Match and Draw Arrays

10 min

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 discussion, ask students to explain the meaning of any terminology they use, such as “rows,” “columns,” “groups,” and “array.”

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A
Group of 15 dots.

B
Group of 15 dots.

C
Group of 15 dots.

D
Array of 9 dots. 3 rows of 3.

Solution Steps (4)
  1. 1
    Count dots in each arrangement
    →A, B, C have 15 dots; D has 9 dots
  2. 2
    Identify which show rows and columns (arrays)
    →A and D show clear rows and columns; B has rows but gaps; C shows diagonal groups
  3. 3
    Find attributes that group 3 together
    →Multiple valid groupings based on: same count, array structure, equal groups, touching dots
  4. 4
    Identify D as a clear array
    →D is 3 rows of 3 - perfect array structure

Sample Response

Sample responses:

A, B, and C go together because:
  • They have 15 dots.
A, B, and D go together because:
  • They are organized in rows and columns.
A, C, and D go together because:
  • The equal groups of dots are right next to each other or touching.
B, C, and D go together because:
  • They show equal groups of 3 in straight lines — horizontal (rows) or diagonal lines.
Activity Synthesis (Teacher Notes)
  • “How would you rearrange each group of dots to make an array?" (For A, I would rearrange the 5 dots on the right side to make a column of 5 dots. For B, I’d push all the dots over to the left so they line up in columns and move the top 2 rows closer to the bottom 3 rows. For C, I’d rearrange the groups of 3 to make rows or columns. I wouldn’t have to do anything for D because it is an array.)”
Standards
Building Toward
  • 3.OA.1·Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. <em>For example, describe a context in which a total number of objects can be expressed as 5 × 7.</em>
  • 3.OA.A.1·Interpret products of whole numbers, e.g., interpret <span class="math">\(5 \times 7\)</span> as the total number of objects in 5 groups of 7 objects each. <span>For example, describe a context in which a total number of objects can be expressed as <span class="math">\(5 \times 7\)</span>.</span>

20 min

15 min