Turns as fractions of a full turn
When you spin on one spot and come back to face the same way, you have made a full turn. Turn only until you face the side wall: that is a quarter turn. Playing "statue" is all about how much you turned.
A turn is a fraction of a full circle. Full turn = 1, half turn = 1/2, quarter turn = 1/4, three-quarter turn = 3/4. Smaller turns: 1/8 (half of a quarter), 1/6 and 1/12.
Formula: Total turn = turn 1 + turn 2 (same direction). Turn left to complete = 1 − turn done.
In the figure: The green line is where we start. The red line shows where we stop. The shaded part is the turn: 1/4, 1/2, 3/4 and a full turn (1).
Rule 1: Add turns in the same direction — Two or more turns in the same direction add up like fractions.
Turns as fractions of a full turn
In the app you can move this figure with your finger.
Open in the app- Easy: 1/2 + 1/4 = 3/4 turn.
- Medium: 1/4 + 1/8 = 2/8 + 1/8 = 3/8 turn.
- Exam-type: 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 turn.
Rule 2: Parts that make a full turn — How many small turns of 1/n make a full turn? Exactly n of them.
- Easy: 4 quarter turns = 1 full turn.
- Medium: 2 turns of 1/8 make a 1/4 turn, and 4 of them make a 1/2 turn.
- Exam-type: 6 turns of 1/6 make a full turn; 12 turns of 1/12 make a full turn.
Half of a quarter turn is 1/8 turn, and half of a 1/6 turn is 1/12 turn. Turns are fractions — compare and add them like fractions.
Adding the denominators: 1/4 + 1/8 = 2/12. Wrong! Make the denominators the same first: 2/8 + 1/8 = 3/8.
Think of a pizza: 8 slices = a full turn. A quarter turn = 2 slices, half turn = 4 slices. Memory clue: "Start line, stop line — the shaded slice is your turn."
Spot the difference
| Point | Quarter turn | Half turn |
|---|---|---|
| As a fraction | 1/4 | 1/2 |
| How many make a full turn | 4 | 2 |
Practice questions
- 1How many quarter turns make a full turn?
- 2Two half turns in the same direction make how much turn?
- 3What is half of a 1/4 turn?
- 4A pointer turns 1/2 and then 1/4 in the same direction. Total turn?
- 5A wheel has turned 5/8 of a full turn. How much more to complete the turn?
- 6How many turns of 1/12 make a quarter turn?
- 71/4 turn followed by 1/8 turn gives what total?
- 8Which is bigger: a 2/3 turn or a 3/4 turn? Give the reason.
Show answers (try them yourself first)
- 14
- 21 (a full turn)
- 31/8
- 43/4
- 53/8
- 63
- 73/8
- 83/4: 3/4 = 9/12 and 2/3 = 8/12.
Acute, right, obtuse and straight angles
Open a pair of scissors a little: small angle. Open a door fully against the wall: a big angle. A turn between two lines creates an angle, so angles arise wherever there is a turn.
Acute: less than a quarter turn. Right: exactly a quarter turn. Obtuse: more than a quarter but less than a half turn. Straight: exactly a half turn. Beyond a half turn the angle is more than a straight angle.
Formula: turn < 1/4 acute; = 1/4 right; between 1/4 and 1/2 obtuse; = 1/2 straight; more than 1/2 → more than straight.
In the figure: The black line is the fixed arm. The coloured arm turns away from it: a little (acute), a quarter (right), more (obtuse) and half (straight).
Rule 1: Name the angle from the turn — Compare the turn with 1/4 and 1/2 to find the kind of angle.
Acute, right, obtuse and straight angles
In the app you can move this figure with your finger.
Open in the app- Easy: 1/8 turn is less than 1/4: acute.
- Medium: 3/8 turn is between 1/4 (2/8) and 1/2 (4/8): obtuse.
- Exam-type: 3/4 turn is more than 1/2: more than a straight angle.
Rule 2: Angles in everyday objects — A notebook corner is a right angle; a slightly open clothes clip is acute; a wide-open book can be obtuse or straight.
- Easy: Clock hands at 3 o'clock: right angle.
- Medium: Clock hands at 6 o'clock: straight angle.
- Exam-type: 2 right angles together = a straight angle.
The kind of angle depends only on how much the arm turns, not on how long the arms are drawn.
Thinking a longer drawn arm means a bigger angle. The angle is the amount of turn only.
Use the corner of your notebook as a right-angle checker: smaller = acute, bigger = obtuse. Memory clue: A-C-O-S: Acute (small), Corner (right), Open wide (obtuse), Straight line.
Spot the difference
| Point | Acute | Obtuse |
|---|---|---|
| Turn | less than 1/4 | between 1/4 and 1/2 |
| Example | 1/8 | 3/8 |
Practice questions
- 1Name the angle made by a 1/4 turn.
- 2Name the angle made by a half turn.
- 3Is a 1/12 turn acute, right or obtuse?
- 4How many right angles make a straight angle?
- 5Name the angle made by a 5/12 turn.
- 6Which angle is made by 3/4 turn?
- 7Can two acute angles add up to a right angle? Give an example.
- 8A right angle plus a 1/8 turn: what turn and which kind of angle?
Show answers (try them yourself first)
- 1Right angle
- 2Straight angle
- 3Acute
- 42
- 5Obtuse (5/12 is more than 3/12 = 1/4 and less than 6/12 = 1/2)
- 6More than a straight angle
- 7Yes: 1/8 + 1/8 = 1/4.
