In this activity, students follow directions for drawing lines, rays, and angles. To create angles precisely and as specified, students need to use a protractor and a ruler or straightedge (MP6). 

Each step in the drawing process involves one or more decisions for students to make. In some cases, the resulting drawing will be the same.

For example, in the first question, students could use the protractors in different ways to create perpendicular lines.

Going from to

(outer set of numbers):

Going from to

(outer set of numbers):

Going from to

(inner set of numbers):

In other cases, the resulting drawings will vary, depending on the decisions made. For example, in the second question, students could choose to draw the first angle () above or below the given ray. When drawing the second angle (), they could choose to draw it inside the angle or adjacent to the angle (and choosing one side or the other)—in both cases, meeting the specifications. Similarly, when drawing the third angle (), students could choose to draw it adjacent to the other angles or with one or both of the other angles inside. 

• Select students to share their drawings and their reasoning for the last question.
• “¿Qué decisiones tuvieron que tomar al crear el dibujo?” // “What decisions did you have to make when creating the drawing?”
• “Muchos de ustedes ubicaron el ángulo de  al lado del ángulo de . Algunos de ustedes lo ubicaron dentro del ángulo de . De manera similar, muchos de ustedes ubicaron el ángulo de  al lado del ángulo de  o del ángulo de . Algunos de ustedes lo ubicaron con los ángulos de y de adentro. ¿Cómo influyeron las distintas elecciones en el tamaño del ángulo de la última pregunta?” // “Many of you placed the angle next to the angle. Some of you placed it inside the angle. Similarly, many of you placed the angle next to the angle or the angle. Some of you placed it with the angle and the angle inside. How did the different choices affect the size of the angle in the last question?” (Putting the angle inside the angle made the last, unlabeled angle larger. Putting the angle and the angle inside the angle made the last, unlabeled angle larger.)

In the first activity, students drew angles with some scaffolding in place: a line and a point were given, each step was described, and the vertex and the measurements of each angle were specified.

In this activity, students continue to draw angles but with less guidance. For each drawing, students are given only a range of angle measurements and no other criteria, prompting them to make additional decisions about how to draw the angles (for instance, where to position the vertex of an angle, how to orient the first ray or line, and so on). After drawing, students trade their cards and use a protractor to measure and check one another’s angles.

The drawings created here will be used in the next lesson. Consider collecting the cards from each group or otherwise supporting students in keeping the cards until then.

• Invite students to share 1–2 examples of an angle that meets each requirement.
• Consider asking:
  • “¿Pueden saber con solo mirar que este ángulo mide _____?” // “Can you tell just by looking that this angle is _____?”
  • “Si dijeron que sí, expliquen” // “If you say yes, explain.”
  • “Si dijeron que no, ¿qué necesitarían para asegurarse de que mide _____?” // “If you say no, what would you need to make sure it is _____?”