Fact Families Worksheet Generator

Three numbers, four facts

Each problem prints three related numbers and four blank lines. Given 4, 6 and 10, the family is 4 + 6 = 10, 6 + 4 = 10, 10 − 6 = 4, 10 − 4 = 6.

Twelve problems by default, numbers to 20. The multiplication families work identically — 3, 4 and 12 give two products and two quotients.

What this is actually teaching

That addition and subtraction are one relationship read two ways. Not two topics.

Learn 4 + 6 = 10 as an isolated fact and you have to learn 10 − 6 = 4 from scratch afterwards. See the family instead and you have four facts for the price of one, plus something considerably more valuable: an understanding of how the numbers relate, rather than another entry on a list to be memorised.

It fixes counting back

Subtraction is where children get slow. The reason is that they count backwards, and counting backwards is harder and less reliable than counting on.

Ask a pupil who knows the family for 13 − 8 and they think "8 plus what makes 13", then recall it. No trick. It is what fluent adults do, and this is how a child gets there.

Times tables work the same way

They are also the fastest route into division facts, which children otherwise treat as a whole new set to be learnt from nothing.

Anyone who knows 7 × 8 = 56 already knows 56 ÷ 8 = 7. Saying so, repeatedly and out loud, halves the tables workload. It is routinely left unsaid.

Use objects first

Before the worksheet, if the child is young. Ten counters split into a group of four and a group of six, physically pushed around a table, will produce all four facts without anybody writing a single thing down.

The part-part-whole language helps: 4 and 6 are the parts, 10 is the whole. Then every fact is either putting parts together or taking one part away from the whole, which is a single idea rather than four.

Setting the ceiling

Twenty covers the number bonds most infant work rests on. Drop it to 10 for a first attempt. Raise it once the pattern has landed, because the pattern is the thing being learnt here, not the arithmetic.

Related: number bonds for the pairs themselves, and multiplication wheels for tables drill.