Question 1(a)
How many half turns make one full turn?
Steps only
A half turn is one-half of a full turn.
2 × 1/2 = 1 full turn.
Answer
2 half turns.
CLASS 5 · MATHS MELA · CHAPTER 3
Angles as Turns
Understand angles as parts of a turn, measure them with folded-circle tools and follow clockwise and anti-clockwise directions.
83 worked answersAll 5 exercise sets
What you will learn
- Compare acute, right, obtuse, straight and reflex angles.
- Express rotations as fractions of a full turn.
- Follow and reverse clockwise and anti-clockwise turns.
83 worked answers · short steps first, explanations when you need them
Turns Around Us
Textbook pages 33–34
Question 1(b)
How many quarter turns make one half turn?
Steps only
1/4 + 1/4 = 2/4 = 1/2.
Answer
2 quarter turns.
Question 1(c)
How many quarter turns make one full turn?
Steps only
4 × 1/4 = 1.
Answer
4 quarter turns.
Question Around us
Name objects around you whose parts turn.
Steps only
Examples: a door knob, bicycle wheel, tap, key, fan and jar lid.
Answer
Any suitable observed examples are correct.
Question Table 1
Estimate the greatest useful turn made by a clothes clip.
Steps only
Open and close the object carefully.
Compare its movement with a quarter turn and a half turn.
Answer
Usually less than 1/4 turn.
Question Table 2
Estimate the greatest useful turn made by a door hinge.
Steps only
Open and close the object carefully.
Compare its movement with a quarter turn and a half turn.
Answer
Usually more than 1/4 turn and can approach 1/2 turn.
Question Table 3
Estimate the greatest useful turn made by a tongs.
Steps only
Open and close the object carefully.
Compare its movement with a quarter turn and a half turn.
Answer
Usually less than 1/4 turn.
Question Table 4
Estimate the greatest useful turn made by a scissors.
Steps only
Open and close the object carefully.
Compare its movement with a quarter turn and a half turn.
Answer
Often more than 1/4 turn.
Question Table 5
Estimate the greatest useful turn made by a file cover.
Steps only
Open and close the object carefully.
Compare its movement with a quarter turn and a half turn.
Answer
Can make about 1/2 turn.
Question Table · full turn
Does any listed hinged object normally need a full turn to open?
Steps only
A clothes clip, door hinge, tongs, scissors and file cover move back and forth through only part of a circle.
Answer
No, none normally makes a full turn while being used.
Recognising and Comparing Angles
Textbook pages 34–36
Question Acute
How does an acute angle compare with a quarter turn?
Steps only
It is smaller than a quarter turn.
Answer
An acute angle is less than 1/4 turn (less than 90°).
Question Right
How large is a right angle?
Steps only
It is exactly one quarter of a full turn.
Answer
A right angle is 1/4 turn (90°).
Question Obtuse
How does an obtuse angle compare with quarter and half turns?
Steps only
It is larger than 1/4 turn but smaller than 1/2 turn.
Answer
An obtuse angle is between 90° and 180°.
Question Straight
How large is a straight angle?
Steps only
It changes a direction to the exact opposite direction.
Answer
A straight angle is 1/2 turn (180°).
Question Two acute angles
Can two acute angles together form an acute, right or obtuse angle?
Steps only
Yes. Their sum depends on their sizes.
30°+40°=70° is acute; 40°+50°=90° is right; 50°+60°=110° is obtuse.
Answer
They can form any of the three types.
Question House A
Classify angle A in the house drawing.
Steps only
Compare angle A with the corner of a square.
Answer
Angle A is acute.
Question House B
Classify angle B in the house drawing.
Steps only
Compare angle B with the corner of a square.
Answer
Angle B is right.
Question House C
Classify angle C in the house drawing.
Steps only
Compare angle C with the corner of a square.
Answer
Angle C is acute.
Question House D
Classify angle D in the house drawing.
Steps only
Compare angle D with the corner of a square.
Answer
Angle D is right.
Question House E
Classify angle E in the house drawing.
Steps only
Compare angle E with the corner of a square.
Answer
Angle E is obtuse.
Question House F
Classify angle F in the house drawing.
Steps only
Compare angle F with the corner of a square.
Answer
Angle F is right.
Question House G
Classify angle G in the house drawing.
Steps only
Compare angle G with the corner of a square.
Answer
Angle G is obtuse.
Question House H
Classify angle H in the house drawing.
Steps only
Compare angle H with the corner of a square.
Answer
Angle H is obtuse.
Question Five-sided shape
Make a five-sided shape with two right angles, two obtuse angles and one acute angle.
Steps only
One possible set of interior angles is 90°, 90°, 150°, 150° and 60°.
Their sum is 540°, which is the interior-angle sum of a pentagon.
