Lesson 1

This warm-up prompts students to generate formal and informal geometric language (lines, points, straight, curved) that will be used in an upcoming task by familiarizing themselves with a context and the mathematics that might be involved.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

• 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.

• “En las observaciones que hicieron y en lo que se preguntaron, ¿qué palabras o términos se mencionaron varias veces?” // “Which words or terms came up multiple times in the observations you made and in the questions you had?” (point, line, straight)
• “Vamos a trabajar con estas características geométricas en esta lección y en las siguientes. Veamos qué podemos descubrir sobre ellas” //“We’ll work with these geometric features in this lesson and in upcoming ones. Let’s see what we can find out about them.”

The purpose of this activity is to motivate a need for more precise geometric language. Students work with a partner to replicate given geometric images—one partner describes the images and the other draws them solely based on the verbal descriptions from their partner. Students do this over several rounds, switching roles after two rounds. As students attempt to produce more accurate drawings, they try to fine-tune their descriptions. They notice that more specific language or terminology is needed to better describe the features in the images (MP6).

Here are the two sets of images:

Set 1

 

Set 2

 

As students are working, listen for and collect the terms or descriptions that come up often or that effectively help the drawer replicate the image (for example: horizontal, vertical, point, lines, segment, top, bottom, and so on).

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

• Create a set of 4 cards from the blackline master for each group of 2.
• Create a poster with the two images shown in activity synthesis. 

• Groups of 2
• Read the instructions together as a class. Demonstrate or clarify the process as needed.
• Give each student a ruler or a straightedge. Give each group four blank (unlined) index cards. 

• Give 4 blank cards to each group.
• Give one partner the first image card from Set 1. When the group is done with the first round and has discussed the drawing, give the second card.
• 3–4 minutes per round.

MLR2 Collect and Display

• Circulate, listen for, and collect the language students use to describe the first and second images. Listen for: line, point, straight, corner, quadrilateral, triangle, rhombus, vertical, horizontal, middle, top, bottom, left, right.
• Record students’ words and phrases on a visual display and update it throughout the lesson.
• Repeat for the second partner, using the cards from Set 2.

• “¿Qué palabras puedes usar para ayudarle a tu compañero a dibujar esa parte de la figura exactamente como tu lo quieres?” // “What words could you use to help your partner draw that part of the figure exactly how you want it?”
• “¿Cómo puedes partir en partes el _____ que ves? ¿De qué manera podrías describir cómo dibujar cada parte?” // “How could you break the _____ you see into parts? How could you describe how to draw each part?”

• “¿Qué otras palabras o frases importantes deberíamos incluir en nuestra presentación?” // “Are there any other words or phrases that are important to include on our display?”

• Display the chart of terms and these images to facilitate discussion. Annotate on them to support students with mathematical terms.

  

  

  

  

• 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.
• “¿Cómo describieron lo que vieron?” // “How did you describe what you saw?” (By describing where the lines start and where they end, their directions, the distances between them, what they look like—if they look like a familiar shape or letter.)
• “¿Qué palabras o descripciones fueron más útiles cuando describieron las figuras y cuáles fueron menos útiles?” // “What words or descriptions were more helpful when describing the figures and which were less helpful?” (Helpful examples: line, point, straight, corner, triangle, rhombus, vertical, horizontal, middle, top, bottom, left, right. Less helpful examples: here, there, a little bit, pointy, slanted.)
• “¿Qué fue fácil de describir?” // “What was easy to describe?” (Lines that start a corner or the middle of an edge, lines that go left and right or up and down.)
• “¿Qué no lo fue?” // “What was not?” (Lines that cross other lines or that stop at hard-to-describe points.)
• “¿Alguien midió algo o uso medidas? ¿En qué casos podrían haber sido útiles las medidas?” // “Did anyone measure something or use measurements? When might measurements have been helpful?” (When describing distances between lines or the position of a starting point.)

The purpose of this activity is to enable students to notice segments as parts of lines and motivate a need for a term to describe them.

Students are asked to draw multiple lines and to notice shapes that intersecting lines might have created. As they look for familiar shapes or figures in their drawing—polygons, letters, or numbers—their attention shifts from the lines to portions of the lines that make up those figures. Certain sections of the lines now have new significance apart from the lines that contain them. The observations here prepare students to better understand the mathematical definition of line segments.

The synthesis introduces the term line segment informally. In the next lesson, the meaning of the term, as well as of the meanings of lines and points, will be formalized.

• Groups of 3–4
• Give each student a ruler or a straightedge.
• Display the image of dots.
• “¿Qué observan?” // “What do you notice?” (There are lots of dots or points. If we connect them, we can make shapes. I see triangles, rhombuses, and hexagons. The dots make straight lines left to right, and they are the same distance apart.)
• “¿Qué se preguntan?” // “What do you wonder?” (Why are the points in one row not lined up with the points in the rows above or below it? Will we be connecting the dots?)
• “En esta actividad, vamos a usar los puntos que hay en la imagen para hacer diferentes figuras” // “In this activity, we will use the dots in the image to make different figures.”
• Demonstrate drawing a line through a set of dots in the isometric dot image, extending them as far as possible.

• 3 minutes: independent work time
• 2 minutes: partner discussion
• As students discuss, listen for informal descriptions of points, lines, and line segments.

• Display the image on the task statement. Invite students to share their drawings and their responses to the discussion questions.
• “¿En qué se parecen sus dibujos?” // “How are your drawings alike?” (They all have long lines. The shapes are made of shorter pieces of the lines. Some of those pieces end in dots. Others are cut off by another line.)
• “¿En qué son diferentes sus dibujos?” // “How are your drawings different?” (The lines made different shapes and letters. Some shapes are made of parts that always end in dots. Others have parts that don’t end in dots.)
• Display the annotated chart from the previous activity.
• “Cada parte de una recta que conforma su figura se llama un segmento de recta o un segmento. Podemos ver dónde empieza un segmento y dónde termina” // “Each part of a line that makes up your shape is called a line segment or a segment. We can see where a segment starts and where it stops.”
• Ask students to point out to their partners some segments in their drawings.
• “Algunos de ustedes han usado la palabra ‘puntos’ para describir ciertos lugares de las figuras que dibujaron” // “Some of you have used the word ‘points’ to describe the dots or certain parts of the figures you drew.”
• “¿Cuántos puntos ven marcados en esta recta o segmento de recta? ¿Dónde están?” // “How many points do you see marked on this line or line segment? Where are they?” (I see 3 points marking the top of my 7.)
• “¿Pueden mostrarle a su compañero algunos puntos en las figuras que dibujaron?” // “Can you show your partner some points in the figures you drew?”