NCERT Solutions for Class 5th Maths Chapter 3 Turning to face a direction — Fun with Turns
Book page 40–41 Updated on2026-09-19
Q1.
The children in a class are playing a game in which the teacher tells them the direction in which they should rotate. Complete the table by filling the direction the children will face on completing the given turns. The starting direction is given in the table.
Starting Direction
Turns
Ending Direction
North
Two right angles, clockwise
South
Two right angles, anti-clockwise
East
Four right angles, anti-clockwise
West
Four right angles, clockwise
North
5 right angles, clockwise
South
3 right angles clockwise, 1/2 right angle clockwise, 1/2 right angle clockwise
West
…… right angles clockwise, four 1/2 right angles anti-clockwise
The table printed on page 41, with the compass rose given beside it. The last column is yours to fill. In the last row the book does not print how many right angles to turn clockwise — that number is missing in the book.
Answer
Two things make every row easy.
One right angle = a quarter turn, and a quarter turn moves you exactly one direction round: N → E → S → W → N going clockwise, and N → W → S → E → N going anti-clockwise.
Four right angles = a full turn, which changes nothing. So if you are told 5 right angles, throw away 4 of them and only 1 is left to do.
Starting Direction
Turns
Ending Direction
North
Two right angles, clockwise
South
South
Two right angles, anti-clockwise
North
East
Four right angles, anti-clockwise
East
West
Four right angles, clockwise
West
North
5 right angles, clockwise
East
South
3 right angles clockwise, 1/2 right angle clockwise, 1/2 right angle clockwise
South
West
(number missing in the book) right angles clockwise, four 1/2 right angles anti-clockwise
see the note
Row by row
North, 2 right angles clockwise. North → East (1st) → South (2nd). South.
South, 2 right angles anti-clockwise. South → East (1st) → North (2nd). North.
East, 4 right angles anti-clockwise. 4 right angles is a full turn. East.
West, 4 right angles clockwise. Again a full turn. West.
North, 5 right angles clockwise. 5 = 4 + 1. The 4 bring you back to North, then 1 more takes you to East.
South, 3 right angles clockwise + 1/2 + 1/2 right angle clockwise. The two halves join to make 1 whole right angle, so this is 4 right angles — a full turn. South.
West, ? right angles clockwise, four 1/2 right angles anti-clockwise. See the note below — a number is missing in the printed book.
Row 1: from North, two right angles clockwise brings you to South.Row 5: 5 right angles clockwise from North is the same as 1 right angle — you end facing East.
Working out the last row: four 1/2 right angles = 4 × 1/2 = 2 right angles anti-clockwise 2 right angles anti-clockwise = a half turn, so West → East If the missing number is 2, then 2 right angles clockwise takes West → East first, and the half turn back takes East → West.
Something odd in the book: In the last row the number of right angles to turn clockwise has been left out in printing — the cell begins straight away with “right angles clockwise”. Ask your teacher which number was meant. Whatever it is, the rule is the same: count the clockwise right angles, take away the anti-clockwise ones, throw away every complete set of 4, and turn by what is left.
Why it happens: There are only four directions on this compass, so turning is like moving round a square of four corners. After every 4 quarter turns you are back at the same corner — which is why only the remainder matters.
Q2.
Padma is facing the toy shop. What place will she face if she takes a half turn clockwise?
Answer
She will face the ice cream cart.
Look at the picture from above.
Padma is standing in the middle of the street.
The toy shop (Toy Dukan) is straight in front of her.
The ice cream cart is straight behind her.
A half turn makes you face the exact opposite way.
So the thing that was behind her comes in front — the ice cream cart.
A half turn: whatever was behind you is now in front of you.
Why it happens: A half turn is 2 right angles, or half of a full circle. It always swaps front with back — and it leaves left and right swapped too.
Check it yourself: Stand facing the blackboard. Take a half turn. You are now facing the back of the classroom — the wall that was behind you.
Q2.
What other way can she turn to face the same place?
Answer
She can take a half turn anti-clockwise instead. She will face the ice cream cart just the same.
Other ways that also work:
two quarter turns clockwise (one after the other)
two quarter turns anti-clockwise
two right angles, either way round
one and a half turns clockwise — the extra full turn changes nothing
1/4 + 1/4 = 1/2 turn ✓ 1/2 turn clockwise = 1/2 turn anti-clockwise (both land on the opposite side) ✓ 1 full turn + 1/2 turn = 1/2 turn ✓
Half turn clockwise …… and half turn anti-clockwise. Both end at the same place.
Why it happens: A half turn is exactly half of the circle, and the circle has only two halves. Going round either half brings you to the very same point on the opposite side. That is special to the half turn — it does not work for a quarter turn.