Lesson 4

This warm-up prompts students to compare four shapes. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about the characteristics of the items in comparison to one another. During the synthesis, emphasize that three of the shapes are quadrilaterals, even though they look very different.

• Groups of 2
• Display the images.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Cuáles figuras son cuadriláteros? ¿Cómo lo saben?” // “Which shapes are quadrilaterals? How do you know?” (A, B, and D. They all have four sides.)
• “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to identify the attributes that make a quadrilateral a rectangle, a rhombus, or a square. They do so by studying examples and non-examples, looking for features that each set has in common and drawing conclusions accordingly (MP7). The goal is not to craft the most precise definition for each, but to develop an understanding of the defining geometric attributes.

• Create a chart with labels showing a rectangle, rhombus, and square for the lesson synthesis.

• Groups of 2–3
• Display the examples and non-examples of right triangles.
• “Los triángulos que están a la izquierda son triángulos rectángulos. Los que están a la derecha, no. Tómense un minuto para pensar en sus diferencias” // “The triangles on the left are right triangles. The ones on the right are not. Take a minute to think about their differences.”
• “Ahora escojan todas las figuras que son triángulos rectángulos del grupo marcado de la A a la H. Escriban qué piensan que hace que una figura sea un triángulo rectángulo” // “Then, choose all the shapes that are right triangles from the set labeled A–H. Write down what you think makes a shape a right triangle.”
• 1–2 minutes: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• “Todos los triángulos que están a la izquierda y el triángulo E del grupo tienen ángulos rectos. Un triángulo que tiene un ángulo recto es un triángulo rectángulo” // “All triangles on the left and triangle E in the set are right angles. A triangle with a right angle is a right triangle.”

• “En grupo, analicen qué hace que una figura sea un rectángulo, un rombo o un cuadrado. Cada grupo va a estudiar un tipo de cuadrilátero” // “Work with your group to analyze what makes a shape a rectangle, a rhombus, or a square. Each group will look at one type of quadrilateral.”
• Assign each group one quadrilateral to analyze.
• 3–5 minutes: small-group work time
• “Ahora compartan su trabajo con otro grupo que haya trabajado con el mismo cuadrilátero. Asegúrense de hacer las preguntas que tengan sobre el trabajo del otro grupo” // “Now, share your work with another group that worked on the same quadrilateral. Be sure to ask any questions you have about each other’s work.”
• 3–5 minutes: small-group discussion

• Invite 1–2 groups who analyzed rectangles to share their responses. Record their responses.
• Ask the class:
  • “¿Están de acuerdo en que las figuras marcadas son rectángulos (o rombos o cuadrados)?” // “Do you agree with the shapes that are marked as rectangles (or rhombuses or squares)?”
  • “¿Están de acuerdo en las descripciones?” // “Do you agree with the descriptions?”
  • “¿Hay alguna parte de las descripciones que dirían de otra manera?” // “Is there any part of the descriptions you’d say differently?”
  • “¿Le agregarían algo a la descripción?” // “Is there anything you'd add to the description?”
• When students have finished describing rectangles, highlight that: “Una figura es un rectángulo solo si es un cuadrilátero que tiene únicamente ángulos rectos y los lados que son opuestos tienen la misma longitud” // “A shape is a rectangle only if it is a quadrilateral with only right angles, and the sides that are across from each other are the same length.”
• Repeat the discussion with rhombuses and squares.