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To achieve 4 lines of symmetry and rotational symmetry of order 4, the three extra squares need to be shaded in such a way that the pattern is symmetrical along both the horizontal, vertical, and diagonal axes. 

Currently, the shaded squares are in positions:
- **B3**, **C2**, **C4**, **D3**, **I3**, **J4**, and **N3**.

We can add the three extra squares as follows:

- **A2**: This balances the position at **M4** (since the grid should reflect diagonally as well as vertically and horizontally).
- **A4**: This balances with **M2**.
- **I5**: This adds symmetry to match with **B3** and **N3** for diagonal and horizontal symmetry.

Thus, shading squares **A2**, **A4**, and **I5** will complete the pattern, ensuring the required lines of symmetry and rotational symmetry of order 4.

Would you like further details or have any questions about this?

Here are some related questions to deepen understanding:
1. What defines rotational symmetry of order 4?
2. How many unique symmetry lines are in a square grid?
3. Can you describe why **A2**, **A4**, and **I5** were chosen for symmetry?
4. How would removing one square affect the symmetry?
5. Can other configurations achieve the same symmetry properties?

**Tip:** When solving symmetry problems, always check reflections and rotations to ensure every part of the pattern is balanced in multiple directions.

Three extra squares can be shaded on this grid so that the resulting pattern has 4 lines of symmetry and rotational symmetry of order 4. Which three squares should be shaded?

Discover how to shade three additional squares in a grid to achieve four lines of symmetry and rotational symmetry of order four. This problem is suitable for students in Grades 6-8, focusing on understanding symmetry and geometric transformations.

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