The purpose of this activity is to introduce the commutative property. Students write array situations for a pair of arrays and discuss similarities and differences. While the situations will have the same total number of objects, how the objects are grouped should be different. Then students write equations to go with the arrays and situations, and make connections between the representations (MP2). Students notice that, while the order of the factors in the multiplication equation changes, the product does not change (MP7).

• “Escribamos las ecuaciones que nos inventamos” // “Let’s write down the equations we came up with.”
• Display and .
• “¿Cómo se conecta cada uno de los números de las ecuaciones con la situación que escribieron?” //“How do each of the numbers in the equations connect to the situation you wrote?” (5 is the number of rows in one situation, but it's how many students are in each row in the other situation. 2 is the number of groups in one situation, but it's how many are in each group in the other situation. 10 is the total number of objects in both situations.)

The purpose of this activity is to reinforce the idea of the commutative property. In this activity, students write two equations to match an array to show again that reversing the order of the factors does not change the product. If students do not immediately see how they might write different equations for the array, encourage them to consider different ways of grouping the dots in the array, similar to the previous activity. Students use the vocabulary they have learned for describing arrays and multiplication to explain why both equations match an array with their partner. The Stronger and Clearer Each Time math language routine allows students to receive feedback and revise their explanation for clarity (MP3, MP6).

If students finish early, consider drawing another array. Have students write two equations for the array and consider how they can think of the rows or columns as equal groups.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• “Escribamos las ecuaciones que nos inventamos” // “Let’s write down the equations we came up with.”
• Display the equations and .

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero por qué ambas ecuaciones pueden representar el arreglo. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share why both equations can represent the array with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion.
• Repeat with 2–3 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time
• Have students share the revisions they made to their initial draft.