Question

In art class, the students each made rectangular quilts using 24 paper squares. They then glued a button onto each square and decorated the squares with markers.1. Create all of the possible arrays for modeling a rectangular quilt with the 24 paper squares. Write an equation to accompany each array. 2. Could the students use 24 paper squares to make quilts with 5 rows of paper squares? How do you know? Use an array to help explain your

Answer 1

To create all possible arrays for a rectangular quilt with 24 paper squares, find the factor pairs of 24. It is not possible to make quilts with 5 rows using 24 paper squares.

Step-by-step explanation:

To create all of the possible arrays for modeling a rectangular quilt with 24 paper squares, we need to find all the factor pairs of 24.

Here are the equations for each array:

• 1 x 24: A rectangular quilt with 1 row and 24 columns
• 2 x 12: A rectangular quilt with 2 rows and 12 columns
• 3 x 8: A rectangular quilt with 3 rows and 8 columns
• 4 x 6: A rectangular quilt with 4 rows and 6 columns
• 6 x 4: A rectangular quilt with 6 rows and 4 columns
• 8 x 3: A rectangular quilt with 8 rows and 3 columns
• 12 x 2: A rectangular quilt with 12 rows and 2 columns

Regarding the second question, if the students want to make quilts with 5 rows using 24 paper squares, it is not possible because there are no factor pairs of 24 which have 5 as one of the factors.

Answer 2

1.

24 rows and 1 column

12 rows and 2 columns

8 rows and 3 columns

6 rows and 4 columns

2. No, you couldn't use 24 paper squares to make quilts with 5 rows.

Step-by-step explanation:

If the total number of squares is 24, the possible arrays for modeling a rectangular quilt will be the possible pairs of numbers that multiply to 24. So, these arrays are

24 rows and 1 column of paper squares

12 rows and 2 columns of paper squares

8 rows and 3 columns of paper squares

6 rows and 4 columns of paper squares

On the other hand, the students couldn't use 24 papers squares to make quilts with 5 rows of paper squares because 5 doesn't divide 24 and we can see in the following diagram, that the quilt will be incomplete with 24 paper squares

Therefore, the answers are:

1. 24 rows and 1 column

12 rows and 2 columns

8 rows and 3 columns

6 rows and 4 columns

2. No, you couldn't use 24 paper squares to make quilts with 5 rows.