Multiplication Tables

UK Secondary (7-11)

Mixed Multiplications 2,4,8

Lesson

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:

Multiplying a number by $2$2 is the same as doubling that number. For example, "double $5$5" would be the same as saying "$5\times2$5×2." This means that instead of $1$1 group of five, there are now $2$2 groups of five.

When we double the number of stars, we can write this mathematically as $5+5$5+5 or $5\times2$5×2 and our answer will be the same: $10$10!

Remember!

Doubling a number is the same as multiplying the number by $2$2.

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

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

Now we know $4$4 groups of $5$5 stars or $4\times5=20$4×5=20.

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

What is $4\times7$4×7?

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

Do:

$2\times7$2×7 | $=$= | $14$14 | (This is $2$2 groups of $7$7) |

$2\times14$2×14 | $=$= | $28$28 | (We've our number of groups to $4$4)doubled |

So: | |||

$4\times7$4×7 | $=$= | $28$28 |

Remember!

Doubling a number, then doubling the answer is the same as multiplying the number by $4$4.

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

So now we know that $8$8 groups of $5$5 or $8\times5=40$8×5=40.

What is $8\times3$8×3?

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

$2\times3$2×3 | $=$= | $6$6 | (This is $2$2 groups of $3$3) |

$2\times6$2×6 | $=$= | $12$12 | ($2\times6$2×6 is the same as $4\times3$4×3) |

$2\times12$2×12 | $=$= | $24$24 | (We've doubled our answer for a third time) |

So: | |||

$8\times3$8×3 | $=$= | $24$24 |

Think

If we doubled the number of groups again, what multiplication tables would be be looking at then?