The purpose of this activity is for students to find all the possible pairs of whole-number side lengths given the area of a rectangle. Each group is assigned 2 areas. Groups find all the possible rectangles for each given area. They draw and cut out possible rectangles with that area. In the next activity, they will display the rectangles in a Gallery Walk. To find all possible rectangles with a given area, students may use tiles. They may also start to observe patterns such as if there are an even number of rows then the number of tiles in the rectangle is an even number (MP7).

Areas to assign (in square units):

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• “Antes de que caminemos y veamos todos los pósteres, tómense un minuto para reflexionar sobre los números con los que trabajaron. ¿Qué observaron y qué se preguntaron mientras trabajaban en esta actividad?” // “Before we walk around and look at all the posters, take a minute to reflect on the numbers you worked with. What did you notice and wonder as you worked on this activity?”
• 1–2 minutes: quiet think time

In this activity, students examine the rectangles drawn by their classmates and learn the term factor pairs. Students recognize the side lengths of each rectangle as a factor pair of its area.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

MLR7 Compare and Connect

• “¿En qué se parecen y en qué son diferentes los rectángulos de los pósteres?” // “What is the same and what is different about the rectangles on the posters?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “¿Cómo saben que encontraron todos los rectángulos posibles para cada área asignada?” // “How do you know that all possible rectangles have been found for the given area?” (We couldn't find any other numbers that multiply together to make the area.)
• Display the rectangles for 21: 1 by 21 and 3 by 7.
• “¿Podemos dibujar más rectángulos? ¿Por qué sí o por qué no?” // “Are there any more rectangles we can draw? Why or why not?” (No, there are no more whole-number factors of 21. Or, no, because to get 21 we can multiply only 1 and 21, 3 and 7, 7 and 3, and 21 and 1.)
• “Decimos que 1 y 21 es una pareja de factores de 21 porque cada uno de ellos es un factor de 21, y al multiplicarlos el producto es 21. Otra pareja de factores de 21 es 3 y 7” //“We call 1 and 21 a factor pair of 21 because each of them is a factor of 21 and multiplying them gives you a product of 21. Another factor pair of 21 is 3 and 7.”
• “Con su compañero, escriban las parejas de factores de las áreas que les asigné” // “Work with your partner to write down the factor pairs for the areas you were assigned.”
• 2 minutes: partner work time