Lesson 17

The purpose of this warm-up is for students to compare four arrangements of dots to elicit the attributes, or structure, of an array. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as rows, corners, groups, and array.

• Groups of 2
• Display the image.
• “Escojan una 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 lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Por qué B no es un arreglo?” // “Why is B not an array?” (It has the same number of dots in each row, but not the same in each column. One of the columns only has 3 dots. The 3rd row is missing.)
• Consider asking:
  • “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to relate drawings of equal groups to arrays. Specifically, students look for arrays that have the same number of objects in each row or column as each drawing has in each group. In some arrays, the equal groups in the drawing are represented as rows, and in some, they are represented in columns. Students have the opportunity to explain the connections they see between the drawings and arrays, receive feedback from their peers, and revise their explanation for precision and clarity (MP3, MP6). This will be useful in future lessons when students record multiplication expressions and equations to represent arrays.

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

Create a set of cards from the blackline master for each group of 2 or 4 students.

• Groups of 2 or 4
• Distribute one set of pre-cut cards to each group of students.

• “Este grupo de tarjetas tiene dibujos de grupos iguales y arreglos. Emparejen cada dibujo con un arreglo. Con su compañero, justifiquen sus elecciones” // “This set of cards includes drawings of equal groups and arrays. Match each drawing to an array. Work with your partner to justify your choices.”
• 8 minutes: partner work time
• “Individualmente, escojan una pareja que hayan hecho con su compañero. Escriban cómo saben que el dibujo le corresponde al arreglo” //   “Independently choose a match you and your partner made. Write down how you know that the drawing matches the array.”
• 2 minutes: independent work time

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero la respuesta de por qué sus tarjetas corresponden. 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 your response to why your cards match 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 2-3 students share the matches they made and describe how they know those cards go together.
• “¿En su grupo estuvieron de acuerdo con las parejas de tarjetas? ¿En qué se fijaron para decidir si emparejaban dos tarjetas?” // “Did your group agree on the matches? What did you look for to decide two cards were matches?” (Yes, we looked for equal groups that had the same number of dots in a group as one of the rows in the array.)
• Listen for language students use to describe their matches and the structure of the arrays. As needed, ask:
  • “¿Qué quieren decir con _____?” // “What do you mean by _____?”
  • “¿De qué otra manera podemos llamar a _____?” // “What else could we call _____?”
  • “¿Cómo pueden usar las palabras ‘grupos iguales’ para explicar lo que emparejaron?” // “How could you use ‘equal groups’ to explain your match?”
• Highlight the use of terms like row, column, and equal groups.

The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rearrange would be helpful in this activity.

• Groups of 2 
• Give students access to connecting cubes or counters.

• “Individualmente, dibujen una manera en la que el primer grupo de puntos del problema 1 se podría organizar en un arreglo” // “Work independently to draw a way that the first group of dots in problem 1 could be arranged into an array.”
• 2 minutes: independent work time
• “Discutan con su compañero cómo organizaron los puntos y cómo se relaciona el arreglo con la multiplicación” // “Discuss how you arranged your dots and how the array is related to multiplication with your partner.”
• 1 minute: partner discussion
• “¿De qué manera reorganizaron los puntos para hacer un arreglo?” // “How did you rearrange the dots to make an array?” (Since there were 3 in each group, I put 3 dots in each row. I saw 2 groups of 6, so I made 2 rows of 6.)
• Consider asking:
  • “¿Alguien hizo un arreglo diferente?” // “Did anyone create a different array?”
• “Ahora van a hacer tantos arreglos como puedan con 16 puntos” // “Now you are going to make as many arrays as you can from 16 dots.”
• 2–3 minutes: independent work time
• “Compartan con su compañero de qué manera reorganizaron los puntos en arreglos. Vean si entre los dos pueden inventarse otros arreglos” // “Share how you rearranged the dots into arrays with your partner. See if together you can come up with any other arrays.”
• 3–5 minutes: partner work time

• “¿Qué tipos de grupos iguales hicieron con 16 puntos? ¿Cómo pueden ver los grupos iguales en los arreglos que hicieron?” // “What kinds of equal groups did you make from 16 dots? How can you see the equal groups in the arrays you made?” (I can make 2 groups of 8. I drew it as 2 rows of 8 dots.)