Lesson 4

This warm-up prompts students to carefully analyze and compare quadrilaterals and their sides. When students make comparisons, they have a reason to use geometric language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about characteristics of two-dimensional figures. The knowledge and ideas that students show here may also be insightful to teachers in the next lesson, when students learn about angles.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Record responses.

• “¿Cómo podemos saber si los lados de una figura son paralelos?” // “How might we know if the sides of a figure are parallel?” (We could extend the lines or measure to see if the two sides are always the same distance apart.)
• “Los cuatro cuadriláteros tienen al menos un par de lados paralelos. En general, ¿todos los cuadriláteros tienen al menos un par de lados paralelos?” // “All four quadrilaterals have at least one pair of parallel sides. Do all quadrilaterals have at least one pair of parallel sides?” (No) “¿Pueden dibujar uno que no tenga lados paralelos?” // “Can you draw one with no pairs of parallel sides?”

In this activity, students practice identifying line segments and both intersecting and parallel lines. First, students find these figures on a map and then in the alphabet. In both contexts, they encounter marks that may appear to be segments, but are not actually perfectly straight, or pairs of lines that appear to be parallel, but are not exactly so. Students have an opportunity to attend to precision when analyzing the given images (MP6).

When analyzing some letters in the alphabet, students may say that J and O have lines or segments that turn. Remind students that we had defined a line as being straight, so a line segment is also straight. In the letter J, the segment can be distinguished from the curve.

• Gather Collect and Display charts from previous lessons.
• Each student will need access to their personal word walls created in previous lessons. 

• Groups of 2
• Display the map of Staten Island, NY.
• Give students access to rulers or straightedges.
• Display the chart of phrases collected during Collect and Display in a previous lesson.
• “Usen su propio muro de palabras o esta tabla de palabras y frases para describir lo que observaron sobre este mapa de Staten Island, Nueva York” // “Use your personal word walls or this chart of words and phrases to describe what you notice about this map of Staten Island, New York.”
• “¿Qué observan acerca de las calles en el mapa?” //  “What do you notice about the streets on the map?” (Some are short and some are long. Some end and some cross others.)

• 5 minutes: quiet think time
• 3–4 minutes: partner work time
• Monitor for students who:
  • notice that some marks on the map are not straight (even if they might appear to be) and are therefore neither lines nor segments
  • recognize that some pairs of lines or segments might appear to be parallel but are not

Students may describe letters as having parallel segments (or as having no intersecting segments) because the segments do not cross. Ask students to explain and show what they mean. If students show segments that meet, but do not cross, consider asking,

• “¿Qué piensas que significa que dos segmentos sean paralelos?” // “What do you think it means for segments to be parallel?”
• “Si dibujas las rectas en las que están estos segmentos, ¿las rectas se cruzarán?” // “If you draw the lines that these segments are on, would the lines ever cross?”

• Select students to share their responses to the first question. Display their work (using a document camera or projection), or display the map and ask them to show their lines on it.
• To elicit the use of precise vocabulary and encourage more participation, consider asking:
  • “¿Hubo pares de rectas que al principio pensaron que eran paralelas, pero después se dieron cuenta de que no lo eran? ¿Cómo lo descubrieron?” // “Were there any pairs of lines that you had assumed to be parallel at first but then realized that they are not? How did you find out?”
  • “¿Alguien más puede mostrar otro par de rectas paralelas? ¿Y otro par de rectas que no sean paralelas?” // “Can someone else show a different pair of parallel lines? A different pair of lines that are not parallel?”
• “¿Dos segmentos tienen que tener la misma longitud para ser paralelos? Por ejemplo, el segmento horizontal de arriba de la ‘E’ y el segmento horizontal del medio tienen longitudes distintas. ¿Son paralelos?” // “Do two segments have to be the same length to be parallel? For example, the top horizontal segment in E and the middle horizontal segment have different lengths. Are they parallel?” (Yes. The segments are part of lines that are parallel. The length of the segments does not determine if they are parallel.)
• “¿Cómo podemos completar estas afirmaciones?” // “How might we finish these statements?”
  • “Todas las rectas que se intersecan _____” // “All intersecting lines _____.” (cross each other)
  • “Algunas rectas que se intersecan _____” // “Some intersecting lines _____.” (form square corners, make an “X” shape)
  • “Todas las rectas paralelas _____” // “All parallel lines _____.” (never cross)

In this activity, students look for parallel and intersecting lines in their environment and record them in a drawing. Students notice that parallel and intersecting segments can be found in logos and symbols and use these figures to design their own logo. When students recognize mathematical features of objects in their classroom and design a logo with intersecting and parallel line segments they model with mathematics (MP4).

If time permits, ask students to display their drawings and logos and do a gallery walk.

• Groups of 2
• Give students access to a ruler or a straightedge.
• “En esta actividad, miren alrededor del salón, encuentren partes que tengan partes geométricas como las que hemos estudiado y dibujen un bosquejo de ellas” // “For this activity, look around the classroom, find parts that have certain geometric parts we've been studying, and draw a sketch of them.”

• 5–7 minutes: independent work time on the first question
• 2–3 minutes: partners trade sketches and verify that the required lines are shown
• Monitor for students who:
  • represent the thickness of objects (of a frame or a countertop, for example) with two parallel lines
  • represent objects abstractly, showing only essential shapes and lines
  • attend to precision by using tools like rulers or straightedges
  • choose to draw freehand
• For students who draw freehand, consider asking:
  • “¿Cómo puedes estar seguro de que lo que dibujas son rectas o segmentos y no curvas?” // “How can you be sure that what you are sketching are lines or segments and not curves?”
  • “¿Cómo sabes si estás dibujando segmentos paralelos?” // “How do you know if you are drawing parallel segments?”
• 5 minutes: independent work time on the second question

• “¿En qué parte de nuestro salón encontraron rectas paralelas?” // “Where did you find parallel lines in our classroom?” (windows, doors, floor tiles, cubbies, desks)
• “¿En qué parte encontraron rectas que formaban esquinas cuadradas?” // “Where did you find lines that make square corners?” (windows, doors, floor tiles, cubbies, desks)
• “¿En qué parte encontraron rectas o segmentos que no formaban esquinas cuadradas cuando se intersecaban?” //  “Where did you find lines or segments that do not make square corners when they intersect?” (design on the doors, slant on the ceiling or floor, railings of stairs, braces or brackets of desks or chairs, hands on the clock)
• If time is limited, ask partners to trade their logo designs, look for the required lines in each other’s work, and share feedback.
• If more time is available, ask students to display their designs and visit others’ work in a gallery walk. As they look at each design, students should look for parallel and intersecting lines and line segments.