# Lesson 2

Características de los triángulos y los cuadriláteros

## Warm-up: Verdadero o falso: Múltiplos de diez (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies students have for multiplying a one-digit number by a multiple of ten. The reasoning students do here helps to deepen their understanding of the properties of operations and develop fluency.

When students use place value or properties of operations as strategies to divide, they look for and make use of structure (MP7).

### Launch

• Display one equation.
• “Hagan una señal cuando sepan si la ecuación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the equation is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each equation.

### Student Facing

En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.

• $$3\times60=9\times10$$
• $$180=3\times60$$
• $$6\times40=24\times10$$
• $$24\times10=240$$

### Activity Synthesis

• “¿Cómo pueden explicar su respuesta sin encontrar el valor de ambos lados?” // “How can you explain your answer without finding the value of both sides?”
• “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
• “¿Alguien quiere agregar algo al razonamiento de _____?” // “Does anyone want to add on to _____’s reasoning?”

## Activity 1: Clasificación de tarjetas: Triángulos (15 minutes)

### Narrative

The purpose of this activity is for students to sort triangles into more specific categories. This requires students to attend to an attribute other than the number of sides. As students sort the triangles, monitor for students who sort by the number of equal side lengths or the presence of a right angle (MP7). Although the terms “equilateral,” “isosceles,” and “scalene” are not introduced in this lesson it is fine if students already know them and use them to describe the groups of triangles.

MLR2 Collect and Display. Direct attention to words collected and displayed from the previous lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Representation: Access for Perception. Synthesis: Use gestures during explanation of triangle sorting to emphasize side lengths of triangles.
Supports accessibility for: Visual-Spatial Processing

### Required Materials

Materials to Copy

### Required Preparation

• Create a set of cards from the blackline master for each group of 2 or 4.
• When copying the card sort triangles, use colored paper to distinguish these cards from the cards in the next activity.

### Launch

• Groups of 2 or 4
• Distribute one set of pre-cut cards to each group of students.
• “¿Qué observan acerca de las figuras que hay en las tarjetas?” // “What do you notice about the shapes on the cards?” (The shapes are all triangles. They all look different. Some of them have sides that are the same length.)
• 1 minute: quiet think time

### Activity

• “Con su compañero, clasifiquen los triángulos en categorías. Asegúrense de explicar sus categorías” // “Work with your partner to sort the triangles into categories. Be sure to explain your categories.”
• 8 minutes: partner work time
• Monitor for students that sort the triangles into groups based on:
• the number of sides with equal length (all, two, none)
• the sides and corners having the same size (the triangles being identical)
• the presence of right angles

### Student Facing

Clasifica los triángulos en categorías. Anota tus categorías y prepárate para explicar cómo clasificaste las figuras.

### Student Response

If students say they aren’t sure how to sort the shapes because they are all triangles, consider asking:

• “¿Qué otras características has usado antes para clasificar figuras?” // “What other attributes have you used before to sort shapes?”
• “¿En qué son diferentes algunos de los triángulos?” // “How are some of the triangles different?”

### Activity Synthesis

• Select groups to share their categories and how they sorted their cards.
• Allow as many categories to be presented as time permits, but be sure to highlight categories based on the number of sides with equal length.
• Highlight the use of terms like “equal side lengths” and “angles.”
• Record and display the attributes students use to categorize the triangles.

## Activity 2: Clasificación de tarjetas: Cuadriláteros (20 minutes)

### Narrative

The purpose of this activity is to sort quadrilaterals by their attributes. By now students may be inclined to look for sides of equal lengths and for right angles. They may not look for parallel sides (and are not expected to know the term “parallel”), but may notice that some quadrilaterals have pairs of sides that are oriented in the same direction (MP7). Encourage students to describe such observations in their own words.

The quadrilateral cards from this activity will be used in the next lesson and in centers.

### Required Materials

Materials to Gather

Materials to Copy

### Required Preparation

• Create a set of cards from the blackline master for each group of 2 or 4.
• Bags or envelopes can be used to store sets of cards from this activity for use in the next lesson.

### Launch

• Groups of 2 or 4
• Distribute one set of pre-cut cards to each group of students.
• “¿Qué observan acerca de las figuras que hay en este grupo de tarjetas?” // “What do you notice about the shapes on this set of cards?” (There are 20 shapes. All the shapes are quadrilaterals. Some have right angles and some don’t.)
• 1 minute: quiet think time

### Activity

• “Como en la actividad anterior, clasifiquen las tarjetas en las categorías que ustedes y su compañero escojan” // “Just like the last activity, sort cards into categories that you and your partner choose.”
• 8 minutes: partner work time
• Monitor for different attributes that students use to sort the shapes.

### Student Facing

Clasifica los cuadriláteros en categorías. Anota tus categorías y prepárate para explicar cómo clasificaste las figuras.

### Activity Synthesis

• “Muestren las tarjetas que clasificaron para que otros puedan verlas” // “Display your sorted cards so that others can see them.”
• “Vayan a ver las tarjetas de otros grupos y traten de descifrar cómo clasificaron sus cuadriláteros. Prepárense para compartir su razonamiento” // “Visit another group’s cards and see if you can figure out how they sorted their quadrilaterals. Be prepared to share your reasoning.”
• 2–3 minutes: Students visit other groups’ displays.
• Invite each group to share how the cards were sorted and their reasoning. Record and display the attributes students use to categorize the quadrilaterals.
• Attend to the language that students use to describe the categories and shapes, giving them opportunities to describe the shapes more precisely.
• Highlight the use of terms like “equal sides” and “right angles.”

## Lesson Synthesis

### Lesson Synthesis

“Hoy clasificamos triángulos y cuadriláteros en categorías más específicas” // “Today we sorted triangles and quadrilaterals into more-specific categories.”

Display the two compiled lists of attributes used to sort triangles and quadrilaterals.

“¿Qué características usamos para clasificar ambos grupos de figuras?” // “Which attributes did we use to sort both sets of shapes?” (The number of sides of the same length. The number of right angles. Whether there were pairs of sides that go in the same direction.)

“¿Cuáles características usamos para un grupo de figuras, pero no para el otro? ¿Por qué razón?” // “Which attributes did we use for one set of shapes but not the other? Why might that be?” (In quadrilaterals we counted the number of right angles, but in triangles we just sorted by whether they had one or not. This is because triangles could only have 1 right angle. We looked at pairs of sides that go in the same direction when sorting quadrilaterals but not when sorting triangles. The sides of triangles can’t go in the same direction.)