Grade by Grade
E. Spatial Sense · Angles, Rectangles, Grids and Measurement

Angles: Right, Acute, Obtuse and Straight

E2.4 A1About 35 minutes
Learning goals
  • I can find the vertex and the arms of an angle.
  • I can use a right angle as a benchmark to compare other angles.
  • I can name an angle as right, acute, obtuse or straight.
  • I can explain how I sorted an angle.

Words to know

angle
The amount of turn or opening between two arms that meet at a point.
vertex
The point where the two arms of an angle meet. More than one are called vertices.
arm
One of the two straight lines that make an angle.
right angle
An angle that is exactly a square corner, like the corner of a sheet of paper.
acute angle
An angle that is smaller than a right angle.
obtuse angle
An angle that is bigger than a right angle but smaller than a straight angle.
straight angle
An angle whose arms make a straight line. It is the same as two right angles together.
benchmark
Something you know well that you use to compare or estimate, like a right angle.

Remember from Grades 2 and 3

You learned that the corner of a sheet of paper is a square corner, also called a right angle. You checked corners of shapes and objects by fitting a paper corner into them.

This year you will give names to angles that are smaller and bigger than a right angle.

Let's start with a door

Open a door just a little. Then open it wider. Then wider still. The door turns around its hinges. The amount of turn is an angle.

An angle has two arms that meet at a point called the vertex. The bigger the opening between the arms, the bigger the angle.

A white bedroom door stands partly open in a hallway.
As a door swings open on its hinges, the opening between the door and the wall makes an angle. The wider it opens, the bigger the angle. AI-generated image

Arm length does not matter

The size of an angle is how far the arms are opened, not how long the arms are. Both angles below are the same size. One just has longer arms.

short armslong arms, same angle
Two angles with the same opening. The arms are different lengths, but the angles are the same size.

Four kinds of angles

We sort angles by comparing them with a right angle. A right angle is our benchmark.

  • A right angle is exactly a square corner. We mark it with a small square.
  • An acute angle is smaller than a right angle. It is a narrow opening.
  • An obtuse angle is bigger than a right angle, but its arms do not make a straight line yet.
  • A straight angle has arms that make a straight line. It is the same as two right angles put together, or a half turn.
acuterightobtusestraight
From left to right: an acute angle, a right angle (marked with a small square), an obtuse angle and a straight angle.

Make a right-angle tester

Take any piece of paper, even one with a torn edge. Fold it in half. Then fold it in half again so the folded edge lines up with itself. The new corner is a perfect right angle!

Put the corner of your tester on the vertex, with one edge along one arm.

  • If the other arm is hidden under the tester, the angle is acute.
  • If the other arm lines up with the edge exactly, it is a right angle.
  • If the other arm sticks out past the tester, it is obtuse (or straight, if the arms make a line).
paper cornerfits insidesticks out
Left: a folded paper corner is a right angle. Middle: this angle fits inside the tester, so it is acute. Right: this arm sticks out past the tester, so the angle is obtuse.
Worked example

Example 1: Angles on a clock

Look at the smaller angle between the two hands on each clock. Name each angle.

  1. At 3:00, the hands point to 12 and 3. That makes a square corner. It is a right angle.
  2. At 6:00, the hands point to 12 and 6, in opposite directions. They make a straight line. It is a straight angle.
  3. At 2:00, the hands point to 12 and 2. The opening is less than the 3:00 angle. It is acute.
  4. At 4:00, the hands point to 12 and 4. The opening is more than the 3:00 angle, but less than 6:00. It is obtuse.

3:00 right, 6:00 straight, 2:00 acute, 4:00 obtuse.

1234567891011123:001234567891011126:001234567891011122:001234567891011124:00
Clocks showing 3:00, 6:00, 2:00 and 4:00.
Worked example

Example 2: Estimate with benchmarks

Pia opens her laptop. The screen and the keyboard make an angle that is a bit more than a right angle, but far from flat. What kind of angle is it?

  1. Compare with the right angle benchmark: it is bigger than a right angle.
  2. Compare with the straight angle benchmark: the laptop is not flat, so it is smaller than a straight angle.
  3. Bigger than right but smaller than straight means obtuse.

