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The problem you're working on involves determining a relationship between the step number in a series of tile formations and the number of tiles used in each step.

### Observations:
- **Middle tower**: Always has the same number of tiles as the step number.
- **Two arms**: Each arm contains one less tile than the step number.

### Pattern Analysis:
- For step \( n \):
  - The middle tower has \( n \) tiles.
  - Each arm (left and right) has \( n - 1 \) tiles.
  - There are two arms, so the total number of tiles in the arms is \( 2(n - 1) \).

### Total number of tiles at step \( n \):
- Middle tower: \( n \) tiles.
- Two arms: \( 2(n - 1) \) tiles.

Thus, the equation for the total number of tiles \( T(n) \) at step \( n \) is:
\[
T(n) = n + 2(n - 1)
\]
This simplifies to:
\[
T(n) = n + 2n - 2 = 3n - 2
\]

### Final Equation:
The equation that fits Dan's way of seeing the relationship is:
\[
T(n) = 3n - 2
\]

Let me know if you'd like further details on this or have any questions!

Here are five relative questions to extend your understanding:
1. How does the number of tiles change if the arms also matched the step number?
2. What would the equation be if the number of tiles in the arms was not fixed but increased by 2 each step?
3. Can you identify the equation for the total number of tiles if each arm had \( n + 1 \) tiles instead of \( n - 1 \)?
4. How does the pattern change if a new arm is introduced on top of the tower, increasing with each step?
5. Can you find a way to graph the equation to visually understand the relationship?

**Tip:** When creating equations from patterns, always identify variables and ensure every part of the structure is accounted for.

Dan explained that the middle tower is always the same number as the step number. He also pointed out that the two arms on each side of the tower contain one less block than the step number. Create an equation that fits Dan’s way of seeing the relationship.

Learn how to create an algebraic equation for tile patterns where the middle tower has the same number of tiles as the step number, and the arms have one less tile. Suitable for Grades 6-8.

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