Lesson 3

Formas de ver cuadriláteros

Warm-up: Cuántos ves: Patrón de ladrillos (10 minutes)

Narrative

This warm-up prompts students to notice the attributes of the parallelograms in a brick pattern. It gives the teacher an opportunity to hear how students use terminology from previous lessons to talk about parallel sides, angles, and side lengths.

Launch

• Groups of 2
• Display the image.
• “¿Cuántos ladrillos tienen 2 pares de lados paralelos?” // “How many bricks have 2 pairs of parallel sides?”
• 1 minute: quiet think time

Activity

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

Student Facing

¿Cuántos ladrillos tienen 2 pares de lados paralelos?

Activity Synthesis

• “¿Cuáles ladrillos tienen solo una pareja de lados paralelos?” // “Which bricks have only one pair of parallel sides?” (Each brick that lays horizontally and is not triangular has one pair of parallel sides. The slanted bricks cut off by the edges of the image also have one pair.)
• “¿Creen que todas las figuras que tienen más de 3 lados tienen por lo menos 1 par de lados paralelos?” // “Do you think all figures with more than 3 sides have at least 1 pair of parallel sides?” (No, but this image does not show any examples. There are some figures with more than 3 sides with no pairs of parallel sides.)

Activity 1: Búsqueda de cuadriláteros (20 minutes)

Narrative

In this activity, students analyze the sides and angles of quadrilaterals with attention to the presence of parallel and perpendicular lines. Students are given a set of shapes (a subset of the cards used in previous lessons) and prompted to look for quadrilaterals that have certain attributes. They also have an opportunity to propose an attribute for their partner to find, and make some general observations about the sides and angles of quadrilaterals.

In the synthesis, when discussing quadrilaterals with two pairs of parallel sides, introduce the term parallelogram. Students are not required to know the definition of this term at this point, however, and should not be assessed on it.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Offer students a subset of the cards to start with. Choose a set of cards that gives students the opportunity to consider all the categories, such as N, Q, D, and W. Introduce additional cards once students have finished examining the first set.
Supports accessibility for: Organization, Attention, Social Emotional Functioning

Required Materials

Materials to Gather

Required Preparation

• Each group needs a set of shape cards from the previous lesson. If time permits, separate the quadrilateral cards from each set in advance.

Launch

• Groups of 2
• Give each group a set of cards from the previous lessons.
• “Para esta actividad, usen solamente las tarjetas que tienen cuadriláteros” // “Use only the cards with quadrilaterals for this activity.”

Activity

• “Completen la búsqueda con un compañero y comparen sus respuestas con las de otro grupo” // “Complete the scavenger hunt with a partner and compare responses with another group.”
• 8–10 minutes: group work time on the first two questions
• Monitor for students who use tools to:
• measure sides and angles
• determine if two sides are parallel
• 2 minutes: individual work time on the last problem

Student Facing

1. Encuentra los cuadriláteros que tengan cada una de las siguientes características. Anota las letras que les corresponden en esta tabla.
característica cuadriláteros que tienen la característica
a. no hay ángulos rectos
b. un par de lados paralelos
c. un par de lados perpendiculares
d. todos los lados tienen la misma longitud
e. todos los ángulos son del mismo tamaño
f. solo dos lados tienen la misma longitud
g. no hay lados paralelos
h. dos ángulos obtusos
2. Escoge una frase y complétala basándote en tu trabajo.

1. Observé que algunos cuadriláteros . . .
2. Observé que todos los cuadriláteros . . .
3. Observé que ningún cuadrilátero . . .

Si te queda tiempo, piensa si es posible que un cuadrilátero tenga:

• más de 2 ángulos agudos
• más de 2 ángulos obtusos
• exactamente 3 ángulos rectos

Si piensas que es posible, dibuja un ejemplo. Si piensas que no lo es, explica o muestra por qué crees que es imposible.

Student Response

Students may identify only one quadrilateral per attribute. Consider asking:

• “¿Cómo te aseguraste de haber encontrado todos los cuadriláteros que tienen cada característica?” // How did you make sure you found all the quadrilaterals that have each attribute?
• “¿Cómo revisarías si un cuadrilátero solo tiene una de las características o si tiene más de una?” // “How would you check if a quadrilateral has only one of the attributes or more than one?”

