- The task is to identify which of the 12 given shapes are nets of a cube.
- A valid cube net must consist of exactly 6 squares that can be folded into a closed cube without overlaps or gaps.
- There are 11 distinct free polyominoes (nets) that form a cube; these are well-documented in geometry.
- Each shape must be checked for connectivity and folding validity.
After analyzing each shape:
1. Shape 1: Invalid — has a “T” with an extra square on top, leading to overlap when folded.
2. Shape 2: Valid — classic “staircase” or “Z” shape, folds cleanly into a cube.
3. Shape 3: Valid — “L” with extensions, forms a cube.
4. Shape 4: Valid — “T” shape with arms, standard cube net.
5. Shape 5: Valid — cross shape (central square with four neighbors), classic net.
6. Shape 6: Valid — “zigzag” or “snake” shape, folds correctly.
7. Shape 7: Valid — “U” shape with two extensions, forms cube.
8. Shape 8: Valid — “L” with three stacked and one offset, works.
9. Shape 9: Valid — vertical stack with side arms, standard net.
10. Shape 10: Valid — “corner” shape with extensions, folds properly.
11. Shape 11: Valid — “staircase” variant, known cube net.
12. Shape 12: Valid — “Z” with offset, folds into cube.
All 12 shapes are valid cube nets.
Final Answer:
[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
Parent Tip: Review the logic above to help your child master the concept of spatial reasoning worksheet.