- 81/4 + 1/8 = 3/8 turn, an obtuse angle.
Turns of the clock hands
The minute hand of a wall clock goes round and round all day. When it goes from 12 to 3 it has moved 15 minutes and made a quarter turn. We can read minutes as turns.
One full turn of the minute hand = 60 minutes. So a turn of 1/n of a full turn is 60 ÷ n minutes. The clock face has 12 equal parts, each worth 5 minutes (a 1/12 turn).
Formula: turn = minutes ÷ 60. minutes = turn × 60.
In the figure: From 12 to 3 the minute hand covers 15 minutes, which is 15/60 = 1/4 of a full turn.
Rule 1: Minutes to turn — Write the minutes over 60 and simplify.
Turns of the clock hands
In the app you can move this figure with your finger.
Open in the app- Easy: 30 minutes = 30/60 = 1/2 turn.
- Medium: 10 minutes = 10/60 = 1/6 turn.
- Exam-type: From 8:15 to 8:50 is 35 minutes = 35/60 = 7/12 turn.
Rule 2: Turn to minutes — Multiply the turn by 60.
- Easy: 1/12 turn = 60 ÷ 12 = 5 minutes.
- Medium: 1/3 turn = 60 ÷ 3 = 20 minutes.
- Exam-type: 2/3 turn = 2 × 20 = 40 minutes.
In 1 hour the minute hand makes 1 full turn; in 2 hours, 2 full turns. The hour hand takes 12 hours for a full turn.
Reading the number 3 as 3 minutes. The number 3 on the dial means 15 minutes (3 × 5).
Number on the dial × 5 = minutes, and number ÷ 12 = turn. Memory clue: 3 → quarter, 6 → half, 9 → three-quarter, 12 → full.
Spot the difference
| Point | 15 minutes | 45 minutes |
|---|---|---|
| Turn | 1/4 | 3/4 |
| Hand points to | 3 | 9 |
Practice questions
- 1How much turn is 15 minutes?
- 2How many minutes make a 1/2 turn?
- 3How many minutes make a 1/6 turn?
- 4The minute hand goes from 12 to 8. What turn?
- 5The minute hand goes from 3:10 to 3:40. What turn?
- 6How many full turns does the minute hand make in 4 hours?
- 7The minute hand turns 5/12 of a full turn. How many minutes?
- 8A class starts at 9:00 and ends at 9:45. What turn does the minute hand make?
Show answers (try them yourself first)
- 11/4
- 230
- 310
- 48/12 = 2/3
- 530 minutes = 1/2 turn
- 64
- 725
- 845/60 = 3/4 turn
Clockwise and anti-clockwise directions
Tighten a bottle cap and you turn it one way; open it and you turn it the other way. A turn needs a direction as well as an amount.
The way the hands of a clock move is clockwise. The opposite way is anti-clockwise. On a compass, a clockwise quarter turn goes North → East → South → West → North.
Formula: Clockwise: N → E → S → W. Anti-clockwise: N → W → S → E.
In the figure: Facing North, a quarter turn clockwise makes you face East.
Rule 1: Count quarter turns — Each clockwise quarter turn moves to the next direction in N → E → S → W. Anti-clockwise goes backwards.
Clockwise and anti-clockwise directions
In the app you can move this figure with your finger.
Open in the app- Easy: Facing South, 1/4 turn clockwise → West.
- Medium: Facing East, a half turn (either way) → West.
- Exam-type: Facing North, 3/4 turn anti-clockwise → East.
Rule 2: Same place, two ways — A clockwise turn of x gives the same direction as an anti-clockwise turn of 1 − x.
- Easy: 1/4 clockwise = 3/4 anti-clockwise.
- Medium: 3/4 clockwise = 1/4 anti-clockwise.
- Exam-type: 1/2 clockwise = 1/2 anti-clockwise.
Tightening is clockwise; loosening or opening a lid is anti-clockwise. A full turn brings you back to where you started.
Mixing up the order: clockwise from North is East (not West).
Stand up and really turn: your body shows clockwise (like clock hands, to your right) and anti-clockwise (to your left). Memory clue: "Never Eat Soggy Waffles" → North, East, South, West, going clockwise.
Spot the difference
| Point | Clockwise | Anti-clockwise |
|---|---|---|
| From North, 1/4 turn | East | West |
| Everyday use | Tightening a nut | Opening a lid |
Practice questions
- 1Facing North, a 1/4 turn clockwise: which direction?
- 2Facing East, a half turn: which direction?
- 3Facing South, a 1/4 turn anti-clockwise: which direction?
- 4In which direction do you turn a lid to open it?
- 5Facing West, a 3/4 turn clockwise: which direction?
- 6Facing North, 1/4 turn clockwise is the same as how much turn anti-clockwise?
- 7Facing South, Ravi makes a 1/2 turn clockwise and then a 1/4 turn anti-clockwise. Which direction does he face?
- 8A tap is turned 1/4 turn clockwise and then 3/4 turn clockwise. How much total turn, and where does the handle end up?
Show answers (try them yourself first)
- 1East
- 2West
- 3East
- 4Anti-clockwise
- 5South
- 63/4
- 7West (South → half turn → North → 1/4 anti-clockwise → West)
- 81/4 + 3/4 = 1 full turn; the handle is back at the start.