Lesson 7
What is an Array?
Warmup: Which One Doesn’t Belong: Counter Collections (10 minutes)
Narrative
Launch
 Groups of 2
 Display the image.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 2–3 minutes: partner discussion
 Record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
 “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.)
 “We call objects arranged in equal rows an array. The rows go from side to side. We are going to explore arrays today.”
Activity 1: What is an Array? (20 minutes)
Narrative
Required Materials
Materials to Gather
Required Preparation

Create containers with 6, 7, and 9 counters for each group of 2.
Launch
 Groups of 2
 Give each group 3 sets of counters with 6, 7, and 9.
 Display A from the warmup or arrange counters to show:
 “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.
Activity
 “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.”
 “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
Student Facing
Arrange each set of counters into equal rows with no extra counters.
 How many counters are there in all? _____
Show how you arranged them using words, drawings, or numbers.
 How many counters are there in all? _____
Show how you arranged them using words, drawings, or numbers.
 How many counters are there in all? _____
Show how you arranged them using words, drawings, or numbers.
Student Response
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Advancing Student Thinking
 “What did you try so far? How many counters were in each row?”
 “_____ counters in each row did not make an array without any leftovers. What other amount of counters in each row could you try?”
Activity Synthesis
 “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:
 “How can we describe this array of 6 counters?” (There are 3 on the top and 3 on the bottom.)
 “Another way to describe this array is to say there are 2 rows with 3 counters in each.”
Activity 2: Rows of Counters (15 minutes)
Narrative
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
Supports accessibility for: Conceptual Processing, Organization, Attention
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to counters.
 Arrange counters to show:
 “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.
 “How many rows are in the array?” (2 rows)
 30 seconds: quiet think time
 Share responses. Circle the 2 rows in the array.
 “How many counters are in each row?” (5 counters)
 30 seconds: quiet think time
 Share responses.
Activity
 “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.”
 Display sentence frames to support students when they describe the structure of the array:
 “There are _____ rows in the array.”
 “There are _____ counters in each row.”
 “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.
Student Facing

 How many rows are in this array?
 How many counters are in each row?
 How many counters are there in all?

 How many rows are in this array?
 How many counters are in each row?
 How many counters are there in all?
 Use 6 counters to make 2 rows with the same number in each row. How many counters are in each row?
 Use 20 counters to make 4 rows with the same number in each row. How many counters are in each row?
Student Response
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Activity Synthesis
 Display student work for the array with 20 counters.
 “Describe _____’s array.” (It has 20 counters, it has 4 rows and 5 counters in each row.)
 “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.)
Lesson Synthesis
Lesson Synthesis
“Today you learned that an array is an arrangement of objects in rows with an equal number of objects in each row.”
Arrange counters to show:
“How could you use the rows to find the total number of counters?” (I know there are 3 rows with 5 in each row. I skip counted by 5. 5, 10, 15)
Share and record responses.
Record \(5 + 5 + 5 = 15\)
Cooldown: Count the Counters (5 minutes)
CoolDown
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