Represent Arrays with Expressions

10 min

Narrative

The purpose of this How Many Do You See? is for students to subitize or use grouping strategies to describe the images they see. When students use the structure of the array to figure out how many objects are shown, they look for and make use of structure (MP7).

Launch

  • Groups of 2
  • “How many do you see? How do you see them?”  
  • Flash the image.
  • 30 seconds: quiet think time
Teacher Instructions
  • Display the image.
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses.

Student Task

How many do you see? How do you see them?

Array. 5 rows of 4 triangles.

Solution Steps (4)
  1. 1
    Observe the array structure
    →5 rows of 4 triangles
  2. 2
    See equal groups by rows
    →5 groups of 4 (5 rows, 4 in each row)
  3. 3
    See equal groups by columns
    →4 groups of 5 (4 columns, 5 in each column)
  4. 4
    Find total using grouping
    →5×4 = 20 or 4×5 = 20 triangles

Sample Response

Sample responses:
  • 20: I saw 4 groups of 5 or 5 groups of 4.
  • 20: I see 2 groups of 10 or 10 groups of 2.
Activity Synthesis (Teacher Notes)
  • “How did seeing equal groups help you know how many triangles there were in the array?”
  • Consider asking:
    • “Who can restate the way _____ saw the triangles in different words?”
    • “Did anyone see the triangles the same way but would explain it differently?”
Standards
Addressing
  • 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