Lesson 16

The purpose of this warm-up is to elicit ideas students have about objects arranged in an array, which will be useful when students arrange equal groups into arrays in a later activity. While students may notice and wonder many things about this image, ideas around arrangement and equal groups are the important discussion points. When students notice the arrangement of the eggs they look for and make use of structure (MP7).

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses. 

• “¿Cómo les ayudó tener los huevos en una caja a ver grupos iguales?” // “How does having the eggs in a carton help you see equal groups?” (I can see how they could be split into equal groups. I can see 6 eggs in each row. I can see 6 groups of 2.)
• “Los huevos están organizados en un arreglo. Un arreglo es una organización de objetos en filas y columnas. Cada columna debe tener el mismo número de objetos que las demás columnas y cada fila debe tener el mismo número de objetos que las demás filas” // “The eggs are arranged in an array. An array is an arrangement of objects in rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number of objects as the other rows.”

The purpose of this activity is for students to describe an array as an arrangement of objects into rows with an equal number of objects in each row and into columns with an equal number in each column. This will be helpful in the next activity when students arrange objects into arrays and describe arrays in terms of multiplication.

When students decide whether or not they agree with Noah about seeing equal groups in the array and explain their reasoning, they construct a viable argument and critique the reasoning of others (MP3).

• Groups of 2
• Display the images.
• “Consideren estos dibujos. A la izquierda hay un dibujo que muestra grupos iguales. A la derecha hay un arreglo. ¿En qué se parecen los dibujos? ¿En qué son diferentes?” // “Consider these drawings. On the left is a drawing showing equal groups. On the right is an array. How are the drawings alike? How are they different?” (Alike: They both have 20 dots. They both have groups of 5. Different: The dots are arranged differently. The second group has the dots in rows. The first drawing has the dots in circles.)
• 1–2 minutes: quiet think time
• Share and record responses.

• “Con su compañero, describan cómo cambia la manera en la que ven el número cuando los puntos están organizados en un arreglo” //  “Work with your partner to describe how arranging the dots into an array affects how you see the number.”
• 2–3 minutes: partner work time
• Share responses.
• “Lean lo que dice Noah sobre los puntos y decidan si están de acuerdo o en desacuerdo. Prepárense para compartir su razonamiento” // “Read what Noah says about the dots and decide whether you agree or disagree. Be ready to share your reasoning.”
• 1 minute: independent work time
• Ahora, discutan con su compañero si están de acuerdo o en desacuerdo con Noah” // “Now discuss whether you agree or disagree with Noah with your partner.” 
• 2–3 minutes: partner discussion

• “¿Cómo se relacionan los arreglos con los grupos iguales?" // “How are arrays related to equal groups?” (There are the same number of dots in each row, so the rows are equal groups. There are the same number of dots in each column, so the columns are equal groups.)

The purpose of this activity is for students to build arrays with physical objects and describe the arrays in terms of multiplication. Students focus on where equal groups can be seen in arrays. Students will write expressions and equations to represent arrays in future lessons. In the activity, students are asked to create different arrays with 24 cubes. It is not an expectation of grade 3 for students to find all the arrays for a given number.

When students notice that the rows or columns in an array have the same number of objects and relate this to equal groups, they look for and make use of structure (MP7).

Keep connecting cubes out for the cool-down.

• Each group of 2 needs 60 cubes.

• Groups of 2
• Give each group of 2 students at least 60 connecting cubes.

• 7–10 minutes: partner work time
• Monitor for students who relate the same number of objects in each row and column in an array to how multiplication expresses equal groups of objects.

• Have students share different arrays they made for the last problem.
• “¿Por qué pudieron crear diferentes arreglos con 24 objetos?” // “Why were you able to create different arrays with 24 objects?” (There are many ways to put 24 things into equal groups.)