Scratch Addition

Scratch Addition


>>Hi, this is Julie Harland and I’m YourMathGal. Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic. All right, I’m going to show you how to do something called Scratch Addition. It’s a quick and easy way to add a column of numbers. So let’s say you have something like these, 8, 9, 3, 5, 7, 6 just a bunch of numbers you had to add, right? So these– a column of numbers. So one way is to think of it in your head but it’s easy to get lost, so normally people say 8, 9 is 17, right, and then 17 and 3 is 20 and then 20 and 5 is 25 and then– oh, you have to think, “Where was I?” Oh yeah, 25. 25 and 7, 32; 32 and 6 is 38 and hopefully, I got that right. But what’s happening is I have to keep all these numbers in my head. Now there are other things people do to add numbers quickly but just not scratch addition and that’s by kind of combining numbers. They kind of add up together or adding a couple numbers at a time. So some people might notice that these three numbers 8, 9 and 3, 17 and 3 add up to 20. So those add up to 20 so far. And then they might say, well these two numbers add up to 12 and then I’ve got 6 and then that’s another way to get 38. Okay that’s not scratch addition but that’s a way of like kind of just adding a few numbers together at a time. Someone else might say, “I wonder if there’s any easy sets of numbers I could add together,” and they’ll notice like the 7 and 3 add up to 10. So that’s up to 10 so far and then they might say, “Well, let’s see.” 6 and 5 here add up to 11, right, plus that 9 is 20.” So then they think that and then you’ve got the 8 again. Different ways of adding these numbers up and where we had actually a 3 here. Okay, I’m going to show something a little bit different though. All right, so this isn’t the only way to obviously quickly add a bunch of numbers up. Instead of keeping numbers in your head that are over in ten, we’re going to scratch out a number. So watch how this works. 8 and 9 is 17, now normally you write 17 like this, right? What I’m going to do is here’s I’m going to write 17. I’m going to scratch and write the number 7 right next to it. Then I’m going to add 7 and 3, 7 and 3 is 10. Look how I’m going to write 10. So instead of writing a 1 you just scratch a number out. Then 0 and 5 is 5. If I want it, I could write that down. 5 and 7 is 12. So, you see I’m writing 12? And then 2 and 6 is 8 and the last thing you get, that’s going to be the one’s column. You see how many numbers you scratch out that’s how many ten’s there were; 10, 20, 30 so this is the number 38. So let’s do that again. We’ve got 8, 9, 3, 5, 7, and 6 and you don’t have to write these numbers on the right ’cause– to do this again, actually, you could just put the video on rewind and watch what I did. Now watch me do this by keeping the numbers in my head. So I think 8 and 9 is 17. I’m going to just remember the 7. 7 and 3 is 10. I’m going to remember the 0. 0 and 5 is 5, 5 and 7 is 12. I’m just going to think 2 and what’s left is an 8. I count the number– how many times I made scratches? And that’s the ten’s column again. So you could either write down that number or keep it in your head. One more time. Okay, so let’s do it again. So what you could think of? Instead of thinking of the number 17, some people actually think about it this way. 8 and 7, scratch 7, 7 and 3 scratch 0. See instead of writing the number 10 you think scratch 0. 0 and 5 is 5. 5 and 7 scratch 2. 2 and 6 is 8 and count those numbers 38. So you see the idea why we call it “scratch,” okay? Whether or not you write this little numbers down or keep that number in your head– oh, by the way, I ended up writing a 2 here. I didn’t keep that number 2 in my head. You still end up with 8 in the one’s column. So let’s try it on in other column of numbers. Right, so here we have a column of numbers again. By the way, I learned this method from a really old book before there were calculators back in– I think the ’30s or ’40s it was written and it was for accountants. How to quickly add a bunch of numbers together, right? So again, lots of ways people might add these numbers. They might just, you know, start 7 and 6 is 13, keep that in their head. 13 and 5 is 18; 18 and 9 is 27; 27 and 8 is 35; 35 and 4 is 39; 39 and 6 let’s say that’s 45; 45 and 7 is 52. So I think it’s 52 if I didn’t make any mistakes. All right, so the question is I wonder if it’s 52. So easy when you’re adding all those digits not to make a mistake somewhere. So let’s do the scratch method. Right, so I’m going to write down the ones just so that you could see what I could be thinking in my head. You could keep that number in your head or you know, if you don’t have a piece of paper, some people just put their finger up instead of writing a scratch. So when they do 7 and 3 they actually put one of their fingers up and think the number 3 for 13 but I’m going to do it with the scratch. 