# Lesson 7

## Warm-up: ¿Qué saben sobre esta figura? (10 minutes)

### Narrative

The purpose of this What Do You Know About...? is for students to share what they know about a square. Students revisit this same question in the lesson synthesis.

### Launch

• Display the image.
• 1 minute: quiet think time

### Activity

• Record responses.

### Student Facing

¿Qué sabes sobre esta figura?

### Activity Synthesis

• “¿Cómo se llama esta figura?” // “What is this shape called?” (a square)
• “¿Cómo saben que es un cuadrado?” // “How do you know it is a square?” (It has 4 equal sides and 4 angles that are 90 degrees.)
• “Vamos a retomar esta pregunta en la síntesis de la lección” // “We are going to come back to this question in the lesson synthesis.”

## Activity 1: Pistas sobre cuadriláteros (15 minutes)

### Narrative

In this activity, students deepen their understanding of the quadrilateral hierarchy. Students recognize quadrilaterals with specific attributes. Students consider the defining attributes of each type of quadrilateral as they decide whether or not certain shapes exist. For example, a square which is not a rectangle does not exist because a square has 4 right angles (and 4 equal sides). However, there are rectangles that are not squares because the 4 sides of a rectangle do not need to have the same length.

As students work on these problems, monitor for those who experiment and try to draw shapes with different attributes and for those who think about the defining attributes of each shape category.

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “Observé _____, entonces emparejé . . .” // “I noticed _____ , so I matched . . .” Encourage students to challenge each other when they disagree.

### Required Materials

Materials to Copy

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.
• Gather diagram from a previous lesson.

### Launch

• Groups of 2
• Give each group of 2 a set of cards.

### Activity

• 2 minutes: independent think time
• 5 minutes: partner work time
• Monitor for statements about properties of shapes and conjectures such as:
• a rhombus has 4 equal sides
• squares are rhombuses
• a trapezoid can be a rectangle because it has at least one pair of parallel sides
• a rectangle is a parallelogram because it has two pairs of parallel sides
• it is impossible to find a square that isn’t a rectangle

### Student Facing

Acomoden sus tarjetas de figura sobre la mesa de manera que ustedes y su compañero las puedan ver todas.

Encuentren juntos una figura para cada pista. Si creen que no es posible encontrar esa figura, expliquen por qué. Pueden usar cada figura solo una vez.

1. Encuentren un cuadrilátero que no sea un paralelogramo.
4. Encuentren un trapecio que no sea un rectángulo.
6. Encuentren un paralelogramo que no sea un rectángulo.

### Activity Synthesis

• Invite previously selected students to share.
• “Clare dice: ‘Algunos rombos son cuadrados y algunos rectángulos son cuadrados’. ¿Están de acuerdo con ella?” // “Clare says, ‘Some rhombuses are squares and some rectangles are squares.’ Do you agree with her?” (Yes, we saw with the toothpicks that a rhombus can be a square but it doesn't have to be. Rectangles are squares when the 4 sides are equal, but the 4 sides don’t need to be equal, so not all rectangles are squares.)
• Display or draw a diagram like the one below or use the diagram from a previous lesson and ask, “¿Cómo se ve en el diagrama la relación que hay entre rombos y rectángulos?” // “How does the diagram show the relationship between rhombuses and rectangles?” (It shows that squares are both rhombuses and rectangles.)
• “¿Todos los cuadrados son rectángulos? ¿Cómo se muestra esto en el diagrama?” // “Are all squares rectangles? How does the diagram show this?” (Yes, a square has 4 right angles and the diagram shows that squares sit inside of rectangles.)

## Activity 2: Siempre, a veces, nunca (20 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of the hierarchy of quadrilaterals to determine if statements relating shape categories are sometimes, always, or never true. Students may draw examples of the shapes to help them answer the questions or they may think of defining attributes. The synthesis gives students an opportunity to have a discussion about these statements and apply what they have learned to make sense of the hierarchy as it is represented in a diagram. For example, as seen in the previous activity, squares are included inside rectangles on the diagram because all squares are rectangles.

Action and Expression: Develop Expression and Communication. Provide access to a variety of tools: colored pencils, markers, etc. Invite students to use the tools in order to help organize the anchor chart to aid in completing the task accurately.
Supports accessibility for: Conceptual Processing, Attention

• Groups of 2

### Activity

• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who:
• make drawings of shapes to help answer each question
• think about defining properties of the different shapes

### Student Facing

Escribe “siempre”, “a veces” o “nunca” en cada espacio en blanco para que la afirmación sea verdadera.

En cada afirmación que hayas completado con “a veces”, dibuja una figura para la que la afirmación sea verdadera y otra figura para la que la afirmación no sea verdadera.

3. Un triángulo ________________________ es un cuadrilátero.
5. Un rectángulo ________________________ es un paralelogramo.
6. Un paralelogramo ________________________ es un rombo.
7. Un trapecio ________________________ es un paralelogramo.

### Activity Synthesis

• “¿Es posible encontrar un rombo que también sea un cuadrado? ¿Cómo lo saben?” // “Is it possible to have a rhombus that is also a square? How do you know?” (Yes. I drew one. Any square has 4 equal sides so it is also a rhombus.)
• Display the diagram from the synthesis of the previous activity.
• “¿Cómo se muestra en el diagrama que a veces un rombo es un cuadrado?” // “How does the diagram show that a rhombus is sometimes a square?” (A part of the rhombus bubble includes squares.)
• “¿Cómo se ve en el diagrama la relación que hay entre los paralelogramos y los trapecios?” // “How does the diagram show how parallelograms are related to trapezoids?” (It shows that a parallelogram is always a trapezoid but there are trapezoids that are not parallelograms.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy observamos las relaciones que hay entre varios tipos de cuadriláteros, como trapecios, paralelogramos, rectángulos, rombos y cuadrados” // “Today we looked at relationships between different types of quadrilaterals including trapezoids, parallelograms, rectangles, rhombuses, and squares.”

Display the image from the warm-up:

“En el calentamiento dijimos que la figura es un cuadrado porque _____. ¿Qué saben ahora sobre esta figura?” // “During the warm-up we said the shape is a square because _____ (include statements students made earlier in the warm up). What do you now know about this shape?” (This is a square, but it also is a rectangle. It can also be called a rhombus or parallelogram.)

“¿Por qué un cuadrado también es un rombo?” // “Why is a square also a rhombus?” (All of its sides are the same length.)

“¿Por qué un cuadrado también es un rectángulo?” // “Why is a square also a rectangle?” (All of the angles are 90 degrees.)

“Si una figura es un rectángulo, ¿también es un cuadrado?” // “If a shape is a rectangle, is it also a square?” (Sometimes. It depends on the lengths of the sides of the rectangle. If all four sides are equal then it is a square, but if all four sides are not equal then it is not a square.)

“Si una figura es un rectángulo y un rombo, ¿también es un cuadrado?” // “If a shape is a rectangle and a rhombus, is it also a square?” (Yes, because it has 4 right angles and 4 equal sides.)