Lesson 5

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Además del tiempo, ¿qué otra cosa cambia cuando giran las manecillas de los relojes?” // “Besides the time, what else changes when the long and short hands of the clocks turn?” (The directions of the hands, the figures created by the two hands, the appearance of the clock.)
• “Es posible que algunos de ustedes se pregunten qué tienen que ver el tiempo y los relojes con las rectas, los puntos, los rayos y los segmentos. Sigamos pensando sobre esto mientras trabajamos en nuestra primera actividad” // “Some of you may wonder what time and clocks have to do with lines, points, rays, and segments. Let’s keep thinking about this as we work on our first activity.”

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 endpoint. Students may also 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 are likely to use terms such as “narrower,” “wider,” or the like. Save the chart that shows the words students use to describe angles during the activity to revisit in future lessons.

Here are the two sets of images for the activity and one set for the extension:

Set 1

Set 2

Set 3 (If time permits)

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

• Create a set of cards (4 cards total) for each group of 2 from the blackline master.
• Each group of 2 needs 2 cards (sets 1 and 2). Additional cards (sets 3A and 3B) can be used for extension.

• Groups of 2
• Read the instructions together as a class. Demonstrate or clarify the process as needed.

• Give one partner the card for set 1. When the partners have discussed the drawings, give the other partner the card for set 2 and repeat the exercise.
• Provide one ruler or straightedge per student.
• 3–4 minutes per round

MLR2 Collect and Display

• Monitor for geometry terms from this section and phrases students use to describe the pace between the rays on each card. (spread apart, slide, moved over)
• Record students’ words and phrases on a visual display and update it throughout the lesson.
• If groups are ready for more, give them a third card to describe and draw.

• “¿En qué se parecen los dos dibujos de cada tarjeta?” // “How are the two drawings on each card the same?” (They each have 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 like 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 extremo” // “The figures that you drew are angles. An angle is a figure that is made up of two rays that share the same endpoint.“

• “El punto en el que los dos rayos se encuentran se llama el vértice del ángulo” // “The point where the two rays meet 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.

• Groups of 2
• Read the prompt to students.

MLR1 Stronger and Clearer Each Time

• 5 minutes: independent work time
• “Compartan con su pareja su respuesta al primer problema. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response to the first problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: partner discussion
• Repeat with 2–3 different partners.
• Monitor for students who hypothesize that there are no angles in figure B or C because no rays are drawn. Address this idea in the synthesis.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

• “¿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.)
• “¿Podrían usar la palabra ‘ángulo’ en nuestra descripción de la figura A? Si es así, ¿cómo?” // “How might you use the word ‘angle’ in our description of figure A? If so how?” (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.)
• “En la discusión de Clare y Kiran, ¿dónde están los dos ángulos que vio Kiran?” // “In Clare and 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 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 an endpoint.

In future lessons, students will look more closely at the properties of angles and consider how they can be measured and whether the length of the segments that form them impacts the size of the angles.

• Groups of 2
• Give each student a ruler or a straightedge.

• 5 minutes: independent work time
• 2 minutes: partner discussion

Students may say they have identified an angle because they have found a vertex. Ask these students to explain what they mean and to describe the angle they see. Consider asking:

• “¿Cómo reconociste los rayos que comparten este vértice? ¿Puedes dibujarlos?” // “How do you see the rays that share this vertex? Can you draw them?”
• “¿Un vértice puede ser compartido por más de un ángulo? ¿Cómo puedes usar la figura A de la actividad anterior para explicarlo?” // “Could more than one angle share a vertex? How could you use figure A from the previous activity to explain?”

• “¿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?”