2nd Grade · 3rd Grade · 2.MD.D.9 · 3.MD.B.4

Line plots in 2nd and 3rd grade

Line plots show measurement data as Xs stacked above a number line, one X for each measurement. In 2nd grade, your child measures objects to the nearest whole inch or centimeter and plots the lengths. In 3rd grade, the ruler and the line plot add halves and quarters of an inch.

What the standards say

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

2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

What it means, in plain words

2nd grade: measuring and plotting whole units 2.MD.D.9

Measurement data is a list of lengths your child collects by measuring. It can come from measuring several objects, such as 8 shells, or from measuring one object several times. Line plots in 2nd grade use whole units, so each length is measured to the nearest whole inch or centimeter.

A line plot is a number line with an X above it for each measurement. The number line must show every whole number from the smallest length to the largest, evenly spaced, including numbers that nobody measured. A length that comes up more than once gets a stack of Xs, so the tallest stack shows the most common length.

Your child should be able to:

Measure several objects to the nearest whole inch or centimeter
Draw a number line that covers every length, from the smallest to the largest
Put one X above the number line for each measurement
Read the line plot to find the most common length

Example

8 shells measure 4, 6, 7, 7, 9, 9, 9 and 10 centimeters. How do you show them on a line plot?

The smallest length is 4 and the largest is 10, so the number line shows every whole number from 4 to 10: 4, 5, 6, 7, 8, 9 and 10.
Put 1 X above 4, 1 X above 6, 2 Xs above 7, 3 Xs above 9 and 1 X above 10.
5 and 8 have no Xs, but they still appear on the line.
The line plot has 8 Xs, one for each shell. The most common length is 9 centimeters.

3rd grade: halves and quarters of an inch 3.MD.B.4

Line plots in 3rd grade use rulers marked with halves and fourths of an inch. Half-inch marks split each inch into 2 equal parts. Quarter-inch marks split each inch into 4 equal parts. A quarter is another name for a fourth. Measuring to the nearest half inch means picking the half-inch mark closest to the end of the object.

Measuring to the nearest quarter inch works the same way with the smaller marks. Between 2 and 3 on the ruler, the quarter-inch marks are $2\frac{1}{4}$ , $2\frac{1}{2}$ and $2\frac{3}{4}$ . The middle one could also be called $2\frac{2}{4}$ , but children learn to say $2\frac{1}{2}$ .

The scale of a line plot is the step between its marks. It depends on the measurements. When some lengths end in halves, the number line is marked in halves. When some end in quarters, it is marked in quarters, and every quarter mark appears even if no X sits above it.

Your child should be able to:

Measure to the nearest half inch and to the nearest quarter inch
Read lengths such as $3\frac{1}{2}$ or $1\frac{3}{4}$ inches on a ruler
Choose a scale in wholes, halves or quarters that fits the data
Make a line plot with a scale marked in halves or quarters

Example

Six feathers measure $2\frac{1}{4}$ , $2\frac{1}{2}$ , $2\frac{1}{2}$ , $2\frac{3}{4}$ , 3 and 3 inches, each to the nearest quarter inch. How do you show them on a line plot?

Some lengths end in quarters, so the scale is marked in quarter inches.
The number line runs from 2 to 3: 2, $2\frac{1}{4}$ , $2\frac{1}{2}$ , $2\frac{3}{4}$ and 3.
Put 1 X above $2\frac{1}{4}$ , 2 Xs above $2\frac{1}{2}$ , 1 X above $2\frac{3}{4}$ and 2 Xs above 3.
The mark for 2 has no Xs. The line plot has 6 Xs, one for each feather.

Where children usually get stuck

Your child writes only the measured lengths on the number line, such as 4, 6, 7, 9 and 10, with equal gaps between them.
The child thinks the line only needs the numbers in the list. A line plot is built on a number line, so every number in between belongs on it, at equal spaces. Leaving numbers out makes the lengths look closer together than they are.
What helps. Draw the number line first, writing every number from the smallest length to the largest. Add the Xs only after the line is complete.
Three shells all measure 9 centimeters, and your child puts just one X above 9.
The child marks each length once, as if the X means that this length showed up. Each X stands for one object.
What helps. Cross off each length in the list as its X goes on the plot. At the end, count the Xs and check that there is one for every object.
On a ruler marked in quarters, your child reads the first mark after 2 inches as $2\frac{1}{2}$ .
Halves came first, so any mark between two whole inches looks like a half. The child has not counted how many equal spaces sit between 2 and 3.
What helps. Count the spaces between two whole-inch marks together: there are 4, so each one is a quarter. Then name the marks in order: $2\frac{1}{4}$ , $2\frac{1}{2}$ , $2\frac{3}{4}$ , 3.

