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Launch

Groups of 2
Display the image or show 20 counters (10 red and 10 yellow) in a random arrangement.
“How many counters do you see?”
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time

Activity

“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:

Groups of dots.

“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.
“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:

Array.

“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.

How many counters do you see?

Group of dots. 10 red. 10 yellow.

Record an estimate that is:

too low	about right	too high

Student Response

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Advancing Student Thinking

Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR8 Discussion Supports

Materials

To Gather

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.
“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:

Array.

“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.
“How many counters are in each column of the array you made?” (3)
30 seconds: quiet think time
Share responses.

Activity

“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:
- “There are _____ columns in the array.”
- “There are _____ counters in each column.”
- “There are _____ counters in all.”
8 minutes: partner work time

1. How many columns are in this array?
2. How many counters are in each column?
3. How many counters are there in all?
1. How many columns are in this array?
2. How many counters are in each column?
3. How many counters are there in all?
Use 10 counters. Make 2 columns with the same number in each column.
1. How many counters are in each column?
2. How many rows are in the array?
3. How can you count these counters without counting by ones?
Use 15 counters. Make 3 columns with the same number in each column.
1. How many counters are in each column?
2. How many rows are in the array?
3. How many counters are in each row?
4. How can you count these counters without counting by ones?

Student Response

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Advancing Student Thinking

Activity Synthesis

Display student work for an array with 10 counters.
“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.)
“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

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

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
“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

“Now you will work with a partner to see if you can make matching arrays.”
“Partner A will make an array using up to 25 counters. Don’t let your partner see.”
“Give your partner clues about your array, so they can try to make it.”
“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.

Four students make arrays.

Han says, “My array has an even number of counters. It has 2 rows with 6 counters in each row.”
Priya says, “My array has more than 10 counters. It has 4 rows with 3 counters in each row.”
Elena says, “My array is very long. It has 6 counters in each column.”
Kiran says, “My array has more columns than rows. It has 3 rows.”

Write the name of each student below their array.

A

B

C

D
Each student used _____ counters to make an array.
Make an array using up to 25 counters. Don’t let your partner see.

Give your partner clues so they can try to make your array. Compare your arrays.

How do you know the total number of counters in each array? Be prepared to explain your reasoning.

Student Response

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Advancing Student Thinking

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

“How many rows does your array have? How many columns does your array have?”
“Does your array have more rows, more columns, or the same number of rows and columns?”

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.
“Which clues helped you most when making your arrays?” (It was easy when they said how many rows and columns.)