Lesson 7
Rectángulos y cuadrados
Warm-up: ¿Qué saben sobre esta figura? (10 minutes)
Narrative
Launch
- Display the image.
- “¿Qué saben sobre esta figura?” // “What do you know about this shape?”
- 1 minute: quiet think time
Activity
- Record responses.
Student Facing
¿Qué sabes sobre esta figura?
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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.
Advances: Conversing, Representing
Required Materials
Materials to Copy
- Quadrilateral Clues
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.
- Encuentren un cuadrilátero que no sea un paralelogramo.
- Encuentren un rombo que también sea un cuadrado.
- Encuentren un rombo que no sea un cuadrado.
- Encuentren un trapecio que no sea un rectángulo.
- Encuentren un rectángulo que no sea un cuadrado.
- Encuentren un paralelogramo que no sea un rectángulo.
- Encuentren un cuadrado que no sea un rectángulo.
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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.
Supports accessibility for: Conceptual Processing, Attention
Launch
- 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.
- Un rombo ________________________ es un cuadrado.
- Un cuadrado ________________________ es un rombo.
- Un triángulo ________________________ es un cuadrilátero.
- Un cuadrado ________________________ es un rectángulo.
- Un rectángulo ________________________ es un paralelogramo.
- Un paralelogramo ________________________ es un rombo.
- Un trapecio ________________________ es un paralelogramo.
Student Response
Teachers with a valid work email address can click here to register or sign in for free access to Student Response.
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.)
Cool-down: Cuadriláteros en el diagrama de Venn (5 minutes)
Cool-Down
Teachers with a valid work email address can click here to register or sign in for free access to Cool-Downs.