Section 26.4 Closing Ideas
In some ways, subtraction is very simple. You start with some objects and you take some away. But we have already seen that there are a number of ways of looking at how we might do this. We have used base-10 blocks (and base-8 blocks, if you did Worksheet 5) and we used the number line. But we also used the number line in several different ways. We saw subtraction as movement, subtraction as a distance, and subtraction reframed as addition.
But there's even more to subtraction that this. What happens if you are being asked to "take away" more than what you started with?
If you try to think about how an early elementary school student might respond, the most common explanation of this is "You can't do that!" As adults, we have other ways of thinking about this that can help us resolve the question, but it also requires a certain level of intellectual sophistication. Whatever explanation we might have is going to be more complex than just saying that you start with a collection and "take away" things from it.
All of this only goes to show that sometimes simple and easy are not synonymous. The idea of subtraction is fairly simple. But as you look deeper at it, the simplicity of it requires some rather complex ideas to fully understand. And this helps us to see the beauty of mathematics. Simple concepts can lead to complex ideas if you simply ask the right questions.