Angles and turns
In this topic you will
- Use angles to measure turns in both clockwise and anticlockwise directions.
- Predict and check how many times a shape looks the same as it completes a whole turn.
Key Words
- angle
- anticlockwise
- clockwise
- half turn
- quarter turn
- right angle
- turn
- whole turn
Show Definitions
- angle: The amount of turn between two lines or directions, measured in degrees.
- anticlockwise: Turning in the opposite direction to a clock’s hands.
- clockwise: Turning in the same direction as a clock’s hands.
- half turn: A turn of $180^\circ$, which points you in the opposite direction.
- quarter turn: A turn of $90^\circ$, which is one-quarter of a full rotation.
- right angle: An angle of exactly $90^\circ$.
- turn: A rotation from one direction to another; the size of the turn can be measured as an angle.
- whole turn: A complete rotation back to the starting direction, equal to $360^\circ$.
Angles on a clock
There are angles everywhere! Look at this clock. The minute hand and hour hand make an angle where they meet.
Clock hands also turn. The direction that they move is called clockwise. Anticlockwise is the opposite direction.
EXERCISES
1.
a. The tortoise always looks in the direction he is walking.
He travels along the green path.
How many times did he turn a quarter turn clockwise? ________
How many times did he turn a quarter turn anticlockwise? ________
How many right angle turns did he make altogether? ________
b. Colour a different path to get the tortoise home.
How many quarter turns clockwise? ________
How many quarter turns anticlockwise? ________
How many right angle turns did he make altogether? ________
👀 Show answer
a.
- Quarter turns clockwise: $2$
- Quarter turns anticlockwise: $2$
- Right angle turns altogether: $4$
b. Answers will vary (it depends on the different path you colour).
Check your path by counting every corner where the tortoise changes direction by a quarter turn ($90^\circ$).
2. Work with a partner.
Look around you and make a list of six angles that you can see.
Try to find at least $3$ right angles.
Draw them.
👀 Show answer
Answers will vary. Example list (includes at least $3$ right angles):
- Corner of a book (right angle, $90^\circ$).
- Corner of a door frame (right angle, $90^\circ$).
- Corner of a window (right angle, $90^\circ$).
- Open scissors (an acute angle, less than $90^\circ$).
- A clock hands position making an obtuse angle (between $90^\circ$ and $180^\circ$).
- The corner where a wall meets the floor (often a right angle, $90^\circ$).
3. Turn the shapes a half turn clockwise and draw them.
Would each shape fit exactly on top of its drawing? ________
Predict and then check how many turns would be needed to make the shapes look identical.
________
👀 Show answer
After a half turn clockwise ($180^\circ$), each shape is upside down and the red spot moves to the opposite side of the shape.
Would each shape fit exactly on top of its drawing? No.
How many turns are needed to look identical again? A whole turn in total ($360^\circ$), which is $4$ quarter turns.
4. Turn the shapes a quarter turn anticlockwise and draw them.
Draw where the red spots would be.
Would they fit exactly on top of each other? ________
Predict and then check how many turns would be needed to make the shapes look identical.
________
👀 Show answer
- Red spot positions after a quarter turn anticlockwise ($90^\circ$): The spot moves with the shape to the next side/position after a $90^\circ$ turn (for example, a spot at the top moves to the left).
- Would they fit exactly on top of each other? No (they are different shapes).
- How many turns to look identical again? A whole turn in total ($360^\circ$), which is $4$ quarter turns.
Think like a Mathematician
You have $2$ sticks:
$1$ red ____________________ $1$ blue ____________________
Task: Draw how you can make one right angle using sticks.
Task: Draw how you can make two right angles using $2$ sticks.
Work on your own. Can you make three and four right angles with $2$ sticks?
If you can, draw them. If you can’t, write why not.
Show Answers
One right angle: Place the $2$ sticks so they meet at one end and form an $L$ shape (a $90^\circ$ corner).
Two right angles: Make a $T$ shape by placing one stick across the other at its midpoint. This creates $2$ right angles where they meet.
Three right angles: Not possible with only $2$ straight sticks. When two straight sticks cross, they make either $4$ right angles (if they are perpendicular) or $0$ right angles (if they are not). There is no way to get exactly $3$ right angles.
Four right angles: Yes. Put the sticks so they cross at $90^\circ$ (a plus sign $+$). That makes $4$ right angles at the intersection.
Activity adapted from NRICH Right Angle Challenge.