Answer
One valid answer is a pentagon with angles 90°, 90°, 150°, 150° and 60°.
Question Pose 1
Classify the marked angle in pose 1 of the gymnast sequence.
Steps only
Compare the opening with a quarter turn and a half turn.
Answer
It is a acute angle.
Question Pose 2
Classify the marked angle in pose 2 of the gymnast sequence.
Steps only
Compare the opening with a quarter turn and a half turn.
Answer
It is a right angle.
Question Pose 3
Classify the marked angle in pose 3 of the gymnast sequence.
Steps only
Compare the opening with a quarter turn and a half turn.
Answer
It is a obtuse angle.
Question Pose 4
Classify the marked angle in pose 4 of the gymnast sequence.
Steps only
Compare the opening with a quarter turn and a half turn.
Answer
It is a obtuse angle.
Question Pose 5
Classify the marked angle in pose 5 of the gymnast sequence.
Steps only
Compare the opening with a quarter turn and a half turn.
Answer
It is a straight angle.
Making and Using Angle Tools
Textbook pages 36–37
Question 2/8 turn
What familiar turn is 2/8 of a full turn?
Steps only
2/8 simplifies to 1/4.
Answer
2/8 turn = 1/4 turn, a right angle.
Question 4/8 turn
What familiar turn is 4/8 of a full turn?
Steps only
4/8 simplifies to 1/2.
Answer
4/8 turn = 1/2 turn, a straight angle.
Question 6/8 turn
Simplify 6/8 of a full turn.
Steps only
6/8 = 3/4.
Answer
6/8 turn = 3/4 turn (270°).
Question 8/8 turn
What is 8/8 of a full turn?
Steps only
All 8 of the 8 equal sectors are used.
Answer
8/8 turn = 1 full turn (360°).
Question Half of 1/6
What is half of a 1/6-turn sector?
Steps only
1/2 × 1/6 = 1/12.
Answer
1/12 turn (30°).
Question Starting points
The endpoint and direction of a turn are shown. How do you locate its starting point?
Steps only
Begin at the shown endpoint.
Move through the same fraction of a turn in the opposite direction.
Mark the ray where this reverse movement ends.
Answer
Reverse every shown turn to find its starting ray.
Question Fold into twelfths
How can a circle folded into sixths be used to make twelfths?
Steps only
Fold each 1/6 sector exactly in half.
Each old sector becomes two equal sectors.
Answer
The circle now has 12 equal sectors; each is 1/12 turn.
Let Us Do
Textbook pages 38–40
Question 1(a)
Estimate the top-left angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/12 turn (30°), acute.
Question 1(b)
Estimate the middle-left angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/8 turn (45°), acute.
Question 1(c)
Estimate the top-middle angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/6 turn (60°), acute.
Question 1(d)
Estimate the top-right angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/3 turn (120°), obtuse.
Question 1(e)
Estimate the bottom-left angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/6 turn (60°), acute.
Question 1(f)
Estimate the bottom-middle angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 1/4 turn (90°), right.
Question 1(g)
Estimate the bottom-right angle with the angle tools.
Steps only
Place the centre of the angle tool on the vertex.
Align one ray and count equal sectors to the other ray.
Answer
The printed angle is about 3/8 turn (135°), obtuse.
Question 2(a)
Find the clockwise turn shown in arrow diagram a.
Steps only
Count the eighth-turn sectors followed by the curved arrow.
Answer
3/8 turn
Question 2(b)
Find the clockwise turn shown in arrow diagram b.
Steps only
Count the eighth-turn sectors followed by the curved arrow.
Answer
5/8 turn
Question 2(c)
Find the clockwise turn shown in arrow diagram c.
Steps only
Count the eighth-turn sectors followed by the curved arrow.
Answer
1/8 turn
Question 2(d)
Find the clockwise turn shown in arrow diagram d.
Steps only
Count the eighth-turn sectors followed by the curved arrow.
Answer
1/2 turn
Question 3(a)
Estimate the marked angles in shape (a).
Steps only
Using the printed rays, A is close to 1/12 turn and B′ is close to 1/6 turn.
Answer
A ≈ 1/12 turn (acute); B′ ≈ 1/6 turn (acute).
Question 3(b)
Estimate the marked angles in shape (b).
Steps only
The two narrow angles use about two sixth-turn sectors; the wider angle uses about two sixths.
Answer
D and D′ ≈ 1/6 turn (acute); E ≈ 1/3 turn (obtuse).
Question 3(c)
Estimate the marked angles in shape (c).
Steps only
Compare each corner with 1/12, 1/4 and 5/12 turn tools.
Answer
F ≈ 1/12 turn (acute); G ≈ 5/12 turn (obtuse); F′ ≈ 1/4 turn (right).
