 + 1 + 1 = 10$

Answer

The line plot below steps by eighths from 0 to 1 inch. It has 1 mark above $\frac{1}{8}$ , 2 above $\frac{1}{4}$ , 2 above $\frac{3}{8}$ , 3 above $\frac{1}{2}$ , 1 above $\frac{3}{4}$ and 1 above $\frac{7}{8}$ .

Line plot

Rain on 10 rainy days, in inches. Each mark is one day, so the 3 marks above

\frac{4}{8}

, or

\frac{1}{2}

, inch stand for 3 different days.

Worked example

Find a total and a difference

Use the rain line plot above. (a) How much rain fell on the 10 days in all? (b) How much more rain fell on the rainiest day than on the least rainy day?

Add one value for every mark, because each mark is a different day. Write each value in eighths, the step size of the scale, so all the values have the same denominator. The stack above four eighths has 3 marks, so four eighths appears 3 times. The sum has 10 values, one for each mark.
$\frac{1}{8} + \frac{2}{8} + \frac{2}{8} + \frac{3}{8} + \frac{3}{8} + \frac{4}{8} + \frac{4}{8} + \frac{4}{8} + \frac{6}{8} + \frac{7}{8}$
Every value is in eighths, so add the numerators and keep the denominator 8.
$\frac{1 + 2 + 2 + 3 + 3 + 4 + 4 + 4 + 6 + 7}{8} = \frac{36}{8}$
Rename 36 eighths as a mixed number. Eight eighths make 1 whole, so 32 eighths make 4 wholes, with 4 eighths left over. Then simplify 4 eighths to one half.
$\frac{36}{8} = 4\frac{4}{8} = 4\frac{1}{2}$
Part (b) asks how much more, so find the difference. The rainiest day is the mark farthest right, at seven eighths of an inch. The least rainy day is the mark farthest left, at one eighth of an inch. Subtract the smaller amount from the larger, then simplify.
$\frac{7}{8} - \frac{1}{8} = \frac{6}{8} = \frac{3}{4}$

Answer

In all, $4\frac{1}{2}$ inches of rain fell on the 10 days. The rainiest day had $\frac{3}{4}$ inch more rain than the least rainy day.

Takeaway: On a line plot, each mark is one measurement, placed above its value on an evenly spaced scale. To make a line plot, choose a scale that every value lands on. For values in halves, fourths and eighths, a scale in eighths fits them all. To find a total, add each value once for every mark above it.