The purpose of this activity is for students to use square tiles to find the areas of rectangles. They use their knowledge of tiling to complete the tiling that is started in each rectangle. Students may use physical tiles on copies of the blackline master or reason directly on the images in the student book, which may not be the right size for physical tiles. The Activity Synthesis focuses on solidifying the idea that area is the number of square units that cover a flat figure, with no gaps or overlaps.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• “¿Por qué las fichas cuadradas del primer, tercer y cuarto rectángulo se debían acomodar antes de que pudiéramos terminar de encontrar el área del rectángulo?” //“Why did the square tiles in the first rectangle, the third rectangle, and the fourth rectangle need to be adjusted before we could finish finding the area of the rectangle?” (In the first rectangle, the square tiles had to be moved over because the rectangle would have gaps if we left the squares in the center. In the third rectangle, the squares in the second and third rows needed to be lined up along the edges. In the fourth rectangle, the squares need to be adjusted so they are not crooked or overlapping and 1 square needs to be removed from the first row.)
• “Si alguien les dijera que en la parte superior del último rectángulo caben 4 cuadrados, pero que en la parte inferior del rectángulo solo caben 3 cuadrados, ¿cómo sabrían que esto no tiene sentido?” // “If someone told you 4 squares would fit across the top of the last rectangle, but only 3 squares would fit across the bottom of the rectangle, how would you know this didn’t make sense?” (The top and bottom have the same length so they should fit the same number of squares.)

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero su respuesta al último problema. 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 to the last problem with your 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.”
• 2 minutes: structured partner discussion.
• Repeat with 1 or 2 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft, based on the feedback you got from your partners.”
• 2–3 minutes: independent work time
• “Acabamos de encontrar el área de algunos rectángulos. Aprendimos que cuando cubrimos un rectángulo con fichas cuadradas, las fichas no pueden tener espacios ni sobreposiciones. Es importante que tengamos en cuenta estas mismas ideas para cualquier figura plana. El área es el número de unidades cuadradas que se necesitan para cubrir una figura plana sin espacios ni sobreposiciones” // “We just found the areas of rectangles, and learned that when we cover a rectangle with square tiles, the tiles can’t have gaps or overlaps. The same ideas are important with any flat figure. Area is the number of square units that it takes to cover a flat figure without gaps or overlaps.”

The purpose of this activity is for students to recognize that different shapes can have the same area. Students sort the cards, first in any way that makes sense to them and then by area. After the cards are sorted by area, students create another rectangle that fits into one of the categories (by having a particular area). This sorting task gives students opportunities to analyze the structure of the rectangles closely and make connections (MP7).

Students may start to notice that the organization of the squares that cover a rectangle makes them efficient to count. The squares can be grouped by row or by column, or in other ways. As students sort and create rectangles with certain areas, monitor for those who leverage the structure of a rectangle to find the area. Invite them to share in the Activity Synthesis.

In this activity, the squares on the gridded rectangles are not the same size as the square tiles, but students could still use tiles as a support. Provide students access to square tiles if they would like to use them, but encourage them to draw what they create on the grid provided.

• Invite students to share the rectangles they created for each category.
• Consider asking:
  • “¿Cómo supieron que su rectángulo pertenecía a esta categoría?” // “How did you know that your rectangle belongs here?”
  • “¿Cómo supieron que el rectángulo que hicieron tenía la misma área que los otros rectángulos de esa categoría?” // “How did you know that the rectangle you created had the same area as the other rectangles in that category?”
• Invite previously selected students to share some of the ways they counted to find the areas of rectangles.