https://file.aiquickdraw.com/mathbot/file/17261859534755mrmfz2w.jpg

The image provided shows a pattern with tile designs and an expression written by Ramone. Let's analyze the given information.

### Problem Context:
- **Ramone's Expression**: \( 8(n - 1) \)
- **Pattern Table**:
  - Design 1: 0 new tiles
  - Design 2: 8 new tiles
  - Design 3: 16 new tiles

According to the text, Ramone's expression \( 8(n - 1) \) is intended to represent the number of new tiles for each design. Let's break it down:

### Ramone's Expression:
- \( n \) represents the design number.
- \( (n - 1) \) indicates a shift in the design number, likely due to the fact that Design 1 starts with 0 new tiles.
- Multiplying by 8 accounts for the increase in tiles between designs.

### Validation of the Expression:
- For Design 1:
  \( n = 1 \), so \( 8(1 - 1) = 8(0) = 0 \), which matches the table.
  
- For Design 2:
  \( n = 2 \), so \( 8(2 - 1) = 8(1) = 8 \), which matches the table.
  
- For Design 3:
  \( n = 3 \), so \( 8(3 - 1) = 8(2) = 16 \), which also matches the table.

Thus, Ramone's expression \( 8(n - 1) \) correctly models the pattern of new tiles.

Would you like further details or explanations?

Here are 5 related questions to consider:
1. What is the pattern for Design 4 and 5 using Ramone's expression?
2. How would the expression change if the first design had 4 new tiles instead of 0?
3. What general mathematical form does \( 8(n - 1) \) represent?
4. How can this pattern be described in terms of arithmetic sequences?
5. How would you graph this relationship between design number and new tiles?

**Tip:** When analyzing patterns, always check whether the formula is consistent with all given values in the sequence.

Analyze the expression Ramone wrote to represent this pattern and his explanation: The expression 8(n - 1) represents Miriam's square floor pattern. The number of new tiles increases by 8 in each new design.

Analyze how the expression 8(n - 1) models the increase in new tiles for Miriam's square floor pattern. This problem covers key algebraic concepts, such as arithmetic sequences and linear functions. Suitable for students in Grades 7-9.

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