ACARA v9 CONTENT DESCRIPTION “estimate, compare and classify angles as acute, right, obtuse or straight, and relate a right angle to a quarter turn and a straight angle to a half turn”
An angle is the amount of turn between two arms that meet at a point. The wider the opening, the bigger the angle, and the size is measured in degrees. A small opening like fifteen degrees is a narrow angle; a wide opening near a hundred and eighty is almost a straight line. Thinking of an angle as an amount of turn, rather than as the length of its arms, is the key idea: the arms can be drawn long or short, but the angle between them is the same. Year 4 measures, compares and names angles by this amount of turn.
An angle is a turn
An angle measures how far one arm has turned from the other, in degrees.
45 degrees: an angle is the amount of turn between two arms.
The right angle
The most important angle is the right angle: a square corner, exactly ninety degrees. It is the angle in the corner of a page, a tile or a window, and it is the benchmark every other angle is measured against. A right angle is a quarter of a full turn, the turn from facing forward to facing directly sideways. Because it is so common and so easy to recognise, the right angle is the reference point for naming all other angles — whether they are smaller than it, equal to it, or larger. Knowing a right angle on sight is the start of classifying angles.
The right angle
A right angle is a square corner, exactly 90 degrees.
This is a square corner. How many degrees is it?
Naming angles by size
Angles are named by how they compare to a right angle. An acute angle is less than ninety degrees, narrower than a square corner; a right angle is exactly ninety; an obtuse angle is more than ninety but less than a hundred and eighty, wider than a square corner but not yet a straight line. Holding an angle up against the corner of a page sorts it at once into acute, right or obtuse. These three names cover every angle from a sliver up to a straight line, and recognising which is which, by eye, is the central skill of this unit.
Acute, right or obtuse
Angles are named by size: acute under 90, right at 90, obtuse over 90.
Is this 45 degree angle acute, right or obtuse?
Comparing angles
Two angles can be compared by their openings: the one with the wider opening has more degrees, whatever the length of its arms. Forty degrees is smaller than eighty; a hundred and twenty is larger than sixty. Comparing angles means looking only at the turn between the arms, ignoring how long they are drawn, which can be misleading. This is why an angle is measured by degrees and not by the length of its sides. Putting angles side by side and judging which opens wider builds the sense of angle size that estimating and measuring both depend on.
Compare two angles
The angle with more degrees has the wider opening.
Which angle is bigger, 40 degrees or 80 degrees?
Angles on a straight line
A straight line is itself an angle: a straight angle of a hundred and eighty degrees, a half turn. Standing a line upright in the middle of a straight line makes two right angles, ninety degrees each, side by side — and ninety plus ninety is a hundred and eighty. This links the right angle to the straight angle: two right angles make a straight line, just as a quarter turn twice makes a half turn. Seeing angles add up along a line is the beginning of working with angles as measured amounts that combine, not just shapes to name.
Angles on a line
Two right angles sit on a straight line: 90 + 90 = 180 degrees.
A straight line is really an angle too. Stand a line up in the middle and see.
Every angle has a name
Pulling the unit together, every angle can be classified by its degrees: acute under ninety, right at ninety, obtuse between ninety and a hundred and eighty, straight at a hundred and eighty. A table makes the ranges plain, and the right angle anchors them all as the quarter turn, with the straight angle as the half turn. With angles seen as amounts of turn, the right angle known, angles named by size, openings compared and the straight line understood as two right angles, a child can estimate, compare and classify the angles all around them — in shapes, clocks and the turns of everyday movement.
Angle types by degrees
Each angle name matches a range of degrees: acute, right, obtuse, straight.
Each kind of angle has a degree range. Reveal each to pair them.
Quick self-check
1. A right angle, the square corner of a page, measures...
2. An angle smaller than a right angle is called...
3. An angle between 90 and 180 degrees is called...
4. Two right angles placed side by side on a line make...
5. The hands of a clock at 3 o’clock form an angle that is...