In art class, the students each made rectangular quilts using 24 paper

Question

squares. They then glued a button onto each square and decorated the
squares with markers. Create all of the possible arrays for modeling a rectangular quilt with
the 24 paper squares. Write an equation to accompany each array.
You can use the attached pre-made quilt squares by cutting and
pasting them, or you can draw the arrays with your own designs on a
separate sheet of paper.

Answer 1

To create all possible rectangular arrays using 24 paper squares, we can first determine the pairs of factors of 24. Each pair of factors will represent one possible layout for the rectangular quilt.

The factor pairs of 24 are:

1. \( 1 \times 24 \)
2. \( 2 \times 12 \)
3. \( 3 \times 8 \)
4. \( 4 \times 6 \)

Here are the rectangular arrays modeled by these pairs, along with the corresponding equations:

1. Array: \( 1 \times 24 \)

   • This means 1 row of 24 squares.
   • Equation: \( 1 \times 24 = 24 \)

2. Array: \( 2 \times 12 \)

   • This means 2 rows of 12 squares.
   • Equation: \( 2 \times 12 = 24 \)

3. Array: \( 3 \times 8 \)

   • This means 3 rows of 8 squares.
   • Equation: \( 3 \times 8 = 24 \)

4. Array: \( 4 \times 6 \)

   • This means 4 rows of 6 squares.
   • Equation: \( 4 \times 6 = 24 \)

In summary, the possible rectangular quilts made with 24 paper squares can be represented in the following arrays, along with their corresponding equations:

1. \( 1 \times 24 \): \( 1 \times 24 = 24 \)
2. \( 2 \times 12 \): \( 2 \times 12 = 24 \)
3. \( 3 \times 8 \): \( 3 \times 8 = 24 \)
4. \( 4 \times 6 \): \( 4 \times 6 = 24 \)

You can create these arrays using paper squares by combining them into the specified rows and columns for each layout.