Lesson 8

El arte de Mondrian (optional)

Warm-up: Observa y pregúntate: El arte de Piet Mondrian (10 minutes)

Narrative

The purpose of this task is to introduce students to the artwork of Piet Mondrian. Students may notice that his paintings are composed of rectangles of various sizes. Students will create their own versions of Mondrian art in the first activity.

To show students additional artwork by Mondrian, consider visiting a virtual installation of Piet Mondrian's work on the website of Museum of Modern Art (MoMA) or visiting the website of the Tate Gallery.

Launch

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

Activity

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

Student Facing

¿Qué observas? ¿Qué te preguntas?

Image consisting of many connected rectangles and squares of different sizes and colors.

Image consisting of many connected rectangles of different sizes and colors.

Student Response

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Activity Synthesis

  • “Estas son copias digitales de pinturas famosas de un pintor holandés llamado Piet Mondrian. Él vivió de 1982 a 1944. Hace un poco más de 100 años, se volvió famoso por pintar con un estilo que se relaciona con las matemáticas que hemos estado estudiando. Muchas de sus pinturas están colgadas en museos de todo el mundo” // “These are digital copies of famous paintings by a Dutch artist named Piet Mondrian. He lived from 1872 to 1944. A little more than 100 years ago, he became known for painting in a style that relates to the math we have been studying. Many of his paintings hang in museums all around the world.”
  • “¿Cómo creen que su arte se conecta con lo que hemos estado estudiando? ¿Por qué estamos viendo esto en clase de Matemáticas?” // “How do you think his art connects with what we’ve been studying? Why are we looking at it during math class?” (He used a lot of rectangles. His art looks very precise. He seemed to have planned for the rectangles to have certain side lengths.)
  • If not mentioned by students, highlight that some of the lines go from edge to edge of the painting while others are shorter, and that some rectangles seem to have the same area.
  • Considering showing students additional artwork by Mondrian.

Activity 1: Mi bosquejo de Mondrian (20 minutes)

Narrative

The purpose of this activity is for students to create an outline for their artwork. In this activity, students draw lines on graph paper, marking out rectangular areas that will be the basis for their Mondrian-inspired artwork. 

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to rephrase directions in their own words. Keep a display of Mondrian’s paintings visible throughout the activity.
Supports accessibility for: Memory, Organization

Required Materials

Materials to Gather

Materials to Copy

  • Centimeter Grid Paper - Standard

Required Preparation

  • Each student will need a black marker or crayon.

Launch

  • “Vamos a crear nuestras propias piezas de arte inspiradas en el trabajo de Mondrian” // “We are going to create our own art pieces that are inspired by Mondrian’s work.”
  • Read the activity statement as a class.
  • Select a student to explain the task in their own words. Invite the class to ask clarifying questions.
  • Give students a copy of the blackline master, a straightedge, and black markers or crayons.

Activity

  • “Usen su regla y su lápiz para partir su cuadrícula. Traten de hacer al menos uno de los retos” // “Use your straightedge and pencil to partition your grid. Try at least one of the challenges.”
  • “Cuando estén contentos con su diseño, trácenlo con un marcador o un crayón negro” // “Once you are happy with your design, trace it with a black marker or crayon.”
  • 13–15 minutes: independent work time
  • Monitor for students who attempt or accomplish one or more of the challenges.

Student Facing

Haz un bosquejo de arte con el estilo de Mondrian. Comienza con una cuadrícula de 18 por 24.

Tu obra de arte debe:

  • estar partida en al menos 12 rectángulos  
  • tener dos rectángulos diferentes que tengan la misma área
  • tener al menos un rectángulo que tenga un área que sea un número primo

Trata de hacer al menos uno de estos retos. Haz un diseño en el que:

  • todos los rectángulos excepto dos tengan un área que sea un número primo
  • no haya dos rectángulos que compartan un lado completo

Student Response

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Activity Synthesis

  • “Comparen su trabajo con el de un compañero. ¿En qué se parecen o en qué son diferentes sus bosquejos?” // “Compare your work with a partner. What is alike or different about your outlines?” (They are alike because they show only rectangles, but the way they are arranged and their sizes are different.)
  • “¿Cómo pueden determinar si algunos de los rectángulos tienen la misma área?” // “How can you determine if any of the rectangles have the same area?” (See if the sides are factor pairs of the same number. Use the side lengths and multiply them to see if the product is the same number.)

