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YEAR 5 · COORDINATES AND TRANSFORMATIONS · 15 MIN

Constructing grids

Build a first-quadrant coordinate grid with named axes, a clear origin and equal intervals.

In this lesson

Before you start
  • Number lines; horizontal and vertical directions
01 / LEARN

Understand the idea.

Two number lines meet

A coordinate grid uses two perpendicular number lines: the horizontal x-axis and vertical y-axis. They meet at the origin, (0,0). Points are located at intersections, rather than inside the square spaces.

Draw straight axes and label them clearly. Choose equal intervals along each axis and show the numbers they represent. A one-unit grid increases by one whenever you cross the next grid line.

A blank first-quadrant coordinate grid with horizontal x-axis, vertical y-axis and a common origin. Both axes are labelled from zero to 6 at equal one-unit intervals. The physical x and y scales match. No plotted points or answers are supplied.

Choose and keep a scale

The scale says how much one interval represents. Five squares can show ten metres if each square represents two metres. Labels then increase by two, even though the spaces on the page remain equal.

Keep each axis consistent from start to finish. The two axes can use different scales when needed, but each scale must be clear. Do not change the numerical jump partway along equally spaced marks.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Construct a small grid

Describe how to make a grid showing coordinates from 0 to 5 in both directions.

Worked solution

  1. 1

    Draw and name the two axes.

    x,y

    The horizontal and vertical axes must be perpendicular so their directions are clear.

  2. 2

    Mark their common origin.

    (0,0)

    Both axes start their positive measurements at the same intersection.

  3. 3

    Mark five equal one-unit intervals on each.

    0,1,2,3,4,5

    Five spaces require six boundary marks when zero is included.

  4. 4

    Complete the matching grid lines.

    Lines through corresponding marks create intersections covering coordinates from 0 to 5 in both directions.

Answer

A grid with named axes, a common origin and equal one-unit intervals from 0 to 5.

EXAMPLE 02

Choose a scale

A path reaches 10 metres east. Your grid is five squares wide. What horizontal scale lets it fit exactly?

Worked solution

  1. 1

    Share the required distance among the squares.

    10÷5=2 metres per square

    All five equal squares must together represent the 10-metre horizontal span.

  2. 2

    Label the horizontal positions.

    0,2,4,6,8,10

    Each successive grid line adds another two metres.

  3. 3

    Check that the path fits exactly.

    5×2=10 metres

    The rightmost grid line represents the full required distance.

Answer

Each square represents 2 metres; label 0, 2, 4, 6, 8, 10.

03 / YOUR TURN

Try it yourself.

Check your understanding

An axis is labelled 0, 3, 6, 9 at equal spaces. What comes next?

Show answer & reasoning

12

The labels increase by 3 each interval. After 9, add the same jump: 9+3=12.

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions
Read the questions online
  1. Name the horizontal axis on a coordinate grid.
    1 mark
  2. Name the point where the axes meet.
    1 mark
  3. Draw a first-quadrant grid from 0 to 4 on each axis. Use one square for one unit and label both axes.
    2 marks
  4. An axis is labelled 0, 2, 4, __, 8 at equally spaced marks. Fill the gap.
    1 mark
  5. You have six squares across to show 12 centimetres. Choose a scale and write the seven labels, including zero.
    2 marks
  6. 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.

  1. Name the horizontal axis on a coordinate grid.
    1 mark

    The horizontal number line is conventionally called x.

    The x-axis.
  2. Name the point where the axes meet.
    1 mark

    Both coordinate values are zero where the axes meet.

    The origin, (0,0).
  3. 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.
    A blank first-quadrant coordinate grid with horizontal x-axis, vertical y-axis and a common origin. Both axes are labelled from zero to 4 at equal one-unit intervals. The physical x and y scales match. No plotted points or answers are supplied.
  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
  5. 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.
  6. 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.
Checking saved progress…
Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics 2026

Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.

Official curriculum source ↗

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