Problem
Draw the top-view outline
An outline keeps only the outer border, with every inner line erased. The top view of a cube solid is given on a dot grid as unit squares. Join dot to dot to draw that footprint's outline.
Reasoning · Grade 2-1 Stacking Cubes
Your answer
Watch out A tall column looks like it should cover more, but from above any column is just one square.
How to solve
Strategy Draw a Diagram — The task is literally to draw the boundary (tool 1), so the work is in deciding which dot-grid segments belong to the border. First picture the solid from straight above to get its footprint of unit squares (tool 17). Then handle the boundary edge by edge - keep an edge if it touches the outside, erase it if it sits between two filled squares (tool 7) - and connect the kept edges into one closed loop.
1STEP 1
Find the top-view footprint
Seen from straight above, each column fills one square of the grid.
Looking from directly overhead flattens a 3D solid into a flat picture of squares - the same as tracing where each cube touches the floor.
K.G.A.3Visualize Spatial Relationships2STEP 2
Mark every edge of the filled squares
Lightly draw all four edges of every filled square.
Drawing the full grid of edges first makes it easy to see which ones are inside and which face the outside.
2.G.A.1Draw A Diagram3STEP 3
Erase shared (interior) edges
The edge between two filled squares is interior, so erase it.
An inside line is shared by two squares, so it cannot be part of the border - the border is only where the shape meets the outside.
1.G.A.1Identify SubproblemsAn edge shared by two filled squares is inside the shape, so only the unshared edges can be part of the outline.
Why?
Every edge belongs to either one filled square or two, and those two situations never happen to the same edge.
🧱Disjoint cases addSplit the possibilities so no case overlaps another and none is left out, and the case counts simply add.
Why?
An edge with a filled square on both sides has no outside to face, so the outline can only run along edges with exactly one filled neighbour.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
4STEP 4
Connect the kept edges into one closed outline
Joining what is left gives one closed border with nothing inside.
Following the outside edges all the way around naturally closes up into the one border polygon, which is the outline.
2.G.A.1Draw A DiagramAnswer
the closed border with inner lines erased — an L of 3 squares gives a hexagon
The result is a single closed loop made only of grid-aligned straight segments, with no leftover interior lines - exactly what 'outline' means. The L-footprint gives 6 corners, which matches an L (boot) shape, so the count of sides is sensible.
Takeaway
An outline is just the outside edge: erase every line shared by two squares, keep the rest, and the leftover lines join up into one neat border!
- Find the top-view footprint
- Mark every edge of the filled squares
- Erase shared (interior) edges
- Connect the kept edges into one closed outline