Subtraction Problems Using Fact Families
The essence of mathematics is not to make simple things complicated, but to make complicated things simple.
– S. Gudder
Today we are going to see an interesting strategy, that you may not know about, to solve problems of addition and subtraction of natural numbers. It is called a fact family, and it is a strategy that helps us memorize basic numerical facts and what they are always going to equal. But, what is it exactly?
It is a collection of operations that uses the same numbers. In each fact family there are three numbers that you can add and subtract in various ways.
For example, we can form a fact family with these three numbers: 3, 6, and 9 in the following way:
3 + 6 = 9
6 + 3 = 9
9 – 6 = 3
9 – 3 = 6
This allows us to understand that:
- A close relationship exists between addition and subtraction, if we know 6 + 3 = 9, then we also know that 9 – 6 = 3 and that 9 – 3 = 6.
- If we add 6 + 3, we will get the same result as when we add 3 + 6. This is to say that it does not matter how we write the addends, because the result will always be the same.
Now, we will solve a subtraction problem using two digits from the fact family:
I have a collection of all types of books at my house: picture books, story books, coloring books … I also have 30 comic books in the collection. If I give David 15 comic books as a present… how many comic books will I have left in my collection?
We can represent the operation like this: 30 – 15 = ?
But, through the fact family formula we can reorganize the terms and change the signs, and we get two possibilities:
15 + __ = 30
__ + 15 = 30
What number added to 15 gives us 30? 15! In that case, this means that 30 – 15 is equal to 15 because it is a numerical term from our fact family whose terms are always related.
- Somewhere in Africa there is a very rare and beautiful flower that can live, in total, for 25 years. In a documentary I saw one of these flowers and they said that it had been alive for 17 years. How many more years could it live?
- I love the movie theater and now that I am on vacation and have a lot of time, I want to watch all 49 movies that I have in my house. I am going to watch one movie each day. If I have seen 20…how many movies do I have left to watch?