Angles

Open a door just a little, so a cat can slip through. Then open it wider, wide enough for a person. Then open it all the way, flat against the wall. The door is the same size every time. So what has changed?

An amount of turn

What changes is how far the door has turned around its hinges. Look at it from above, as if you were a fly on the ceiling. The wall is a line, the door is another line, and both start at the same point: the hinge. The space between them, the amount of turn from the wall to the door, is an angle.

A door seen from above, three times. The wall is a straight line, and the door is a line that starts at the hinge. The door is open a little, then wider, then all the way to a quarter turn. The space between wall and door is coloured amber each time and grows each time

An angle is made by two rays that start at the same point. The point is where the turning happens. Clock hands make angles too: both hands start at the centre of the clock, and as the time changes, the angle between them opens and closes.

The right angle

One angle is so useful that it has its own name. Turn a door from shut until it points straight out from the wall, at the corner where floor and wall meet. That is a quarter turn: four of them would take you all the way round. The angle of a quarter turn is called a right angle.

Right angles are everywhere people build: the corner of a page, of a door, of a tile, of a window. At 3 o'clock, the hands of a clock make a right angle.

Two clocks. At 3 o'clock the hands make a right angle, like the corner of a page. At 1 o'clock the hands make a much smaller angle

You can make a right angle with any scrap of paper, even one with torn edges. Fold it once, then fold it again so the fold lies on top of itself. The corner of the folded paper is a right angle. It is a tool for testing angles.

Smaller or bigger

Put the corner of your folded paper into an angle, one edge along one line.

If the other line hides under the paper, the angle is smaller than a right angle.
If the other line runs exactly along the paper's other edge, it is a right angle.
If you can still see a gap beyond the paper, the angle is bigger than a right angle.

Three angles, each with a folded-paper corner laid in it. In the first, the second line is hidden under the paper: smaller than a right angle. In the second, the line runs along the paper's edge: a right angle. In the third, there is a gap between the paper and the line: bigger than a right angle

Two right angles side by side make a half turn, and the two lines then lie in one straight line. Four right angles make a full turn, all the way round.

Try it at home

Fold a scrap of paper twice to make a right-angle tester.
Test the corners of a book, a phone, a plate's edge and a slice of pizza. Which are right angles?
Look at a clock at 3 o'clock and at 9 o'clock. What angle do the hands make?

Answers: 1. The corner of the double fold is a right angle. 2. The book and the phone have right angles; a slice of pizza has a smaller one at its tip; a round plate has no corners at all. 3. A right angle both times.

Words to know

angle - the amount of turn between two lines that start at the same point
quarter turn - a quarter of the way round; four make a full turn
right angle - the angle of a quarter turn, like the corner of a page

Big idea

An angle measures turning, not length. The right angle, a quarter turn, is the one we compare every other angle with: smaller, the same, or bigger.