Rolling-face route
Predict which face is on top after a sequence of physical rolls.
Adult planning suggestion: about6–9 · Shape & spatial thinking
- Players
- 2–3 per group
- Time
- 15–20 minutes
- Materials
- A large cube labelled U,D,N,S,E,W on its six faces, 4×4 grid, one position marker and pencil.
Prepare
With the grid north at the page top, place U up, D down, N toward north, S south, E east and W west beside the board, with a separate position marker at A1. These are face identities and never change their letters. Use a large block with removable paper labels; do not use an unlabelled die as if its opposite faces were specified.
Play
Choose a route on the four-by-four board. Move the position marker one adjacent grid square and roll the cube one quarter-turn in that direction on the table beside the grid, without sliding, spinning in place or lifting to reset. The cube and printed grid need not be the same physical size. Before each move, predict the next top identity, then roll and record. Reset only at the start of a new challenge.
Worked example
From A1, roll east to B1, north to B2, west to A2. The top faces are W, S, U. A route returning to its starting square need not return all faces to the original orientation. Test this claim with actual rolls rather than relying only on the printed answer.
Finish and check
Complete the supplied route, then invent a legal four-step route for another pair. A solution needs both legal coordinates and correct orientation after every step. If a roll leaves the board, undo that move and record the boundary error. Stop after two exchanged challenges.
Adaptation and limits
For a class of thirty, ten groups share ten large labelled blocks. One learner rolls, one predicts, one logs. Allow tactile inspection and adult writing. Age bands are planning suggestions; this is not an assessment of lasting spatial ability.
Purpose, observation and provenance
Within this activity: Predict which face is on top after a sequence of physical rolls.
Ask the learner to name old and new top faces before checking with the cube.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
NRICH — Rolling That Cube — Cube-orientation task background; our labelled block, route and sheets are original.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Rolling-face route
Start A1: top U / bottom D / north N / south S / east E / west W.
Route: A1 → B1 → B2 → A2; before rolling, top prediction ___ .
Player record · keep the host key separate
| From→to | Predicted top | Actual top |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host key · separate from players
Top sequence W,S,U. East roll moves the old west face to the top.
Run the round
With the grid north at the page top, place U up, D down, N toward north, S south, E east and W west beside the board, with a separate position marker at A1. These are face identities and never change their letters. Use a large block with removable paper labels; do not use an unlabelled die as if its opposite faces were specified.
Choose a route on the four-by-four board. Move the position marker one adjacent grid square and roll the cube one quarter-turn in that direction on the table beside the grid, without sliding, spinning in place or lifting to reset. The cube and printed grid need not be the same physical size. Before each move, predict the next top identity, then roll and record. Reset only at the start of a new challenge.
From A1, roll east to B1, north to B2, west to A2. The top faces are W, S, U. A route returning to its starting square need not return all faces to the original orientation. Test this claim with actual rolls rather than relying only on the printed answer.
Complete the supplied route, then invent a legal four-step route for another pair. A solution needs both legal coordinates and correct orientation after every step. If a roll leaves the board, undo that move and record the boundary error. Stop after two exchanged challenges.
For a class of thirty, ten groups share ten large labelled blocks. One learner rolls, one predicts, one logs. Allow tactile inspection and adult writing. Age bands are planning suggestions; this is not an assessment of lasting spatial ability.