Activity Synthesis

• “Usemos nuestros brazos para mostrar cómo se ven unas rectas paralelas” // “Let’s use our arms to show what parallel lines look like.” (Students hold up two arms parallel to each other.)
• “¿Cómo decidieron si los lados de una figura son paralelos?” // “How did you decide if the sides of a figure are parallel?” (Check if the distance between them is always the same. Extend the sides to see if the lines would eventually meet.)
• As needed, place a ruler between the extended arms of a student to illustrate checking for parallelism.
• “¿Cómo supieron si había lados perpendiculares?” // “How did you know if any sides are perpendicular?” (Check if the sides make a right angle.)
• Ask students to share their completed sentences for the last question. Record their responses and invite the class to agree or disagree.
• Some quadrilaterals . . .
• All quadrilaterals . . .
• No quadrilaterals . . .
• Explain to students that quadrilaterals with two sets of parallel sides are called parallelograms.
• Ask students to identify all the parallelograms in the set of cards. (D, K, N, U, Z, AA, EE, JJ)
• “Así conozcamos estas figuras con otros nombres, como rectángulo o rombo, siempre que los cuadriláteros tienen dos pares de lados paralelos también son paralelogramos” // “We may know some of these figures by other names like rectangle or rhombus, but as long as the quadrilaterals have two pairs of parallel sides, they are also parallelograms.”

Activity 2: ¿Qué es verdad sobre estos cuadriláteros? (15 minutes)

Narrative

In this activity, students begin to formalize their understanding of the attributes of some shapes they have worked with since grades 2 and 3. Students use their observations from the previous activity to draw general conclusions about rectangles, squares, parallelograms, and rhombuses. The conclusions may be incomplete at this point.

Students are not expected to recognize that the attributes of one shape may make it a subset of another shape (for example, that squares are rectangles, or that rectangles are parallelograms). They may begin to question these ideas, but the work to understand the hierarchy of shapes will take place formally in grade 5. During the synthesis, highlight how sides and angles can help us define and distinguish various two-dimensional shapes.

When students describe the sides and angles in the shapes they use language precisely (MP6) and observe common structure in the different sets of quadrilaterals (MP7).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain their statements. Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing

Required Preparation

• Each group needs a set of shape cards from the previous activity.

Launch

• Groups of 2
• Give each group a set of cards from the previous activity and a large sheet of paper for each shape (square, rectangle, rhombus, parallelogram).
• Provide access to rulers, protractors, and patty paper.
• “Hagan una lista de 4 o 5 afirmaciones que sean verdaderas para cada grupo de cuadriláteros” // “List 4–5 statements that are true for each set of quadrilaterals.”

Activity

• 5 minutes: group work time
• Rearrange students into groups of 3–4. Assign each group one set of quadrilaterals (squares, rectangles, parallelograms, or rhombuses).
• “En su nuevo grupo, discutan las afirmaciones sobre el grupo de figuras que les asignaron” // “In your new group, discuss the statements about the set assigned to you.”
• “Juntos, creen un póster que muestre todo lo que encontraron que era verdadero para su grupo de figuras” // “Work together to create a poster that lists everything you found to be true for your set.”
• 3 minutes: group work time
• Consider allowing groups working on the same set to compare lists before the synthesis.

Student Facing

Estos son cuatro grupos de cuadriláteros.

Los cuadriláteros K, Z y AA son rectángulos.

Los cuadriláteros N, U y Z son paralelogramos.

Los cuadriláteros AA, EE y JJ son rombos.

Escribe 4 o 5 afirmaciones sobre los lados y los ángulos de los cuadriláteros de cada grupo. Cada afirmación debe ser verdadera para todas las figuras del grupo.

Student Response

Students may wonder how shape AA and Z can belong to multiple groups. Invite students to make a “notice and wonder” chart to record their questions during the activity and to share them in the synthesis. Consider asking:

• “¿Qué dijiste que era verdadero para todos los cuadrados?, ¿para todos los rectángulos?, ¿para todos los rombos?” // “What did you say was true for all squares? For all rectangles? For all rhombuses?”
• “¿La figura en la que estás pensando tiene todas esas características?” // “Does the shape you are wondering about have all of those attributes?”
• “¿Puedes pensar en otras figuras que tengan más de un nombre?” // “Can you think of other shapes that have more than one name?”

