# Lesson 6

Todo tipo de características (optional)

## Warm-up: Cuántos ves: Punto tras punto (10 minutes)

### Narrative

The purpose of this How Many Do You See is to allow students to use subitizing or grouping strategies to describe the images they see. Students may identify lines of symmetry within the dot arrangement and use this as a strategy to determine the total number of dots. The may also consider smaller arrays, or chunk the image into small groups and multiply or add.

In this activity, students have an opportunity to look for and make use of structure (MP7) because the arrangement contains smaller arrays and line symmetry.

### Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Display the image.
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

### Student Facing

¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?

### Activity Synthesis

• “¿Cómo les ayuda la forma en la que están organizados los puntos a encontrar el número?” // “How does the arrangement of dots help you find the number?” (It has lines of symmetry. We can count the dots on one side of the line and double it, without counting one by one.)
• “¿Alguien puede expresar con otras palabras la forma en la que _____ vio los puntos?” // “Who can restate the way _____ saw the dots in different words?”
• “¿Alguien vio los puntos de la misma manera, pero lo explicaría de otra forma?” // “Did anyone see the dots the same way but would explain it differently?”
• “¿Alguien quiere compartir otra observación sobre la manera en la que _____ vio los puntos?” // “Does anyone want to add an observation to the way _____ saw the dots?”

## Activity 1: Vas a dibujarla: Es simétrica (20 minutes)

### Narrative

In this activity, students create their own figures that have certain symmetry-based attributes. Students are given a pair of parallel segments on a grid. They then add more segments to create figures with one, two, and zero lines of symmetry.

To create their own figures, students rely on their understanding of symmetry and parallel lines. They consider where possible lines of symmetry could be, how many segments to add, and where to place them. They may also experiment, rely on familiar shapes and their lines of symmetry, or imagine a line of symmetry and what it would tell them about the figure. As they do so, they look for and make use of structure (MP7).

Action and Expression: Develop Expression and Communication. Offer grid paper and copies of the pair of parallel line segments from the task. Invite students to use this paper to create multiple drafts, examining and refining their own thinking as they work. Supports accessibility for: Conceptual Processing, Visual Spatial Processing, Organization

### Required Materials

Materials to Gather

### Launch

• Groups of 2–4

### Activity

• 2–3 minutes: independent work on the first question
• 2 minutes: group discussion
• “Compartan el dibujo que hicieron para la primera pregunta. Si es necesario, ajusten sus ideas y su dibujo” // “Share your drawing for the first question. If needed, revise your thinking and drawing.”
• 5 minutes: independent work time on the remaining questions
• 3–5 minutes: group discussion
• “Asegúrense de discutir cómo saben que sus dibujos tienen el número de líneas de simetría que les piden” // “Be sure to discuss how you know that your drawings have the specified number of lines of symmetry.”
• Listen for attention to precision in students’ justifications. For instance, they may say the figure has line symmetry because:
• the angles are the same
• the sides have the same length and create the same angles when folded on top of each other
• they measured all the parts and found them to be the same
• they traced the figure and placed the copy on top of the original

### Student Facing

1. Este es un par de segmentos paralelos que tienen la misma longitud.

Agrega uno o más segmentos para formar una figura que tenga solamente 1 línea de simetría.

2. Estos son otros dos pares de segmentos paralelos. Agrega más segmentos para formar:

1. una figura que tenga 2 líneas de simetría

2. una figura que no tenga líneas de simetría

Si te queda tiempo: Estos son otros pares de líneas paralelas. Agrega más segmentos para formar una figura que tenga 1 línea de simetría.

### Student Response

If students create figures with more or fewer lines of symmetry than planned, consider asking:

• “¿Cuántas líneas de simetría querías que tuviera tu figura? ¿Cuántas líneas de simetría tiene?” // “How many lines of symmetry did you want your figure to have? How many lines of symmetry does it have?”
• “¿Cómo puedes cambiar tu figura para que tenga menos (o más) líneas de simetría?” // “How could you change your figure so it has fewer (or more) lines of symmetry?”

### Activity Synthesis

• Invite students to share their drawings and how they determined how and where to add segments.
• “¿Qué partes de la figura tuvieron en cuenta para dibujarla? ¿Cómo se aseguraron de que su dibujo fuera simétrico con respecto a una línea?” // “Which parts of the figure did you pay attention to when drawing? How did you make sure your drawing has line symmetry?“ (The segment lengths, angles, and distances from the line of symmetry all have to be the same on both sides of a line of symmetry.)
• “En esta tarea, ¿qué fue complicado al crear figuras simétricas con respecto a una línea?” // “What was tricky about creating figures with line symmetry in this task?” (Sample response: It was hard to figure out what to draw to get the exact number of lines of symmetry.)

