Rotate, Reflect & Identical Shapes

The official test drew an F-shape made of squares and asked how it would look after a quarter turn anticlockwise, with five pictures to choose from. Turning changes the shape's direction but not its size or its parts. Clockwise is the way clock hands move, so the top of the shape swings to the right; anticlockwise swings it to the left; a half turn puts it upside down. The fastest method is to follow one feature: the F's long top bar must end up on the right after a clockwise quarter turn, on the left after an anticlockwise one. And a tall shape becomes a wide shape after any quarter turn — that alone rules out the options that are still tall.

Quarter turns add up: two make a half turn, four bring the shape back to where it started, and three clockwise give exactly the same picture as one anticlockwise. That lets you simplify 'turned clockwise three times' to a single turn before you look at the pictures. The other idea here is the difference between turning and flipping. A shape's mirror image looks similar but is not the same shape by turning — an F turned any way still has its bars pointing the F way, while a mirror F has them pointing the other way. Test questions that ask whether shapes are 'identical' mean identical by turning, unless they say the pieces may be turned over.

The official test asked which three squares to shade so a dashed line became a line of symmetry, with the answers given as grid references. Two skills are chained. First the reflection rule: each shaded square's twin sits the same number of columns from the mirror line, on the opposite side, in the same row — count to the line, then count the same again past it. Second, naming the square correctly: column letter first, then row number, so Q3 reflects to V3, not 3V. Finish by folding the grid in your head along the line; every shaded square must land exactly on another.

A 'find the shapes that are not identical' question shows a set of shapes and a second set that should match it, and asks how many in the second set do not. Every shape has a fingerprint: how many squares, how long its longest arm is, and which side its short arm hangs off. A turned shape keeps all three. A mirror image keeps the first two but the short arm hangs off the other side — and no turn fixes that. So work through the second set one shape at a time, fingerprint it, and try to turn it into something from the first set. Count the failures. With sixteen shapes you have about four seconds each, so fingerprint rather than stare.

The official test showed a wall made of identical tiles, some rotated, and asked which of four designs the tile could be. Do not try to see the whole pattern at once. Find one tile in the wall you can see completely and note where its features sit — a corner square here, a stripe there. Turning a tile keeps those features in the same relationship to each other: a square next to a stripe stays next to it whatever the turn. So take each option, turn it in your head, and ask whether its features could ever line up the way the wall's do. Every wrong option breaks one feature; the right one survives every check. Quiz and exercises now!