Question 4(a)
Draw an angle of 1/2 turn.
Steps only
Use the matching folded-circle tool and trace its two boundary rays.
Answer
Draw two opposite rays from one point; the angle is 180°.
Question 4(b)
Draw an angle of 1/4 turn.
Steps only
Use the matching folded-circle tool and trace its two boundary rays.
Answer
Draw perpendicular rays; the angle is 90°.
Question 4(c)
Draw an angle of 1/4 turn.
Steps only
Use the matching folded-circle tool and trace its two boundary rays.
Answer
Any rotated pair of perpendicular rays is correct.
Question 4(d)
Draw an angle of 1/8 turn.
Steps only
Use the matching folded-circle tool and trace its two boundary rays.
Answer
Draw a 45° acute angle.
Question 4(e)
Draw an angle of 1/12 turn.
Steps only
Use the matching folded-circle tool and trace its two boundary rays.
Answer
Draw a 30° acute angle.
Question 5(a)
Find and classify a turn of 1/2 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
180°, a straight angle
Question 5(b)
Find and classify a turn of 1/4 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
90°, a right angle
Question 5(c)
Find and classify a turn of 2/4 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
180°, a straight angle
Question 5(d)
Find and classify a turn of 1/6 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
60°, an acute angle
Question 5(e)
Find and classify a turn of 4/6 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
240°, a reflex angle
Question 5(f)
Find and classify a turn of 3/12 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
90°, a right angle
Question 5(g)
Find and classify a turn of 1/2 + 1/4 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
270°, a reflex angle
Question 5(h)
Find and classify a turn of 1/8 + 1/6 of a full turn.
Steps only
Multiply the fraction of a turn by 360°.
Answer
105°, an obtuse angle
Question 6(a)
Relate 15 minutes to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
1/4 turn
Question 6(b)
Relate 30 minutes to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
1/2 turn
Question 6(c)
Relate 45 minutes to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
3/4 turn
Question 6(d)
Relate 1/12 turn to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
5 minutes
Question 6(e)
Relate one full turn to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
60 minutes
Question 6(f)
Relate 1/6 turn to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
10 minutes
Question 6(g)
Relate 4/12 turn to the minute hand’s turn.
Steps only
The minute hand makes one full turn in 60 minutes.
Answer
20 minutes
Direction and Turns
Textbook pages 40–41
Question Ladybird
Which way did the ladybird turn in the picture?
Steps only
Follow the head direction from the first picture to the second.
Answer
clockwise.
Question Snail
Which way did the snail turn in the picture?
Steps only
Follow the head direction from the first picture to the second.
Answer
clockwise.
Question Bee
Which way did the bee turn in the picture?
Steps only
Follow the head direction from the first picture to the second.
Answer
anti-clockwise.
Question Ant
Which way did the ant turn in the picture?
Steps only
Follow the head direction from the first picture to the second.
Answer
anti-clockwise.
Question Opening objects
In which direction are common taps, bottle caps and screws usually turned to loosen them?
Steps only
Most standard threaded objects loosen when turned to the left.
Answer
Usually anti-clockwise.
Question Direction 1
Face North and make two right-angle turns clockwise. Which way do you face?
Steps only
North → East → South.
Answer
South.
Question Direction 2
Face South and make two right-angle turns anti-clockwise. Which way do you face?
Steps only
South → East → North.
Answer
North.
Question Direction 3
Face East and make four right-angle turns anti-clockwise. Which way do you face?
Steps only
Four right angles make one full turn.
Answer
East.
Question Direction 4
Face West and make four right-angle turns clockwise. Which way do you face?
Steps only
Four right angles make one full turn.
Answer
West.
Question Direction 5
Face North and make five right-angle turns clockwise. Which way do you face?
Steps only
Four turns return to North; one more turn points East.
Answer
East.
Question Direction 6
Face South. Turn three right angles clockwise, then two half-right-angles clockwise. Which way do you face?
Steps only
Two half-right-angles equal one right angle.
The total is 3+1=4 right angles, one full turn.
Answer
South.
Question Direction 7
Face West, make an unspecified number of right-angle turns clockwise, then four half-right-angle turns anti-clockwise. Can the final direction be fixed?
Steps only
Four half-right turns equal two right-angle turns, or a half turn.
The first number is missing from the printed prompt, so different values give different final directions.
Answer
A unique final direction cannot be found until the missing number of clockwise right-angle turns is given.
Question Padma
Padma faces the toy shop. After a half turn clockwise, what does she face? Can she reach it another way?
Steps only
A half turn points to the place directly behind her.
A half turn anti-clockwise reaches the same final direction.
Answer
She faces the ice-cream cart; she can also make a half turn anti-clockwise.