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.

• “¿En qué se parecen los dos dibujos de cada tarjeta?” // “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.)
• “¿En qué son diferentes?” // “How are they different?” (The rays are pointing in different directions on some cards. The rays are farther apart in some cards.)
• “¿Cómo describieron lo que vieron? ¿Qué términos les ayudaron a describir en qué direcciones iban los rayos?” // “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.
• “¿Alguien usó el término ‘ángulo’? ¿Alguien midió algo o uso medidas?” // “Did anyone use the term ‘angle’? Did anyone measure something or use measurements?”
• “Las figuras que dibujaron son ángulos. Un ángulo es una figura formada por dos rayos que comparten el mismo punto de inicio” // “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.“

• “El punto que comparten los dos rayos que forman un ángulo se llama el vértice del ángulo” // “The point that two rays share when they form an angle is called the vertex of the angle.”

  Display:

  

• “¿Dónde vemos ángulos a nuestro alrededor?” // “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.

• “¿Cómo decidieron si había al menos un ángulo en cada figura? ¿Qué buscaron?” // “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.)
• “¿Cómo podrían usar la palabra ‘ángulo’ en nuestra descripción de la figura A?” // “How might you use the word ‘angle’ in our description of Figure A?” (Two intersecting lines make 4 angles.)
• “En la figura B, los lados del cuadrilátero son segmentos en vez de rayos. ¿Eso significa que no hay ángulos en la figura?” // “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.)

• “¿Pueden mostrar los rayos que forman los ángulos en la figura B?” // “Can you show the rays that make the angles in Figure B?”

  Display:

  

• “¿Podemos mostrar un ángulo en la figura C dibujando rayos, tal como lo hicimos con la figura B?” // “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.)
• “Piensen en el argumento de Kiran. ¿En dónde están los dos ángulos que vio Kiran?” // “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.

• “¿Cómo encontraron los ángulos?” // “How did you find the angles?” (We looked for intersections of segments. When the segments meet or cross, angles are formed.)
• “¿Dónde está el vértice de cada ángulo que encontraron?” // “Where is the vertex of each angle you found?”