In a previous lesson, students described an angle to a partner so that they might draw the angle accurately, without seeing it. Students learned what an angle is and have reasoned about how to describe the size of an angle.

In this activity, students use the features of an analog clock (minute hand, hour hand, and position of numbers) to explain how to draw a given angle. In doing so, they use language related to turning one or both hands on the clock. In future activities, students will relate this idea to turning a ray around a fixed point. 

The hands on an actual clock are designed so that moving the minute moves the hour hand. The examples here disregard this constraint. For the purposes of this activity, it is assumed that both hands can be moves freely, or that one hand can be held in place while the other moves freely.

• “Escuchemos algunas instrucciones diferentes sobre cómo dibujar estos ángulos. Mientras escuchan, intenten dibujar el ángulo y adivinen cuál ángulo se está describiendo” //  “Let’s listen to some different directions for how to draw these angles. As you listen, try to sketch the angle and guess which angle they are describing how to draw.”
• Invite 2–3 students to share the directions they wrote for drawing one of the angles. Choose students to share in a different order than the angles are presented in the task.
• For each, consider asking:
  • “¿Cuál ángulo describieron ellos (a, b o c), y cómo lo saben?” // “Which angle did they describe (a, b, or c), and how do you know?”
  • “¿Qué palabras les ayudaron a imaginarse cómo dibujar el ángulo?” // “What words help you picture how to draw the angle?” (turn right, turn left, point at 4)
• “Podemos describir el tamaño de un ángulo explicando cuánto giró un rayo desde el otro rayo” // “We can describe the size of an angle by explaining how much one ray has turned from the other.”

In this activity, students compare the sizes of angles by thinking in terms of a turn of one ray from the other ray. They continue to use the clock as a tool for reasoning and for talking about “how much” of a turn. This work helps to elicit a need for more formal units and tools for measuring degrees while building the foundation for understanding angle measurement as additive. Students may describe the unit of measurement as “minutes,” “hours,” or other informal names (turn-units). They will learn about degrees as a unit of measurement in the upcoming lessons. 

The final question gives students an opportunity to describe the size of an angle in as many ways as they can, using the clock face, benchmark angles, or other informal descriptions (MP6), which prepares them for the introduction of a numerical way to measure angles.

• Invite 2–3 previously identified students to share their responses. 
• “¿Cómo pudo cada estudiante ver el ángulo formado por las manecillas de una manera diferente?” // “How did each student see the angle formed by the hands in different ways?” (Some thought about moving the _____ hand toward the _____ hand, in the same direction it really moves on the clock. Others thought about the minute hand starting at the same spot as the hour hand, and moving it in either direction.)  
• “¿Esto cómo cambió cuál era el ángulo que ellos pensaban que era el más grande?” // “How did this change which angle they thought was larger?” (It changed how far they thought one ray turned.)
• “Cuando le describimos un ángulo a otras personas, con frecuencia dibujamos un ‘arco’, o una parte de un círculo, entre los rayos para mostrar a cuál giro nos referimos” // “When we describe an angle to others, we often draw an ‘arc,’ or part of a circle, between the rays to show which turn we are talking about.”