Discover Mathematics P4: Term 2, Unit 13, Lessons 1–4
GoalMeasure turns in degrees: a quarter turn is 90°, a half turn 180° and a full turn 360°.
New words
degree (°) · the unit for measuring angles and turnsfull turn · a turn all the way round back to the start, 360°quarter turn · a quarter of a full turn; it makes a right angle, 90°
Explanation
We measure how far something turns with a unit called the degree, written °. A full turn, all the way round to where you started, is 360°. A half turn is half of that: 360° ÷ 2 = 180°, and it makes a straight angle. A quarter turn is 360° ÷ 4 = 90°, and it makes a right angle. Three quarter turns make 3 × 90° = 270°. An angle is the amount of turning between its two arms. A bigger turn means a bigger angle. If a turn is split into equal smaller turns, we can find the size of each one by dividing: a full turn of 360° made of 12 equal turns gives 360° ÷ 12 = 30° each.
Turn
quarter
half
three-quarter
full
Fraction of a circle
1/4
1/2
3/4
1
Degrees
90°
180°
270°
360°
Worked examples
Mariam stands facing the door and turns. A quarter turn is 90°. Two quarter turns make a half turn: 90° + 90° = 180°, and she faces the opposite way. Four quarter turns make a full turn: 4 × 90° = 360°, and she faces the door again.
How many equal turns make a full turn? 360° ÷ 90° = 4, so four 90° turns. And 360° ÷ 30° = 12, so twelve 30° turns. The picture shows a circle cut into 12 equal turns of 30° each, like the hours on a clock.
Omar turns his chair by three quarter turns. The total turn is 3 × 90° = 270°. That is a full turn of 360° less one quarter turn: 360° − 90° = 270°. The angle shown is larger than a straight angle.
Class activity
Turning game. Stand up and face a wall. A grown-up calls out a turn, for example: quarter turn to the right, half turn, or three quarter turns. Say how many degrees you turned and which wall you face now. After four quarter turns you must face the first wall again. Why?
Practice
1
A turn of 180° is what fraction of a full turn?
One half, 1/2, because 180° is half of 360°.
2
What fraction of a full turn is 90°?
90° out of 360° is one quarter, 1/4.
3
A wheel makes 3 quarter turns. How many degrees is that?
