The purpose of this Warm-up is to elicit strategies for quantifying numbers 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 discussion, ask students to explain the meaning of any terms they use, such as “row,” “column,” “array,” “group,” “line,” “grid,” and “rectangle.”

• “¿Cómo encontraron la cantidad total en cada imagen?” // “How did you determine the total number for each image?” (In D, I counted by 4 since I saw equal groups of 4. In C, I counted by 5 since each row had 5 dots. In B, I counted by 5 since each row had 5 squares. In A, 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 how they are different. Students should describe their rectangles to their partners without revealing the total numbers of squares they used, so that the focus is on understanding the rectangular structure. In the Activity Synthesis, students share language that helped them understand the rectangles their partners built. When students revise their language to be more precise in the descriptions of their rectangles, they attend to precision (MP6).

The purpose of this activity is for students to find the areas 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 10. If students finish quickly, encourage them to confirm their areas by counting another way. Emphasize that each area is in square units.