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Count Only What
You See, and You'll Get It Wrong

Stacking-block pictures can be deceptive. Behind the blocks you can see from the front, there can be just as many hidden ones you can't.

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1A unit cube stack is built from "how high each square is stacked"

Divide the floor into a grid like a checkerboard, and stack some number of cube blocks on each square — that's a unit cube stack. One square might have just 1 block stacked on it, another might have 3.

2Writing it as numbers is far more accurate

Counting purely from the picture makes it easy to miss anything hidden in the back. That's why looking at a "number grid" — the count of blocks stacked on each square, written as numbers — alongside the picture lets you see the top-down shape and each square's height at a glance.

Add up every square in the number grid to get the total count

If a 2×2 grid reads 1, 2, 2, 1, the total count is 1+2+2+1 = 6 blocks.

1 2 2 1 1+2+2+1 = 6 blocks
Each square in the number grid shows how high that stack is — add them all up for the total number of blocks

3Staircase shapes are especially tricky

In a staircase shape that steps down in height, the front squares block the ones behind them, so it's hard to be sure from the picture alone whether there are blocks stacked in back or not. This is exactly where a number grid is a huge help.

The same picture can sometimes have more than one correct answer.
Looking at the picture alone, without any numeric information, there are cases where you can't be sure whether a completely hidden square has blocks on it or not. That's exactly why schools usually present views from several directions (top, front, side) together.

4Spatial reasoning grows with practice

At first, counting a solid shape purely by eye can be tough. But practice going back and forth between the picture and the number grid, and eventually you'll be able to imagine the hidden parts naturally, just by looking at the picture.

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