NCERT Class 5 Maths · Chapter 3
Angles as Turns
Full, half, and quarter turns; right, acute, obtuse, and straight angles; clockwise and anti-clockwise. Learn it all by moving your own body!
📌 What you’ll learn in this chapter
- What full, half, and quarter turns are
- How a turn makes an angle
- Right, acute, obtuse, and straight angles
- How to make and use your own angle measuring tool (⅛, ⅙, and 1/12 turns)
- Clockwise and anti-clockwise directions
🔄 Let’s Begin: Turn Around!
In the PT period, Sir says, “Everyone face the blackboard. Now turn right!” Everyone faces the window. “Turn right again!” Now they face the back wall. “Again!” Now the door. “Once more!” And they’re back facing the blackboard. 😄
You just made 4 quarter turns, which is 1 full turn. Turns are all around us: a fan blade, a steering wheel, a door opening, the hands of a clock, and a spinning top (lattu).
| Turn | What it means | Real-life example |
|---|---|---|
| Full turn | You come back to where you started | A lattu spinning once |
| Half turn (½) | You face the opposite side | Turning to see who is behind you |
| Quarter turn (¼) | Half of a half turn | Turning from the front door to face a side wall |
| Three-quarter turn (¾) | 3 quarter turns | The minute hand going from 12 to 9 |
💡 Adding turns
2 quarter turns = 1 half turn · 2 half turns = 1 full turn · 4 quarter turns = 1 full turn
📐 Part 1: Turns Make Angles
Take two pencils and hold them together at one end. Keep one pencil still and turn the other. The opening between them is an angle. The bigger the turn, the bigger the angle.
| Amount of turn | Name of angle | Looks like |
|---|---|---|
| Less than ¼ turn | Acute angle | Open mouth of a crocodile clip, a slice of pizza tip |
| Exactly ¼ turn | Right angle | Corner of your notebook, the letter L |
| Between ¼ and ½ turn | Obtuse angle | A laptop screen pushed back, a reclining chair |
| Exactly ½ turn | Straight angle | An open book lying flat, a straight road |
💡 Quick check with your notebook corner
Put the corner of a notebook into the angle. If the angle fits inside the corner, it’s acute. If it matches exactly, it’s a right angle. If it’s wider, it’s obtuse.
⚠️ Common mistake
Thinking that longer arms make a bigger angle. ❌
✅ The size of an angle depends only on how much it has turned, not on how long the lines are.
✅ The size of an angle depends only on how much it has turned, not on how long the lines are.
🧰 Part 2: Your Own Angle Measuring Tool
Take a circle of tracing paper (or roti-shaped paper). Fold it in half, then half again, then half again. Open it and you’ll see 8 equal parts. Each part is a ⅛ turn.
- ⅛ turn = half of a right angle
- 2/8 turn = ¼ turn = right angle
- 4/8 turn = ½ turn = straight angle
- 6/8 turn = ¾ turn
- 8/8 turn = full turn
Now fold another circle in half and then into 3 equal parts. You get 6 equal parts, and each is a ⅙ turn. Fold one ⅙ part in half and you get a 1/12 turn.
Example: A ⅛ turn and a ¼ turn together make ⅛ + 2/8 = 3/8 turn. That’s more than ¼ but less than ½, so it’s an obtuse angle.
Example: ⅙ + 1/12 = 2/12 + 1/12 = 3/12 = ¼ turn, a right angle!
🕒 Part 3: Turns on a Clock
The minute hand takes 60 minutes to make a full turn. So:
| Minutes moved | Turn |
|---|---|
| 5 minutes | 1/12 turn |
| 10 minutes | 2/12 = ⅙ turn |
| 15 minutes | ¼ turn |
| 30 minutes | ½ turn |
| 45 minutes | ¾ turn |
| 60 minutes | Full turn |
💡 Clock trick
Each number on a clock is a 1/12 turn apart and is worth 5 minutes.
↻ Part 4: Clockwise and Anti-clockwise
The direction in which clock hands move is clockwise ↻. The opposite direction is anti-clockwise ↺.
