Lesson 17

Match and Draw Arrays

Warm-up: Which One Doesn’t Belong: Arrangements (10 minutes)

Narrative

The purpose of this warm-up is for students to compare four arrangements of dots to elicit the attributes, or structure, of an array. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as rows, corners, groups, and array.

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

• 2–3 minutes: partner discussion
• Share and record responses.

Student Facing

Which one doesn't belong?

Activity Synthesis

• “Why is B not an array?” (It has the same number of dots in each row, but not the same in each column. One of the columns only has 3 dots. The 3rd row is missing.)
• “Let’s find at least one reason why each one doesn’t belong.”

Activity 1: Card Sort: Arrays (20 minutes)

Narrative

The purpose of this activity is for students to relate drawings of equal groups to arrays. Specifically, students look for arrays that have the same number of objects in each row or column as each drawing has in each group. In some arrays, the equal groups in the drawing are represented as rows, and in some, they are represented in columns. Students have the opportunity to explain the connections they see between the drawings and arrays, receive feedback from their peers, and revise their explanation for precision and clarity (MP3, MP6). This will be useful in future lessons when students record multiplication expressions and equations to represent arrays.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Attention, Organization

Required Materials

Materials to Copy

• Card Sort Arrays

Required Preparation

• Create a set of cards from the blackline master for each group of 2 or 4 students.

Launch

• Groups of 2 or 4
• Distribute one set of pre-cut cards to each group of students.

Activity

• “This set of cards includes drawings of equal groups and arrays. Match each drawing to an array. Work with your partner to justify your choices.”
• 8 minutes: partner work time
• “Independently choose a match you and your partner made. Write down how you know that the drawing matches the array.”
• 2 minutes: independent work time

MLR1 Stronger and Clearer Each Time

• “Share your response to why your cards match with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion
• Repeat with 2–3 different partners.
• “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

Student Facing

1. Match the drawings of equal groups and arrays that are alike. Be prepared to explain your reasoning.

2. Choose a match you and your partner made. Write down how you know the drawing matches the array.

Activity Synthesis

• Have 2-3 students share the matches they made and describe how they know those cards go together.
• “Did your group agree on the matches? What did you look for to decide two cards were matches?” (Yes, we looked for equal groups that had the same number of dots in a group as one of the rows in the array.)
• Listen for language students use to describe their matches and the structure of the arrays. As needed, ask:
• “What do you mean by _____?”
• “What else could we call _____?”
• “How could you use ‘equal groups’ to explain your match?”
• Highlight the use of terms like row, column, and equal groups.

Activity 2: Draw Arrays (15 minutes)

Narrative

The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rearrange would be helpful in this activity.

MLR8 Discussion Supports. To support partner discussion, display the following sentence frames: “This array matches the diagram because . . .”, and “This array shows multiplication because . . . .”

Required Materials

Materials to Gather

• Groups of 2

Activity

• “Work independently to draw a way that the first group of dots in problem 1 could be arranged into an array.”
• 2 minutes: independent work time
• “Discuss how you arranged your dots and how the array is related to multiplication with your partner.”
• 1 minute: partner discussion
• “How did you rearrange the dots to make an array?” (Since there were 3 in each group, I put 3 dots in each row. I saw 2 groups of 6, so I made 2 rows of 6.)
• “Did anyone create a different array?”
• “Now you are going to make as many arrays as you can from 16 dots.”
• 2–3 minutes: independent work time
• “Share how you rearranged the dots into arrays with your partner. See if together you can come up with any other arrays.”
• 3–5 minutes: partner work time

Student Facing

1. Draw 1 way the dots could be rearranged into an array.

2. Explain or show how the array is related to multiplication.
1. Draw ways that the dots could be arranged into arrays. Draw as many ways as you can.

2. Explain or show how each array is related to multiplication.

Activity Synthesis

• “What kinds of equal groups did you make from 16 dots? How can you see the equal groups in the arrays you made?” (I can make 2 groups of 8. I drew it as 2 rows of 8 dots.)

Lesson Synthesis

Lesson Synthesis

“Today we made drawings that showed how groups of dots could be rearranged into arrays.”

“What do you need to think about when you draw an array?” (Make sure the rows and columns all have the same number of dots. Make the number of groups the number of columns or row in the array and then draw how many are in each group in each column or row. All the dots have to be used.)