Number Chain Generator: Mental Maths

Hold the number in your head

Start with 12. Double it. Add 7. Halve that. Subtract 5.

Nothing gets written down until the end, which is the whole exercise. The arithmetic itself is easy; carrying a result from one step to the next without losing it is not, and that is a different skill from anything a column of sums assesses.

Chains run from three steps to eight. Four to twenty chains on a sheet, and you can ask for several worksheets at once so different groups get different sets out of one PDF.

The four bands

Easy stays with adding and subtracting, plus doubling and halving, all on small numbers. Medium brings in multiplying and dividing by single digits.

Hard widens the ranges and adds squaring and percentages, which is where the chain stops being arithmetic and starts being strategy: a child who knows that 25 per cent is halving twice is a long way ahead of one computing it properly. Ninja uses everything at awkward values, and it is genuinely hard for an adult.

The generator refuses steps that would produce a negative, a non-integer, or a number too big to hold, so a chain never becomes impossible by accident. Percentages and halving are the exceptions, where a decimal is sometimes the point.

Chain length matters more than difficulty

Three steps at ninja is a puzzle. Eight steps at easy is a memory test, and it will defeat children who can do every individual operation without hesitating.

That is worth knowing before you pitch a sheet. If the class is failing, look at the length before you look at the band, because working memory and arithmetic fluency are separate things and only one of them is being taught in the maths lesson.

Three to five steps is a warm-up. Seven or eight is a session in itself.

A Monday starter

Medium, six steps, four chains. Start with 18, double to 36, add 12 to get 48, divide by 4 for 12, subtract 7 for 5, multiply by 3 for 15, halve it to 7.5.

Children write 7.5 and nothing else. The answer key on the back page carries every intermediate value, which is what makes marking diagnostic rather than binary: when a child is wrong you can usually see which step they dropped, and it is nearly always the same step for the same child.

Next Monday, a fresh PDF with different starting values and a different sequence. Same format, no preparation.

Same seed, same sheet

Generation is seeded, so a given seed always produces the same chains. Print an in-class version and a matching homework version from one seed, or regenerate a lost worksheet weeks later.

Change nothing but the seed and you get an entirely different set at the same difficulty, which is how you make four versions for four groups in about a minute.

Limits

• Eight steps is the maximum. Longer chains stop measuring arithmetic and start measuring only memory.
• You cannot specify the operations yourself. The steps are drawn at random from the pool that the difficulty band allows.
• Static PDFs. Nothing here tracks a pupil across weeks.