Number pyramid worksheets

What this worksheet is for

A number pyramid practises exactly the same addition as a page of sums, and children treat it as a puzzle rather than as work — which is the whole reason it belongs in the collection. The structure also does something a list of sums cannot: a mistake low down changes every brick above it, so the pyramid announces its own errors and a child who checks the top can find the slip themselves. With gaps placed anywhere, the same shape stops being addition and becomes reasoning — knowing a brick and one of the two below it means subtracting to find the other.

Who it suits

Grade 1 to Grade 5, ages six to eleven, and popular well outside school. A three-brick base with small numbers suits the first year; a five or six brick base with gaps anywhere is a genuine challenge for Grade 4 and 5, and for adults at a rainy kitchen table.

How to use the settings

Start with the base given and work upwards — that version is pure addition, and it is where the shape gets learned. Move to gaps anywhere once the class is comfortable: it needs subtraction as well, and the pupil has to look for the brick they can work out rather than starting at the left. Keep the starting numbers small when the base is wide, because the top of a six-brick pyramid is thirty-two times the size of the numbers underneath it.

What goes wrong

The commonest error is adding a brick to the one diagonally above rather than to its neighbour, which produces a pyramid that looks plausible and is wrong from that point up. The second, on the gaps version, is trying to work strictly upwards and getting stuck — the fix is a habit rather than a method: look for a brick with two of its three neighbours known.

Questions

How is a number pyramid solved?

Every brick is the sum of the two directly beneath it. Given the base you add upwards; given a brick and one below it, you subtract to find the other.

Does every puzzle have exactly one answer?

Yes. Puzzles with gaps anywhere are checked before printing: the generator works out whether the gaps can all be deduced, and throws away any arrangement that cannot.

Why do the numbers at the top get so large?

Because each level roughly doubles. With a six-brick base, the top brick is a weighted sum of all six, so starting numbers around ten give a top brick in the hundreds. Lower the starting range if the arithmetic is running ahead of the class.