Minds On

Angles around us

Explore the following traffic signs. The signs have been sorted into three groups.

As you explore the groups, answer these questions, and record your thinking in a notebook or a method of your choice:

  • What do you notice about the signs in each group?
  • What do the signs in Group 1 have in common with each other? What about the signs in Group 2 and Group 3?
  • What is different between the groups? What do you think the sorting rule might have been?

Group 1

A square bike route sign.
A square parking sign.

Group 2

Caution sign. A triangular sign with an exclamation point.
A yield sign. An upside-down triangle with the word yield in the middle.

Group 3

A stop sign. An octagonal-shaped sign with the word STOP in the middle.
A moose-crossing sign. An octagonal-shaped sign with a moose on it.

Test Your Skills

One more sign

Explore the following sign.

Which of the groups would you sort this sign into?

Explain your thinking. You can record your ideas using a method of your choice.

A pentagonal school sign with 5 sides. In the middle are two children walking with bags.

Action

All about angles

Explore this video entitled “Angles” to learn more about the different classifications of angles.

As you explore the video, consider these questions:

  • What makes a right angle, acute angle, and obtuse angle?
  • What is a straight angle?

Angle review

Let’s review some of the information that Teacher Charmaine shared in the video.

An angle is a shape formed by two rays (‘arms’ of an angle) or two line segments that meet at a common endpoint (vertex).

2 straight lines that meet to form an angle. The point where the 2 lines meet is labelled vertex.

Now let’s explore four different classifications of angles: right, acute, obtuse, and straight.

Press on the tabs to learn more about angles.

A right angle is an angle that measures 90 degrees.

  • a right angle is a quarter turn
  • it is sometimes called a “square angle” because all angles of a square (or rectangle) are right
  • if two lines meet at a right angle, the lines are perpendicular (meaning they intersect at 90 degrees)
A right angle. It is two lines meeting to form a corner. The inside is labelled 90 degrees.

An acute angle measures between 0 degrees and 90 degrees.

  • this angle is smaller than a 90-degree angle
An acute angle. It is 2 lines meeting to make a point that is less than 90 degrees.

An obtuse angle is more than 90 degrees but less than 180 degrees.

An obtuse angle. It is two lines meeting to make a large angle that is more than 90 degrees.

A straight angle measures 180 degrees.

  • this occurs when the rays lie opposite of each other
  • this creates a straight line
Straight angle. It is 2 horizontal lines meeting. The angle is a semi-circle labelled 180 degrees.

Task 1: Classifying angles

Some shapes have all the same type of angle, and some have a variety of angles.

A stop sign has eight obtuse angles. A stop sign is an octagon, and all the angles are the same size.

The following image displays a stop sign, with all the obtuse angles identified.

An octagonal-shaped sign with the word STOP in the middle. Each angle on the sign is obtuse.

A yield sign has three acute angles. A yield sign is approximately an equilateral triangle. Therefore, all the angles will be the same size.

The following image displays a yield sign, with all the acute angles identified.

An upside-down triangle with the word YIELD in the middle. Each angle on the sign is acute.

Practice

Explore the following shapes and determine the types of angles.

Record your ideas in a notebook or a method of your choice.

A rhombus with 4 equal sides, opposite sides are parallel, and the opposite angles are equal.
A trapezoid with 4 sides, 1 pair of parallel sides. Top angles are same and the lower angles are same.

When you’re ready, press ‘Answers’ to reveal some suggested answers for this activity.

Rhombus

Has two acute angles and two obtuse angles

A rhombus with 4 equal and opposite sides, which two are parallel. The rhombus has opposite angles with two acute angles and two obtuse angles.

Trapezoid

Has 2 acute angles and 2 obtuse angles.

A trapezoid with 4 sides, and 1 pair of parallel sides. Top angles are obtuse and the same. The lower angles are acute and the same.

Task 2: Time for angles

Analog clocks are another example of where angles are found within real world objects.

The analog clock is a circle which has numbers from 1 to 12.

The 12 starts at the very top of the clock, then goes to 1, 2, 3, 4, and so on, around back to 12.

