4th Grade · 5th Grade · 4.MD.B.4 · 5.MD.B.2

Line plots with fractions in 4th and 5th grade

Line plots with fractions show a set of measurements, such as the lengths of pencils, on a number line marked in halves, fourths or eighths. In 4th grade, your child makes the line plot and adds or subtracts the measurements on it. In 5th grade, your child also multiplies and divides, for example to share a total out equally.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit ( $\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{1}{8}$ ). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit ( $\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{1}{8}$ ). Use operations on fractions for this grade to solve problems involving information presented in line plots.

What it means, in plain words

4th grade: making a line plot and adding or subtracting 4.MD.B.4

A line plot is a number line with an X above it for each measurement. If three pencils are each $4\frac{1}{2}$ inches long, three X's stack above $4\frac{1}{2}$ . The stacks show at a glance which lengths came up most often.

In line plots with fractions in 4th grade, the measurements are in halves, fourths or eighths of a unit. Your child first marks the number line in steps that fit the data, such as every $\frac{1}{4}$ inch, and then puts one X above each measurement.

Then your child uses the line plot to answer questions, such as how much longer the longest item is than the shortest. This means adding and subtracting fractions with the same denominator, the bottom number of a fraction. Many of the numbers are mixed numbers, a whole number and a fraction together, like $2\frac{3}{4}$ .

Your child should be able to:

Mark a number line in halves, fourths or eighths
Make a line plot with one X for each measurement
Read a measurement from a line plot
Add and subtract fractions and mixed numbers to answer questions about the data

Example

A class measured 6 earthworms: $2\frac{1}{4}$ , $2\frac{1}{2}$ , $2\frac{1}{2}$ , $3$ , $3\frac{1}{4}$ and $3\frac{3}{4}$ inches. Make a line plot. How much longer is the longest worm than the shortest?

Draw a number line from 2 to 4 inches, marked every $\frac{1}{4}$ inch.
Put one X above each length. $2\frac{1}{2}$ gets two X's.
The longest worm is $3\frac{3}{4}$ inches and the shortest is $2\frac{1}{4}$ inches.
$3\frac{3}{4} - 2\frac{1}{4} = 1\frac{2}{4}$ , which is the same as $1\frac{1}{2}$ .
The longest worm is $1\frac{1}{2}$ inches longer than the shortest.

5th grade: using all four operations on the data 5.MD.B.2

In 5th grade, the line plot is made the same way, but the questions take more steps. Your child now adds fractions with different denominators, such as $\frac{1}{2}$ and $\frac{3}{8}$ , by first rewriting them as eighths. Your child also multiplies a fraction by a whole number, for example to add up several X's at the same mark.

A common question in line plots with fractions 5th grade lessons is a fair share. Several containers hold different amounts. If all of it were poured together and shared out equally, how much would each one hold? Your child finds the total of all the measurements and then divides by the number of containers.

Your child should be able to:

Add fractions with different denominators from a line plot
Multiply a fraction by the number of X's at one mark
Find the total of all the measurements on a line plot
Share a total equally by dividing it by the number of items

Example

A line plot shows the milk in 4 identical glasses: $\frac{3}{8}$ cup, $\frac{1}{2}$ cup, $\frac{5}{8}$ cup and $\frac{1}{2}$ cup. If the milk were shared equally among the 4 glasses, how much would each glass hold?

Write each amount in eighths: $\frac{3}{8}$ , $\frac{4}{8}$ , $\frac{5}{8}$ and $\frac{4}{8}$ .
Total: $\frac{3 + 4 + 5 + 4}{8} = \frac{16}{8} = 2$ cups.
Share 2 cups among 4 glasses: $2 \div 4 = \frac{2}{4} = \frac{1}{2}$ .
Each glass would hold $\frac{1}{2}$ cup of milk.

Where children usually get stuck

On a line marked in eighths, your child puts the X for $\frac{3}{4}$ at the third tick after 0.
The child counts tick marks without checking what each space is worth. On this line, the third tick is $\frac{3}{8}$ , and $\frac{3}{4}$ is the sixth tick.
What helps. Before plotting, ask what one jump on this line is worth. Label the first few ticks together ( $\frac{1}{8}$ , $\frac{2}{8}$ , $\frac{3}{8}$ ) before adding any X's.
Your child adds $\frac{1}{4} + \frac{1}{4}$ and writes $\frac{2}{8}$ .
The child adds the top numbers and the bottom numbers, as if they were two separate whole numbers. The bottom number names the size of the pieces, and that size does not change when you add.
What helps. Use the line plot itself. Start at $\frac{1}{4}$ , jump one more $\frac{1}{4}$ and read where you land: $\frac{2}{4}$ , which is $\frac{1}{2}$ .
To share the milk equally, your child divides the total by the number of different marks on the line instead of the number of glasses.
Two glasses with the same amount make one stack, so the stacks are easy to count as if each were one glass. Each X is one glass.
What helps. Ask how many glasses there are, and count the X's together before dividing.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
What number does the X mark on the line plot below?
Answer format:
Show the answer and how to solve it
Answer. 1
The X is on the first half tick after $0$ , so it shows $\frac{1}{2}$ . Equivalents like $\frac{2}{4}$ and $\frac{3}{6}$ are also accepted.
1. 1Look at the X on the line plot. The X is between $0$ and $1$ .
2. 2The space from $0$ to $1$ is divided into $2$ equal parts. Each tick is $\frac{1}{2}$ .
3. 3Count the half ticks past $0$ : $\frac{1}{2}$ . The X is on the first tick, so it shows $\frac{1}{2}$ .
Common mistake. A common mistake is to read the half tick as a whole number and write $1$ . The space from $0$ to $1$ is divided into $2$ equal parts, so each tick is $\frac{1}{2}$ , not $1$ . Count one tick for each $\frac{1}{2}$ starting from $0$ .
The idea underneath. Between any two whole numbers on a line plot, the number of equal divisions tells you the denominator of the fraction, and counting ticks from the lower whole number gives you the numerator.
2Warm-up
The line plot below shows string lengths in inches.
Length (inches)
Select how many strings are exactly $1\frac{1}{4}$ inches long.
A
1
B
2
C
3
D
5
Show the answer and how to solve it
The answer is $2$ because there are $2$ X marks directly above $1\frac{1}{4}$ on the line plot.
1. 1Find the tick labeled $1\frac{1}{4}$ on the line plot.
2. 2Count the X marks stacked directly above $1\frac{1}{4}$ . Each X is $1$ string, and there are $2$ X marks.
3. 3So $2$ strings are $1\frac{1}{4}$ inches long. Select $2$ .
Common mistake. A common mistake is reading the $3$ X marks at $1\frac{1}{2}$ instead of the stack at $1\frac{1}{4}$ . Match the tick label first, then count only the X marks directly above that value.
The idea underneath. On a line plot, the count for a value is the height of the stack directly above that exact tick label.

