The purpose of this activity is to make connections between arranging objects to make an array and making a rectangle from equal-size squares. Students use the language of arrays to describe the rectangles they create (MP6) and learn that a rectangle composed of equal-size squares is an example of an array.

• Display student work.
• “Describan este rectángulo” // “Describe this rectangle.” (It has _____ rows of squares. It has _____ columns of squares. It has _____ squares in all.)
• If needed, ask:
  • “¿Cuántos cuadrados hay en cada fila?” // “How many squares are in each row?”
  • “¿Cuántos cuadrados hay en cada columna?” // “How many squares are in each column?”
  • “¿Qué ecuaciones podemos escribir para representar el número de cuadrados que hay en este rectángulo?” // “What equations could we write to represent the number of squares in this rectangle?”

The purpose of this activity is for students to finish partitioning a rectangle into equal-size squares. This work will prepare students for partitioning rectangles on their own in later lessons. In the Synthesis, students are invited to use what they know about the structure of arrays to anticipate how many equal-size squares will fill the rectangle without drawing any lines (MP8).

If students create squares one by one or create squares that are significantly different in size, consider pairing them with a peer who uses a ruler or looks for ways to draw longer lines across rows and columns and consider asking:

• “¿En qué se parecen las maneras en las que partiste los rectángulos? ¿En qué son diferentes?” // "How is the way you partitioned your rectangles the same? How are they different?"
• “¿Cuál de los pasos de _____ podrías intentar al partir los rectángulos en cuadrados de igual tamaño? ¿En qué te puede ayudar?” // "Which of _____'s steps could you try when partitioning rectangles into equal-size squares? How would it help?"

• Display the rectangle that has 4 squares in the first row, but is missing squares in each column (from the second problem).
• “Sin dibujar las líneas, ¿cómo podrían encontrar el número total de cuadrados que llenarían este rectángulo?” // “How could you find the total number of squares that would fill this rectangle without drawing the lines?” (I can tell there will be 4 columns based on the top row. I can tell there will be 5 rows based on the first column, even though it is missing 1 square.)