7 and 6 is 13; 3 and 5 is 8; 8 and 9 is 17; 7 and 8 is 15; 5 and 4 is 9; 9 and 6 is 15; 5 and 7 is 12. Here, count the scratches, 1, 2, 3, 4, 5, I did get 5. Looks like I did it right. Now of course, like I said, you could keep those numbers in your head. So just listen and see if you could follow along what’s going on when I do it in my head. 7 and 6, 3; 3 and 5, 8; 8 and 9, 7; 7 and 8, 5; 5 and 4, 9; 9 and 6 is 5; 5 and 7 is 12, so I write the 2 at the bottom and I’m adding that to 5. So you could say it to yourself or you could write the digits down. It’s easier to write the digits down if you have a piece of paper anyway. And lastly, you know, if you don’t find this any easier, by all means don’t use it. It’s just kind of a fun method. You could just put groups of numbers together. Other people do that. So they might notice that let’s say 4 and 6 add up to 10, right? And then I notice right here, I’ve got a 6 and 5; 11 and 9 is 20. So I’m up to 20 so far and then I’ve got 7 and 8, that’s 15 and then I have that 7 and then that’s another way to do it. You just sort of add, you know, pairs of numbers or three numbers together to get easy numbers and then go ahead and add and you’re still going to get 52. So just different ways, this is not the scratch method the way I did it in green although it looks like it, kind of. I was just scratching up the numbers I already used that. So this is just, you know, a method that if you find it useful you could use for adding a column of numbers. How about you try one? So here’s a big column of numbers. So why don’t get a piece of paper and try it. See if you can get it using the scratch method. Okay, here I’m going to go for it. I’m going to write down the digits. To me it’s just as easy as like keeping anything in my head. So 8 and 6, 4; 4 and 3 is 7; 7 and 9 is 16. I’m actually, I was just saying the one’s digit. Let me say the actual number. Okay, 8 and 6, 14; 4 and 3, 7; 7 and 9, 16; 6 and 7, 13; 3 and 6, 9; 9 and 4, 13; 3 and 8, 11; 1 and 5 is 6. Count the scratches 1, 2, 3, 4, 5. I’ve also seen people do this just using a dot instead of a scratch so let’s do it that way. 8, 6, 3, 9, 7, 6, 4, 8, 5. Put a dot every time it adds up to, instead of writing– scratching out a number you just put a dot. So 8 and 6 is 13; 3 and 3 is 6. Oops I’m sorry. 8 and 6 is not 13; 8 and 6 is 14; 4 and 3 is 7; 7 and 9 is 16; 6 and 7 is 13; 3 and 6 is 9; 9 and 4 is 13; 3 and 8 is 11; and 1 and 5 is 6. So did you see what I did? Instead of scratching I just put a dot? Instead of writing 14, I put a dot 4, a dot 6, a dot 3, et cetera. So I still want to put the 6 and now I just count the dots, 1, 2, 3, 4, 5. Okay I did it twice and I got 56 so, you know, I think that’s the right answer. And those of you who wanted to do it some other way like combining couple numbers at a time, that works as well or combining two numbers at a time, that’s another strategy people used just in a row. They might say, well the first two numbers add up to– I do this a lot actually. The first two numbers are 14, the 6– next two numbers are 12, the next two numbers are 13, the next two numbers are 12 and I’ve got a 5. And then they add. You’ve got less numbers to add at a time but then you stop five numbers here over here, right? You could do it again. But let’s just do it from here. You’ve got 4 and 2 is 6; 7, 8, 9, 10, 11, 16. Oh, I just keep getting 56 no matter how you look at it. [ Pause ] Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.  

2 thoughts on “Scratch Addition”

  1. Your strategies are very interesting because, as a child to compensate for my inattentive mindset I needed a quick way to get through my test. Thus, this scratch method, though it was against my teacher's, was something I developed to overcome my shortcomings.

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