# Lesson 16

Arrange Objects Into Arrays

## Warm-up: Notice and Wonder: Eggs (10 minutes)

### Narrative

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).

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Activity Synthesis

• “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.)
• “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.”

## Activity 1: Compare Equal Groups and Arrays (15 minutes)

### Narrative

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).

### Launch

• Groups of 2
• Display the images.
• “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.

### Activity

• “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.
• 1 minute: independent work time
• “Now discuss whether you agree or disagree with Noah with your partner.”
• 2–3 minutes: partner discussion

### Student Facing

1. How does arranging the dots into an array affect how you see the number?
2. Noah says he sees equal groups in the drawing with 4 circles and 5 dots in each circle, but says there are no equal groups in the array. Do you agree with Noah? Explain your reasoning.

### Activity Synthesis

• “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.)

## Activity 2: Arrange Into Arrays (20 minutes)

### Narrative

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.

MLR8 Discussion Supports. Synthesis: Create a visual display of the various arrays created by the students. As students discuss each array, annotate the display with the language used, such as “array”, “rows”, “columns”, and “equal groups”.
Representation: Internalize Comprehension. Synthesis: Invite students to identify what is important or most useful to pay attention to. Display the sentence frame, “The next time I arrange objects in an array, I will remember to . . . .“
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Memory

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 60 cubes.

### Launch

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

### Activity

• 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.

### Student Facing

1. Use cubes to make 6 groups of 5.

• Arrange them into an array.
• Explain or show how the array is related to equal groups.
2. Count out 20 cubes.

• Arrange them into as many arrays as you can.
• Explain or show how each array is related to equal groups.
3. Count out 24 cubes.

• Arrange them into as many arrays as you can.
• Explain or show how each array is related to equal groups.

### Activity Synthesis

• Have students share different arrays they made for the last problem.
• “Why were you able to create different arrays with 24 objects?” (There are many ways to put 24 things into equal groups.)

## Lesson Synthesis

### Lesson Synthesis

“Today we arranged objects into arrays and described how arrays are related to equal groups.”

“What did you think about when you arranged cubes into arrays?” (I dealt the cubes into equal groups and then arranged them into an array. I thought about equal groups I could use to make the total and made each group a row with the same number of things in each row. I arranged them until there were the same number of cubes in each row and the same number of cubes in each column.)