How to explain to kid why subtraction is not commutative

Question

My 7-year old daughter (pre-school) asked why subtraction is not commutative. How to explain that in simple way, in relation to real world concepts? (I am not looking for abstract mathematical proof)

It is easy to explain why addition is commutative. It is also easy to give real world examples of non-commutative operations (putting on underwear and trousers, etc).

But I cannot figure out example with subtraction.

Answer 1

The idea that it isn't commutative seems, to me at any rate, to be more intuitive than the idea that it is. Try this: If you laid out 5 coins on the table, you can take away 2, but if you laid out 2 coins on the table, you can't take away 5!

EDIT: Also, if she understands negative numbers, you can explain it using that concept as well (e.g. I can gave you 7 dollars, and you can give me 5. what would it mean if I gave you 5 and you gave me 7?)

Answer 2

To make things simple, let's consider a way to make sense of $$1-0 = 1 \ne -1 = 0-1$$ in real life, say the temperature.

• $1-0 = 1$: yesterday's temperature way $1\mathrm{°C}$, and there's a $0\mathrm{°C}$ drop in temperature today, so the temperature now is $1\mathrm{°C}-0\mathrm{°C} = 1\mathrm{°C}$.
• $0-1 = -1$: yesterday's temperature way $0\mathrm{°C}$, and there's a $1\mathrm{°C}$ drop in temperature today, so the temperature now is $0\mathrm{°C}-1\mathrm{°C} = -1\mathrm{°C}$.

Both cases give different temperatures.

Answer 3

Sounds to me like she's smart enough to understand that addition is commutative. So, for example, $$7 - 4 = 7 + (-4).$$ Then $$7 + (-4) = (-4) + 7.$$ But $$4 - 7 = 4 + (-7)$$ and $$4 + (-7) \neq7 + (-4).$$

Answer 4

Some more real-live examples of substractions. They make it easier to understand why substraction is not commutative

• bank account operations (deposit, withdrawals)
• sports/games when you can have negative score
• elevator (negative floor numbers are nowadays common)