Lesson 7

This warm-up prompts students to carefully analyze and compare different arrangements of circles, including an array. Listen for the ways student describe how they see equal groups in each arrangement and use the language they developed in previous lessons to determine if a group of objects was even or odd.

• 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
• Record responses.

• “Observen como están organizados los círculos en B. ¿En qué se diferencia de los otros grupos?” // “How are the circles in B arranged differently than in the other groups?” (They are all lined up. They are arranged in rows. There are the same number of circles in each row. There are the same number of circles in columns, too.)
• “A un grupo de objetos organizados en filas iguales lo llamamos un arreglo. Las filas van de lado a lado. Hoy vamos a explorar arreglos” // “We call objects arranged in equal rows an array. The rows go from side to side. We are going to explore arrays today.”

The purpose of this activity is for students to create arrays with counters. Students get sets of 6, 7, and 9 counters. Based on their experiences with images that show an even number of objects arranged in 2 equal groups, they may make an array with 3 rows and 2 columns or 2 rows and 3 columns with 6 counters. They may wonder if 7 or 9 counters can be arranged in an array since they are not even numbers.  Encourage students to experiment with other ways of arranging the counters that include more than 2 rows or columns. They may also make an array with 1 row. Arrays with 1 row or 1 column will be studied in future grades, so for the rest of this unit, students should be encouraged to make arrays with more than 1 row and more than 1 column.

•   Create containers with 6, 7, and 9 counters for each group of 2.

• Groups of 2
• Give each group 3 sets of counters with 6, 7, and 9.
• Display A from the warm-up or arrange counters to show:

• “Las fichas rojas están organizadas en filas, pero este no es un arreglo. ¿Cómo podemos reorganizar las fichas para hacer un arreglo como el de la imagen B?” //  “The red counters are arranged in rows, but it is not an array. How could we rearrange the counters to make an array like image B?” (We could move the bottom two counters to the middle row. We could move one from the top row to the next row. We could move 1 from the third row to the bottom row.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

• “Organicen cada grupo de fichas en un arreglo. Sus arreglos deben tener el mismo número de fichas en cada fila y no pueden usar fichas adicionales. Prepárense para explicar cómo hicieron su arreglo con cada grupo de fichas” // “Arrange each of your sets of counters into an array. Your arrays should have the same number of counters in each row with no extra counters. Be prepared to explain how you made an array out of each set.”
• “Si les queda tiempo, traten de descubrir otra manera de hacer un arreglo con cada grupo de fichas” // “If you have time, try to figure out a different way to make an array out of each set of counters.”
• 12 minutes: partner work time

If students create arrangements with unequal rows or only try to make arrays that have 2 rows or 2 columns (2 equal groups), consider asking:

• “¿Qué has intentado hasta ahora? ¿Cuántas fichas había en cada fila?” // “What did you try so far? How many counters were in each row?”
• “Poner _____ fichas en cada fila no sirve para hacer un arreglo sin que sobren fichas. ¿Con qué otra cantidad de fichas en cada fila podrías intentar?” // “_____ counters in each row did not make an array without any leftovers. What other amount of counters in each row could you try?”

• “7 y 9 son números impares. ¿Qué observaron acerca de los arreglos que podían hacer con ellos?” // “7 and 9 are both odd numbers. What did you notice about the arrays you could make with them?” (I couldn't make an array with 2 rows. With 9 counters, I could do 3 rows with 3 counters in each row. For 7, the only way we did it was with 1 row with all 7 counters.)
• Display student work for array of 6 or arrange counters to show:

• “¿Cómo podemos describir este arreglo de 6 fichas?” // “How can we describe this array of 6 counters?” (There are 3 on the top and 3 on the bottom.)
• “Otra forma de describir este arreglo es decir que hay 2 filas que tienen 3 fichas en cada una” // “Another way to describe this array is to say there are 2 rows with 3 counters in each.”

The purpose of this activity is for students to describe the number of rows in an array, the number of objects in each row, and the total number of objects. They use this vocabulary to describe arrays and create arrays given a number of counters and a number of a rows (MP6). They may use trial and error to build these arrays.

This activity uses MLR8 Discussion Supports. Advances: speaking, conversing

• Groups of 2
• Give students access to counters.
• Arrange counters to show:

• “¿Cuál de estas imágenes muestra 10 fichas en un arreglo? ¿Cómo lo saben?” // “Which of these images shows 10 counters in an array? How do you know?” (The yellow counters are in an array because the rows have the same number of counters in each.)
• 30 seconds: quiet think time
• Share responses.
• “¿Cuántas filas hay en el arreglo?” // “How many rows are in the array?” (2 rows)
• 30 seconds: quiet think time
• Share responses. Circle the 2 rows in the array.
• “¿Cuántas fichas hay en cada fila?” // “How many counters are in each row?” (5 counters)
• 30 seconds: quiet think time
• Share responses.

• “Ahora van a examinar unos arreglos para decidir cuántas filas tiene cada uno, cuántas fichas hay en cada fila y cuál es el número total de fichas. Después, van a usar fichas para hacer arreglos” // “Now you will look at a few arrays to decide how many rows each one has, how many there are in each row, and the total number of counters. Then you will make arrays using counters.”

MLR8 Discussion Supports

• Display sentence frames to support students when they describe the structure of the array:
  • “Hay _____ filas en el arreglo” // “There are _____ rows in the array.”
  • “Hay _____ fichas en cada fila” // “There are _____ counters in each row.”
  • “Hay _____ fichas en total” // “There are _____ counters in all.”
• 8 minutes: partner work time
• Monitor for students who build an array with 5 in each row for 20 counters.

• Display student work for the array with 20 counters.
• “Describan el arreglo de _____” // “Describe _____’s array.” (It has 20 counters, it has 4 rows and 5 counters in each row.)
• “¿Cómo podemos mostrar que hay 20 fichas en este arreglo?” // “How can we prove there are 20 counters in this array?” (We can count them. We can skip count by 5. We can add \(5 + 5 + 5 + 5\). The top 2 rows have 10 and the bottom 2 rows have 10.)