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Year 5 Maths Data

Interpret line graphs

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Theory

A line graph shows how something changes over time, such as temperature through a day or water in a tank. This Year 5 maths page shows how to read values, find how much the line rises or falls, and describe the overall pattern (the trend).

On a line graph, time goes along the horizontal axis and the measurement goes up the vertical axis. The points are joined because the quantity changes continuously.

A line going up shows an increase; down shows a decrease; flat means no change.

The steeper the line, the faster the change. The biggest rise between two readings is the steepest upward part.

The trend is the overall direction: rising, falling, or rising then falling.

Line graph of temperature during a day A line graph of temperature in degrees Celsius against time: 9 at 6 am, 14 at 9 am, 22 at 12 pm, 24 at 3 pm and 17 at 6 pm. The vertical scale goes from 0 to 30 in steps of 5. Temperature during one day 051015202530 Temperature (°C) 6 am9 am12 pm3 pm6 pm Time
Warmest at 3 pm (\(24^\circ\)C). Steepest rise: 9 am to 12 pm (\(8^\circ\)C).
Line graph of water in a tank A line graph of the water in a tank on the first day of each month: January 700 L, February 650 L, March 400 L, April 450 L and May 300 L. The scale goes from 0 to 800 in steps of 100. Water in a tank 0100200300400500600700800 Water (L) JanFebMarAprMay Month
Biggest fall: February to March, \(650 - 400 = 250\) L.

Reading change on a line graph:

\[ \text{change} = \text{later reading} - \text{earlier reading} \]
change = later reading − earlier reading
\[ \text{steeper line} \Rightarrow \text{faster change} \]
steeper line means faster change
Steepest, not lowest. The biggest fall is where the line drops most steeply, not where it is lowest.
Flat means no change. A flat section shows the value stayed the same.

Reading a line graph

  1. Read the title, axes and the scale step.
  2. Find the time on the horizontal axis, go up to the line, then across to read the value.
  3. Subtract two readings to find a rise or fall.
  4. Compare the changes to find the biggest one, and describe the trend.
Example 1 — Read a value
Use the first diagram. What was the temperature at 9 am?
Solution

\(14^\circ\)C.

Example 2 — Rise over the day
Use the first diagram. How much warmer was it at 3 pm than at 6 am?
Solution
\(24 - 9\)\(=\)\(15\)
24−9=15

\(15^\circ\)C warmer.

Example 3 — Biggest rise
Use the first diagram. Between which two times did the temperature rise the most?
Solution
\(14 - 9\)\(=\)\(5\)
\(22 - 14\)\(=\)\(8\)
\(24 - 22\)\(=\)\(2\)
5,8,2

9 am to 12 pm, a rise of \(8^\circ\)C.

Example 4 — Biggest fall
Use the second diagram. Between which two months did the water fall most?
Solution
\(700 - 650\)\(=\)\(50\)
\(650 - 400\)\(=\)\(250\)
\(450 - 300\)\(=\)\(150\)
250 is the largest fall

February to March, \(250\) L.

Example 5 — Count the falls
Use the second diagram. In how many of the four changes did the water fall?
Solution

\(3\) (Jan to Feb, Feb to Mar, Apr to May). From March to April it rose \(50\) L.

Example 6 — Trend
Describe the trend in the first diagram.
Solution

The temperature rose all morning to a peak at 3 pm, then fell in the evening.

Example 7 — Why a line graph?
Why is a line graph better than a column graph for the temperature data?
Solution

Temperature changes continuously over time, so the line shows the values in between the readings too.

Example 8 — Find the mistake
Ali says the tank lost the most water from April to May because the line is lowest there. What is wrong?
Solution

He looked for the lowest point, not the steepest fall. The biggest fall is February to March (\(250\) L, compared with \(150\) L).

Common pitfalls

Lowest point is not the biggest fall. Compare the size of each drop.
Ignoring the scale step. On a scale of \(100\)s, half a step is \(50\).
Reading the wrong time. Go straight up from the time on the horizontal axis.
Missing a rise among falls. Check every pair of readings.

Frequently asked questions

What does a line graph show?

How a quantity changes over time.

What does a steep line mean?

A fast change.

What does a flat line mean?

No change between those readings.

What is a trend?

The overall direction of the line.

How do I find how much something rose?

Subtract the earlier reading from the later one: \(22 - 14 = 8\).

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