Slides, Turns and Flips

Pick up a book from your table and put it down somewhere else. Maybe you pushed it along, maybe you spun it round, maybe you turned it face down. The book is still the same book: no longer, no wider. Mathematicians count three ways of moving a shape like that. What are they, and what stays the same?

Slide

A slide moves every point of a shape the same distance in the same direction. Nothing turns: the shape still points the same way. On a grid you can say exactly how far it went, for example 4 squares across and 1 square up. Mathematicians call a slide a translation.

Turn

A turn spins the shape round one fixed point, by an angle: a quarter turn (90°), a half turn (180°) and so on. The fixed point doesn't move, and every other point travels round it in a circle. The hands of a clock turn about the centre of the clock. The mathematicians' word is rotation.

Flip

A flip reflects the shape in a mirror line, as if you picked it up and put it down face down on the other side of the line. Each point lands on the other side, just as far from the line as it was. A flip is the only one of the three moves that changes which way round a shape is. Its other name is reflection.

Three grids, each with a blue flag shape and an amber copy. Slide: the copy is 4 squares to the right and 1 up, pointing the same way. Turn: the copy has been turned a quarter turn about a dot at the foot of the pole. Flip: the copy is the mirror image of the flag on the other side of a dashed mirror line

Left and right

Your left footprint can be slid anywhere on the beach and turned any way you like, and it is still a left footprint. To get a right footprint, you need a flip. That is why a left shoe never fits a right foot: it is the same shape, but the wrong way round.

A left footprint and a right footprint on either side of a dashed mirror line: each one is the flip of the other

Same shape, same size

A slide, a turn and a flip all move a shape without stretching, shrinking or bending it. Every side keeps its length and every angle its size. Two shapes that match exactly like that, when one is moved onto the other, are called congruent. The tiles on a floor are congruent: one tile, slid and turned, again and again.

Try it at home

Cut a shape like a flag from card. Draw round it, slide it, draw round it again. Do the same with a turn and a flip.
Put your left hand flat on a table. Can you slide and turn your right hand to fit exactly on it, palm down too?

Answers: 2. No. Your right hand is a flip of your left hand. To match them, one would have to be face up.

Words to know

slide (translation) - every point moves the same distance in the same direction
turn (rotation) - the shape spins about a fixed point by an angle
flip (reflection) - the shape is reflected in a mirror line
congruent - the same shape and the same size

Big idea

A shape can be moved by a slide, a turn or a flip without changing it. The copy is congruent to the original: the same shape and size. Only a flip changes which way round it is.