Year 5 · Mathematics · Space
Angles and shapes
Compare angles with a right angle, describing them as acute, right, obtuse, straight or a full turn, and identify angles in shapes and objects.
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These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.
Learning goals
Learners will
- Understand an angle as an amount of turn between two arms.
- Compare angles with a right angle and name them as acute, right, obtuse, straight or a full turn.
- Identify angles in two-dimensional shapes and everyday objects.
Success looks like
- I can make a right-angle checker and use it to test angles.
- I can name an angle as acute, right, obtuse or straight by comparing it with a right angle.
- I can find and describe right angles and other angles in shapes around my home.
The big idea
An angle is an amount of turn. Picture two arms joined at one point, like the hands of a clock or a pair of scissors. When the arms open wider, the angle gets bigger. The length of the arms does not change the size of the angle; only the amount of turn matters.
The most important angle to know is the right angle. It is a quarter turn, the shape of the corner of a book or a sheet of paper. Right angles are often marked in diagrams with a small square in the corner.
Make a right-angle checker: fold any piece of paper in half, then fold it in half again so the folded edges line up. The corner you have made is a right angle. Hold it against other angles to compare them.
We name angles by comparing them with a right angle:
- An acute angle is smaller than a right angle.
- A right angle is exactly a quarter turn.
- An obtuse angle is bigger than a right angle but smaller than a straight line.
- A straight angle is a half turn, which makes a straight line. It is two right angles.
- A full turn goes all the way around back to the start. It is four right angles.
Angles are everywhere in shapes. A square and a rectangle each have four right angles. Every angle in an equilateral triangle is acute. A regular hexagon has six obtuse angles. Clock hands make angles too: at 3 o'clock they make a right angle, and at 6 o'clock they make a straight angle.
Worked examples
Using a right-angle checker
The two arms of an angle are opened wider than the corner of a sheet of paper, but not as wide as a straight line. What type of angle is it?
- Place the corner of the right-angle checker into the angle, lining up one edge with one arm.
- The other arm is outside the checker, so the angle is bigger than a right angle.
- The arms do not make a straight line, so it is smaller than a straight angle.
Answer: It is an obtuse angle.
Angles on a clock
Name the angle made by the hands of a clock at 1 o'clock, 3 o'clock and 6 o'clock.
- At 1 o'clock the minute hand points to 12 and the hour hand to 1. The gap is less than a quarter turn, so it is acute.
- At 3 o'clock the hands point to 12 and 3. That is a quarter turn, so it is a right angle.
- At 6 o'clock the hands point to 12 and 6, making a straight line, so it is a straight angle.
Answer: 1 o'clock: acute. 3 o'clock: right angle. 6 o'clock: straight angle.
Angles in a shape
How many right angles does a rectangle have, and how many right angles make a full turn?
- Test each corner of a rectangle with the right-angle checker. All four corners match exactly.
- Stand facing a wall and make quarter turns: after 1 quarter turn you face a new wall, and after 4 quarter turns you are facing the first wall again.
Answer: A rectangle has 4 right angles, and 4 right angles make a full turn.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What is an angle that is smaller than a right angle called?
Acute — An acute angle is smaller than a right angle.
What type of angle is the corner of a sheet of paper?
Right — The corner of a sheet of paper is a quarter turn, which is a right angle.
What angle do the hands of a clock make at 3 o'clock?
Right angle — At 3 o'clock the hands point to 12 and 3, which is a quarter turn: a right angle.
What angle do the hands of a clock make at 6 o'clock?
Straight angle — At 6 o'clock the hands point to 12 and 6 and form a straight line, which is a straight angle.
How many right angles does a rectangle have?
4 — Every corner of a rectangle is a right angle, and a rectangle has 4 corners.
How many right angles make a straight angle?
2 — A straight angle is a half turn, and two quarter turns make a half turn.
An angle is bigger than a right angle but smaller than a straight angle. What type of angle is it?
Obtuse — Angles between a right angle and a straight angle are called obtuse.
You stand facing a door, then turn all the way around until you are facing the door again. What is this turn called?
A full turn — Turning all the way around back to the start is a full turn, which is the same as four right angles.
Watch out for
- Thinking that longer arms make a bigger angle. Draw two angles of the same size with short and long arms and check them with the right-angle checker.
- Believing an angle is only a right angle when it “sits” the usual way, with one arm flat and one straight up. Turn a book on a slant and show that its corner is still a right angle.
- Mixing up acute and obtuse. A memory hook: “a-cute angle is small and cute”.
Tips for parents
- Go on an angle hunt around the house and garden. Look for right angles in doors and windows, acute angles in a slice of pizza and obtuse angles in an open laptop.
- Use your arms or two pencils to make angles and ask the learner to name each one.
- Make turning games: give directions such as “make a quarter turn”, “make a half turn” or “make a full turn”.
Go further
- Draw a picture made only of straight lines, then colour every right angle red, every acute angle blue and every obtuse angle green.
- Open a door slowly from closed to wide open and describe the angle at each stage: acute, right, then obtuse.
- Look at an analogue clock every hour for a morning and record whether the hands make an acute, right, obtuse or straight angle.
About 40 minutes
You'll need
- A sheet of scrap paper to fold into a right-angle checker
- Two strips of card joined at one end with a split pin, or two pencils
- An analogue clock (optional)
- Paper, pencil and ruler
Key words
- Angle
- The amount of turn between two lines (arms) that meet at a point.
- Right angle
- A quarter turn, like the corner of a sheet of paper. It is 90 degrees.
- Acute angle
- An angle smaller than a right angle.
- Obtuse angle
- An angle bigger than a right angle but smaller than a straight angle.
- Straight angle
- A half turn, which makes a straight line. It is the same as two right angles.
- Full turn
- A complete turn back to where you started. It is the same as four right angles.
Still tricky?
For parents
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