New Math Series Part 2: Making Tens
Hello all! In this series I am going to be discussing a few of the ways that math has changed since I was in school. For some context, I am 30. I graduated from high school in 2004, and from the University of Oregon with a BA in Mathematics and a Secondary Education emphasis in 2008. A lot of changes have happened in Oregon's math curriculum since then, with the adoption of common core educational standards and mandatory testing placed as a graduation requirement. Some of the changes in curriculum have been good, some have been bad, but all of them are changes none the less! The purpose of this series is to familiarize parents with a few of the "big picture" changes I have seen in my 11 years as a private tutor so they can broaden their understanding of their students' homework and classwork.
This is a method of addition that can also lead into a twin method of subtraction. In making tens we split up addition problems into a portion that makes a multiple of ten and then the remaining portion.
Let's first look at all the ways to add to 10:
0+10
1+9
2+8
3+7
4+6
5+5
6+4
7+3
8+2
9+1
10+0
These should all be familiar to someone who has been using them for a decade or two. However, throughout this article please keep in mind that the people learning these methods have not been doing addition for 80% of their life like many of us have.
Now let's look at an addition problem. We'll start with something simple, like 9 + 8. We first think about what would be needed to add up from 9 to 10. This would simply need 1. Now we will break the problem up into 9 + 1 + 7. We get the 7 by taking 1 away from the 8, since we in essence "separated" the 1 out to go with the 9.
Now we have 9 + 1 + 7 = 10 + 7 = 17.
By "making a ten" we turned the problem into a multiple of ten and a single digit number, which is simple in our base ten number system.
Let's try it with bigger numbers. We'll try 34 + 7. In order to go from 34 to the next multiple of ten we have to add 6. So let's re-write this as 34 + 6 + 1. This gives us 40 + 1, or 41. Remember, we need to keep in mind that while these facts may be obvious to some of us, they are less intuitive for students who are learning addition for the first time.
Many of the objections that have been raised to this method of addition have to do with time. People say this is a time-consuming way of doing simple addition problems, and in that they are correct. This takes longer than simply counting with your fingers or memorizing more extensive addition facts.
However, the long term benefits of knowing how to use this method may be greater than people realize. This is really just a formal process constructed for a trick that many adults use to quickly do addition in their heads. While it may not be efficient for small addition, the process it teaches allows students to do larger problems in their heads. How would you add 45+25 quickly? Chances are, you would put the 5 from the 25 with the 45 to get it to a multiple of ten, then add the 20. This is a perfect example of the problem-solving skills being taught in this method.
Let's formalize the process for a 2-digit number. Hmm, what about 34 + 19?
34 + 19 = 34 + 6 + 13 = 40 + 13 = 53. Easy!
Maybe this isn't the most efficient way to add small numbers. However, with so much emphasis being placed on "real world" applications for math in recent changes to standardized tests and curriculum, this is certainly a step in the more applicable direction.
