Previously, students learned that angles are geometric figures made up of two rays that share the same starting point. The purpose of this activity is for students to compare angles, using the language that makes sense to them. As students look for ways to sort the cards into different categories, they have a reason to look for and describe the parts of the angles that make them different (MP7).

MLR2 Collect and Display is used during the Activity Synthesis of the lesson to record and organize the language students use to describe parts of angles and their sizes. Encourage students to notice differences in the ways they attempt to compare the angles. This work helps elicit the need for more precise vocabulary to describe angle size and ways to measure angles.

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

• “¿En qué fue parecida la manera de clasificar del otro grupo a la de ustedes?” // “How was the other group’s way of sorting like your group's way of sorting?” (We all looked at the lengths of the drawn rays.) 
• “¿En qué fue diferente la manera de clasificar del otro grupo a la de ustedes?” // “How was their way of sorting different from yours?” (They sorted based on if a ray was pointing horizontally or not. We sorted based on if the rays were open wide or whether they looked like they were closing.)
• “¿Qué palabras usaron para ponerles un nombre a las categorías que crearon? ¿Qué palabras escucharon que otros usaron?” // “What words did you use to name the categories you created? What words did you hear others use?”
• As students share, update the display of words they use to describe the angles.
• Remind students to borrow language from the display as needed.

Previously, students sorted angles in ways that made sense to them. In this activity, students reason about how to compare angles, based on a measurable attribute. They are asked to sort the angles from smallest to largest. Students may interpret this prompt in many ways, but all students must begin to reason about how to describe the size of an angle. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

Accept any way that students compare the angles as long as they can explain how they determine whether an angle is smaller or larger than another. Students may use informal language to describe the sizes of the angles. For example, they may use “less wide,” “more pointy,” or “less space” to describe smaller angles. They also may reason that an angle that “can fit inside” another angle is smaller. Continue to collect student language during the activity and to offer formal language when appropriate.  

• Invite 2–3 groups, who ordered the angles in different ways, to share.
• With each group, consider asking:
  • “¿En qué características del ángulo se enfocaron?” // “What features of the angle did you focus on?”
  • “¿Cómo decidieron si un ángulo era más pequeño o más grande?” // “How did you determine whether an angle was smaller or larger?”
• “Hay una manera estándar de medir el tamaño de un ángulo” // “There is a standard way of measuring the size of an angle.”
• Display angles organized from smallest to largest: L, B, G, H, C, D, A (and F, K, P), O, J, E, M, N, I.
• “Estos ángulos están ordenados según su medida, de la menor a la mayor” // “These angles are ordered from the least angle measure to the greatest angle measure.”
• “¿En qué se parece esta forma de ordenar los ángulos a como ustedes lo hicieron? ¿En qué se diferencia?” // “How is this the same as how you ordered the angles? How is it different?” (The smallest angle is the same in both. The largest angles are different, and the angles in the middle also are different.)