Coordinates come up in the 11+ maths section, and the awkward part is the timing: describing positions on all four quadrants is Year 6 content, and the test is sat in September of Year 6.
So a child can meet a negative coordinate in the exam months before their class reaches it. Not always, because primaries vary in when they teach it, but often enough to be worth checking rather than assuming.
Maths carries 25% of the marks, according to the partnership entrance test page. The partnership publishes no syllabus. What it does say is that the section draws on what has been taught in class, with some questions more challenging than a child is used to. That is the whole basis for working out what might appear, and it is why the national curriculum matters here.
What the curriculum actually requires, and when
Coordinates are statutory primary content. The national curriculum programme of study for KS2 mathematics sets out when:
| Year | What is required | Taught before a September Year 6 test? |
|---|---|---|
| Year 4 | Describe positions on a 2-D grid as coordinates in the first quadrant | Yes |
| Year 4 | Describe movements between positions as translations, left, right, up, down | Yes |
| Year 4 | Plot specified points and draw sides to complete a given polygon | Yes |
| Year 5 | Identify a shape's position after a reflection or translation | Yes |
| Year 6 | Describe positions on the full coordinate grid, all four quadrants | Often not yet |
| Year 6 | Draw and translate simple shapes on the coordinate plane, and reflect them in the axes | Often not yet |
Everything in the Year 4 and Year 5 rows is fair game and should be secure. The two Year 6 rows are the gap worth closing over the summer before the test, because they are the rows a school may not have reached.
x before y, every single time
The most common lost mark on this topic is the simplest one. A coordinate is written (x, y): along first, then up.
The phrase children remember is "along the corridor, then up the stairs". It sounds childish and it works, which is the only test that matters under time pressure.
Reversing a pair turns (3, 7) into (7, 3), a different point and a wrong answer. In a multiple-choice paper the reversed pair is very often one of the options on offer, so the error does not announce itself.
Negative coordinates, and the sign that goes missing
Once the grid extends past zero, both numbers can be negative. The four quadrants work like this, reading anticlockwise from the top right:
- Top right: x positive, y positive, so (4, 3).
- Top left: x negative, y positive, so (-4, 3).
- Bottom left: both negative, so (-4, -3).
- Bottom right: x positive, y negative, so (4, -3).
A child who has only ever worked in the first quadrant will usually read the position correctly and then drop the minus sign while writing it down. Practise reading points out of all four quadrants, rather than plotting points into them, because reading is what the paper asks for.
Translation: counting, not calculating
A translation slides a shape without turning or resizing it. Every vertex moves by the same amount, so finding one new vertex gives the rest for free.
A triangle has a vertex at (2, 5). The shape is translated 3 right and 4 down. Where is that vertex now?
- 3 right adds to x: 2 plus 3 is 5.
- 4 down subtracts from y: 5 minus 4 is 1.
- The vertex is at (5, 1).
Right and up add. Left and down subtract. Children who do this by eye on a diagram make counting slips; children who treat it as two small sums do not.
Completing a polygon from its corners
A standard question gives three corners of a rectangle or square and asks for the fourth. There is nothing to calculate: a rectangle's corners share their coordinates in pairs.
Given (1, 2), (1, 6) and (5, 2), the missing corner takes the x it has not used with the y it has not used, which is (5, 6). Sketching the three points settles it faster than reasoning about it, and a sketch takes seconds.
This is maths coordinates, not non-verbal reasoning
Worth separating, because the two feel similar and are assessed differently. Reflecting a shape in an axis on a numbered grid is maths. Spotting which option is the mirror image of a pattern, with no grid and no numbers, is non-verbal reasoning, which carries its own 25% of the marks. Our guide to 11+ reflection and symmetry questions covers that side.
For the wider picture of what the maths section asks and where the marks actually go, start with our guide to 11+ maths topics.
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[TUTOR INSIGHT] Needed: the coordinates mistake you actually see
[TUTOR INSIGHT] To fill before publish. Two questions, both yours rather than sourceable:
[TUTOR INSIGHT] 1. Is the four-quadrant gap real in practice? Do the primaries you see children from teach negative coordinates before September of Year 6, or do you fill it?
[TUTOR INSIGHT] 2. Which error costs more marks: reversing x and y, or dropping the minus sign. One line on which you drill first, and why.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
Are coordinates tested in the West Midlands 11+?
The partnership does not publish a syllabus, so no list of tested topics exists. It states that the mathematics section draws on what has been taught in class. Coordinates are statutory primary content in the national curriculum from Year 4, so they are within scope. Nobody can tell you how many coordinate questions will appear, and any site that gives you a number is guessing.
Do children need negative coordinates for the 11+?
Possibly. Describing positions on the full coordinate grid, meaning all four quadrants, is Year 6 content in the national curriculum, and the West Midlands test is sat in September of Year 6. A child may therefore meet a negative coordinate in the exam before their class has covered it. Ask the primary school when they teach it, and fill the gap over the summer if the answer is the spring term.
What order do coordinates go in?
Along first, then up: a coordinate is written as (x, y). So (3, 7) means 3 along and 7 up. Reversing the pair gives a different point, and in a multiple-choice paper the reversed pair is often offered as one of the wrong answers, so the mistake does not look like a mistake.
How do you translate a shape on a coordinate grid?
Move every vertex by the same amount. Right and up are added, left and down are subtracted. A vertex at (2, 5) translated 3 right and 4 down becomes (5, 1). Because every point moves identically, working out one vertex gives you the position of the rest.
How do you find the fourth corner of a rectangle from the other three?
A rectangle's corners share coordinates in pairs, so the missing corner uses the x value and the y value that appear only once among the three you have. Given (1, 2), (1, 6) and (5, 2), the fourth corner is (5, 6). Sketching the three points is quicker than reasoning it out.