The 12 and the 6 are directly across from each other. 1 and 7 are across from each other, and 2 and 8 are across from each other. Other pairs of numbers that are across from each other on an analog clock are:

  • 3 and 9
  • 4 and 10
  • 5 and 11

As an example, let’s explore the following analog clock. This clock indicates the time of 11:06:

The hour hand is at 11, and the minute hand is just past the 1. The angle that the minute and hour hand makes is less than a right angle. It makes an acute angle.

Analog clock with the time 11:06. The hour hand is at 11, and the minute hand is just past the number 1. The clock's hands form an acute angle.

An analog clock displaying the time 11:06. The hour hand is pointing up and slightly to the left, to the number 11, and the minute hand is pointing up and slightly to the right, just past the number 1. The hands of the clock form an acute angle.

Next, consider the following clock at 12:35.

The hour hand is between the 12 and the 1 and the minute hand is at 7.

In this example, the minute and hour hand do not make a 90-degree angle. The two hands are closer to making a perfect straight angle, as this would be the case if the hour hand was at 1 and the minute hand stayed at 7.

Since it is less than a straight angle, it is an obtuse angle.

Analog clock with the time 12:35. The hour hand points between 12 and 1. The minute hand points to 7. The clock's hands form an obtuse angle.

An analog clock displaying the time 12:35. The hour hand is pointing up and slightly to the right, between the 12 and the 1. The minute hand is pointing down and slightly to the left, at the 7. The hands of the clock form an obtuse angle.

Practice

Consider the clocks listed in the following chart. What angles are produced by the hands of the analog clocks?

Complete the Clock Angles activity in your notebook or using the following fillable and printable document. You can also record your responses using a method of your choice.

Clock Angles

Press the Activity button to access Clock Angles.

Activity (Open PDF in a new tab)

When you’re ready, press ‘Answers’ to reveal the angles for each time.

Time Angle

11:20

Clock is 11:20. Hour hand between 11 and minute hand at 4. The hands form an obtuse angle.

obtuse

9:00

Clock is 9 o'clock. Hour hand at 9 and minute hand at 12. The hands form a right angle.

right

6:00

Clock is 6 o'clock. Hour hand at 6 and minute hand at 12. The hands form a straight angle.

straight

1:12

Clock is 1:12. Hour hand at 1 and minute hand between 2 and 3. The hands form an acute angle.

acute

4:10

Clock is 4:10. Hour hand at 4 and minute hand at 2. The hands form an acute angle.

acute

Consolidation

House of angles

Explore the following house. The house has different angles labelled A to J. Your task is to classify the labelled angles as right, straight, acute, or obtuse.

Press ‘Hints’ to reveal the types of angles.

Right angle: an angle that measures 90 degrees

  • A right angle is a quarter turn.
  • It is sometimes called a “square angle” because all angles of a square (or rectangle) are right.
  • If two lines meet at a right angle, the lines are perpendicular (meaning they intersect at 90 degrees).

Acute angle: an angle whose measure is between 0 degrees and 90 degrees

  • This angle is smaller than a 90-degree angle.

Obtuse angle: an angle that is more than 90 degrees, but less than 180 degrees

Straight angle: an angle that measures 180 degrees

  • This occurs when the rays lie opposite of each other.
  • This creates a straight line.
An image of a house. Different angles on the house are labelled with the letters A to J.

A basic drawing of a house. The different angles on the house are labelled A through J. Angle A is 90 degrees. Angle B is more than 90 degrees, and less than 180 degrees. Angle C is larger than a quarter turn, and smaller than a half turn. Angle D is a quarter turn. Angle E is a straight line. Angle F is smaller than a quarter turn. Angle G is less than 90 degrees. Angle H measures between 90 degrees and 180 degrees. Angle I is less than 90 degrees. Angle J is sometimes called a square angle.

House of angles: Multiple choice

Identify each angle on the house by completing the following multiple choice questions.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.

An open paper fan.

Consider a paper fan or decorative fan. What angles can be produced when the fan is partially open at about 30 degrees? How about 90 degrees? How about when the fan is open at 140 degrees?

Record your ideas in a notebook or a method of your choice.