In this activity, students work with a partner to replicate images of angles. One partner describes the figure, and the other draws, based on the verbal descriptions. The purpose of the activity is to draw students’ attention to how they use the vocabulary they have learned from previous lessons to describe the figures (MP6). In this Synthesis, students learn that an angle is a geometric figure that is made up of two rays that share the same starting point. Students also may become aware that they need a clear way to describe the size of the figure. Angle measurement is not addressed in this lesson, but in the process of describing or drawing the figures, students likely will use terms such as “narrower,” “wider,” and the like. Save the chart that shows the words students use during the activity to describe angles, to revisit in future lessons.

This activity uses MLR2 Collect and Display. Advances: conversing, reading, writing.

• “How are the two drawings on each card the same?” (Each has 2 rays. The rays start at the same point. One ray is pointing in the same direction in both drawings.)
• “How are they different?” (The rays are pointing in different directions on some cards. The rays are farther apart in some cards.)
• “How did you describe what you saw? What terms did you use to help you describe the directions of the rays?” (We tried to explain by describing the hands on a clock. We tried using words such as “north,” “south,” “east,” “and “west.” We described them in relation to vertical and horizontal.)
• As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
• Remind students to borrow language from the display as needed.
• “Did anyone use the term ‘angle’? Did anyone measure something or use measurements?”
• “The figures that you drew are angles. An angle is a figure that is made up of two rays that share the same starting point.“

• “The point that two rays share when they form an angle is called the vertex of the angle.”

  Display:

  

• “Where around us do we see angles?”

In the previous activity, students learned what constitutes an angle. In this activity, they identify angles within geometric figures and explain their reasoning. Listen for the ways students show their understanding of rays even when they are not explicitly labeled in a given geometric figure.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• “How did you decide if there’s at least one angle in each figure? What did you look for?” (I looked for two lines or segments that intersect.)
• “How might you use the word ‘angle’ in our description of Figure A?” (Two intersecting lines make 4 angles.)
• “In Figure B, the sides of the quadrilateral are segments rather than rays. Does that mean there are no angles in the figure?” (No, there are angles. We can think of the segments as being parts of longer rays.)

• “Can you show the rays that make the angles in Figure B?”

  Display:

  

• “Can we show an angle in Figure C by drawing rays, just as we have done with B?” (No, because one of the marks is not straight and can’t be a part of a ray.)
• “Think about Kiran’s argument. Where are the two angles that Kiran saw?” (Kiran saw angles where each ray meets the line segment. The line segment is part of angles made with the rays that start at either of its endpoints.)

In this activity, students identify and sketch angles in their environment—in the text, graphics, and shapes in their physical surroundings—and reinforce the idea of an angle as a figure made up of two rays that share the same starting point.

In future lessons, students will look more closely at the properties of angles and consider how they can be measured and whether the lengths of the segments that form them impact the sizes of the angles.

• “Can you explain how you found angles in the figure?”
• “How do you see the rays that share this vertex? Can you draw them?”

• “How did you find the angles?” (We looked for intersections of segments. When the segments meet or cross, angles are formed.)
• “Where is the vertex of each angle you found?”