A scale says how much each square on the graph paper stands for. A good scale uses most of the paper and is easy to read.
How do you choose a scale?
Work out the range of your data, which is the largest value minus the smallest. Divide by the number of big squares available, then round up to an easy step such as 1, 2, 5 or 10.
Always start at a value that suits the data, often 0. If all values are far from zero, you may start higher and show that with a break mark.
Worked example
An original experiment records the temperature of cooling water every 5 minutes. The times run from 0 to 40 minutes, and the temperatures run from 35 °C to 90 °C. The graph paper allows 10 big squares across and 12 up.
For time: the range is 40, and 40 ÷ 10 = 4 per square. Rounding to an easy step gives 5 minutes per square, which uses 8 of 10 squares. It is easy to read because every square is a multiple of 5.
For temperature: starting at 30 °C, the range to 90 °C is 60, and 60 ÷ 12 = 5 per square. The scale of 5 °C per square fits exactly.
| Axis | Range | Scale chosen | Why |
|---|---|---|---|
| Time | 0 to 40 min | 1 square = 5 min | Easy multiple, 8 squares used |
| Temperature | 35 to 90 °C | 1 square = 5 °C, start at 30 | Fits 12 squares |
What does the common mistake look like?
A student picks 1 square = 3 minutes for time because 3 divides 40 roughly. Reading 35 minutes then means counting 11 and two-thirds squares, and points are misplaced by eye.
A second slip is using an uneven scale, such as 0, 10, 20, 50, because a value was awkward. Each square must stand for the same amount. The fix is to choose the scale before plotting and write the values along the axis first.
Steps to follow
- Write the smallest and largest value for each axis.
- Divide the range by the number of squares, then round up to 1, 2, 5 or 10.
- Mark and label the axis values, add the quantity and unit, then plot.
Self-check
A plant grows from 0 cm to 46 cm over 12 weeks. You have 12 big squares across and 10 up. Suggest a scale for each axis.
Answer
Weeks: range 12 and 12 squares, so 1 square = 1 week. Height: range 46 and 10 squares gives 4.6 per square, so round up to 5.
With 1 square = 5 cm, 46 cm sits near the ninth or tenth square and fits. A scale of 4 cm per square would need 11.5 squares, which overflows the paper.
Where to go next
With a scale chosen and points plotted, measure steepness in calculating a straight-line gradient. The map and graph reading practice gives more scale-reading drills. Return to plotting ordered pairs if points still land in the wrong place.