Try four practice questions

Real 2nd 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
Liam measured some objects in inches. He made a line plot of his measurements.
Object Length (in)
Eraser 2
Leaf 3
Crayon 4
Key 2
Length (inches)
Select the statement that best describes the line plot.
A
One value has too few Xs.
B
One value has too many Xs.
C
All Xs are correctly placed.
D
One X is in the wrong column.
Show the answer and how to solve it
The plot has 4 Xs matching all 4 table measurements, and every column count is correct. All Xs are correctly placed.
1. 1Look at the table. Count the measurements: there are 4 in all.
2. 2Now count the Xs on the line plot. The plot has 4 Xs in total. The totals match.
3. 3Check each column. At 2 inches: the table has 2 measurements (eraser and key) and the plot has 2 Xs. At 3 inches: table has 1, plot has 1. At 4 inches: table has 1, plot has 1. Every column matches.
4. 4Every column on the plot matches the table. All Xs are correctly placed.
Common mistake. A common mistake is only checking the total number of Xs instead of comparing each column to the table.
The idea underneath. When both the total and every column count match the table, all Xs are correctly placed.
2Warm-up
Look at the ruler. How long is the mushroom?
A
$\displaystyle 2$
B
$\displaystyle 2\frac{1}{2}$
C
$\displaystyle 3$
D
$\displaystyle 4$
Show the answer and how to solve it
The mushroom is $2$ inches long because it starts at $0$ and ends at the whole-inch mark on the $2$ mark.
1. 1Look at the ruler. The left side of the mushroom lines up with 0.
2. 2Find where the right side of the mushroom ends. It lines up with the $2$ mark — a whole-inch mark, not a shorter half-inch tick.
3. 3So the mushroom is $2$ inches long.
Common mistake. A common mistake is to add an extra half inch that is not there. The mushroom ends exactly on the $2$ -inch mark, so the length is $2$ inches, not $2\frac{1}{2}$ .
The idea underneath. Each whole inch on a ruler is split in half by a slightly shorter tick mark. When an object ends on that tick, the length is the whole-inch number plus $\frac{1}{2}$ .
3On level
Pierre wants to plot the lengths 1, 3, 6, and 9 inches on a number line. Pierre's number line is shown below.
Select the statement that best describes Pierre's number line.
A
Pierre's number line ends before the largest measurement.
B
Pierre's number line includes every measurement.
C
Pierre's number line skips whole numbers between ticks.
D
Pierre's number line starts after the smallest measurement.
Show the answer and how to solve it
Pierre's line ends at 7, but his largest measurement is 9 inches. His line ends before the largest measurement.
1. 1Look at Pierre's measurements and his number line.
2. 2The largest measurement is 9 inches. Pierre's number line ends at 7.
3. 3Since 9 is bigger than 7, Pierre can't plot 9 on this line. The line ends before the largest measurement.
Common mistake. A common mistake is checking only the start of the line and forgetting to check the end. Always check the start AND the end of the number line against the smallest AND largest measurements.
The idea underneath. A number line works for plotting measurements only when it goes from at most the smallest measurement to at least the largest, with a tick at every whole number.
4Stretch
Carlos used the ruler to find the length of the scissors. Carlos says it is $5\frac{1}{2}$ inches long. Which statement best describes Carlos's work?
A
Carlos's $5\frac{1}{2}$ comes from leaving out the fraction part.
B
Carlos's $5\frac{1}{2}$ comes from reading the next quarter-inch mark to the right of the end.
C
Carlos's $5\frac{1}{2}$ comes from using the distance to the next whole-inch mark as the fraction part.
D
Carlos's reading of $5\frac{1}{2}$ is correct to the nearest quarter-inch.
Show the answer and how to solve it
Carlos's $5\frac{1}{2}$ comes from reading the next quarter-inch mark to the right of the end. The next quarter-inch mark to the right of $5\frac{1}{4}$ is $5\frac{1}{2}$ .
1. 1Look at the ruler. The scissors start at $0$ and the right end lands on the first quarter-inch tick after $5$ , which is $5\frac{1}{4}$ inches.
2. 2Carlos says the scissors are $5\frac{1}{2}$ inches long. The actual length is $5\frac{1}{4}$ inches, so Carlos's claim is wrong by $\frac{1}{4}$ inch.
3. 3Leaving out the fraction part of $5\frac{1}{4}$ gives $5$ . The next quarter-inch mark to the right of $5\frac{1}{4}$ is $5\frac{1}{2}$ .
4. 4The end is $\frac{3}{4}$ inch before $6$ . That is the distance back from $6$ , not the fraction after $5$ . Using $\frac{3}{4}$ as the fraction after $5$ gives $5\frac{3}{4}$ .
5. 5Only reading the next quarter-inch mark to the right of the end gives Carlos's $5\frac{1}{2}$ . Choose the statement that describes that mistake.
Common mistake. Count forward from $5$ to find the fraction part. Counting back from $6$ gives $\frac{3}{4}$ , but the end is $\frac{1}{4}$ inch after $5$ .
The idea underneath. First read the ruler. Then check which statement gives the number the student reported. The student may have read correctly.

Object	Length (in)
Eraser	2
Leaf	3
Crayon	4
Key	2