L4 · Fact families and patterns in multiplication tables

Learning goal

“I can write the whole fact family for a multiplication - two multiplications and two divisions with the same three numbers - and I can see and use patterns in the multiplication table, like the 5s endings and the 9s digit pattern.”

Fact family — the multiplications and divisions that share the same three numbers: 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6, 24 ÷ 6 = 4.

Multiple — a number you land on when you count by a number: the multiples of 5 are 5, 10, 15, 20, ...

Turnaround fact — the multiplication with the factors swapped: 6 × 4 is the turnaround of 4 × 6. The product does not change.

Pattern — a change that happens the same way every time, like the 9s: 9, 18, 27, 36, ...

Worked example

Start with one fact: 4 × 6 = 24. The same three numbers - 4, 6, 24 - make a whole family: 4 × 6 = 24; 6 × 4 = 24 (the turnaround); 24 ÷ 4 = 6; 24 ÷ 6 = 4. Four facts, one family. Learn ONE fact well and you own FOUR. Draw the array to see why: 4 rows of 6 is 24; read it sideways it is 6 rows of 4; split 24 into 4 equal rows and each row is 6; split it into 6 equal columns and each column is 4.

Check yourself — explain it

Why does the family of 4 × 6 = 24 have exactly two divisions?

Paired problem — example still visible

Write the two divisions in the family of 7 × 3 = 21. -> 21 ÷ 7 = 3 and 21 ÷ 3 = 7

Faded completion — last step is yours

"Family of 8 × 2 = 16: 16 ÷ 8 = ___ and 16 ÷ 2 = ___." -> 2; 8

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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