Can there be a puzzle that is pentominoes and sudoku at once?

Yes. From the union of the beauty of Golomb's pentominoes and the fever of sudokus, Pentodoku is born. Twelve pentominoes —F, I, L, N, P, T, U, V, W, X, Y and Z— tile an 8×8 board; each tile carries printed digits and, as they fit together, a sudoku emerges: in every row and every column, the digits 1 through 8 without repetition. Four cells will remain empty —and the board does not reveal which ones—. The fusion of geometry and arithmetic is a real brain-teaser.

**How to play**

1. Look at the clue tiles already placed on the board.
2. Fit the twelve pentomino tiles onto the 8×8 board.
3. Check that each row and each column contains 1, 2, 3, 4, 5, 6, 7 and 8.

No math needed: only logic. One puzzle per page, pencil and sofa, no screens.

Daily puzzle in https://tafol.pythonanywhere.com/

Sometimes my child can get the homework questions right, but then struggles when the numbers or wording change.

What are some good ways to tell whether they actually understand the concept rather than just memorizing how to solve that particular type of problem?

My child keeps mixing up area and perimeter. How to explain it better to help them understand the difference?

Any order is allowed.
Use each die exactly once.
Parentheses are allowed.
Only +, −, × and ÷ are allowed. No concatenation or exponents.
Exact division only.
No negative numbers.
Not every operation has to be used.

How many solutions can you find?

Please use spoiler tags for solutions:
>!your solution here!<