Activity Synthesis

• For each set of quadrilaterals, select one group to share their poster of statements. Invite other students to suggest amendments or corrections if they disagree.
• “Los rectángulos y los paralelogramos tienen varias características en común. ¿Qué los hace diferentes?” // “Rectangles and parallelograms share many attributes. What makes them different?” (To be a rectangle, all angles must be equal or must be right angles.)
• “Los rectángulos y los cuadrados tienen varias características en común. ¿Qué los hace diferentes?” // “Rectangles and squares share many attributes. What makes them different?” (To be a square, all sides must have the same length.)
• “Los rombos y los cuadrados tienen varias características en común. ¿Qué los hace diferentes?” // “Rhombuses and squares share many attributes. What makes them different?” (To be a square, all angles must be equal or must be right angles.)

Activity 3: Adivina otra vez [OPTIONAL] (10 minutes)

Narrative

In this optional activity, students work with a partner to practice naming and looking for certain attributes in quadrilaterals. Each partner has a chance to select a particular attribute that a quadrilateral might have and to find examples and non-examples. Their partner must deduce the attribute they chose based on the examples and non-examples.

Students may choose familiar attributes—lengths of sides, presence of certain types of angles, parallelism, or perpendicularity—or pick a one that is much narrower or broader. In the synthesis, consider discussing how the specificity of an attribute affects the guessing process.

Launch

• Groups of 2
• Read the task statement as a class. Clarify the directions as needed.

Activity

• “Jueguen dos rondas del juego de adivinanzas con su compañero. Intercambien roles para la segunda ronda. Escriban la característica correcta al finalizar cada ronda” // “Play two rounds of the guessing game with your partner. Switch roles for the second round. Write down the correct attribute at the end of each round.”
• If time permits, encourage students to play another round.

Student Facing

Compañero A:

• Escribe una característica que puede tener un cuadrilátero. No se la muestres a tu compañero.
• Busca 3 cuadriláteros que tengan esa característica y 3 cuadriláteros que no la tengan. Ponlos en las columnas de la tabla.

Compañero B:

• Estudia los cuadriláteros que escogió tu compañero.
• Escoge otro cuadrilátero del conjunto. Pregunta: “¿Este cuadrilátero tiene la característica?”.
• Encuentra por lo menos 1 cuadrilátero que tenga la característica y 1 cuadrilátero que no la tenga.
• Adivina la característica. Si no la puedes adivinar, haz más preguntas antes de tratar de adivinar de nuevo.

Intercambia roles con tu compañero después de que adivines correctamente cuál es la característica.

• Característica del compañero A:

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tienen la característica no tienen la característica
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• Característica del compañero B:

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tienen la característica no tienen la característica
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Activity Synthesis

• Invite students to share the attributes they chose. Ask them to reflect on the process of deducing the attributes from examples and non-examples.
• “¿Hubo alguna característica particularmente complicada de descubrir? ¿Qué cosas de los ejemplos y de los no-ejemplos hicieron que fuera difícil adivinar?” // “Was there an attribute that was particularly tricky to figure out? What about the examples and non-examples might have made it hard to guess?” (Students may say:
• The examples had many attributes in common, likewise with the non-examples.
• There are not enough examples in the set.
• The attribute is very specific—for example, one angle that is greater than $$90^\circ$$ but less than $$120^\circ$$.)

Lesson Synthesis

Lesson Synthesis

“Hoy miramos de cerca los cuadriláteros y sus características” // “Today we looked closely at quadrilaterals and their attributes.”

“¿Qué características tienen estos cuadriláteros en común?” // “What attributes do these quadrilaterals share?” (Both have at least one pair of parallel sides, and at least one obtuse angle and one acute angle.)

“¿Qué características son diferentes?” // “What attributes are different?” (Side lengths: N has two pairs of sides that are the same length and O has sides of different lengths. O has perpendicular sides and N doesn’t.)

“¿Qué podemos decir sobre los lados paralelos de los cuadriláteros?” // “What can we say about parallel sides in quadrilaterals?” (Students may say:
• They could be one, two, or no pairs of parallel sides.
• Parallel sides may not always be the same length.
• If a shape has two pairs of parallel sides, each pair of sides are the same length.
• Rectangles, squares, and rhombuses have two pairs of parallel sides. )