3Warm-up

Maya is finding how many feet of ribbon each of

2

gift bags will get after the pieces in the line plot are combined with

\frac{1}{2}

foot of additional ribbon and shared equally. The line plot and Maya's work are shown below.

Ribbon pieces

Ribbon length (feet)

Step 1	$\displaystyle \frac{1}{2}+\frac{3}{4}+1+1\frac{1}{4}=3\frac{1}{2}\text{ ft}$
Step 2	$\displaystyle 3\frac{1}{2}+\frac{1}{2}=4\text{ ft}$
Step 3	$\displaystyle 4\div 2=2\text{ ft for each gift bag}$

Select the statement that best evaluates Maya's solution.

Maya added the additional

\frac{1}{2}

foot after dividing, but the additional ribbon should be added to the total before sharing.

Maya's work is correct.

Maya forgot to include the additional

\frac{1}{2}

foot in the total before dividing equally between the

2

gift bags.

Maya divided by 4 ribbon pieces instead of by 2 gift bags.

Show the answer and how to solve it

Maya's work is correct. She totaled $3\frac{1}{2}$ feet, added the additional $\frac{1}{2}$ foot before dividing, and shared equally between $2$ gift bags to get $2$ feet each.

1First, use the line plot to identify all $4$ ribbon lengths.
2Add all $4$ ribbon pieces. Maya's sum of $3\frac{1}{2}$ feet is correct.
3Maya added the additional $\frac{1}{2}$ foot to the total before dividing by $2$ gift bags. This is the correct order.
4Each step in Maya's work matches the correct procedure: sum the pieces, add the additional ribbon to the total, then divide equally.
5Maya's work is fully correct. Each gift bag receives $2$ feet of ribbon.

Common mistake. Students evaluating this work may wrongly flag an error, but Maya correctly added the additional $\frac{1}{2}$ foot to the total before sharing.

The idea underneath. In equal-sharing line plot problems, combine all pieces and any additional amount first; only then divide by the number of equal shares.

4On level
Jordan wants to find how many more Xs are at $\frac{3}{4}$ inch than at $\frac{1}{2}$ inch on the line plot below.
Length (inches)
Jordan's work:
$\displaystyle \begin{array}{l} \text{Xs at } \frac{3}{4} \text{ in.}: 4 \\[0.5em] \text{Xs at } \frac{1}{2} \text{ in.}: 3 \\[0.5em] 4 - 3 = 1 \end{array}$
Select the statement that best describes Jordan's work.
A
Jordan's comparison is correct.
B
Jordan counted the Xs at $\frac{3}{4}$ inch incorrectly.
C
Jordan counted the Xs at $\frac{1}{2}$ inch incorrectly.
D
Jordan added the counts at $\frac{3}{4}$ and $\frac{1}{2}$ instead of subtracting them.
Show the answer and how to solve it
The correct statement is: "Jordan counted the Xs at $\frac{3}{4}$ inch incorrectly." The stack at $\frac{3}{4}$ has $5$ Xs, but Jordan wrote $4$ , so the calculation was $4 - 3 = 1$ instead of the correct $5 - 3 = 2$ .
1. 1Jordan is comparing the stack at $\frac{3}{4}$ inch and the stack at $\frac{1}{2}$ inch. Look at the line plot to count the Xs at each value.
2. 2The stack at $\frac{3}{4}$ inch has $5$ Xs. The stack at $\frac{1}{2}$ inch has $3$ Xs.
3. 3The correct difference is:
4. 4Now compare to Jordan's work. Jordan wrote $4$ for the stack at $\frac{3}{4}$ inch, but the actual count is $5$ . The count at $\frac{1}{2}$ ( $3$ ) matches the line plot, and the subtraction $4 - 3 = 1$ is arithmetically correct — only the count at $\frac{3}{4}$ is wrong.
Common mistake. A common mistake is glancing at the subtraction $4 - 3 = 1$ and assuming the operation went wrong. The arithmetic is fine — the error is in counting the stack at $\frac{3}{4}$ inch.
The idea underneath. When checking someone else's data work, verify both the data they read AND the operation they performed — a correct procedure on incorrect data still produces the wrong answer.