Once you know your facts, the multiplication table is full of patterns. A pattern is more useful when you can explain why it happens.
| × | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 2 | 2 | 4 | 6 | 8 | 10 | 12 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 |
Por qué funciona
Each number in the 4s row is double the number above it in the 2s row, because 4 groups is 2 groups twice. The 6s row is double the 3s row for the same reason. Every number in the 4s row is even, because 4 groups can be split into two equal halves. Even and odd come from pairs: an even number of things pairs up with none left over.
Idea clave
Patterns in the tables come from what multiplying means. Explain a pattern with equal groups or pairs, and you can trust it.
Ejemplo resuelto: Why is 4 times any number even?
Explain why $4 \times 7$ is even.
- $4 \times 7$ is 4 groups of 7.
- Split them into 2 groups of 7 and 2 groups of 7: two equal halves.
- A number that splits into two equal halves is even. $4 \times 7 = 28$.
Respuesta: It is 2 equal halves, so it is even.
Ejemplo resuelto: Continue a pattern
What comes next: 6, 12, 18, 24, ?
- Each number is 6 more than the one before.
- These are the 6s facts. Next is $6 \times 5 = 30$.
Respuesta: $30$
Ejemplo resuelto: Sums of odd numbers
Is $7 + 9$ even or odd? Is that always true for two odd numbers?
- Each odd number is pairs plus one left over.
- The two left-over ones make one more pair, so nothing is left over.
- So the sum of two odd numbers is always even: $7 + 9 = 16$.
Respuesta: always even
Error común
Trusting a pattern too soon. 3, 9 and 15 are odd, but "the 3s are all odd" is false: $3 \times 2 = 6$. Look for a reason, or keep checking more numbers, before you believe a pattern.