Corridor then stairs: coordinates

What is a coordinate question?

Reading a point off a grid, or plotting one, or doing something to a point — reflecting it, translating it, finding the middle of two.

Your child could read a point off a grid last year. What has changed is that the grid no longer stops at zero.

Corridor, then stairs

The across number comes first, then the up number.

Corridor, then stairs. You walk along the corridor before you go up the stairs.

It is a physical picture rather than a rule about which letter comes first, and children who have it stop reversing their coordinates almost at once — which matters, because a reversed coordinate is wrong in a way that produces a perfectly plausible point.

The grid carries on past zero

Extend both axes straight through the origin and the grid opens into four sections — quadrants. Same grid, four times the size.

The rule is short:

• Left of the origin, the across number goes negative
• Below the origin, the up number goes negative

So a point four to the left and three up is (−4, 3). A point two right and five down is (2, −5).

Reflections change one sign

If your child is unsure, plotting the original point and looking at where its mirror image has to be is faster than trying to recall which rule applies.

Midpoints land on halves

The midpoint is the average of each pair of coordinates.

The midpoint of (2, 3) and (6, 9) is (2+6)÷2 and (3+9)÷2 — (4, 6).

The midpoint of (1, 2) and (4, 5) is (2.5, 3.5) — which sits between the grid lines, and is completely correct.

Children who expect every answer to land on a crossing assume they have gone wrong and go back to check working that was right. Averages do not have to be whole numbers.

Where do pupils lose marks?

Reversing the two numbers, which corridor-then-stairs fixes.

Losing a minus sign, particularly in the third quadrant where both are negative.

Changing both signs in a reflection, when only one should change.

Rejecting a half in a midpoint answer.

Try it yourself

Read along first, then up. Watch the signs — left is negative on the first number, down on the second.

1. A point sits 4 to the left of the origin and 3 above it. What are its coordinates?
2. Reflect the point (−4, 3) in the y-axis. Where does it land?
3. Reflect the point (2, −5) in the x-axis. Where does it land?
4. What is the midpoint of (2, 3) and (6, 9)?
5. What is the midpoint of (1, 2) and (4, 5)?

Show Answers

How much practice does this type need at home?

Squared paper, four quadrants drawn once, and battleships. Genuinely — a version played on a four-quadrant grid with negative coordinates makes reading and saying points automatic within a single game, and it does it without anybody practising.

Beyond that, the useful drill is saying points aloud: four left, two down. Minus four, minus two. Ten seconds, and it builds the sign instinct that carries the rest of the topic.