The problem in the image asks students to arrange tiles representing letters of the alphabet on a classroom wall in a rectangular grid, adhering to the following instructions:

1. The tiles must form a rectangle.
2. The rectangle should have 6 rows.
3. The rectangle should use the least possible number of columns.

Let's solve part b based on the following information:

• The total number of letters in the alphabet is 26.
• The rectangle must have 6 rows, so we can divide 26 by 6 to figure out how many columns are needed.

Now, $26 \div 6 = 4$ with a remainder of 2. This means that there will be 4 full tiles per row, and the last row will need 2 extra tiles (which will likely be blank to complete the rectangle).

Thus, to fill the rectangle, there will need to be 5 columns (4 full tiles and 1 column to accommodate the remaining 2 tiles in the last row), which is already confirmed as the answer in part a.

Answer for part b:

• There will be 4 blank tiles used in total. Two blank tiles are required to fill the incomplete rows after placing the 26 letters into the rectangle.

Do you want further details on how I reached this conclusion? Here are some questions to extend this problem:

1. How would the solution change if the number of letters were 30 instead of 26?
2. What is the mathematical process to generalize this approach for any number of letters?
3. If the rectangle could have more than 6 rows, how would you find the best arrangement?
4. How could the blank spaces be minimized with a different arrangement?
5. What if you were asked to form the rectangle with exactly 5 columns instead of the smallest possible number?

Tip: When dividing objects into grids or rows, consider both the quotient and remainder to determine if extra blank spaces are needed to complete the arrangement.