KA-0016Dice and cube face relationships
4 points, difficulty 2 of 3Level 3–4about 75sOn a standard die opposite faces add to 7. Two dice are stacked. The touching faces show 3 on the upper die and 5 on the lower. What number is on the bottom face?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Only the lower die matters here.
2The strategy
The bottom face of the lower die is opposite its own top face, and its top face is the one touching the die above. Opposite faces add to seven.
3The full solution
The lower die's top face shows 5, so its bottom face is 7 - 5 = 2. The 3 belongs to the upper die and never enters the calculation.
Solution— no shortcut on this one
The bottom face of the lower die is opposite that die's top face. The lower die's top face is the one in contact with the upper die, which shows 5. Since opposite faces add to 7, the bottom face is 7 - 5 = 2. The 3 belongs to the upper die and is irrelevant. The transferable idea: identify which object and which face before applying the rule.
Why this is on the test: Dice problems test whether a student tracks which face belongs to which object before applying the opposite-faces rule.