Reasoning · Grade 5-2 Exploring the Cube
Problem
Address each corner by left-right, front-back, top-bottom.
This is the coordinate idea from Grade 5 with one extra direction: a point is pinned down by how far along each of three perpendicular directions it sits, and looking along one direction simply stops you from seeing how far along that one direction things are.
5.G.A.1Visualize Spatial RelationshipsFix how each empty square is oriented.
Above, below, in front of and behind are the only words needed here, but they have to be pinned to the paper before drawing, or the answer comes out mirrored.
K.G.A.1Draw A DiagramTake one segment and drop one address part per view.
A line drawn on a face is seen true to shape from the direction facing that face, and flattens onto a single side of the square from either of the other two directions — those are the only two things that can happen.
5.G.A.1Visualize Spatial RelationshipsFollow the other segments the same way.
Taking the segments strictly in order and writing down three lines for each one turns a spatial puzzle into a short list; nothing has to be held in the head at the same time.
4.G.A.1Make A Systematic ListTogether they complete part (1).
Each view of a cube face-on is a square, so every image is either one of the square's four sides or one of its two diagonals — there are very few possible answers, and the end points say which one it is.
4.G.A.1Draw A DiagramIn (2) upright segments become points from above.
Look down a pencil held upright and you see only its rubber: length along your line of sight simply does not show, which is why an upright line is worth nothing in the top view.
5.G.A.1Visualize Spatial RelationshipsThe two upright segments vanish from the top view, because looking straight down flattens them to single points.
Looking from directly above sends every point straight down to the floor, so a whole upright line lands on one spot.
The view is a shadow of the solid, and a shadow keeps the shapes lying flat in it while collapsing what points at the viewer.
From the front only the upright middle line remains.
The middle of an edge stays the middle of a side in every view, so a segment that starts halfway along an edge gives a half-length mark, not a whole side.
4.G.A.1Make A Systematic ListFrom the side it is a plain square.
A closed loop of lines drawn on a box can flatten onto the outline of the square itself; that is not a mistake or an empty answer, it is the correct picture.
5.G.A.1Visualize Spatial RelationshipsTurning a real box confirms all three views.
Views are about where you stand, so moving your head is a fair and fast way to test an answer that was worked out on paper.
K.G.A.1Create A Physical RepresentationLooking at a see-through cube from one direction just forgets one of the three directions, so lines pointing straight at you become dots and lines on a face you see edge-on hide in the square's own border!