Noun Challenge: July 14, 2014
Today’s noun: Addition
I’ve been hearing a lot recently about school systems switching over to the common core method of math. So, I looked it up. I figured if I was going to have an educated opinion on the topic, I needed to try to understand exactly what it was. I forgot about the fact that everyone else my age seemed to hate it, and looked at it from the point of view of my nine-year-old self. That was the only way I would be able to decide if it would make sense to kids now. Here is what I found.
Let me explain how common core works. I looked into how kids will be taught addition, subtraction, multiplication, and division. Okay, I’ll start with addition since that is what the kids will learn first. You are given two numbers to add together. I’ve generated two random numbers: 159, and 1,607. Now, most of use were taught the stacking method. You would write 1,607 on a piece of paper, then write 159 under it, lining up the numbers. You then add vertically, carrying the “1” when you add up to more than ten. You all know how to add.
So let’s talk about common core now. This method is a bit more visual. It uses pictures to help the kids add the two numbers together. First, some basics. A cube represents 1,000. A square represents 100. A line represents 10. And a dot represents 1. Okay so for our fist number, 1,607, we would draw one cube. That takes care of 1,000 and we are left with 607. Next we draw six squares. That represents 600 and we are left with 7. So we draw seven dots. This picture now represents 1,607.
We do the same for the second number, 159. We start with one square to represent 100. Now we have 59 left. We now draw five lines to represent 50, which leaves us 9. So we draw nine dots. Now we have a picture that represents 159.
Now we take our two pictures and put all the cubes together, all the squares together, and all the lines and dots together. So we have seven dots in the first picture, and nine dots in the second picture. This equals 16 dots. I hope they teach the kids to carry the 1.
I think you get the picture. I don’t need to walk you through this, do I? Here is a visual to help you:
Basically, this method teaches the kids to do math using a picture to help guide them. If your child is a more visual learner, this might be useful. I’ll get into that a little bit later. Let’s move on to subtraction.
Let’s get two numbers to subtract; 29, and 196.Now again, you probably know the stacking method. You stack the two numbers and subtract one column at a time. Visuals below.
Common core take a different approach. It focuses on starting from the lower number, and counting up to the higher number. For our example, we’ll start at 29, and count up to 196. First you are going to get to the closest tens place, 30. That’s one away. So, write the number ‘1’. Now, we need to get to the nearest hundreds place, 100. We need to count from 30, all the way to 100. That’s 70. So, next to the ‘1’ that we wrote earlier, we write ‘+70’. Now we have ‘1+70’. Now we have less than one-hundred to go, so we will go to the closest tens place to our final number of 196. So we will go to 90, which means we need to add ‘+90’ to our equation, giving us ‘1+70+90’. now we just add the 6 left in the ones place to get to our final number. so we have ‘1+70+90+6’. The last step is to just add those together. 1+70+90+6= 167. Again, the addition would be done by drawing pictures. If that was a little hard to follow here are some pictures.
Again, the common core method is a bit more visual.
Now, let’s multiply.
I’ll randomly generate two more numbers that are smaller. I’ll use smaller numbers so that our solution doesn’t end up too big. So our numbers are: 43, and 38. Okay, so with the stacking method, you know to write 43, then write 38 directly below it. You then multiply the numbers. Again, I’m not going to explain it because I am assuming you know and understand the stacking method. There will be visual below.
So what’s the common core method? I believe there are a few ways, maybe? The one that I looked into was called the box method of common core. It took the numbers being multiplied, turned them each into an addition equation. For example, 43 would become 40+3, and 38 would become 30+8. Next, you draw a box (a square). On the top of the box, you write ’40+3′ and down the side, write ’30+8′. Now, you multiply similarly to how you would with punnet squares (biology, anyone?). So, 30×40=1200. 8×40=320, 3×30=90, and 3×8=24. (Now, for simplification, the kids are taught that if you have to multiply big numbers like 30×40, you can multiply 3×4=12, and then add 2 zeroes to get 1200). After you’ve multiplied all of those, you can just add the four together; 1200+230+90+24= 1634. Again, visuals are below.
Again, Visual. Let’s move on to division.
We were taught the bracket method, where you put the larger number inside the bracket and the smaller number outside. You then divide into each number. Pictures below.
Two random numbers please. How about 200, and 5. These are not random because I don’t want a number with a decimal 3 miles long.
Alright, common core teaches children to draw circles for the smaller number. So we would draw 5 circles. Next you draw little lines inside of the circles, starting with one line in each circle, and going around until you’ve drawn 200 lines. Then you count the lines in one circle and you have your answer. Visuals below.
Again, the common core method works best for visual learners.
Now that you understand common core methods, lets get into why I like it.
I like this method because it explains how the math works. I don’t like it because it’s time consuming and kind of ridiculous to ask students to do every time they are confronted with a problem. I think this method would be best suited for teaching only. In other words, teachers should present the common core method when teaching students the math, but also present the stacking method as a faster way to do the math. For example, when teaching division, if teachers presented the common core method to explain what division is, and how it works, the students might get a better understanding. Then they should teach the students how to use the bracket for a faster, simpler way to get the answer.
What I’m really saying is, Students should be taught the way that we were taught, with common core as an option for students who do not understand that way.
I know when I was learning math, I understood the stacking method. I didn’t struggle at all. Needless to say, I went on to study astronomy and particle physics. So I had a knack for math from the beginning. But my dad taught me how to multiply bigger numbers, quickly, and in my head. And guess what? It was really the common core method that he taught me. Break the numbers down into their bases, 40 and 3. and multiply them that way, then add it together. That’s still, to this day, how I can multiply numbers quickly in my head.
So, the reason for me telling you this is because the common core method is not actually changing the way that we do math, but just explaining it a little differently. That’s why I have no problem with schools using this method.
The problem that I do have, not that I get any say in the matter, is that school are not allowing students to use that stacking method. While researching this method, I came across a student who was explaining the common core method to reporters, or someone who asked about it. She showed them the common core method, and then explained that she was taught the stacking method at home by her parents. She said that she liked the stacking method better, but she wasn’t allowed to use it in school.
This meant a lot to me. When I was in school, I struggled with fractions. Still, I can not do it the way that I was taught in elementary school. So, when presented with fractions, I asked my dad for some help. He explained to me that fractions were just decimals, written a different way and That if I could convert the fraction into a decimal, I could add or subtract it easier, and then convert it back to a fraction, if that’s what the problem called for. So I did that, and I started getting the answers right. But then my teachers started taking off points for not solving the equations the way we were taught in class.
How is that fair? I got the answers right, consistently. I was marked down simply because I didn’t do it the teacher’s way.
I told you this because its the same thing. If the student finds a way to solve the problem, and it works every time, then I see no problem. If one student likes common core, and another likes stacking, then that’s fine. Both method will get you the same answer.
This is why I like that schools are teaching an alternate method, but I absolutely hate that they ban the other. Children are all different. One method will work for some and not for others. Let them use what works for them.
As always, sorry for spelling and grammatical errors. Have a luxurious day and I’ll see you tomorrow!
P.S. Sorry for the crazy long post.
P.P.S. Also, sorry for my poor Microsoft Paint skills.