Line Plots for Kids: Read, Make and Use Fractions

What Is A Line Plot In Math?

A line plot is a graph that shows data as marks above a number line, one mark for each value. The number line holds every possible value in order, and the stack of Xs above each number shows how often that value appears. That "how often" has a name: the frequency.

Some books call it a dot plot, because the marks can be dots instead of Xs. The idea is identical. What makes it different from other graphs is that it keeps the individual data visible: you can count every answer, not just read a total off a bar.

Line plots suit small data sets of numbers, usually measurements or counts, such as:

• The length of ten pencils in centimetres.

• The number of pets each child in a class has.

• The heights of bean plants after two weeks.

• How much juice is left in each of six glasses.

What Are The Parts Of A Line Plot?

A line plot has four parts, and a missing part is the most common reason a plot cannot be read.

How Do You Read A Line Plot?

You read a line plot by counting stacks, then asking what the stacks say about the whole group. Work through it in this order:

1. Read the title and the label. Say what was measured: "how many pets each child has".

2. Check the number line. Note the smallest and largest values and the step between ticks (1, or a half, or a quarter).

3. Count each stack. The number of Xs above a value is how many times it appears.

4. Count all the Xs. The total number of Xs is the number of data values, here the number of children.

5. Describe the shape. Where do the Xs bunch up? Are there gaps? Is one X sitting far away from the rest?

Three ideas come out of step 5, and they are the start of statistics. The tallest stack is the mode, the most common value, which is the same idea as the mode your child will meet in later grades. The range is the largest value minus the smallest. An outlier is a value far from the others, like the one child with 6 pets when everyone else has 4 or fewer.

Line plots also make the middle value easy to find, because the Xs are already in order; that middle value is the median, which usually arrives around Grade 6.

How Do You Make A Line Plot?

You make a line plot by collecting data, drawing a number line that covers every value, and placing one X per data value. Measuring things at home makes the best first data set, because your child produces the numbers.

1. Collect the data. Measure ten pencils, ten leaves or ten toy cars, writing each length down.

2. Find the smallest and largest values. These set the ends of the number line.

3. Draw the number line with even spacing. Include every value between the ends, even ones nobody measured.

4. Place the Xs. Cross off each value in the list as its X goes on, so nothing is counted twice.

5. Make the Xs the same size and spacing. Stacks are compared by height, so a stack of big Xs can look taller than a stack with more, smaller Xs.

6. Add a title and the label with units. Then ask three questions: most common, range, and anything unusual.

Grid paper helps: one square per X keeps every stack honest. It is tempting to start drawing the line while the measuring is still going on. Actually, wait until every value is written down, because the ends of the line depend on the smallest and largest values, and a line drawn too early runs out of room.

How Do You Make A Line Plot With Fractions?

A line plot with fractions works exactly like one with whole numbers, except the number line is split into halves, quarters or eighths. The key step is choosing the smallest unit in the data and marking every tick at that unit, so the spacing stays even.

Choosing that unit is the one genuinely fiddly part of this topic, and textbooks rarely say it out loud. For lengths of 2 1/4, 2 1/2, 2 3/4 and 3 1/4 inches, the smallest unit is a quarter, so the number line runs 2, 2 1/4, 2 1/2, 2 3/4, 3, 3 1/4, with every quarter marked. These lengths are mixed numbers, a whole number plus a fraction, and placing them on a line is excellent practice for seeing their size.

Once the plot is built, the questions turn into fraction arithmetic: how much longer is the longest than the shortest, what is the total of all the lengths, and what would each be if the total were shared equally. If fractions are the sticking point rather than the graph, why fractions are so hard explains what usually goes wrong underneath.

Examples Of Line Plots For Kids

All the data below is invented for practice, and every answer has been worked twice.

Example 1

A line plot of pets per child shows: 0 pets (1 X), 1 pet (3 Xs), 2 pets (4 Xs), 3 pets (2 Xs), 4 pets (1 X), 6 pets (1 X). How many children were asked, what is the mode, and what is the range?

Count every X:

$$1 + 3 + 4 + 2 + 1 + 1 = 12$$

Twelve children were asked. The tallest stack sits above 2, so the mode is 2 pets. The range is

$$6 - 0 = 6$$

The single X at 6 is an outlier, far from the bunch between 0 and 4.

Example 2

Using the same plot, how many pets do the children have altogether?

A tempting first answer: count the Xs again and say 12 pets.

That answer is the number of children, not the number of pets. The four children with 2 pets already own 8, and the child with 6 pets adds 6 more, so 12 is far too small. Each X stands for one child, and the number under it is how many pets that child has, so multiply each value by its count:

$$0 \times 1 + 1 \times 3 + 2 \times 4 + 3 \times 2 + 4 \times 1 + 6 \times 1$$

$$= 0 + 3 + 8 + 6 + 4 + 6 = 27$$

The children have 27 pets altogether.

