Non-verbal Reasoning · Spatial Reasoning
Dice Partner
On every ordinary dice, the numbers on opposite faces add up to 7. Which number is hiding on the face opposite the 3?
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Why this works
A standard dice is built so that every pair of opposite faces adds to 7. That gives exactly three pairs: 1 with 6, 2 with 5, and 3 with 4. So the face opposite the 3 must be 4, because 3 plus 4 is 7. The strategy that saves you in the exam is to learn those three pairs by heart and then subtract: opposite face equals 7 minus the face you can see. It also lets you check a dice question quickly, because any two numbers shown next to each other on the same dice can never be a pair that adds to 7.
Helping a child through Dice Partner
Hints, least revealing first
- You can see 1, 3 and 5. The three numbers you cannot see are on the opposite faces.
- Opposite faces always pair up to make 7. Write the three pairs out: 1 and ?, 2 and ?, 3 and ?
- You need the number that goes with 3 to make 7. What do you add to 3 to reach 7?
When they finish it: “Turned it over, and there it is!”
What usually goes wrong here
- Treats faces separated on the flat net as necessarily opposite.
This is the wrong answer 11+ papers are built to offer, so it is worth watching for directly: a child who does this will look confident and still lose the mark. If it keeps happening on track opposite cube faces, the fix is the misunderstanding rather than more questions.
11+ skill this exercise practises
It has its own page, with a worked example and the mistake that skill attracts.
All non-verbal reasoning 11+ skillsYou can reuse this. Here is exactly how far that goes
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Dice Partner practises one skill. Non-verbal Reasoning has 22 of them
A free diagnostic covers every non-verbal reasoning skill and the other three subjects, and comes back with a shortlist rather than a list.