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Launch

Groups of 2
Display the image or show 20 counters (10 red and 10 yellow) in a random arrangement.
“¿Cuántas fichas ven?” // “How many counters do you see?”
“¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high?” “Too low?” “About right?”
1 minute: quiet think time

Activity

“Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Arrange counters to show 2 circular arrangements of 10 red and 10 yellow counters:

“Estas son las mismas fichas, pero organizadas de otra manera. ¿Quieren revisar lo que pensaron antes?” // “Here are the same counters in a different arrangement. Would you like to revise your thinking?” (I counted the red and there were 10. I think there’s the same amount of yellow, so I said 20.)
1 minute: quiet think time
Share responses.
“¿Cómo les ayuda esta imagen a pensar si el total es par o es impar?” // “How does this image help you think about whether or not the total is even or odd?” (It helps me see the number of counters as 2 equal groups. So, it must be an even number.)
Arrange the counters into an array of 2 rows of 5 red counters and 2 rows of 5 yellow counters with some space to separate the two colors:

“Esta imagen muestra el mismo número de fichas, pero organizadas de otra manera. ¿Quieren revisar lo que pensaron antes?” // “This image shows the same number of counters, but in a different arrangement. Would you like to revise your thinking?” (It’s easy now to see that it’s 20. There’s 10 red and 10 yellow.)
30 seconds: quiet think time
Share responses.

Student Task Statement

¿Cuántas fichas ves?

Escribe una estimación que sea:

muy baja	razonable	muy alta

Student Response

to access Student Response.

Advancing Student Thinking

Are You Ready for More?

Activity 1

15 mins

Contemos por columnas

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR8 Discussion Supports

Materials

To Gather

Counters

Activity Narrative

The purpose of this activity is for students to describe the structure of an array by identifying the number of columns, the number of objects in each column, and the total number of objects. Students learn that the columns of an array go up and down. Students begin to reason about how they can use the structure of an array to find the total number of objects without counting by 1.

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

Representation: Develop Language and Symbols. Support understanding of the rows and columns by inviting students to act it out. For example, use students to create the first array (3 rows of 2). Discuss the students who create the rows. Now switch to talking about columns (2 columns of 3). Discuss the difference between how students create the rows and how they create the columns.
Supports accessibility for: Visual-Spatial Processing, Organization

Launch

Groups of 2
Give students counters.
“Usen sus fichas para hacer un arreglo que tenga 3 filas con 4 fichas cada una. Asegúrense de que las fichas de cada fila estén alineadas con las fichas de las otras filas” // “Use your counters to make an array with 3 rows with 4 in each row. Make sure the counters in each row line up with the counters in the other rows.”
Display counters in an array as shown:

“Los arreglos están formados por filas, pero también tienen columnas que van de arriba hacia abajo. ¿Cuántas columnas hay en este arreglo?” // “Arrays are made up of rows, but they also have columns that go up and down. How many columns are in this array?” (4)
30 seconds: quiet think time
Share responses.
“¿Cuántas fichas hay en cada columna del arreglo que hicieron?” // “How many counters are in each column of the array you made?” (3)
30 seconds: quiet think time
Share responses.

Activity

“Ahora van a examinar unos arreglos. Van a encontrar cuántas columnas tiene cada uno, cuántas fichas hay en cada columna y cuál es el número total de fichas. Después, van a usar fichas para hacer arreglos y a responder unas preguntas” // “Now you will look at a few arrays to find how many columns each one has, how many counters are in each column, and the total number of counters. Then you will make arrays using counters and answer a few questions.”

MLR8 Discussion Supports

Display sentence frames to support students when they describe the structure of the array:
- “Hay _____ columnas en el arreglo” // “There are _____ columns in the array.”
- “Hay _____ fichas en cada columna” // “There are _____ counters in each column.”
- “Hay _____ fichas en total” // “There are _____ counters in all.”
8 minutes: partner work time

Activity Synthesis

Display student work for an array with 10 counters.
“Describan el arreglo de _____” // “Describe _____’s array.” (It has 10 counters. It has 2 columns with 5 counters in each column. It has 5 rows with 2 counters in each row.)
“¿Cómo podemos mostrar que hay 10 fichas en este arreglo?” // “How can we prove there are 10 counters in this array?” (We can skip-count by 2. We can add . We can add .)