## Activity 2: Figuras escondidas (10 minutes)

### Narrative

In this activity, students apply their understanding of symmetry, parallel and perpendicular lines, and types of quadrilaterals to create shapes with certain attributes on isometric dot paper. The arrangement and equal spacing of the dots give students structure for drawing parallel and perpendicular lines and to determine symmetry.

MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous activities. Invite students to borrow language from the display as needed, and update it throughout the lesson.

### Launch

• Groups of 2
• Display the isometric dot image.
• “¿Qué observan?” // “What do you notice?” (lots of dots forming lines, triangles, rhombuses)
• “¿Qué se preguntan?” // “What do you wonder?” (Are the dots spaced apart equally? Why is every other vertical stack of dots higher or lower than the stack next to it?)

### Activity

• 10 minutes: group work time
• Monitor for students who:
• use the equal distance between dots to draw parallel lines
• notice that the dots in alternate columns form horizontal lines, which can be used to create right angles with vertical lines
• use the dots to create equal lengths and angles

### Student Facing

Este es un campo de puntos.

¿Puedes unir puntos para crear cada una de las siguientes figuras? Si es así, dibújalas. Si no, prepárate para explicar cómo razonaste.

1. Un triángulo que tenga solamente una línea de simetría
2. Un cuadrilátero que tenga solamente una línea de simetría
5. Un rectángulo
6. Una figura de seis lados que tenga solamente una línea de simetría

### Activity Synthesis

• Invite students to share their drawings. Highlight that many different drawings are possible for each description.
• “¿Cómo se aseguraron de que las primeras dos figuras fueran simétricas con respecto a una línea?” // “How did you make sure that the first two figures have line symmetry?” (Check that the figure has a line that splits it into two halves that mirror one another and match up when folded.)
• “¿Cómo crearon lados paralelos y cómo supieron que en realidad son paralelos?” // “How did you create parallel sides and know that they are indeed parallel?” (Use the spacing of the dots to draw segments that are the same distance apart.)
• “¿Cómo crearon segmentos que fueran perpendiculares?” // “How did you create segments that are perpendicular?” (Connect dots that line up vertically and those that line up horizontally.)
• “¿Qué partes específicas tuvieron que dibujar para crear un rectángulo?” // “What parts, specifically, did you need to draw to create a rectangle?” (2 sets of parallel segments—the same length for opposite sides—and 4 right angles)

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos nuestra comprensión de las características de las figuras para dibujar figuras con diferentes líneas de simetría y diferentes números de lados paralelos o perpendiculares” // “Today we used our understanding of the attributes of figures to draw figures with varying lines of symmetry and varying numbers of parallel or perpendicular sides.”

Display the images:

“Cuando las figuras se muestran en una cuadrícula hecha con líneas o puntos, a menudo podemos conocer muchas de sus características. Estas son dos figuras: una está en una cuadrícula cuadrada y la otra está en una cuadrícula triangular punteada” // “When figures are shown on a line grid or dotted grid, we can often learn a lot about their attributes. Here are two figures, one on a square grid and the other on a dotted triangular grid.”

“Díganme cómo podríamos usar las cuadrículas para ver si:” // “How might we use grids to see if:”

• “dos segmentos tienen la misma longitud” // “two segments have the same length?” (On a grid with lines, we can count the units. On dot paper, we can use the distance between dots to see segments are the same length.)
• “dos segmentos son paralelos” // “two segments are parallel?” (On a square grid, the horizontal lines are parallel, and so are the vertical lines. On dot paper, any two rows or columns of dots that are always the same distance apart are parallel.)
• “dos segmentos son perpendiculares” // “two segments are perpendicular?” (On a square grid, the vertical and horizontal lines are perpendicular. On dot paper, there are vertical stacks of dots and horizontal rows.)
• “una figura es simétrica con respecto a una línea” // “a figure has line symmetry?” (Use the grid or the dots to check if the figure has two parts that are the same size and mirror each other across a line.)

## Student Section Summary

### Student Facing

En esta sección, examinamos diferentes características de las figuras, como el número de lados y sus longitudes, la medida de los lados y de los ángulos, y si las figuras tenían lados paralelos o perpendiculares. Después, usamos estas características para clasificar cuadriláteros y triángulos.

Los triángulos que tienen un ángulo recto son triángulos rectángulos.