It is an obtuse angle.

Turn it around

An angle can point any way: up, down or sideways. A right angle is still a right angle if you turn the page. Always check with your tester, not just by looking at which way the arms point.

Math talk

When you name an angle, say why: "It is acute because it fits inside my right-angle tester." Explaining your thinking helps you catch mistakes.

Just for fun

Q: Why are angles smaller than a right angle always so adorable?

A: Because they're a-cute angles!

Hands-on activity

Angle hunt

You need: a sheet of paper for a right-angle tester, a pencil, and two drinking straws or two pencils.

  1. Fold your right-angle tester (fold the paper in half, then in half again).
  2. Make a table with four columns: acute, right, obtuse, straight.
  3. Hunt around your home. Check corners and openings with your tester: a book cover, a door that is part open, the hands of a clock, a slice of pizza, the legs of a folding chair, a coat hanger.
  4. Write or draw each thing in the right column. Try to find at least two of each kind.
  5. Hold two straws so they touch at one end. Make an acute, a right, an obtuse and a straight angle. Ask a grown-up to check with your tester.

Math talk: "Which kind of angle was easiest to find at home? Which was hardest? Why do you think so?"

ABCDE
Angles A, B, C, D and E for the questions below.

Your turn

1

Look at angle A above. Is it acute, right, obtuse or straight?

2

Look at angle B. It is tilted. What kind of angle is it?

3

Look at angle C. What kind of angle is it?

4

Look at angle D. What kind of angle is it?

5

Look at angle E. What kind of angle is it?

6

What kind of angle do the hands of a clock make at 9:00?

7

Two right angles are put side by side so they share an arm. What kind of angle do they make together?

More practice: warm-up

1

What is the point called where the two arms of an angle meet?

2

An angle is smaller than a right angle. What is it called?

3

What kind of angle is the corner of a sheet of paper?

4

An angle's arms make a straight line. What is it called?

5

An angle is bigger than a right angle but smaller than a straight angle. What is it called?

More practice: on your own

1

Name the smaller angle between the clock hands at 1:00.

2

Name the smaller angle between the clock hands at 5:00.

3

Sam draws an angle with very long arms. He says it must be obtuse because it is big. Is he right?

4

A book is lying open flat on a table. What angle do the two covers make?

5

Look at the capital letter V. What kind of angle is at the bottom point?

Challenge

1

Find a time when the smaller angle between the clock hands is obtuse, and a different time when it is acute. Use o'clock times only.

2

Mia says: "If I put an acute angle and a right angle side by side so they share an arm (without overlapping), I always get an obtuse angle." Is she right? Explain.

3

A pizza is cut into 4 equal slices from the centre. What kind of angle is at the point of each slice? What if it is cut into 8 equal slices?

Check your understanding

Quiz

1.

Which angle is smaller than a right angle?

2.

What kind of angle do the clock hands make at 6:00?

3.

An angle's other arm sticks out past your right-angle tester, and the arms do not make a straight line. What kind of angle is it?

4.

Which of these changes the size of an angle?

5.

How many right angles make one straight angle?

6.

What kind of angle do the clock hands make at 3:00?

For parents and teachers

Big idea: The Ontario curriculum (E2.4) asks Grade 4 students to identify angles and classify them as right, straight, acute or obtuse. Students do not measure in degrees yet (that comes in Grade 5 with a protractor). Instead, they use a right angle as a benchmark. If you want to mention it, a right angle measures 90 degrees and a straight angle 180 degrees, but your child does not need these numbers this year.

Common difficulties:

  • Judging by arm length. Children often think an angle with long arms is "bigger". Show two same-size angles with different arm lengths.
  • Only recognizing angles in one position. A right angle that is tilted is still a right angle. Practise with the page turned.
  • Mixing up acute and obtuse. A memory trick: an "a-cute" angle is small and cute.

How to help: Make a paper right-angle tester together and keep it handy. Point out angles in daily life: a partly open door, the hands of a clock, the hinge of a laptop, a hockey stick blade against its shaft. Ask "Is that bigger or smaller than a right angle? How do you know?"