Example 3

Ten pencils measure 12, 15, 14, 12, 17, 15, 15, 13, 12 and 15 centimetres. Make a line plot, then find the mode and range.

Tally first: 12 appears 3 times, 13 once, 14 once, 15 four times, 16 never, 17 once. Check the count:

$$3 + 1 + 1 + 4 + 0 + 1 = 10$$

Draw the number line from 12 to 17, including 16 with no Xs. The mode is 15 cm, and the range is

$$17 - 12 = 5\ \text{cm}$$

Example 4

Eight leaves measure $2\tfrac{1}{4}$, $2\tfrac{1}{2}$, $2\tfrac{1}{2}$, $2\tfrac{3}{4}$, $3$, $2\tfrac{1}{2}$, $2\tfrac{1}{4}$ and $3\tfrac{1}{4}$ inches. What is the difference between the longest and shortest leaf, and what is the total length of the leaves that measured $2\tfrac{1}{2}$ inches?

The first instinct with mixed numbers is to mark only 2 and 3 and squeeze the quarters in by eye; mark every quarter from 2 to $3\tfrac{1}{4}$ instead. The stacks are: $2\tfrac{1}{4}$ (2 Xs), $2\tfrac{1}{2}$ (3 Xs), $2\tfrac{3}{4}$ (1 X), $3$ (1 X), $3\tfrac{1}{4}$ (1 X).

Longest minus shortest:

$$3\tfrac{1}{4} - 2\tfrac{1}{4} = 1 \text{ inch}$$

Total of the three leaves at $2\tfrac{1}{2}$ inches:

$$3 \times 2\tfrac{1}{2} = 7\tfrac{1}{2} \text{ inches}$$

Example 5

Six glasses hold $\frac{1}{8}$, $\frac{1}{4}$, $\frac{1}{4}$, $\frac{3}{8}$, $\frac{1}{2}$ and $\frac{3}{4}$ of a litre of juice. If all the juice is poured together and shared equally, how much does each glass get?

Rewrite everything in eighths so it can be added:

$$\frac{1}{8} + \frac{2}{8} + \frac{2}{8} + \frac{3}{8} + \frac{4}{8} + \frac{6}{8} = \frac{18}{8} = \frac{9}{4}$$

Share the total among 6 glasses:

$$\frac{9}{4} \div 6 = \frac{9}{24} = \frac{3}{8}$$

Each glass gets $\frac{3}{8}$ of a litre. Sharing a total equally is finding the average, and on the line plot, $\frac{3}{8}$ sits right among the Xs, which is a quick way to check it.

Example 6

Nine bean plants measure 8, 8.5, 9, 9, 9, 9.5, 10, 10 and 11.5 centimetres. How many plants are taller than 9 cm, and what fraction of the plants are exactly 9 cm?

The stacks are: 8 (1), 8.5 (1), 9 (3), 9.5 (1), 10 (2), 11.5 (1). Plants taller than 9 cm sit to the right of 9, not on it:

$$1 + 2 + 1 = 4$$

Four plants are taller than 9 cm. Exactly 9 cm:

$$\frac{3}{9} = \frac{1}{3}$$

One third of the plants are exactly 9 cm. Notice the number line needs half-centimetre ticks from 8 to 11.5, including 10.5 and 11 with no Xs.

When Do Kids Learn Line Plots?

Line plots usually arrive in Grade 2 in the US, at about age 7, and grow into fraction work by Grades 4 and 5. The UK National Curriculum does not name line plots, so the table pairs the US Common Core (CCSS) with the nearest UK requirement.

If your child is ahead, Example 5 is the Grade 5 target. If they are behind, step back to whole-number plots made from things they measure themselves.

What Is The Difference Between A Line Plot And A Bar Graph?

A line plot puts an X for every single data value on a number line; a bar graph draws one bar for each group and shows only the total. A line plot keeps the individual answers, while a bar graph summarises them.

A quick test for your child: if the answers are numbers that could be put in order, use a line plot; if the answers are names, use a bar graph.

Is A Line Plot The Same As A Line Graph?

No. A line graph joins points with a line to show one thing changing over time, such as the temperature each hour. A line plot has no joining line at all; its Xs sit in stacks above a number line. The names are confusingly close, and plenty of adults mix them up too, which is why it is worth saying the difference out loud the first time your child meets each one.

What Signs Show Your Child Needs More Practice?

Line plot trouble usually shows up in how the plot is drawn or counted. Watch for these:

• Missing values on the number line. The rusher writes only the numbers that appeared, so 16 vanishes and the gaps lie.

• Xs of different sizes. Stacks can no longer be compared by height.

• "Total" answered by counting Xs. The memorizer counts marks for every question, including ones that need multiplying.

