Using 6 tiles make a pattern that uses four more toothpicks then tiles 

To create a pattern with 6 tiles and 4 more toothpicks than tiles, let's break down the situation.

- **Tiles**: There are 6 tiles.
- **Toothpicks**: We need to use 6 + 4 = 10 toothpicks.

Now let's visualize a pattern with tiles and toothpicks:

1. **Basic unit**: Each tile can be surrounded by 4 toothpicks (forming a square), but we need to overlap some edges to reduce the total number of toothpicks.

2. **Pattern design**: One possible arrangement is to place the tiles in a row or some other compact arrangement where shared edges reduce the overall number of toothpicks. 

Here's how it works:
- Place all 6 tiles in a straight line (like forming a rectangle).
- For 6 tiles placed side by side, there are shared edges between adjacent tiles.

- Without shared edges, we’d need 6 tiles × 4 toothpicks = 24 toothpicks.
- However, every shared edge between two tiles reduces the total number of toothpicks by 1.

### Detailed arrangement:
- Place the 6 tiles in a row, this creates 5 shared edges between adjacent tiles.
- Thus, the total number of toothpicks required is:
  
  \[
  6 \times 4 - 5 = 24 - 5 = 19 \text{ toothpicks}.
  \]

- We want exactly **10 toothpicks**, so we need a different arrangement where fewer toothpicks are needed.

Try a different compact arrangement like a T- or L-shaped arrangement, and look for ways to increase shared edges to lower the total toothpicks to exactly 10.

Would you like a diagram for better visualization, or further details on this arrangement?

### 5 Related Questions:
1. What is the fewest number of toothpicks that can be used to enclose 6 tiles?
2. How does changing the shape (e.g., L-shape or T-shape) affect the number of toothpicks?
3. Can you create patterns with tiles using fewer shared edges?
4. What’s the maximum number of toothpicks you can use with 6 tiles?
5. How would adding more tiles affect the number of required toothpicks?

### Tip:
When designing patterns with tiles, always look for shared edges to minimize the number of surrounding toothpicks!

Using 6 tiles, make a pattern that uses four more toothpicks than tiles.

Learn how to make a pattern using 6 tiles and 10 toothpicks, optimizing shared edges to minimize toothpick usage. This geometric puzzle challenges students to think about tiling patterns and edge-sharing principles. Suitable for students in Grades 5-7.

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