Lesson 7 The Size of Angles on a Clock

    • Let’s describe angles using the hands of a clock.

Warm-up Notice and Wonder: Two Sets of Angles

What do you notice? What do you wonder?

Set 1
set of 3 angles. From left to right, angle measurements appear to increase, angle segments appear to remain the same.
Set 2
set of 3 angles. From left to right, angle measurements appear to increase, angle segments appear to decrease.

Activity 1 Draw Angles Andre’s Way

Problem 1

Andre used the hands of a clock to explain how to draw an angle to his partner.

“Imagine both hands are pointing at the 12. Turn the minute hand so it’s pointing at the 3.”

clock with both hands on 12

  1. Draw Andre’s angle.

  2. What is another way to describe how to draw the same angle using the clock?

Problem 2

Use Andre’s way to explain how to draw these angles:

  1. angle formed by two rays
  2. angle formed by two rays
  3. angle formed by two rays

Activity 2 Compare Angles on the Clock

Problem 1

Here are some angles formed by the two hands of a clock.

In each pair of angles, which angle is larger? Explain or show your reasoning.

  1. 5:00

    clock showing 5:00

    3:00

    clock showing 3:00

  2. 1:15

    clock showing 1:15

    1:20

    clock showing 1:20

  3. 2:50

    clock showing 2:50

    11:20

    clock showing 11:20

  4. 8:58

    clock showing 8:58

    9:35

    clock showing 9:35

Problem 2

How large is this angle?

Describe its size in as many ways as you can.

clock showing 12:20

Practice Problem

Problem 1

A
clock showing 3:00
B
clock showing 5:05

  1. Which set of clock hands make a greater angle? Explain how you know.

  2. Choose one of the clocks and describe how to use the clock to draw the angle represented by the hands on the clock.