 What you need to know

Things to remember:

• We can split big numbers into smaller numbers to make multiplying easier.
• We can use doubling and halving for the 4 and 8 times tables..

Multiplying by 3 is the hardest, so let’s start there by looking at the times table up to 12:

1×3      2×3      3×3      4×3      5×3      6×3      7×3      8×3      9×3      10×3    11×3    12×3

3          6          9          12        15        18        21        24        27        30        33        36

If we look at the 3 times table, we can see that there isn’t any sort of repeating pattern until we multiply by 10, which is why it is so difficult. But we do have one neat trick we can use.

Think of multiplication as “lots of”, so $11\times3$ would be the same as saying “11 lots of 3”. But, 11 lots of 3 is the same as 10 lots of 3 and an extra 1 lot of 3.

$$10 \times 3 + 1 \times 3 = 30 + 3 = 33$$

We need to be careful if we use this method with division.

What is $24 \div 3$?

$24 \div 3 = 20 \div 3 + 4 \div 3 =$ Something not very nice

So, instead of splitting it up into tens and units, we need to split it int two numbers we can divide by 3. Here, we can actually split it into two lots of 12.

$$24 \div 3 = 12 \div 3 + 12 \div 3 = 4 + 4 = 8$$

With practice though, eventually you will just be able to “see” the answer.

The 4 and 8 times tables are much nicer, and we will look at them together with the 2s!

1            2          3          4          5          6          7          8          9          10        11        12

2          4          6          8          10        12        14        16        18        20         22        24

4         8          12        16        20        24        28        32        36        40        44        48

8        16         24        32       40       48        56         64       72        80        88        96

Luckily here, there is a nice repeating pattern after the 5!

What is nice here, is that we can use doubling (Multiplying by 2) to help find an answer.

Notice how 2 times table we is just double the 1 times table; the 4 times table is doubled again; the 8 times table is doubled a third time.

So, to figure out 8 times table, we just need to double, double, and double again!

What is $9\times8$?

$$9 \times 2 = 18 \rightarrow 18 \times 2 = 36 \rightarrow 36 \times 2 = 72$$

So, $9\times8=72$.

Multiplication and division are opposites, so to divide 2, 4, or 8 we need to do the opposite of doubling… which is halving!

What is $48\div4$?

$$48\div 2 = 24 \rightarrow 24 \div 2 = 2$$

Example Questions

Remember we can split up our number if we need to.

$$15\div3 +12\div3 = 5+4=9$$

$27\div3=9$.

Remember, when multiplying by 8 we can double, double, and double again.

$$7 \times 2 = 14 \rightarrow 14 \times 2 = 28 \rightarrow 28 \times 2 = 56$$