We were doing a lesson on multiplying decimals with models when a student asked a question:

**“Why does our answer get smaller if we’re multiplying?”**

Great question!

This makes us stop and think “How are we teaching the basic understanding of multiplication?” Is it right for us to be saying ‘the number gets larger when we multiply’?

Let’s go back to the basics of multiplication

## 4 x 3

4 equal groups of 3

3 + 3 + 3 + 3 = 12

## 3 x 4

3 equal groups of 4

4 + 4 + 4 = 12

## 4 x 0.54

4 equal groups of 54/100

0.54 + 0.54 + 0.54 + 0.54 = **2.16**

Now what do we notice here?

We’re adding 0.54 together four times to get 2.16. We don’t necessarily get a ‘smaller’ number or answer but instead we just proved when we take 0.54 and add 4 groups of them together, we get a total of 2.16.

## 0.2 x 0.4

2 tenths equal groups of 4 tenths.

Or of these 4 tenths – we need to take 2 tenths of it.

When we multiply two tenths and four tenths together, we get a total of 8 hundredths

0.2 x 0.4 = 0.08

This is why the strategy of overlaying works!

Let’s try another one

## 0.5 x 0.3

5 tenths equal groups of 3 tenths.

Of these 3 tenths – we need to take 5 tenths of it.

When we multiply five tenths and three tenths together, we get a total of 15 hundredths

0.5 x 0.3 = 0.15

So next time we talk about multiplication – instead of saying “remember when we multiply the numbers get larger” reiterate the **concept** “remember when we multiply, we take the number and add it over and over again” or be specific with your** verbiage **“when we multiply two whole numbers together, the quantity gets larger” 😀