Times tables as equal groups
Maths · Key Stage 1 · The School
Groups of
Multiplication is repeated addition of EQUAL groups. 4 × 3 means four groups of three: 3 + 3 + 3 + 3 = 12. Draw four circles and put three dots in each. If the groups are not equal, it is not multiplication — that is the whole idea in one sentence.
Arrays turn it around
Arrange 12 counters in 4 rows of 3. Now turn the paper a quarter turn: it is 3 rows of 4. Same counters, same total. So 4 × 3 = 3 × 4. This is commutativity, and it halves how much you have to learn: know 3 × 8 and you already know 8 × 3.
The tables worth knowing cold
The 10 times table: just add a zero — 7 × 10 = 70. The 5s: always end in 5 or 0, and they are half of the 10s. The 2s: doubling. Get these three instant, and the rest of the tables become much easier because you can build them: 6 × 4 = 5 × 4 + 4 = 20 + 4 = 24.
Building a fact you cannot yet recall
Suppose 7 × 6 will not come. Do not guess, and do not draw 42 dots. Build it from a fact you already have. 7 × 6 is one more group of six than 6 × 6, and 6 × 6 is 36, so 7 × 6 = 36 + 6 = 42. Or come at it from the other side: 7 × 6 is 7 × 5 with one more seven added, and 7 × 5 = 35, so 35 + 7 = 42. Both routes land on 42, and that agreement IS the check — a fact you can reach two different ways is a fact you have got right.