Activity 2: Analicemos los rectángulos (20 minutes)

Narrative

In this activity, students use their understanding of factor pairs, prime, and composite numbers to analyze their peers’ artwork. They look for rectangles that have the same area and those with a prime number or a composite number for their area. Students practice communicating with precision as they identify rectangles and how they know the rectangles meet these conditions (MP6). 

After students share their analyses with their partner and a brief class discussion, give students time to color their artwork and to prepare it for display.

MLR8 Discussion Supports. Synthesis: Display the following sentence frames to support whole-class discussion: “Para encontrar rectángulos que tuvieran la misma área, busqué . . .” // “To find rectangles with the same area I looked for . . .”, “Para encontrar rectángulos que tuvieran un área que fuera un número primo, busqué . . .” // “To find rectangles with an area that is prime, I looked for . . .”, and “Para encontrar rectángulos que tuvieran un área que fuera un número compuesto, busqué . . . .” // “To find rectangles with an area that is composite, I looked for . . . .”

Advances: Speaking, Representing

Required Materials

Launch

  • Groups of 2
  • “Intercambien sus obras de arte con su pareja” // “Switch artwork with your partner.”
  • “Miren la obra de su pareja y traten de encontrar tres tipos de rectángulos: rectángulos que tengan la misma área, rectángulos que tengan un área que sea un número primo y rectángulos que tengan un área que sea un número compuesto” // “Look at your partner’s work and try to find three kinds of rectangles: rectangles with the same area, rectangles with an area that is a prime number, and rectangles with an area that is a composite number.”
  • “Luego, revisen si su pareja hizo alguno de los retos de la primera actividad” // “Then, if your partner completed a challenge from the first activity, see which one they did.”

Activity

  • 5–7 minutes: independent work time
  • 2–3 minutes: partner discussion
  • Monitor for students who consider factor pairs of a number as they look for rectangles with the same area in their partner's artwork.

Student Facing

Intercambia tu obra de arte con tu pareja.

Busca y describe cada uno de los siguientes en la obra de arte de tu pareja:

  1. Rectángulos que tengan la misma área
  2. Rectángulos que tengan un área que sea un número primo
  3. Rectángulos que tengan un área que sea un número compuesto
  4. El reto que hizo tu pareja

Student Response

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Activity Synthesis

  • Invite 1–2 previously selected students to share how they found rectangles with the same area. (The sides are factor pairs of the same number.)
  • “Ahora, tómense un momento para colorear su obra de arte con 3 o 4 colores. Más adelante, van a exhibir sus obras para que otros las vean” // “Now, take a moment to color your artwork with 3–4 colors. Later, you’ll display your work for others to see.”
  • Give students colored pencils, crayons, or markers.
  • 8–10 minutes: independent work time
  • Give students materials needed for the gallery walk: glue or tape for displaying their artwork and sticky notes for writing comments or questions.

Lesson Synthesis

Lesson Synthesis

Direct students to display their artwork for all to see.

“Ahora van a caminar por el salón y van a observar las obras de arte que creó la clase. Mientras lo hacen, piensen en preguntas que le harían a los artistas sobre su diseño. Escojan al menos una pieza de arte y escriban una pregunta sobre esta en una nota adhesiva” // “You will now walk around and look at the art the class has made. As you do so, consider questions that you might ask the artists about their design. Choose at least one piece of artwork and write a question about it on a sticky note.”

5–6 minutes: gallery walk

Monitor for questions that are related to the artist's intent or mathematics in the design. Invite a couple of students to whom those questions are directed to answer questions about their art.

“Hoy tuvieron la oportunidad de crear obras de arte y exhibirlas, como se hace en una galería de arte” // “Today you had a chance to create artwork and display it like in an art gallery.”

“¿Qué fue lo más retador de hacer la obra de arte?” // “What was the most challenging part about creating the artwork?” (I was limited to only using rectangles. I had to make sure two rectangles had the same area.)

“¿Qué conexiones ven entre las matemáticas y el arte que vivimos hoy?” // “What connections do you see between the mathematics and art we experienced today?” (The art we made uses rectangles. We can use multiplication to figure out if the areas are the same or different. We had the same requirements, but our art was different because we chose different side lengths.)