In this activity, students are given cards that contain illustrations, definitions, and descriptions of points, lines, rays, and segments. They sort the cards into groups so that each group describes one of the four geometric figures.

When students sort the cards, they begin to connect the terms to their formal definitions and attributes (MP6).

Students may have trouble making sense of a point having “no size.” It is not necessary to discuss this in depth at this point, but during the Activity Synthesis, clarify that a point marks a location, and we need a symbol or a mark to represent it. The symbol or the mark has size, but the location itself doesn’t. It is important that students recognize that points make up lines even though we do not always identify them or label them with a dot. If needed, revisit the isometric grid from the previous activity as a reference.

• Invite students to share how they decided which cards go together.
• “¿Con cuáles tarjetas fue más largo el debate en grupo?” // “Which cards did you spend the most time debating as a group?” (“I have no size.” or “My length cannot be measured.”)
• “Puede ser complicado pensar en un punto. Con frecuencia se representa con una bolita o un círculo, que puede ser grande o pequeño. Pero el punto en sí mismo no puede ser grande o pequeño ya que solo marca una ubicación” // “A point might be tricky to think about. It is often represented by a dot or a circle, which could be large or small. But the point itself cannot be large or small since it only marks a location.”
• “¿Qué pasa con una recta? ¿Por qué no se puede medir?” // “What about a line? Why can it not be measured?” (It just keeps going in both directions so we don’t know where to start or stop measuring.)
• “¿Por qué un rayo tampoco se puede medir?” // “Why is a ray also impossible to measure?” (There is a starting point for measurement but there is no endpoint.)
• Consider displaying a graphic organizer (as shown in the Task Statement) for all to see and placing the cards in the correct boxes along the way.
• Ask students to write a sentence and draw an image to represent each figure in the graphic organizer.

The purpose of this activity is for students to use line segments and rays to draw familiar two-dimensional figures, letters, and numerals. Drawing on dot paper helps to reinforce the idea that segments have a defined endpoint on both ends. It also helps to distinguish rays from segments. As they describe and compare figures, students use vocabulary from the previous activity.

The activity also enables the teacher to hear the geometric vocabulary students are bringing from earlier grades. Consider displaying a chart with an image of each shape listed in the first problem during the Launch.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• “¿Cuántos triángulos posibles podemos dibujar en el papel de puntos? ¿Cuántos trapecios posibles? ¿Y hexágonos?” // “How many possible triangles can we draw on the dot paper? How many possible trapezoids? Hexagons?” (There are countless ways to create and connect a specified number of line segments to make a certain type of shape.)
• “¿Alguien no comenzó o terminó sus segmentos de recta o sus rayos en un punto del papel de puntos? ¿Los resultados aún cuentan como segmentos o rayos?” // “Did anyone not start or end their line segments or rays on a dot? Do the results still count as segments or rays?” (Yes. A line segment stops at 2 endpoints, but the endpoints don’t have to be on a dot of the paper.)
• “¿Cómo diferenciaron los segmentos de recta y los rayos cuando dibujaron números y letras en la segunda pregunta?” // “How did you distinguish line segments and the rays when drawing numbers and letters in the second question?” (Line segments stop on both ends. On the end marked with an arrow, the rays go on.)