Lesson 2

The purpose of this warm-up is for students to describe a point which will be useful when students locate points on a coordinate grid in a later activity. While students may notice and wonder many things about this image, the relationship between the point and the numbers on the vertical and horizontal axes is the main focus of the discussion. 

• 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. 

• “¿Cómo podemos describir la ubicación del punto?” // "How can we describe the location of the point?” (It is kind of in the middle of the grid, but toward the top. It is where two lines intersect. It is where line 5 and line 6 cross each other.)

The purpose of this activity is for students to describe coordinates for points. After playing a round of What’s the Point, students have an opportunity to write a description of the location of a point in the coordinate plane. The structure of this part of the activity mirrors what students did in the previous lesson when they were describing a rectangle. Some students may use the coordinates on the grid while others may use words to describe the location of the point.

Students make choices about how to revise their thinking based on what makes the description stronger and clearer to them. This activity not only supports students developing language to describe the location of a point but also develops a deeper understanding of the coordinate grid (MP6). Invite students to use language from the display from an earlier lesson if they find it helpful.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

• Create a set of cards from the blackline master for each group of 2.

• Groups of 2.

• 10 minutes: partner work time
• Monitor for students who:
  • revise their thinking
  • refer to the numbers on the coordinate grid to communicate the location of the point

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero su descripción de la ubicación del punto en la cuadrícula. 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 description of the location of the point on the grid 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: structured partner discussion
• Repeat with 1–2 different partners.
• If needed, display question starters and prompts for feedback, such as:
  • “¿Pueden usar los números de la cuadrícula de coordenadas en su explicación?” // “Can you use the numbers on the coordinate grid in your explanation?”
• “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 partner.”
• 2–3 minutes: independent work time

If students do not reference the axes or the directionality of the gridlines, show them point \((3, 4)\) and point \((4, 3)\) on a grid and ask, “¿En qué se parecen y en qué son diferentes estos dos puntos?” // “What is the same and different about these two points?”

• Select previously identified students to share how they revised their explanation for the location of the point in the last problem.
• Display the image of the coordinate grid with a point from the student workbook.
• “El punto se puede describir usando las coordenadas \((3, 4)\). ¿De dónde creen que vienen estas coordenadas?” // “The point can be described using the coordinates \((3, 4)\). Where do you think these coordinates come from?” (They describe the location of the point. The point is on gridline 3 and gridline 4. The point is where these gridlines intersect.)

The purpose of this activity is for students to write ordered pairs of numbers to represent points in the coordinate plane and to plot points with given coordinates. Students may interpret the horizontal and vertical coordinates backward. With time and practice they will learn the convention that the first coordinate represents the horizontal location of the point and the second coordinate represents its vertical location.

• Groups of 2
• Display images of points \(P\) and \(Q\) from student workbook.
• Poll the class:
  “¿Cuáles son las coordenadas de los puntos \(P\) y \(Q\)?” // “What are the coordinates of point \(P\) and \(Q\)?”
• “Las coordenadas de estos puntos tienen los mismos números. Tenemos una convención: siempre escribimos de primero el número que corresponde al eje horizontal y de segundo el número que corresponde al eje vertical. Las coordenadas del punto P son \((3, 4)\). ¿Cómo está representado el punto \(P\) con estas coordenadas?” // “The coordinates for these points have the same numbers. We have a convention that we always list the number that corresponds with the horizontal axis first and the number that corresponds with the vertical axis second. The coordinates for point P are \((3, 4)\). How do these coordinates represent point \(P\)?” (The 3 is on the horizontal axis and the 4 is on the vertical axis.)
• “¿Cuáles son las coordenadas del punto \(Q\)?” // “What are the coordinates for point \(Q\)?” \((4, 3)\)
• “En esta actividad, van a nombrar coordenadas de puntos y a ubicar puntos que tienen ciertas coordenadas dadas” // “In this activity, you are going to name coordinates of points and plot points with given coordinates.”

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

• “¿Qué retos hay al nombrar las coordenadas de un punto?” // “What is challenging about naming the coordinates for a point?” (I need to remember which coordinate goes first and which one goes second. I have to be careful to make sure I get the right horizontal and vertical location of the point.)
• “¿Qué retos hay al ubicar puntos en la cuadrícula de coordenadas?” // “What is challenging about plotting points on the coordinate grid?” (I have to remember which coordinate goes with which axis. It is hard to remember the coordinates while you are also trying to find them on the grid. I could find each coordinate but finding the point with both of those coordinates is hard.)