Number Chain Puzzle

Chains written as instructions, not as sums

Each chain gives a starting number and then a short list of instructions — Add 7. Double it. Find half of that. Subtract 9. — ending in a box for the answer. The point is to carry a running total in your head from one line to the next.

Up to twenty chains a sheet, and up to ten sheets in one download, each with its own randomly chosen title.

The four difficulty levels change which operations appear

• Easy — add and subtract (1 to 10), double, halve. Nothing else.
• Medium — adds and subtracts grow to 3–20, and multiply and divide join in with small factors.
• Hard — adds and subtracts reach 40, factors reach 6, and percentages and squaring appear.
• Ninja — everything at once.

The jump worth watching is easy to medium. Doubling and halving are single moves a child can do without a strategy; multiplying by 4 is a fact they either know or must build. A class that flies through easy chains and stalls on medium has a times-table gap, not a working-memory one, and the two need completely different help.

Halving and dividing never leave a fraction

A halving step is only used when the running total is even, and a division step only when the number divides exactly. If the chain has arrived somewhere awkward, the generator picks a different operation instead.

That constraint is what keeps the whole thing mental. One decimal in the middle of a chain and the child is reaching for paper, at which point they are doing four separate sums rather than one chain.

Chain length is the working-memory dial

Three steps to eight. Three is a warm-up. Eight is genuinely demanding, and the errors change character: at three steps children get sums wrong, and at eight they get the arithmetic right and lose the total.

Watch which is happening before you change the difficulty. Shortening the chain helps the second problem and does nothing for the first.

Running it out loud

The sheet is written as instructions on purpose, so it can be read aloud. Cover the page, read one chain line by line at whatever pace suits the class, and have everyone write only the final answer.

That version is harder than the printed one and much closer to what mental arithmetic actually is, since a child reading the page can go back and check step two. Do both. The gap between a pupil's written score and their spoken score tells you how much of their fluency depends on being able to re-read.

What the form offers

Difficulty, steps per chain (3–8), chains per sheet (4–20), sheets per download (1–10), a title, the answer key, and a seed. A4 or US Letter.

Ten sheets in one download is a half-term of daily starters, printed once.