Lesson 5.4 of Exploding Dots

Okay, the division problems I've been doing so far all worked out very nicely. So for example, we did 276 divided by 12 was 23. We saw that as follows. We drew a picture of 276, we drew a picture of 12. We looked for groups of 12 in a picture of 276. One dot next to two dots, one at that level. One dot next to two dots, one at that level. One dot next to two dots, one at that level. Another one at that same level. And another one at that level yet again. So, two at the tens level, three at the ones level, twenty-three groups of twelve. Grand. Okay, indeed, that was a very nice problem. It worked out to be good whole numbers. So my question now is, what if I change this problem? So say 277 divided by 12. What would we see? What would be the difference? Okay, well our picture wouldn't be this anymore. It'd be now a picture of 277 which is two dots, seven dots and one extra dot yonder. We'll still go up ahead looking for groups of twelve and we'll see exactly this but we see this one extra dot. How do we interpret that one extra dot? Well we have to say then that 277 dived by 12 is 23, yep, two groups and three groups, with one extra remaining dot. Well, depending on what grade level you're in, you might write remainder one. Or some countries might write dot, dot, dot one. You might write different ways but maybe probably the correct way to write it in terms like if you want to be truly mathematically correct to say it's 23 plus one more dot still waiting to be divided by 12. So it's 23 plus one twelfth. My point is, this long division approach with pictures, is kind of brilliant. I love it so much because if it turns out there are remainders, do you know what? You'll just see them. They'll just sit there right before your very eyes and you'll know exactly what to do with them. So even if the division problems not nice, remainders are a piece of cake. You can see what's going on. Loads of fun. Good stuff.