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A graph answers questions you never calculated, if you can read it. Learn how to go from an x value to its y value, and find three of them in a playground.

A graph is not a picture of an equation — it is every solution of it, plotted at once. Learn what the line means and match three equations in a playground.

A graph is straight when the rise per step never changes. Learn what steepness means, what a downward line says, and match three steps in a playground.

Area is not a formula to remember — it is a count of the squares that fit inside a shape. Once you can see the squares, length × width stops being a rule and becomes the fastest way to count rows. Match each multiplication to the rectangle it describes in an interactive playground.

A square is a rectangle whose sides happen to match, so its area is still a count of the squares inside it — you just only need to measure once. That is why it is written s², and why area and square numbers are the same idea. Pick the real squares out of a grid in an interactive playground.

Every triangle fits inside a rectangle and fills exactly half of it. That single fact is where the half-base-times-height formula comes from, and seeing it means you never have to trust the formula again. Match each triangle to its area on an interactive grid.

A circle has no sides to measure, so everything is measured from its centre instead. The radius reaches out to the edge, the diameter crosses the whole way through, and telling them apart is what every circle calculation depends on. Place each name on a real circle in an interactive playground.

A circle has no rows of squares to count, so its area is measured against a square built on its own radius. It always holds a little over three of them, and that little-over-three is pi. Match each circle to its area on an interactive grid.

Every shape you will ever meet is built from four ideas, and they differ in nothing except whether they end. A point has no size, a line never stops, a segment stops twice and a ray stops once. Tell them apart on a real drawing in an interactive playground.

Two straight lines on a flat page either cross somewhere or never do — there is no third option. Parallel means the gap never changes, which is a claim you can check by measuring in two places rather than trusting your eye. Sort real pairs of lines in an interactive playground.

A right angle is a quarter turn, and two lines that cross at one are perpendicular. It is the one angle buildings, screens, paper and tiles are all built around, which is why a crossing that is nearly square is a problem rather than a near-enough. Pick the true right angles out of six crossings.

An angle is not the corner and it is not the two lines — it is the amount of turning between them. That is why a long arm and a short arm can hold exactly the same angle, and why stretching a drawing changes nothing. Name the parts of a real angle in an interactive playground.

Every angle there is falls into one of five kinds, and the boundaries are set by two landmarks: the quarter turn and the half turn. Once those are fixed, acute, right, obtuse, straight and reflex sort themselves. Match five sizes to the angles that show them in an interactive playground.

A polygon has to pass two tests: every side straight, and the outline joined up. Pass both and the shape earns a name, and the name is nothing more than how many sides it has. Sort real shapes from near-misses in an interactive playground.

Square, rectangle, rhombus, parallelogram and trapezium are not five separate boxes to sort shapes into — they are conditions, and a shape can satisfy several at once. That is why every square is also a rectangle. Match each name to the shape that earns it on a grid.

Perimeter is the distance around the outside of a shape — the fence, not the grass. It is measured in lengths rather than squares, which is the whole of what separates it from area. Walk six shapes round the edge and match each to its perimeter on a grid.

Once a circle has a centre and a radius, the rest of its vocabulary describes pieces: a straight cut across it, a stretch of its edge, a wedge from the middle and the cap left over. Place all four on real circles in an interactive playground.

A line of symmetry is a fold that makes both halves land exactly on top of each other. Cutting a shape into two equal halves is not the same thing, which is why a parallelogram has no lines of symmetry at all. Count the folds on six shapes in an interactive playground.

A solid shape is described by three counts: its flat surfaces, the lines where they meet, and the corners. Counting them is easy once you remember the ones hidden round the back. Match each set of counts to the solid it belongs to in an interactive playground.

Eight planets, in an order that never changes, and the two most people mix up look nearly identical. Learn the single feature that gives each planet away, then label all eight yourself in an interactive playground.