NZ Level 3
Extending multiplication to larger numbers
Lesson

When we looked at the 10 times tables, we discussed how important place value is because each column in the place value table is $10$10 times larger than the previous one.

$10$10 units make a ten, $10$10 tens make a hundred, $10$10 hundreds make a thousand and so on.

Let's build on that knowledge and discuss how we can use it to multiply larger numbers.

## What is $6\times7$6×7?

As we know our multiplication fact of $6\times7$6×7 is $42$42.

We can use this to answer questions like $6\times70$6×70, or $6\times700$6×700 or even $60\times70$60×70

Let's see how.

## $6\times70$6×70

$6\times70$6×70 is the same as $6\times\left(7\times10\right)$6×(7×10) which we can write as $6\times7\times10$6×7×10

As multiplication is commutative, we can complete this multiplication in any order we like, so as we know $6\times7$6×7 is $42$42, then the final multiplication is by $10$10 which is a final easy step.

$6\times7\times10=42\times10=420$6×7×10=42×10=420

## $6\times700$6×700

The same process can be applied to $6\times700.$6×700.

 Rewrite (or imagine) $6\times700$6×700 $=$= $6\times7\times100$6×7×100 Do the $6\times7$6×7 component $=$= $42\times100$42×100 Then the multiplication of $100$100 $=$= $4200$4200

## $60\times70$60×70

 Rewrite (or imagine) $60\times70$60×70 $=$= $6\times10\times7\times10$6×10×7×10 Regroup the multiplication by $10$10's $=$= $6\times7\times100$6×7×100 Do the $6\times7$6×7 component $=$= $42\times100$42×100 Complete the multiplication $=$= $4200$4200

#### Worked Examples

##### Question 1

If $2\times8=16$2×8=16, what is $20\times8$20×8?

##### Question 2

Using your knowledge of place value, solve these related number facts.

1. $3\times12$3×12=

2. $30\times120$30×120=

##### Question 3

Using your knowledge of place value, solve these related number facts.

1. $2\times18$2×18=

2. $20\times18$20×18=

3. $2\times180$2×180=

4. $20\times180$20×180=

### Outcomes

#### NA3-6

Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality

#### NA3-7

Generalise the properties of addition and subtraction with whole numbers