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On the 4 × 4 square (Fig. AS 5) show that 16 = 1 + 3 + 5 + 7. 

To explain the equation \(16 = 1 + 3 + 5 + 7\) using the 4×4 grid of dots:

### Breakdown:
- The grid shows 16 red dots arranged in a 4×4 square.
- The sum \(1 + 3 + 5 + 7\) refers to the consecutive odd numbers.
  
### Interpretation:
- You can count the dots layer by layer starting from the center. Think of it like growing outward in odd-numbered rings.

1. **First layer (center)**: There is 1 dot in the center of the grid, which corresponds to the first term, \(1\).
2. **Second layer**: Around the center dot, the next layer forms a cross of 3 dots, contributing the next term, \(3\).
3. **Third layer**: The next outer layer forms a larger cross with 5 dots, giving us the third term, \(5\).
4. **Fourth layer**: The outermost layer is made of 7 dots, representing the last term, \(7\).

### Total: 
- \(1 + 3 + 5 + 7 = 16\), which matches the total number of dots in the grid (4×4).

This pattern shows how the sum of consecutive odd numbers builds up to form a perfect square. In this case, the sum \(1 + 3 + 5 + 7 = 16\) corresponds to \(4^2\), the number of dots in the grid.

Let me know if you'd like more details on the concept! Here are some related questions for further exploration:

1. How does the pattern of odd numbers relate to other perfect squares?
2. Can you extend this idea to a 5×5 or larger grid?
3. What is the general formula for the sum of the first \(n\) odd numbers?
4. Why does the sum of the first \(n\) odd numbers always give a perfect square?
5. How can you visualize other mathematical concepts using grids or patterns like this?

**Tip**: Summing consecutive odd numbers is a useful way to understand how perfect squares are constructed geometrically.

On the 4 × 4 square (Fig. AS 5) show that 16 = 1 + 3 + 5 + 7.

Learn how the equation 16 = 1 + 3 + 5 + 7 is visualized using a 4×4 grid of dots. This problem demonstrates how the sum of consecutive odd numbers results in perfect squares, a key concept in number theory, suitable for Grades 6-8.

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