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Arrange Objects into Arrays

Grade 3: Unit 1: Lesson 16

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Lesson Purpose

The purpose of this lesson is for students to describe arrays and arrange objects into arrays.

Lesson Narrative

In grade 2, students were introduced to arrays and related them to addition expressions and

equations. In this lesson, students deepen their understanding of arrays as they arrange physical

objects and relate arrays to multiplication and equal groups. Students use connecting cubes to

represent arrays in Activity 2 and in the cool-down.

When working with array situations, students may see the equal groups in an array in either the

rows or the columns. For example, when representing 3 rows of 5 chairs, they may create a 3 by 5

array or a 5 by 3 array. This is fine as long as students can correctly describe where the “3 rows of 5

chairs” are in their array. Students will learn about commutativity in the last lesson in this section,

so if questions about commutativity arise, record them publicly for discussion in that lesson.

Learning Goals

• Build arrays with physical objects and describe them in terms of multiplication.

• 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.

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Let’s make some arrays!

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Notice and Wonder: Eggs

Warm-Up

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What do you notice? What do you wonder?

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Let’s talk about it!

How does having the eggs in a carton help you see equal groups?

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Compare Equal Groups and Arrays

Activity 1

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How does arranging the dots into an array affect how you see the number?�
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.

• 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.

• “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.

• “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

• “Now discuss whether you agree or disagree with Noah with your partner.”

• 2–3 minutes: partner discussion

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Let’s talk about it!

How are arrays related to equal groups?

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Arrange into Arrays

Activity 2

MLR 8: Discussion Supports
Representation

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a. Use cubes to make 6 groups of 5.

◦ Arrange them into an array.

◦ Explain or show how the array is related to equal groups.�

b. Count out 20 cubes.

◦ Arrange them into as many arrays as you can.

◦ Explain or show how each array is related to equal groups.�

c. Count out 24 cubes.

◦ Arrange them into as many arrays as you can.

◦ Explain or show how each array is related to equal groups.

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Let’s Talk About it!

Why were you able to create different arrays with 24 objects?

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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?

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Array Arrangement

Cool-Down

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Arrange 12 cubes into an array.

Explain or show how the array is related to multiplication.

Cool-Down: Array Arrangement

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Image Citations

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRQmJ0jf8zd-5C9zDin_7ykTZ9gwJOBo_QtloyW764fca8xpUM&s

https://pixabay.com/photos/woman-thinking-thought-5692050/

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