1. When he was ten years old, Mattie's illness got worse.

2. At the age of ten years old, Mattie's illness got worse.

3. Aged ten years old, Mattie's illness got worse.

(Are the three sentences the same and grammatical?)

4. When he was ten, Mattie's illness got worse.

5. At the age of ten, Mattie's illness got worse.

6. Aged ten, Mattie's illness got worse.

(Are the three sentences the same and grammatical?)

1, 4, and 5 are correct.

The others are not. Do you see why?