In previous activities, students used the features of a clock to describe and compare angles. This activity introduces students to the degree as a unit of measure.

Because one degree is much more abstract than one inch or one square-inch tile, students are first introduced to 360 degrees as a full rotation of a ray around its starting point. Students use this information to reason about other angle measurements. They may use their understanding of fractions of a circle to determine the sizes (MP7).

In the Activity Synthesis, students describe angle measurement as additive. Students will continue to build this understanding and reason about the size of 1 degree in subsequent lesson activities.

• Invite previously identified students to share how they estimated the turn of each ray in degrees.
• “¿En qué se parecieron sus métodos? ¿En qué fueron diferentes?” // “How were your methods the same? How were they different?” (We all used the first diagram to figure out how much of a turn. Some of us used one measure to find the next measure. Some of us thought about addition and some thought about division).
• Consider displaying the equation and discussing:
  • “¿Cómo corresponde esto a una manera de estimar el tercer ángulo?” // “How does this match a way to estimate the third angle?”
  • “¿Qué otra ecuación podemos usar para describir ese ángulo?” // “What’s another equation we could use to describe that angle?”
• “Un ángulo que mide 90 grados se llama un ángulo recto” // “An angle that measures 90 degrees is called a right angle.”
• “¿En dónde han visto ángulos rectos antes?” // “Where have you seen right angles before?” (Corners of squares or rectangles. Corners of paper. The angle made by the hands of a clock when it is 3 o'clock or 9 o'clock.)

In this activity, students construct a protractor-like tool that shows some benchmark angles. They do so by decomposing given angles— and —and then looking for other ways to compose or decompose the subsequent angles identified along the way.

The activity serves several goals. The first is to familiarize students with the structure of a protractor, using tactile processes (folding paper and aligning lines or edges). The second goal is to develop students’ intuition for thinking of a larger angle as composed of smaller angles, preparing them to see (in future lessons) that a angle is of a full turn. A final goal is to motivate the need for a tool that can measure angles more precisely.

Some students may use a square corner of a sheet of paper to find a angle on their semicircle and others may choose to fold their semicircle in half. Expect most students to fold their paper to find all subsequent angles.

• “¿Cómo encontraron un ángulo de ?” // “How did you find a angle?” (I folded the semicircle into halves.)
• “¿Cómo encontraron todos los demás ángulos?” // “How did you find all the other angles?” (For , fold to line up the thick ray with the segment, splitting 120 into two. For , fold to line up the ray with the segment, splitting 90 into two. Repeat in a similar fashion to find the others.)
• Invite students to share how they might find a angle in their half circle. Highlight explanations that involve finding some fraction of smaller and smaller angles.
• Solicit some estimates of the angle measurements in the last problem. Record and display them for comparison later, when the same four angles are measured, using a protractor.
• Students likely will notice that their tool is imprecise and not reliable or practical for measuring angles beyond estimations. Explain that we will look at another tool in the next activity.