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Cube Stacks and Their Views

A pile of unit cubes described by what it looks like from above, in front and from the side. Each view is a projection that keeps only the tallest cube in its line, so views constrain the pile without fixing it -- some positions are pinned down and others are still free, which is what makes counting all the possible piles a real question.

grade 6–7 Geometry Visualize Spatial RelationshipsMake a Systematic List

Builds on: Net and Solid StructureSystematically Count Shapes in a Figure

Progression (8)

g6 1. Height on a plan makes it a solid Geometry · core
g6 2. The longest side sets the cube's edge GeometryNumber system · advanced
g6 3. Spot the piece added onto a shape Geometry · core
g6 4. See the shape after cubes are removed Geometry · core
g6 5. Per-cell counts give the front and side views Geometry · core
g6 6. Layer and position fix how many faces show Geometry · advanced
g7 7. Start where the front and side views pin the count down Geometry · advanced
g7 8. Find the cubes removed twice over Geometry · advanced