11+ Prep
Learn the opposite-face rule for folding cube nets, and a reliable method for counting blocks in a 3D stack without missing any.
Spatial reasoning — cube nets, opposite faces and 3D block structures
11+ spatial reasoning has two common question types. Cube-net questions show a flat, unfolded net and ask which faces end up opposite each other once it's folded into a cube -- this always comes down to counting POSITIONS in the net, not imagining the fold. Block-counting questions show a grid of column heights and ask for the total number of blocks -- this is really just careful addition, as long as you don't lose track of a column.
In a straight strip of 4 faces, opposite pairs are 1st-and-3rd, 2nd-and-4th
If a net is a plain row of 4 squares, folding it into a cube always pairs the 1st face with the 3rd, and the 2nd with the 4th.
Circle (1st) is opposite Square (3rd). Triangle (2nd) is opposite Star (4th).
This rule only applies to a plain strip of 4 -- a cross-shaped net (with extra flaps above/below) needs the extra flaps thought about separately.
In a cross-shaped net, the top and bottom flaps are opposite each other
A cross net has 4 faces in a row plus one flap above and one below a chosen square in that row.
Sun (top flap) is opposite Cloud (bottom flap). In the middle row, Circle is opposite Star, and Moon is opposite Triangle.
Never assume two faces are opposite just because they look far apart on the flat net -- always count positions using the rule.
Block counting: add column heights, don't estimate
A structure's column heights are given as a grid of numbers (one number per column, showing how many blocks are stacked there).
2 + 4 + 3 = 9 blocks in total.
Work through the grid row by row, ticking off each column height as you add it, so none get missed or counted twice.
A net is a straight strip of 4 squares in this order: Sun, Moon, Star, Cloud. Which face is opposite Moon when folded into a cube?
Apply the opposite-face rule or the column-addition method to each question.
A net is a straight strip of 4 squares: Circle, Triangle, Square, Star (in that order). Which face is opposite Circle?
Using the same net (Circle, Triangle, Square, Star), which face is opposite Triangle?
A structure has 3 columns with heights 2, 4 and 3. How many blocks are there in total?
A structure has 2 rows of 3 columns. Row 1 heights are 1, 2, 3. Row 2 heights are 2, 2, 1. How many blocks in total?
In a cross-shaped cube net, which two faces become opposite each other when folded?
Watch for these when working through the lesson.
These ideas fit closely with this lesson.