Line Plots
4A · Chapter 9 · Lesson 3 · MATH-4A-C09-L03
Learning goal. Construct and interpret frequency X marks on a number line, including repeated observations.
Before you begin
Recall: Grade 3A: picture and bar graphs, tables; 4A: data comparisons; Drawing Line Graphs. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Construct a correctly labeled line graph for daily rainfall in millimeters: Mon: 20, Tue: 19, Wed: 15, Thu: 8, Fri: 4. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 20; plot all five points in weekday order, connect adjacent points, and identify the maximum of 20.
Construct a correctly labeled line graph for daily book checkouts: Mon: 5, Tue: 6, Wed: 5, Thu: 20, Fri: 6. State the highest value.
Show answer & reasoning
Choose a consistent axis scale from zero to at least 20; plot all five points in weekday order, connect adjacent points, and identify the maximum of 20.
From the line graph below, read the number collected on Tue.
Show answer & reasoning
Read the plotted point above Tue on the vertical scale: 7.
Key vocabulary
- line graph
- ordered measurements connected to display change
- line plot
- frequency display using marks above values
- axis
- reference line for labels or quantities
- scale
- equal numeric intervals on an axis
Understand the concept
A line plot uses X marks above a number line to record individual observations. If five people have a score of 4, there must be five X marks above the number 4. Count marks to find frequencies or totals; the height of a stack is a count, not the measurement value itself.
Model it: number line with stacked X marks. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
On the line plot below, how many observations equal 3?
Count the X marks stacked directly above 3: 4.
Check your understanding 1
On the line plot below, how many observations equal 1?
Show answer & reasoning
Count the X marks stacked directly above 1: 1.
Worked example 2
On the line plot below, how many observations equal 8?
Count the X marks stacked directly above 8: 2.
Check your understanding 2
On the line plot below, how many observations equal 2?
Show answer & reasoning
Count the X marks stacked directly above 2: 2.
Worked example 3
What is the total number of observations recorded by the line plot?
Count the X marks: there are 12 observations.
Check your understanding 3
What is the total number of observations recorded by the line plot?
Show answer & reasoning
Count the X marks: there are 12 observations.
Guided practice
On the line plot below, how many observations equal 3?
Show answer & reasoning
Count the X marks stacked directly above 3: 3.
On the line plot below, how many observations equal 3?
Show answer & reasoning
Count the X marks stacked directly above 3: 1.
What is the total number of observations recorded by the line plot?
Show answer & reasoning
Count the X marks: there are 12 observations.
How many values in the line plot are greater than 6?
Show answer & reasoning
Count the X marks above values larger than 6: 3.
What is the greatest frequency shown on the line plot?
Show answer & reasoning
The tallest stack of X marks contains 3 observations.
Independent practice
On the line plot below, how many observations equal 5?
Show answer & reasoning
Count the X marks stacked directly above 5: 2.
What is the total number of observations recorded by the line plot?
Show answer & reasoning
Count the X marks: there are 12 observations.
How many values in the line plot are greater than 6?
Show answer & reasoning
Count the X marks above values larger than 6: 3.
What is the greatest frequency shown on the line plot?
Show answer & reasoning
The tallest stack of X marks contains 3 observations.
Draw a line plot for these values: 1, 1, 3, 3, 5, 5, 5, 6, 6, 7, 8, 8. How many X marks should appear in total?
Show answer & reasoning
Put one X above the number line for every recorded value: 12 marks total.
On the line plot below, how many observations equal 8?
Show answer & reasoning
Count the X marks stacked directly above 8: 1.
On the line plot below, how many observations equal 1?
Show answer & reasoning
Count the X marks stacked directly above 1: 1.
What is the total number of observations recorded by the line plot?
Show answer & reasoning
Count the X marks: there are 12 observations.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A line plot has three X marks above 2 and four X marks above 5. How many observations does it record?
Show answer & reasoning
Each X represents one observation; three plus four gives seven.
On the line plot below, how many observations equal 7?
Show answer & reasoning
Count the X marks stacked directly above 7: 2.
Exit check
How many values in the line plot are greater than 4?
Show answer & reasoning
Count the X marks above values larger than 4: 8.
What is the greatest frequency shown on the line plot?
Show answer & reasoning
The tallest stack of X marks contains 3 observations.
Draw a line plot for these values: 1, 1, 2, 3, 4, 4, 5, 5, 5, 6, 8, 8. How many X marks should appear in total?
Show answer & reasoning
Put one X above the number line for every recorded value: 12 marks total.