- Tightening a bottle cap or a screw: usually clockwise
- Opening a bottle cap, tap, or nut: usually anti-clockwise
Turns and directions
Imagine you face North. A ¼ turn clockwise makes you face East. Another ¼ turn clockwise and you face South. Another and you face West.
Example: Tanu faces East and makes 3 right-angle turns anti-clockwise. East → North → West → South.
Shortcut: 3 turns anti-clockwise is the same as 1 turn clockwise! East → South ✅
❌ Common Mistakes to Avoid
Calling a straight line “no angle”
✅ A ½ turn makes a straight angle.
✅ A ½ turn makes a straight angle.
Mixing up the directions
✅ Clockwise = the way clock hands move.
✅ Clockwise = the way clock hands move.
Thinking two acute angles always make an acute angle
✅ They can make a right or even an obtuse angle.
✅ They can make a right or even an obtuse angle.
Counting turns from the wrong starting line
✅ Always mark the starting position first.
✅ Always mark the starting position first.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
Q1. Name the angle: (a) corner of a door (b) the hands of a clock at 2:00 (c) the hands at 4:00
✅ Answer(a) Right angle (b) Acute (2/12 turn = ⅙) (c) Obtuse (4/12 = ⅓ turn, more than ¼)
Q2. How many ⅛ turns make a ¾ turn?
✅ Answer¾ = 6/8, so 6
Q3. The minute hand moves from 12 to 8. What part of a turn is this? How many minutes?
✅ Answer8/12 = ⅔ turn, and 8 × 5 = 40 minutes
Q4. Ravi faces West. He takes a half turn clockwise. Which direction does he face now?
✅ AnswerEast (a half turn always makes you face the opposite side)
Q5. Is ⅙ + ⅙ turn acute, right, or obtuse?
✅ Answer2/6 = ⅓ turn. That’s more than ¼ and less than ½, so it’s obtuse.
Q6. In which direction do you turn a key to lock most doors?
✅ AnswerIt depends on the lock, but most locks close with a clockwise turn. Try it at home and check!
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Page 33 · Reema’s turnsAdding turns and everyday objects
✅ Answer
Two half turns = a full turn. Two quarter turns = a half turn. Four quarter turns = a full turn.
Objects with turns: taps, doors, fans, bottle lids, door handles, scissors, a screw.
Maximum turn: Clothes clip: less than ¼ · Tongs: less than ¼ · Scissors: usually less than ¼ (can open wider with force) · Door with hinge: more than ¼ · File cover: more than ¼ (it can open flat, a ½ turn).
A file cover can make a half turn. None of these makes a full turn, but a tap or a fan can!
Pages 34–35 · Straws and fanObjects with turns: taps, doors, fans, bottle lids, door handles, scissors, a screw.
Maximum turn: Clothes clip: less than ¼ · Tongs: less than ¼ · Scissors: usually less than ¼ (can open wider with force) · Door with hinge: more than ¼ · File cover: more than ¼ (it can open flat, a ½ turn).
A file cover can make a half turn. None of these makes a full turn, but a tap or a fan can!
Can two acute turns make another acute turn?
✅ AnswerSometimes. Two small acute turns (like ⅛ + 1/12) together stay acute. But two bigger acute turns (like ⅙ + ⅙ = ⅓) become obtuse. Two ⅛ turns make exactly a right angle.
Page 35 · (b) Cardboard houseAngles in the house
✅ AnswerUse your notebook corner to test each marked angle. The pointed roof top (A) is narrow, so it’s acute. The corners where walls meet the floor and the flat roof are right angles. The slanted walls that open wide make obtuse angles. Compare with your classmates, since the picture is small.
Page 35 · (c) 5-sided shape2 right, 2 obtuse, 1 acute
✅ AnswerDraw a “house with a sharp roof”: two right-angle corners at the bottom, two walls going up and then slanting inward (these corners are obtuse), and a narrow pointed top (acute). Check each corner with the notebook corner.
Page 36 · (d) GymnastsAngles between the legs
✅ AnswerLegs slightly apart: acute. Legs apart like an L: right. Legs wide apart but not flat: obtuse. Full split in a straight line: straight. In the first picture, the angle is acute. In the second, it is a right angle.
