Problem
A small cube's painted faces are the outer faces reaching it: corners meet 3, edges 2, face centres 1, the buried one none.
A fifth grader who has counted unit cubes filling a box can imagine which little cubes are on the skin of the big cube and which are tucked inside.
5.MD.C.4Visualize Spatial RelationshipsTwo painted faces means an edge spot, and along an edge of 3 only the middle cube is not a corner.
An edge is like a row of 3 cubes; chop off the two corner ends and exactly one cube is left in the middle, and that middle one shows two outside faces.
5.MD.C.3Draw A DiagramA small cube shows exactly two painted faces only when it sits along an edge of the big cube without being a corner.
A small cube's painted faces are exactly the big cube's outer faces that reach it, one paint job for each outer face it touches.
A spot along an edge but away from the corners is touched by exactly two outer faces, while a spot in the middle of a face is touched by one and a corner by three.
The big cube's surface is made of its faces, its edges, and its corners, so where a small cube sits is what decides how many outer faces can reach it.
A cube has 12 edges, and each one holds exactly one such middle cube.
Holding a real box, you can run your finger along its 12 edges and feel that each edge has one cube between its two corners.
5.MD.C.3Create A Physical RepresentationThere are 12 edges and 1 two-face cube on each edge, so the total number of small cubes with exactly two painted faces is 12 times 1.
Repeated equal groups (one cube per edge, 12 edges) is just multiplication, the same skill used to count cubes in a box layer by layer.
5.MD.C.5Visualize Spatial RelationshipsCubes with two painted faces live in the middle of each edge, and a cube has 12 edges, so there are 12 of them.