ACARA v9 CONTENT DESCRIPTION “estimate, construct and measure angles in degrees, using appropriate tools including a protractor, and relate these measures to angle names”
Builds on recognising angles as an amount of turning and identifying right angles. Year 5 measures angles properly: in degrees, using a protractor to measure and construct them, estimating their size by eye, and relating those measures to the names acute, right, obtuse, straight and reflex. Being able to estimate, measure and name an angle turns a vague sense of how open a corner is into an exact figure that can be compared and constructed.
Angles and their names
An angle measures the amount of turn between two arms meeting at a point called the vertex. Angles are named by their size. An acute angle is smaller than a right angle; a right angle is a square corner, marked with a small square; an obtuse angle is larger than a right angle but less than a straight line; a straight angle is a straight line; and a reflex angle is larger than a straight angle. Naming an angle is the first way to describe it, before any measuring, simply by comparing it to a right angle and a straight line.
Angles and their names
Acute, right, obtuse, straight or reflex.
What kind of angle is this?
Measuring angles in degrees
Angles are measured in degrees. A full turn, all the way around, is three hundred and sixty degrees, so a half turn, a straight angle, is one hundred and eighty degrees, and a quarter turn, a right angle, is ninety degrees. The degree is the unit that gives every angle an exact size, so that two angles can be compared precisely rather than just by eye. Knowing these benchmarks, ninety for a right angle and one hundred and eighty for a straight angle, anchors the whole scale and makes other angles easy to judge.
Measuring angles in degrees
A full turn is 360; a right angle 90; a straight angle 180.
Degrees give every angle an exact size; 90 for a right angle and 180 for a straight angle anchor the scale.
Estimating an angle
Before measuring, it is useful to estimate an angle by eye, using the benchmarks. An angle a little smaller than a square corner is around sixty degrees; one a little larger, around one hundred and twenty. Comparing an angle to a right angle of ninety degrees and to a straight angle of one hundred and eighty gives a sensible estimate, and estimating first is a good habit because it catches mistakes: a measurement far from the estimate is a sign that something has gone wrong. A good estimate is rarely exact, but it should be close.
Estimating an angle
Judge by eye against 90 and 180 degrees.
Estimate this angle in degrees.
Using a protractor
A protractor measures angles exactly. It is a half-circle marked from zero to one hundred and eighty degrees. To measure an angle, the centre of the protractor is placed on the vertex and the zero line along one arm, and the size is read where the other arm crosses the scale. To construct an angle of a given size, the same setup is used in reverse, marking the point at the required degree and drawing the arm to it. Reading the correct scale, since most protractors have two, is the key to measuring accurately.
Using a protractor
Centre on the vertex, zero on one arm, read the other.
Read the angle from the protractor.
Naming angles from their size
Once an angle is measured, its size tells its name. An angle between zero and ninety degrees is acute; exactly ninety degrees is a right angle; between ninety and one hundred and eighty is obtuse; exactly one hundred and eighty is a straight angle; and more than one hundred and eighty is reflex. So an angle of fifty degrees is acute, one of one hundred and thirty degrees is obtuse, and one of two hundred degrees is reflex. The name and the measure describe the same angle, one in words and one as a number, and moving between them shows a full understanding of the angle.
Naming angles from their size
The measure in degrees gives the name.
Name the angle from its measure in degrees.
Working with angles confidently
Working with angles confidently means putting these skills together: name an angle by comparing it to a right angle and a straight line, measure it in degrees with a protractor, estimate its size first to check the measurement, and relate the degrees back to the name. The benchmarks of ninety and one hundred and eighty degrees guide both estimating and naming. With these habits a child can estimate, measure, construct and name any angle, ready for the geometry and the angle relationships of later years.
Quick self-check
1. An angle smaller than a right angle is called...
2. A right angle measures...
3. A full turn, all the way around, is...
4. The tool used to measure angles in degrees is a...