The idea, step by step
Two number lines meet
A coordinate grid uses a horizontal x-axis and a vertical y-axis. They meet at the origin, labelled 0. Here both axes go from 0 to 6. A point sits at an intersection, not in the middle of a square.
A clear grid has straight lines, axis names and readable numbers. Put equal steps of the same value along each axis. In the example one square represents one unit.
Choose and keep a scale
If a grid must show distances up to 12, one square could represent 2 units. Label 0, 2, 4, 6 and so on. The distance between neighbouring labels must stay the same.
The two axis scales can be chosen separately when needed, but each axis must be internally consistent. State the scale so another person can read the graph correctly.
A common trap
Equally spaced marks can be labelled 0, 1, 3, 6.
Instead: Those number gaps are unequal. On a linear coordinate axis, equal physical spacing represents equal numerical changes.
See the thinking
Construct a small grid
Describe how to make a grid showing coordinates from 0 to 5 in both directions.
- Draw perpendicular x- and y-axes meeting at 0.
- Mark five equally spaced one-unit steps on each axis, label 0 to 5, and draw matching grid lines.
Choose a scale
A path reaches 10 metres east. Your grid is five squares wide. What horizontal scale lets it fit exactly?
- Divide the span by the number of squares: 10 ÷ 5 = 2.
- Increase each horizontal label by 2 metres.
Check your understanding
An axis is labelled 0, 3, 6, 9 at equal spaces. What comes next?
Show answer
12
Each interval adds 3.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Name the horizontal axis on a coordinate grid.1 mark
- Name the point where the axes meet.1 mark
- Draw a first-quadrant grid from 0 to 4 on each axis. Use one square for one unit and label both axes.2 marks
- An axis is labelled 0, 2, 4, __, 8 at equally spaced marks. Fill the gap.1 mark
- You have six squares across to show 12 centimetres. Choose a scale and write the seven labels, including zero.2 marks
- A pupil labels consecutive equally spaced marks 0, 1, 2, 5. Explain what needs correcting.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Name the horizontal axis on a coordinate grid.1 mark
The horizontal number line is conventionally called x.
The x-axis. - Name the point where the axes meet.1 mark
Both coordinate values are zero where the axes meet.
The origin, (0, 0). - Draw a first-quadrant grid from 0 to 4 on each axis. Use one square for one unit and label both axes.2 marks
Use a ruler; mark four equal steps from 0 in both directions.
x horizontal, y vertical, common origin, equal one-unit intervals labelled 0 to 4. - An axis is labelled 0, 2, 4, __, 8 at equally spaced marks. Fill the gap.1 mark
The scale increases by 2 each time.
6 - You have six squares across to show 12 centimetres. Choose a scale and write the seven labels, including zero.2 marks
12 ÷ 6 = 2; both endpoints are labelled.
2 centimetres per square; 0, 2, 4, 6, 8, 10, 12. - A pupil labels consecutive equally spaced marks 0, 1, 2, 5. Explain what needs correcting.2 marks
The final jump is 3, unlike the earlier jumps of 1.
The labels or positions need equal numerical intervals. For one-unit steps use 0, 1, 2, 3.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.
Official curriculum source ↗