Lesson 4

The purpose of this warm-up is to elicit strategies for quantifying the number of objects arranged in rows and columns and the language used to describe such arrangements. It gives students a reason to use language precisely (MP6). During the synthesis, ask students to explain the meaning of any terminology they use, such as row, column, array, group, line, grid, and rectangle.

• Groups of 2
• Display the image.
• “Escojan uno 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.

• “¿Por qué B es diferente?” // “Why doesn’t B belong?” (It doesn’t have 20 dots.)
• “¿Cómo encontraron el número total en cada imagen?” // “How did you determine the total number for each image?” (In D, I counted every dot. In C I counted by 5 since each row had 5 dots. In A, I counted by 5 since each row had 5 squares. In B, I just added 20 and 4 for the extra column.)

The purpose of this activity is for students to create and describe rectangles of a certain area. Students work in groups of 2. One partner creates a rectangle and describes it, and the other partner creates a matching rectangle based on the description. Then students compare how their rectangles are the same and different. Students should describe their rectangle to their partner without revealing the total number of squares they used, so that the focus is on understanding the rectangular structure. In the synthesis, students share language that helped them understand the rectangle their partner built. When students revise their language to be more precise in the descriptions of their rectangle, they attend to precision (MP6).

• Each group of 2 needs one folder.

• Groups of 2
• Ask students to place an object between them that obstructs their view, such as a folder.

• “El objetivo de esta actividad es lograr que los dos compañeros dibujen el mismo rectángulo sin mirar el dibujo del otro. Si son el compañero A, dibujen un rectángulo y descríbanselo a su compañero. No pueden decirle cuántos cuadrados usaron para dibujar su rectángulo” //  “The goal of this activity is to get both partners in a group to draw the same rectangle without looking at each other’s drawing. If you are partner A, draw a rectangle and describe it to your partner. You can’t tell them how many squares you used to draw your rectangle.”
• “Si son el compañero B, dibujen el rectángulo que creen que les describe su compañero y luego comparen los dibujos” // “If you are partner B, draw the rectangle that you think your partner is describing and then compare the drawings.”
• “Después de que terminen de describir y dibujar el primer rectángulo, intercambien roles y repitan estos pasos” // “After you finish describing and drawing the first rectangle, switch roles and repeat.”
• 10–12 minutes: partner work

• “¿Qué lenguaje usó su compañero que les resultó más útil para dibujar el mismo rectángulo que dibujó su compañero?” //  “What language did your partner use that was most helpful for you to draw the same rectangle they drew?” (The number of squares in each row or column and the number of rows or columns.)

The purpose of this activity is for students to find the area of rectangles by counting squares. Larger rectangles provide more opportunities for students to practice counting strategies using the structure of the rectangles to group the individual squares (MP7). Rectangles in this activity lend themselves to show groups of twos, fives, or tens in rows or columns. Students may also see other ways to create equal groups within rectangles. For example, the second rectangle with an area of 30 square units can be seen as 3 groups of ten. If students finish quickly, encourage them to confirm the area by counting another way. Emphasize that each area is in square units.

• Groups of 2

• “Encuentren el área de cada rectángulo. Prepárense para explicar su razonamiento” // “Find the area of each rectangle. Be ready to explain your reasoning.”
• 5–7 minutes: independent work time
• Monitor for counting strategies such as:
  • Counting the squares in a row or a column and then skip-counting by that number for subsequent rows or columns.
  • Grouping by twos, fives, tens, or other numbers.
• “Ahora, compartan sus estrategias con su compañero” // “Now share your strategies with your partner.”
• 2–3 minutes: partner discussion

If students miscount the square units in the rectangles, consider asking:

• “Dime cómo contaste los cuadrados” // “Tell me how you counted the squares.”
• “Cuando cuentas los cuadrados, ¿cómo puedes saber qué cuadrados ya contaste?” // “How could you keep track of your count as you count the squares?”

• Invite 3–4 previously selected students to share how they found the area of one of the rectangles. Try to highlight a variety of strategies.
• Consider asking, “¿Su estrategia cambió de un rectángulo a otro?” // “Did your strategy change from rectangle to rectangle?”