Reasoning · Grade 6-2 Counting Cubes and Stackings
Problem
Put all three views into one picture.
Writing the front and side numbers around the edge of the top view is exactly like labelling the edges of a seating chart, and it means no picture has to be remembered while another is being read.
K.G.A.1Draw A DiagramEach stack is capped by the smaller of two limits.
Two people setting a height limit on the same thing means the stricter one wins, which is the same 'take the smaller' comparison a first grader makes when ordering objects by height.
1.MD.A.1Visualize Spatial RelationshipsEvery stack is squeezed between a floor and a ceiling set by the views, so filling to the ceiling gives the largest possible count.
A stack cannot climb past the smaller of the two silhouettes it appears in, so those two bounds pin it from above.
Any filling that exceeds a ceiling is ruled out at once, so the greedy filling is the only candidate for the maximum.
For the most, fill right up to each cap.
Once every cell carries its own private ceiling, finding the biggest total needs no searching at all -- you simply write the ceiling in every cell.
1.MD.A.1Organize Information In More WaysEven filled, the three views are unchanged.
Checking each bar is reached is the half of the argument that is easy to forget, and it is what turns 'no more than 15' into 'exactly 15 is possible'.
1.MD.A.1Visualize Spatial RelationshipsCounting gives 15 cubes.
Adding one row at a time keeps ten numbers from turning into a single long sum where a cube is easy to drop.
5.MD.C.5Identify SubproblemsWrite the front numbers under the columns and the side numbers beside the rows, then give every square the smaller of its two numbers -- that is the fullest solid the three pictures allow.