Lesson 5 What is an Angle?

    • Let’s look for angles and find out ways to describe them.

Warm-up Notice and Wonder: A Wall of Clocks

What do you notice? What do you wonder?

picture of 6 rows of 8 clocks. No numbering on the clocks. The times are different on the clocks, each showing 3 hands.

Activity 1 Tricky Figures

Problem 1

Work with a partner in this activity. Choose a role: A or B. Sit back to back, or use a divider to keep one person from seeing the other person’s work.

Partner A:

  • Your teacher will give you a card. Don’t show it to your partner.

  • Describe both images on the card—as clearly and precisely as possible—so that your partner can draw the same images.

Partner B:

  • Your partner will describe two images. Listen carefully to the descriptions.

  • Create the drawings as described. Follow the instructions as closely as possible.

  1. When done, compare the drawings to the original images. Discuss:

    • Which parts were accurate? Which were off?

    • How could the descriptions be improved so the drawing could be more accurate?

  2. Switch roles and repeat the exercise. Compare the drawings to the original images afterwards.

Problem 2

If you have time… Request two new cards from your teacher (one card at a time). Take turns describing and drawing the geometric figure on each card.

Activity 2 Angles or Not Angles?

  1. Decide if each figure shows at least one angle. Explain or show your reasoning for each.

    4 images. A, two intersecting lines. B, parallelogram. C, line segment connected to a curve at one endpoint. D, two parallel rays.

  2. Clare and Kiran are looking at this diagram. Clare says there are no angles because the rays do not meet at a point. Kiran says he sees two angles.

    two rays connected by a line segment

    Do you agree with either of them? How many angles do you see?

Activity 3 Discover Angles

Problem 1

Here are two figures.
Find 2–3 angles in each figure. Draw pairs of rays to show the angles.

  1. the letter k
  2. the number 7

Problem 2

Sketch a part of your classroom that has 2–3 angles. Draw pairs of rays to show the angles.

Practice Problem

Problem 1

  1. Find one angle in the figure. Draw a pair of rays to show the angle and extend them as far as you can.

  2. Find another angle in the figure. Draw a pair of rays to show it. Extend the rays as far as you can. (If you’d like, you can use a different colored pencil for this pair of rays.)

  3. Now that you have drawn some rays, do you see other angles that you didn’t see before? If you see one or more, label each one with a letter.

triangle. two acute angles and one angle about 90 degrees