Mixed Multiplications 2,4,8

We've already looked at our 2 times tables, our 4 times tables and our 8 times tables. Now we're going to look at the really cool relationship between these three sets of multiplication tables.

Let's start by watching this video:

 

x 2: Double

Multiplying a number by $$2 is the same as doubling that number. For example, "double $$5" would be the same as saying "$$5×2." This means that instead of $$1 group of five, there are now $$2 groups of five.

When we double the number of stars, we can write this mathematically as $$5+5 or $$5×2 and our answer will be the same: $$10!

 

x 4: Double, Double

What happens when we double the $$2 groups in the last picture? Now we have $$4 groups of $$5! 

We know that in $$2 groups there are $$10 stars. So since we have doubled the number of groups, we need to double our answer. This means there are now $$20 stars! 

Now we know $$4 groups of $$5 stars or $$4×5=20.

So multiplying a number by $$4 is the same as doubling the number and then doubling the answer.

Another example 

What is $$4×7?

Think: Let's use the double, double strategy!

Do:

$$2×7	$$=	$$14	(This is $$2 groups of $$7)
$$2×14	$$=	$$28	(We've doubled our number of groups to $$4)
So:
$$4×7	$$=	$$28

 

x 8: Double, Double, Double

Let's double the number of groups again. $$4+4=8, so now we have $$8 groups of $$5 stars. Now we have $$2 groups of $$20, which means that there are $$40 stars in total.

So now we know that $$8 groups of $$5 or $$8×5=40.

Example

What is $$8×3?

Think: This time we are going to use a double, double, double strategy.

$$2×3	$$=	$$6	(This is $$2 groups of $$3)
$$2×6	$$=	$$12	($$2×6 is the same as $$4×3)
$$2×12	$$=	$$24	(We've doubled our answer for a third time)
So:
$$8×3	$$=	$$24