• Fraction ticks squeezed in by eye. The quarters drift, so $2\tfrac{3}{4}$ ends up closer to 3 than to $2\tfrac{1}{2}$.

• Joining the Xs with a line. A sign that line plot and line graph have merged in your child's mind.

Where Do Kids Go Wrong With Line Plots?

Four mistakes cause most wrong answers on line plots, and each has a simple fix.

Mistake 1: Leaving Out Values Nobody Chose

Where it slips in:

Drawing the number line for data such as 12, 13, 14, 15, 17.

Don't do this:

Write only the values that appeared, so 16 disappears and 15 sits right next to 17.

The correct way:

Mark every value from the smallest to the largest, evenly spaced, and leave empty values with no Xs.

Children who have just learned bar graphs leave out the empty values almost every time, because a bar graph never needed a category nobody chose. Pointing at the gap and asking "what number lives here?" fixes it within a session or two.

Mistake 2: Counting Xs When The Question Asks For A Total

Where it slips in:

Questions such as "how many pets altogether?" or "what is the total length?"

Don't do this:

Count the Xs and give that number; that only tells you how many data values there are.

The correct way:

Multiply each value by the number of Xs above it, then add, as in Example 2.

Mistake 3: Uneven Fraction Spacing

Where it slips in:

Grade 4 and 5 plots with quarters or eighths.

Don't do this:

Mark the whole numbers and place fractions by eye, so $\frac{3}{8}$ lands anywhere between $\frac{1}{4}$ and $\frac{1}{2}$.

The correct way:

Find the smallest unit in the data, then mark every tick at that unit. For eighths, that means nine ticks from 0 to 1, including $\frac{2}{8}$, $\frac{4}{8}$ and $\frac{6}{8}$, which double as $\frac{1}{4}$, $\frac{1}{2}$ and $\frac{3}{4}$. A little practice with mental math with fractions makes the equivalent names automatic.

Mistake 4: Turning The Line Plot Into A Line Graph

Where it slips in:

Right after a lesson on line graphs, or when the word "line" in the name does the thinking.

Don't do this:

Join the tops of the stacks with a line, as if the data changed over time.

The correct way:

Keep the Xs as separate stacks. A joining line belongs only to data that changes over time, such as temperature through a day.

When Should You Get Outside Help With Line Plots?

Line plots are usually quick to learn once the number line is drawn correctly. Talking to your child's teacher, or getting structured help, makes sense when:

• After several weeks, your child still cannot draw an evenly spaced number line with every value.

• Fraction line plots stall because your child cannot yet place $\frac{1}{4}$, $\frac{1}{2}$ and $\frac{3}{4}$ on a number line at all.

• Questions needing a total or a difference regularly get the wrong operation, even when the plot is correct.

• Data homework ends in frustration more often than not.

The trouble behind a stuck line plot is usually fractions or number lines, not graphing. Fixing that underneath skill tends to fix the plots too.

How Does Bhanzu Teach Data And Fractions?

Bhanzu's live online classes start each topic from why it exists, so line plots are introduced as a way to see every answer in a set of measurements before any rules about ticks and stacks. Trainers start from your child's real level rather than their school grade, which matters here: a Grade 5 child stuck on fraction line plots often needs fractions on a number line first. Classes run from UKG through Grade 10, with peers from more than 20 countries.

This fits best if your child understands graphs but keeps stalling when fractions enter the plot, and you want a teacher to find the gap. It fits less well if your child is already confident with Grade 4 and 5 line plots, or if you mainly want printable practice sheets.

Where Can Your Child Get Extra Help With Line Plots And Fractions?

If you want a teacher to work on the skills behind line plots, these options match the grades where they are taught:

• 3rd grade math tutor for halves, quarters and first measurement plots.

• 4th grade math tutor for eighths and adding fractions from a plot.

• 5th grade math tutor for totals, equal sharing and fraction operations.

• Elementary math curriculum for a structured path through primary data and fractions.

Bottom Line

• A line plot is a number line with one X for every data value, so every answer stays visible.

• Draw every value on the number line, evenly spaced, even values with no Xs.

• Counting Xs gives the number of data values; a total needs each value multiplied by its count.

• Line plots for kids grow from whole numbers in Grade 2 to halves, quarters and eighths in Grades 3 to 5.

• Use a line plot for numbers you can order and a bar graph for named groups.

What Should Your Child Measure This Week?

Hand your child a ruler and ten pencils, leaves or toy cars, and have them measure, plot and find the mode and range. If the number line comes out with gaps missing, go back to Mistake 1; if a "total" question goes wrong, rework Example 2. To have a Bhanzu trainer pinpoint the fraction gap behind a stalled line plot: Book a free demo class.

Read More

• What is a denominator

• Fractions, decimals and percentages

• Math word problems

• How to improve math skills

• What is a unit