• building conceptual understanding
• # Multiplying Decimals | Why does it get smaller? 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” 😀

• best teaching practices
• # Decimal Investigation Building a strong understanding of how our base ten system works is always so important. Taking the time to help students understand this will help with ‘regrouping’ when it comes to adding, subtracting, multiplying, and dividing – it’s worth the time! Ones – Tenths – Hundredths – Thousandths  One whole 1.00 One whole is […]

• building conceptual understanding
• # Do we just add a zero at the end? Creating number sense is something students struggle with throughout their elementary school career – I know that I definitely wrestled with this as a child. We operate on a base ten number system, but we often fail to develop the conceptual understanding behind operating on a ‘base ten’ number system. Many teachers will say “just […]