Page 36 · Angle measuring toolTurns with the ⅛ tool
✅ Answer2/8 turn = a right angle (¼ turn). 4/8 turn = a straight angle (½ turn). 6/8 = ¾ turn. 8/8 = a full turn.
Page 37 · Let Us ThinkFind the starting points
✅ AnswerFrom the end point, count back: for a ½ turn, the start is on the opposite side of the circle. For a ⅛ turn, go back one-eighth (half of a right angle). For a ¼ turn, go back one right angle. Half of a ⅙ turn is a 1/12 turn.
Page 38 · Let Us Do, Q1–Q3Guess and measure
✅ Answer
Q1: Place your tools on each angle. Narrow angles (smaller than ¼) are acute, angles matching the notebook corner are right, and wider ones are obtuse.
Q2: (b) ½ + ⅛ = ⅝ turn · (c) ⅛ turn · (d) the arrow starts at ⅛ and stops just after ½, about 5/12 turn (a bit less than ½)
Q3: In the triangle (a), all three angles are acute. In shapes (b) and (c), the wide angles are obtuse, the narrow ones are acute, and F’ (marked with a square) is a right angle.
Page 39 · Q4, Q5Q2: (b) ½ + ⅛ = ⅝ turn · (c) ⅛ turn · (d) the arrow starts at ⅛ and stops just after ½, about 5/12 turn (a bit less than ½)
Q3: In the triangle (a), all three angles are acute. In shapes (b) and (c), the wide angles are obtuse, the narrow ones are acute, and F’ (marked with a square) is a right angle.
Drawing angles
✅ AnswerUse your tools: ¼ turn = right angle · ½ = straight line · ⅛ = half a right angle · 1/12 = half of a ⅙.
In Q5: 2/4 = ½ turn (straight) · 4/6 = ⅔ turn (more than a straight angle) · ½ + ¼ = ¾ turn · ⅛ + ⅙ = 7/24 turn (a little more than ¼, obtuse).
Pages 39–40 · Q6 ClockIn Q5: 2/4 = ½ turn (straight) · 4/6 = ⅔ turn (more than a straight angle) · ½ + ¼ = ¾ turn · ⅛ + ⅙ = 7/24 turn (a little more than ¼, obtuse).
Minute hand turns
✅ Answer(a) 15 min = ¼ turn (b) 30 min = ½ turn (c) 45 min = ¾ turn (d) 1/12 turn = 5 minutes (e) full turn = 60 minutes (f) ⅙ turn = 10 minutes (g) 4/12 turn = 20 minutes
Page 40 · Which direction?Creatures making a quarter turn
✅ AnswerLadybird (facing left → facing up): clockwise. Bee (facing left → facing down): anti-clockwise. Ant (facing up → facing left): anti-clockwise. For the snail, follow where its head points and check which way it moved around the clock.
Try these: Opening a tap, unscrewing a lid, and loosening a nut are usually anti-clockwise.
Page 41 · Fun with TurnsTry these: Opening a tap, unscrewing a lid, and loosening a nut are usually anti-clockwise.
Direction table and Padma
✅ Answer
(The number before “right angles” is missing in the last row. If it is 2, the two turns cancel out and she faces West again.)
Padma: After a half turn clockwise, she faces the ice cream cart (the place behind her). She can also take a half turn anti-clockwise to face the same place.
| Start | Turns | End |
|---|---|---|
| North | 2 right angles clockwise | South |
| South | 2 right angles anti-clockwise | North |
| East | 4 right angles anti-clockwise | East |
| West | 4 right angles clockwise | West |
| North | 5 right angles clockwise | East |
| South | 3 + ½ + ½ = 4 right angles clockwise | South |
| West | 2 right angles clockwise, then four ½ right angles (= 2 right angles) anti-clockwise | West |
Padma: After a half turn clockwise, she faces the ice cream cart (the place behind her). She can also take a half turn anti-clockwise to face the same place.
👨👩👧 Tips for Parents
- Play “Statue” at home: ask your child to make a quarter, half, or three-quarter turn.
- Hunt for angles in the house: door corners (right), a half-open door (acute), and a laptop screen (obtuse).
- Use a wall clock: “The minute hand moved from 3 to 6. What turn is that?”