Area of a Rectangle

10 min

Narrative

The purpose of this Warm-up is to elicit strategies for quantifying numbers of objects arranged in rows and columns, and the language used to describe such arrangements. It gives students a reason to use language precisely (MP6). During the discussion, ask students to explain the meaning of any terms they use, such as “row,” “column,” “array,” “group,” “line,” “grid,” and “rectangle.”

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 arrangements 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
A rectangle with 24 same-size squares in 4 rows of 6. Dots in the middle of the first column of squares.

B
A rectangle with 20 same-size squares in 4 rows of 5. Dots in the middle of the first row of squares.

C
Array. 4 rows of 5 dots.

D
5 groups of 4.

Solution Steps (4)
  1. 1
    Examine each arrangement for structure
    →A: 4×6 grid with dots, B: 4×5 grid with dots, C: 4×5 dot array, D: 5 groups of 4
  2. 2
    Identify which show array/rectangular arrangement
    →A, B, C arranged in rows and columns (arrays)
  3. 3
    Count total objects in each
    →A: 24, B: 20, C: 20, D: 20
  4. 4
    Group 3 based on shared characteristic
    →B, C, D go together (all have 20 objects)

Sample Response

Sample responses:

A, B, and C go together because:
  • They have objects arranged as a rectangle.
  • They have objects arranged in an array.
A, B, and D go together because:
  • They show dots (circles) inside another shape.  
A, C, and D go together because:
  • They show at least 1 group of 4 dots. 
B, C, and D go together because:
  • They have 20 squares or 20 dots (circles).
Activity Synthesis (Teacher Notes)
  • “How did you determine the total number for each image?” (In D, I counted by 4 since I saw equal groups of 4. In C, I counted by 5 since each row had 5 dots. In B, I counted by 5 since each row had 5 squares. In A, I just added 20 and 4 for the extra column.)
Standards
Building Toward
  • 3.MD.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  • 3.MD.C.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

20 min

15 min