# Lesson 6

### Narrative

The purpose of this Notice and Wonder is to consider examples of some of the shapes that students will build and study in this lesson, namely squares and rhombuses. The key attributes students may notice in the shapes are the side lengths and the angles.

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “¿En qué se parecen estas figuras? ¿En qué son diferentes?” // “How are these shapes the same? How are they different?” (They have the same side lengths, but the angle measurements are different. The square or the one on the left has all 90 degree angles, but the shape on the right does not have any 90 degree angles.)
• “¿Qué nombres podemos usar para describir cada una de las figuras?” // “What names can we use to describe each of the shapes?” (square, rectangle, rhombus, or parallelogram for the one on the left, and rhombus or parallelogram for the one on the right)

## Activity 1: Figuras con palillos (15 minutes)

### Narrative

The purpose of this activity is for students to notice that a square is a special kind of rhombus and that a rectangle is a special kind of parallelogram. Working with toothpicks, students construct quadrilaterals with the same side lengths but different angles. When the side lengths are all the same, the shapes are rhombuses since the defining property of rhombuses is having 4 equal sides. The only way to make a square with the toothpicks, however, is to make 4 right angles. Hence building quadrilaterals with 4 toothpicks helps students visualize why a square is always a rhombus but a rhombus is only sometimes a square. In the same way they see that a rectangle is always a parallelogram but a parallelogram is only sometimes a rectangle.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 6 toothpicks.

• Groups of 2

### Activity

• 5 minutes: independent work time.
• 5 minutes: partner work time
• Monitor for students who:
• explain that the square and rhombus have the same side lengths, but different angles
• explain that the rectangle and parallelogram have the same side lengths, but different angles

### Student Facing

2. Usa los mismos cuatro palillos para construir esta figura. ¿Qué se mantuvo igual? ¿Qué cambió?

3. Construye un rectángulo con seis palillos. ¿Cómo sabes que este es un rectángulo?
4. Usa los mismos seis palillos para construir esta figura. ¿Qué se mantuvo igual? ¿Qué cambió?

### Activity Synthesis

• Ask previously selected students to share their thinking.
• “¿Cuáles de las figuras que hicieron son paralelogramos? ¿Cómo lo saben?” // “Which of the shapes you made are parallelograms? How do you know?” (They are all parallelograms. The opposite sides are parallel in all of these shapes.)
• “¿Cuáles de las figuras que construyeron tienen 4 lados iguales?” // “Which of the shapes you built have 4 equal sides?” (The first two, the ones using 4 toothpicks.)
• Display: rhombus
• “Un cuadrilátero con 4 lados iguales es un rombo” // “A quadrilateral with 4 equal sides is a rhombus.”

## Activity 2: Tres cuadriláteros (20 minutes)

### Narrative

The purpose of this activity is for students to determine if quadrilaterals are squares, rhombuses, rectangles, or parallelograms. Then they begin to outline the relationships between these different types of quadrilaterals, leading to the overall hierarchy of quadrilateral types which students investigate more fully in the next lesson.

When students draw quadrilaterals belonging or not belonging to different categories they reason abstractly and quantitively (MP2), using the definitions of the shapes to inform their drawings.

This activity uses MLR3 Clarify, Critique, and Correct. Advances: Reading, Writing, Representing.

Representation: Develop Language and Symbols. Synthesis: Represent the problem in multiple ways to support understanding of the situation. For example, use a video or pattern blocks to show the connections between the quadrilaterals.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

• Groups of 2

### Activity

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

### Student Facing

1. Dibuja 3 cuadriláteros distintos en la cuadrícula. Asegúrate de que al menos uno sea un paralelogramo.

• rombo
• rectángulo
• paralelogramo
Explica o muestra cómo razonaste.

3. Dibuja un rombo que no sea un cuadrado. Explica o muestra cómo sabes que es un rombo y que no es un cuadrado.
5. Diego dice que es imposible dibujar un cuadrado que no sea un rombo. ¿Estás de acuerdo con él? Explica o muestra cómo razonaste.

### Activity Synthesis

MLR3 Clarify, Critique, Correct

• Display the following partially correct answer and explanation:
• “Mai dice: ‘Todos los cuadrados son rombos. Si una figura es un cuadrado, también es un rombo. Los rombos no son cuadrados’” // “Mai says: All squares are rhombuses. If a shape is a square, it is also a rhombus. Rhombuses are not squares.”
• “¿Qué piensan qué Mai quiere decir? ¿Hay algo que no es claro?” // “What do you think Mai means? Is anything unclear?”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• “Con su pareja, escriban una explicación ajustada” // “With your partner, work together to write a revised explanation.”
• Display and review the following criteria:
• Specific words and phrases: all, some
• Labeled table/graph/diagram
• 3–5 minutes: partner work time
• Select 1–2 groups to share their revised explanation with the class. Record responses as students share.
• “¿En qué se parecen y en qué son diferentes las explicaciones?” // “What is the same and different about the explanations?” (They all explain why a rhombus does not have to be a square.)
• Display or draw a diagram like this:
• “¿Cómo podemos usar este diagrama como ayuda para ajustar la explicación de Mai?” // “How can we use this diagram to help us revise Mai’s thinking?” (The diagram shows that all squares are rhombuses but not all rhombuses are squares.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy relacionamos cuadrados con rombos y relacionamos rectángulos con paralelogramos” // “Today we related squares to rhombuses and rectangles to parallelograms.”

“¿Qué hace que un cuadrado sea un rombo?” // “What makes a square a rhombus?” (It has 4 equal sides.)

“¿Son todos los rombos cuadrados?” // “Are all rhombuses squares?” (No, there are rhombuses that have no right angles and they are not squares.)

Display or draw a diagram like this or use the diagram from a previous lesson.

“¿En dónde dibujaríamos un rombo que no sea un cuadrado?” // “Where would we draw a rhombus that is not a square?” (In the rhombus box, but not the square box.)

“¿Cómo muestra este diagrama que un cuadrado es un rombo y un paralelogramo?” // “How does this diagram show that a square is a rhombus and a parallelogram?” (It shows the squares inside the rhombuses that are inside the parallelograms, which means that a shape that is a square is also a rhombus and a parallelogram.)