I'm working as an aide in an elementary school resource room and have, more or less, been charged with conveying the idea of regrouping with several special ed fifth graders. It's something they have all been exposed to before, but for one reason or another, have lost their understanding of over the summer. We've tried trading chips, using base ten blocks, drawing base-ten type diagrams, writing numbers in expanded notation (or I guess that's what it's called, where 347 is written as 300 + 40 +7?), to try to communicated both the ideas of place value and regrouping. It's been suggested by administrators that we put the "why we do it"s on the back burner and try to teach them steps they can memorize and use instead. Some of them are okay with the regrouping algorithm, but some of them don't even have that. We've been doing subtraction since August! I'm at a loss. It's my understanding that subtraction was pretty much under their belts at the end of last year, also, so I'm discouraged that it's taking so long to get a firm grasp on it again. So... does anyone have any ideas about what I can try, or what tools might help them in remembering? Are there rhymes or songs about subtraction? Or fail-proof books that veteran teachers use? I'm not new to education- I've tutored for years!- but I'm new to the special ed classroom, and to teaching (as teaching and tutoring are, in practice, very different animals). Thanks for any suggestions you all may have!

I know one teacher teaches borrowing as going to the neighbors...I'll try to explain. say tnumber in 37-19. The kids look at the 7 & 9 . Is there enough hot dogs (7) to feed the 9 family members, nope. So we have to go to the neighbors (3) & borrow 10 hotdogs. Now we add the 10 to the 7 to get 17 (I think she just puts a small 1 in front of the 7 to get the 17. Look it over again... can 17 hot dogs feed 9 people yes so we can subtract. I hope that made some sense. It really clicked with the youngers ones.

How did you use the base ten blocks? They should work pretty well, though, of course, I don't know your students. If you model each number with the blocks, it becomes very clear that there aren't enough ones to take away so you can 'borrow' a ten from the tens place. Just following steps is okay, but make sure they realize that the one they borrow from the place to the left means one ten or one hundred or whatever. Don't let them think they get 1 them just attach it to the digit on the right. I don't know if that makes any sense or not .....

We have demonstrated subtraction with regrouping using the base ten blocks as you suggested, "trading in" tens for ones, or hundreds for tens. And it will work for these students so long as you prompt them at every step. However, when allowed to work problems on their own, it's as though we never went over anything with them. Baffling! I've also used the neighbor analogy in saying "we have to go right next door", but I haven't tried associating the numerals with objects being borrowed. They're fifth grade students, and word problems are the name of the game, so I'm hesitant to make general associations like that, outside of the context of a word problem, for fear that they might not be able to adapt the strategy later. But I don't know, maybe that's underestimating them? We've also discussed rounding and estimation, in order to help them check their work... but they seem to have no concept of reasonableness, so when they mis-borrow or align their numbers strangely, they don't realize that the answers they come up with aren't even close. I'm in over my head, I think, and I'm glad I'm not the teacher in this classroom- I'd be so frustrated! As it is, I'm only a little frustrated, and happy to ask questions. Thanks for your suggestions! It wouldn't hurt to go back and try things again!

I've also used play money to help them understand regrouping. You can use ones and tens or pennies and dimes and have them practice trading and showing numbers on the place value mat. This only works if they have solid knowledge of money concepts. Some kids find it motivating to work with "money."