Skip to content
Math Games Central — horizontal lockupMath Games Central Print something

Coordinate plane

A coordinate grid is two number lines crossed at zero, and every point on it has a name made of two numbers: how far across, then how far up. The order is the whole convention — (3, 5) and (5, 3) are different places — and once that is automatic, graphs, map references and later algebra all become readable. The questions here ask for one thing at a time: one coordinate, or which quarter of the grid a point sits in, or how far apart two points are. That keeps every answer a single number, which is the only kind a printed sheet can mark fairly.

Start the levels Print a worksheet

Reading a coordinate

What is the x-coordinate of point A? (point A drawn 3 squares right of the origin and 2 squares up)

  1. Find the origin first: the middle, where the two number lines cross.
  2. The x-coordinate is how far across, so read along the bottom line and ignore the side one for now.
  3. Point A sits directly above the 3, so it is 3 squares right of the origin.
  4. The x-coordinate is 3.

Worth knowing. The same point has a y-coordinate of 2, and that is the other question this figure can be asked. Across first, up second — swapping them names a different place.

Naming the quadrant

Which quadrant is point A in? (point A drawn 4 squares left of the origin and 2 squares up)

  1. The two lines cut the grid into four quarters, numbered 1 to 4.
  2. Quadrant 1 is the one up and to the right. The numbering runs anticlockwise from there: 2 is up and left, 3 is down and left, 4 is down and right.
  3. Point A is left of the origin and above it.
  4. Up and left is quadrant 2.

Worth knowing. You never need the coordinates for this, only their two signs. Left of the middle means a negative x, above it means a positive y, and that pair is quadrant 2 every time.

Measuring between two points

How many units apart are point A and point B? (point A drawn 2 squares left of the origin and 3 up, point B drawn 4 squares right of the origin and 3 up)

  1. Both points are 3 squares up, so they are on the same row and the gap runs straight across.
  2. Count from A in to the vertical line down the middle: 2 squares.
  3. Count on from the middle out to B: 4 more squares.
  4. 2 and 4 is 6, so the points are 6 units apart.

Worth knowing. Counting in to zero and out again is safer than subtracting a negative, and it is the same journey: 2 back to nothing, then 4 forward.

Where it usually goes wrong

  • Reading up before across. The first number is always the one along the bottom, so (3, 5) is three across and five up. (5, 3) is a different point.
  • Starting the count at one. The origin is zero, so the first line you step to is 1 — counting it as 2 shifts every answer by one square.
  • Dropping the minus sign. A point left of the middle has a negative x and a point below the middle has a negative y; the digit on its own is only half the answer.
  • Numbering the quadrants clockwise. They run the other way — anticlockwise from the top right — which is why quadrant 2 is up and to the left, not down and to the right.

The Professor says the same thing every time he reads a point: along the corridor, then up the stairs. You cannot go up before you have walked along.

Practise it

All level paths

Questions teachers and parents ask

Why does nothing here ask a child to plot a point?

Because a printed sheet cannot mark one. A plotted dot is right or wrong by a fraction of a square, and there is no fair way to grade that from a photocopy — so a child who understood perfectly could still be marked down for a wobbly pencil. Asking for one coordinate at a time keeps every answer a single number that is either correct or not. Plotting is very much worth doing with a pencil and a real grid; these questions are what makes it possible.

Why are the distance questions only along a row or a column?

Because a diagonal distance is a square root, and it is almost never a whole number. Measuring straight across or straight up is what the grade 6 standard actually asks for (6.G.A.3), and it is the honest version of the skill. The diagonal case is Pythagoras, and it lives in the area, perimeter and volume topic, where the triangle is drawn and labelled for it.

What if a point sits on one of the lines?

Then it is in no quadrant at all, which is why the quadrant questions never draw one there — there is no fifth answer to give. A point on an axis has a zero in it, and zero is neither positive nor negative, so it belongs to neither side. The reading questions do use those points on purpose: noticing that the x-coordinate is 0 is a genuinely useful thing to be able to say.

When does a child actually need this?

Sooner than most topics, and then permanently. Reading a graph in science, following a map reference, and every line and curve in algebra are this same skill wearing different labels. It is also unusually cheap to over-practise — the reading questions take a few seconds each — so it is worth being fluent rather than merely able.

Where this shows up

Standards

  • 5.G · Geometry
  • 6.NS · The number system
  • 6.G · Geometry
  • CCSS.MATH.CONTENT.5.G.A.1 — Use a pair of perpendicular number lines to define a coordinate system, and understand that the first number in an ordered pair says how far to travel along the x-axis and the second how far along the y-axis.
  • CCSS.MATH.CONTENT.6.NS.C.6 — Extend the number line and the coordinate axes to negative numbers, and find and position points with negative coordinates in all four quadrants.
  • CCSS.MATH.CONTENT.6.G.A.3 — Draw polygons in the coordinate plane given their vertices, and find the length of a side joining two points that share a first coordinate or a second coordinate.

Formats