The purpose of this activity is to draw students’ attention to intersecting lines and parallel lines. Students may not have had a reason to consider how to describe the characteristics of lines that cross. To motivate them to do so, they are given three intersecting lines and asked to add a fourth—first to make any quadrilateral, and then to make a rectangle.

Students notice that creating a quadrilateral is not a problem, but creating a rectangle is. They analyze the given lines and consider the attributes of a rectangle that make the second task difficult. Along the way, students likely will recognize that, to form a rectangle, they would need two pairs of lines, with each pair always pointing in the same direction and never converging, and where the first pair make square corners when they cross the second pair (MP7).

• Display the image on the Task Statement. Invite students to share their responses and reasoning.
• “¿Qué tiene que ser cierto acerca de las cuatro rectas para que estas formen un rectángulo?” // “What must be true about the four lines for them to form a rectangle?” (Sample responses:
  • The lines need to make square corners whenever they cross.
  • We need 2 pairs of lines, each pair going in the same direction and never coming together, and where they cross, they need to make square corners.)
• Record examples to match student explanations or invite students to draw examples of their thinking for all to see.
• “Las rectas que nunca se intersecan, como las que están en lados opuestos de un rectángulo, se llaman rectas paralelas” // “Lines that never intersect—such as those on opposite sides of a rectangle—are called parallel lines.”
• Display or add to student examples to emphasize lines and line segments:

  

• If time permits, consider asking, “¿Pueden encontrar un par de rectas paralelas aquí en nuestro salón de clase?” // “Can you find a pair of parallel lines here in our classroom?” (Lines on either side of a row of floor tiles, the top and bottom sides of the board, or the left and right sides of the door.)

In this activity, students are prompted to draw intersecting and parallel lines, and to explain how they know a pair of parallel lines would never intersect.

Students are not expected to formally justify that two lines are parallel. They are expected to make a case that goes beyond appearance (such as “it looks like they would never cross”) and to notice that the parallel lines maintain the same distance apart (MP3). Students also are introduced to the convention of naming lines with letters to support precision when describing and comparing lines. They are not expected to formally name lines or line segments with letters.

• Discuss the first three questions. Select a few students to show or explain how they know their lines would never cross.
• If students suggested that they extended the lines and the lines didn’t cross, ask if there is a chance that the lines would cross if they continue to be extended.
• “¿Cómo supieron que sus rectas nunca se cruzarían?” // “How did you know that your lines would never cross?” (I lined up one side of a ruler with Line H, or Line G, and traced the other side of the ruler to make a new line, and the two sides of the ruler never crossed. The distance between the dots is always the same, so if one line is always, for instance, 2 dots away horizontally from the other line, then they would never cross.)
• If students discovered after extending them that the lines would cross, ask: “¿Qué observan acerca de la distancia entre las dos rectas que en algún momento se van a cruzar?” // “What do you notice about the distance between the two lines that would eventually cross?” (They are getting closer.)
• “¿Qué observan acerca de la distancia entre dos rectas paralelas?” // “What do you notice about the distance between two parallel lines?” (The distance doesn’t change.)
• Discuss students’ responses to the last question. Ask students to support their predictions by extending the sides of the trapezoid (or display the image in the Student Responses).