Lesson 17

The purpose of this warm-up is for students to discuss the context of mosaics and the mathematics that might be involved, which will be useful when students create their own mosaics in a later activity. While students may notice and wonder many things about this image, the different smaller shapes used to create the mosaic are the important discussion points.

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

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

• “Un mosaico es un patrón o una imagen que se crea usando pequeñas piezas de cerámica, piedra o vidrio para cubrir una superficie” // “A mosaic is a pattern or picture created using small pieces of ceramic, stone, or glass to cover a surface.”
• “Los antiguos artistas griegos y romanos decoraban edificios importantes con mosaicos. Los artistas judíos y musulmanes en Oriente Medio crearon mosaicos para decorar construcciones religiosas” // “Ancient Greek and Roman artists decorated important buildings with mosaics, and Jewish and Muslim artists in the Middle East created mosaics to decorate religious buildings.”
• “Las piezas que cortamos para armar un mosaico pueden tener formas distintas. ¿Qué figuras observan en este mosaico?” // “The pieces that create a mosaic can be cut in different shapes. What shapes do you notice in this mosaic?”
• “En la siguiente actividad, van a usar rectángulos para hacer sus propios mosaicos” // “In the next activity, you’ll create your own mosaics with rectangles.”

The purpose of this activity is for students to create rectangles from colored paper. Students make identical rectangles that have one side length that is a whole number and one side length that is a fraction greater than 1. Then, as a group they create one mosaic. It is not necessary for students to use all of the rectangle pieces. It is important that all students in each group measure their rectangles using the same unit, either inches or centimeters.

• Each student needs a few sheets of the same colored paper.
• Each group of 4 needs a ruler, scissors, glue and one large piece of poster paper.

• Groups of 4 
• Distribute materials. Make sure each student in the group gets a different color paper.

• 10 minutes: independent work time
• 5 minutes: group work time
• Monitor for students who:
  • write numerical expressions to represent the area of the rectangles.
  • use a diagram or write on the physical rectangles.

• Invite a few students to share and describe their mosaic.
• “¿Qué preguntas podemos hacer sobre estos mosaicos?” // “What are some questions we can ask about the mosaics?” (Which color rectangle did we use the most of? What are some other ways we can arrange the same pieces? What are some other pieces that can make the same pattern? How much would this cost if we actually made this using hard materials?)

The purpose of this activity is for students to apply their understanding of multiplying whole numbers by fractions greater than 1 to determine the cost of making a mosaic with different materials. It is not necessary for students to find the exact cost for the mosaic. Encourage students to use estimation strategies. Some students may find the exact cost as a fraction of a dollar, for example \(131\frac{3}{5}\) dollars. Encourage students to make sense of the fraction with respect to money.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

• Group of 4
• Display table from student task.
• “Tradicionalmente los mosaicos están hechos de piezas de piedra, baldosa o vidrio. Imaginen que están haciendo su mosaico para un proyecto de arte en la escuela. En esta actividad van a averiguar el costo de su mosaico” // “Traditionally mosaics are made of stone, tile, or glass pieces. Imagine you are making your mosaic as art for the school. In this activity, you will figure out the cost of your mosaic.”

• 8-10 minutes: Group work time
• Monitor for students who:
  • Determine the cost for each color rectangle needed and then determine the total cost.
  • Find the approximate total area of the materials needed for the mosaic and then determine the cost.
  • Write clear expressions that show multiplication of whole numbers by fractions greater than 1.

MLR1 Stronger and Clearer Each Time

• “Compartan su respuesta con un compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response with a partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion. 
• Repeat  with 2–3 different partners.
• If needed, display question starters and prompts for feedback.
  • “¿Pueden agregar una expresión que muestre . . . ?” // “Can you add an expression to show . . .?”
  • “La parte que mejor entendí fue . . .” // “The part I understood best was . . .”
  • “Me gustó la forma en que tú . . .” // “I liked how you . . .”
• “Ajusten su borrador inicial basándose en los comentarios que sus compañeros les hicieron” //“Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time