Activity 2

20 mins

Adivina cuál es mi arreglo

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Counters

Activity Narrative

The purpose of this activity is for students to distinguish between rows and columns of arrays based on given clues. The Activity Synthesis invites students to use the vocabulary they have learned in this lesson and the previous lesson to describe and create arrays (MP6). When making arrays based on clues, it might be helpful to have partners sit back to back.

Launch

Groups of 2
“Cuatro estudiantes usaron el mismo número de fichas para hacer arreglos. Marquen cada arreglo con el nombre del estudiante y encuentren el número total de fichas” // “Four students made arrays using the same number of counters. Label each array with the student’s name and find the total number of counters.”
6 minutes: independent work time
Share and record responses.
Give each student 25 counters.

Activity

“Ahora van a trabajar con un compañero para ver si pueden hacer arreglos que coincidan” // “Now you will work with a partner to see if you can make matching arrays.”
“El compañero A va a hacer un arreglo con fichas. Puede usar hasta 25 fichas. No va a dejar que su compañero vea el arreglo” // “Partner A will make an array using up to 25 counters. Don’t let your partner see.”
“Después, le da pistas sobre su arreglo a su compañero para que intente hacerlo” // “Give your partner clues about your array, so they can try to make it.”
“Comparen sus arreglos para ver si hicieron el mismo arreglo. Después, intercambien roles” // “Compare to see if your partner made the same array, and then switch.”
10 minutes: partner work time
Monitor for students who gave clues using “odd” or “even” and those who used the “rows” and “columns” language correctly to share in the Synthesis.

Student Task Statement

Cuatro estudiantes hacen arreglos.

Han dice: “Mi arreglo tiene un número par de fichas. Tiene 2 filas con 6 fichas cada una”.
Priya dice: “Mi arreglo tiene más de 10 fichas. Tiene 4 filas con 3 fichas cada una”.
Elena dice: “Mi arreglo es muy largo. Tiene 6 fichas en cada columna”.
Kiran dice: “Mi arreglo tiene más columnas que filas. Tiene 3 filas”.

Escribe el nombre de cada estudiante debajo de su arreglo.

A

B

C

D
Cada estudiante usó _____ fichas para hacer su arreglo.
Usa fichas para hacer un arreglo. No dejes que tu compañero lo vea. Puedes usar hasta 25 fichas.

Dale pistas a tu compañero para que intente hacer tu arreglo. Compara tu arreglo con el de tu compañero.

¿Cómo sabes cuál es el número total de fichas de cada arreglo? Prepárate para explicar tu razonamiento.

Student Response

to access Student Response.

Advancing Student Thinking

If students give clues that are not related to the rows and columns of their array, consider asking or displaying:

“¿Cuántas filas tiene tu arreglo? ¿Cuántas columnas tiene tu arreglo?” // “How many rows does your array have? How many columns does your array have? ”
“¿Tu arreglo tiene más filas, tiene más columnas o tiene el mismo número de filas y de columnas?” // “Does your array have more rows, more columns, or the same number of rows and columns?”

Are You Ready for More?

Activity Synthesis

Invite previously identified students to share their clues.
Students can use their counters to see if they make an array that matches the chosen student’s.
“¿Cuáles fueron las pistas que más les ayudaron a hacer sus arreglos?” // “Which clues helped you most when making your arrays?” (It was easy when they said how many rows and columns.)

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Lesson 8

Contemos columnas y objetos en columnas

Warm-up

Exploración de estimación: Reorganicemos los puntos

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Activity Synthesis

Activity 1

Contemos por columnas

Standards Alignment

2.OA.4

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Adivina cuál es mi arreglo

Standards Alignment

2.OA.4

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Activity Synthesis

Lesson Synthesis

Have feedback on the curriculum?

Standards Alignment

2.OA.2

2.OA.3

2.OA.4

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?