Lesson 2

The purpose of this warm-up is to elicit observations about tiled squares by comparing four images. The work here prepares students to reason about unit squares later in the lesson and gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the shapes in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as longest, largest, and area.

• Groups of 2
• Display the image.
• “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 cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Qué características de estas imágenes compararon?” // “What are some different attributes you compared in these images?” (How many squares were in each image, the size of the smaller squares, the overall shape, and shading.)

• Consider saying: “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 explore area by making shapes out of square tiles and ordering the shapes from smallest to largest. Students may consider the size of the shapes in a variety of ways.

For example, they may see the first shape as larger than the second shape because the squares in the former are more spread out than in the latter, which is completely filled with tiles.

If needed, encourage students not to stack the tiles. In the synthesis, students learn they can count the square tiles to determine the amount of space a shape covers.

• Each group of 4 needs 80 square tiles.

• Groups of 4
• Give each group inch tiles.
• “Tomen algunas fichas y construyan su figura” // “Take some tiles and build your shape.”
• 2 minutes: independent work time

• “Ahora, ordenen las figuras con su grupo. Prepárense para explicar cómo ordenaron las figuras” //  “Now work with your group to order the shapes. Be prepared to explain how you ordered the shapes.”
• 5 minutes: group work time
• Monitor for groups who order by:
  • the amount of space the shape takes up on the table
  • the length of the shape
  • the number of tiles used to create the shape

• “¿Cómo hicieron para ordenar las figuras de la más pequeña a la más grande?” // “How did you order the shapes from smallest to largest?” (We compared the length of each shape. We counted how many tiles it took to make each shape.)
• As students share, consider asking: “¿Cómo decidieron cuánto espacio cubría cada figura?” // “How did you decide how much space each shape covered?”
• “Se suelen usar cuadrados como las fichas cuadradas que usamos en esta actividad para determinar que cada ficha cuadrada tiene un área de una unidad cuadrada. Si contamos el número de fichas que conforman una figura, podemos encontrar el área de la figura. Por ejemplo, si a una figura la cubren 12 fichas cuadradas, la figura tiene un área de 12 unidades cuadradas” //  “It is common to use squares like the square tiles we used in this activity to determine each square tile has one square unit of area. If we count the number of tiles that make up a shape, we can find the area of the shape. For example, if a shape is covered by 12 square tiles, it has an area of 12 square units.”

The purpose of this activity is for students to use square tiles to measure area. Students are given square tiles and a variety of figures. Students learn that they can use the term “figure” to describe a shape that doesn’t have a specific name. Students cover the figures completely with square tiles and use the number of tiles to describe the area of the figure. In the synthesis, students share ideas about how to tile shapes in any way that makes sense to them. They also consider why it’s important to make sure they don’t leave gaps when they use square tiles to measure area (MP6).

Here are the figures on the blackline master for reference:

1.

2.

3.

4.

5.

6.

There is an opportunity to ask students about the figures whose area is the easiest to find. There is no right or wrong answer, but the question may elicit the idea that the structure of rectangles is helpful. This idea will be explored fully in future lessons.

• Each group of 2 needs 80 square tiles.

• Groups of 2
• “Ahora que sabemos que podemos contar fichas cuadradas para encontrar el área, podemos pensar en cubrir las figuras con fichas para encontrar su área. A esto lo llamamos recubrir. En esta actividad recubrirán cada figura con fichas cuadradas para encontrar el área” // “Now that we know we can count square tiles to find area, we can think about covering shapes with tiles to find their area. We call this tiling. In this activity you will tile each shape with square tiles to find the area.”
• Give each group a copy of the blackline master and inch tiles.
• “Para algunas de estas no tenemos nombres, como un cuadrado o un triángulo. Por esta razón, podemos llamarlas ‘figuras’ mientras trabajamos con ellas en esta actividad. Esta palabra será útil para describir otras figuras para las que no tenemos nombres” //  “Some of these aren’t shapes that we have names for like a square or triangle. Because of this, we can call them ‘figures’ as we work with them in this activity. This word will be helpful in describing other shapes that we don’t have names for.”

• 7–10 minutes: partner work time
• Monitor for students who:
  • keep tiling the whole figure all the way to the edges
  • do not leave gaps between the square tiles as the figure is tiled

• Display the first, fourth, and fifth figures.
• “¿Cómo recubrieron cada figura?” // “How did you tile each figure?” (I filled the whole figure with tiles until I couldn’t fit any more. I started with the bottom row, then made the row above it until the figure was full.)
• “¿Cómo encontraron el área de cada figura?” // “How did you determine the area of each figure?” (I counted the number of tiles it took to fill each figure completely.)
• Consider asking, “¿De cuáles figuras les pareció más fácil encontrar su área?” // “Which figures did you and your partner think were easiest to find the area of?” (The rectangle, because there were clear rows and columns. The third one, because we could split it into 2 rectangles. All of them, because they could all be covered completely with square tiles and had no uncovered space.)
• “¿Por qué fue importante no dejar ningún espacio al recubrir sus figuras?” // “Why was it important not to leave any gaps as you tiled your figures?” (Because the whole figure needs to be completely covered. If there are gaps between tiles or around the edge, then the whole figure isn’t covered.)