To create an algebraic expression for how many small squares the frame consists of when there are $n$ tiles along the edge, let's break it down:

1. The frame surrounds a square area. So, the total number of small squares in a square with $n$ tiles along each side is $n^2$.
2. However, we are interested only in the frame of the square, which consists of the tiles along the edges, not the entire area.

Frame Structure:

• There are $n$ tiles on the top and bottom edges. So, both the top and bottom edges contribute $2n$ tiles.
• For the left and right sides, we also have $n-2$ tiles each (since the corners are already counted in the top and bottom edges).
• Therefore, the left and right edges contribute $2(n-2)$ tiles.

Total Expression:

Summing these up, the total number of small squares in the frame is: $2n + 2(n-2) = 2n + 2n - 4 = 4n - 4$ Thus, the algebraic expression for the number of small squares in the frame is:

$\boxed{4n - 4}$

This expression counts the number of small squares in the frame when there are $n$ tiles along each edge.

Would you like a detailed breakdown of how this expression was derived or have any further questions?

Related Questions:

1. What happens to the frame size if $n = 5$?
2. How does the formula change if you want to include the full area, not just the frame?
3. What if the frame consists of two rows of small squares instead of one?
4. How can this expression be applied to a rectangular frame instead of a square?
5. How many small squares are there in the frame when $n = 10$?

Tip: Understanding how different parts of the shape contribute to the frame is crucial when forming such algebraic expressions.