I spent several class periods teaching this skill. We used base ten blocks to discover it, I've used all the things I can think of, and now as I grade a few errant papers, I notice that they still don't get it. I thought most had it, so I moved on to a new concept. Now I see that many more don't have it than do. I'm looking for any and all ideas! BTW, this is a 4th grade spec ed class, so the more concrete & visual, the better. I'm teaching the same material as the regular math teacher, but spending much more time on each concept.

By "renaming" do you mean regrouping/borrowing? I've never heard that term before...I want to check that we're talking about the same thing before I answer!

In student teaching, I used base ten blocks, games, place value order sheets, and whiteboards. I introduced the concept in very, very small increments, like so: 1. Made sure students knew how to use the blocks (some were still shaky) 2. Showed how a ten block could be exchanged for ten one blocks (took a few days) 3. Played a few games to reinforce (mostly just exchanging the blocks for numbers written on my whiteboard) 4. Showed how ten one blocks could be exchanged for one ten block (didn't take much time at all) 5. Played games where they had to make a certain number with the blocks and take a certain number away... basically subtraction w/ regrouping but I walked them through it 6. Introduced the number figures... wrote a lot of things like 23 - 9 = ? on my whiteboard. Kids had to use the blocks to make the numbers and subtract. 7. Did 28349023 practice problems/games to reinforce. 8. Told the kids we were going to try doing the subtraction problems without the blocks, just using the whiteboards and our brains. Some of them got it immediately, some needed lots of reteaching and practice. I did this until they got it... it took us about 4-5 weeks for almost all of the kids to master. Apparently several of the kids had still not mastered it at the end of the year (I did my unit in the fall)... I guess it just comes with the special ed territory!! Hope this helps!

Yes, waterfall, I am referring to regrouping/borrowing. My math methods professor called it renaming as you are renaming tens as ones, hundreds as tens, etc. Thanks for the tips so far. I'm trying to come up with some new lessons for this...

Could you tie it into money? Rename $1 as 10 dimes?? Start the problems with giving change in multiples of 10 cents?

Sometimes my students get more confused if I use manipulatives to teach them, or let them use it. Sometimes, I just have to withdraw the concrete manipulatives and show them how to do it. I make a checklist of the steps. They might not get the concept, but if your state requires kids to do it for the test, they can at least do it.

Have you had the kids draw out the problems in base ten blocks before going to the abstract? When I taught second, several kids had to use that method for much of the year.

I admit I do this too. The 10's/1's is too abstract. I have a checklist of things they follow as well for multiple digit problems... 1. First check to see if I'm adding/subtracting (most of my kids circle the sign to help them remember) Once they see they're subtracting... I always start on this side (farthest from the subtraction sign) Can I take __(bottom number) things away from ____(top number) things? If you're not sure, get out your fingers. So, "yes, I can take 6 things away from 10. So I keep going" or "no, if I try to take 8 things away from 6 things, I run out. I have to borrow from the other side." Add your one, and take one away from the other side. Solve. It sounds weird typed out, but it makes sense when you say it when you're looking at the problem, lol. I've never had a kid not be able to do it after several lessons. They tend to need practice (even when we're doing other concepts, I'll throw a couple of these in at least once every few weeks), but it's not something I really have to spend weeks and weeks on or something.

Is place value an issue for these kids? For students that have had a hard time with regrouping, I've gone back to basic place value and reviewed/gamed a lot there. Then, when I re-taught the borrowing/regrouping lesson, it went much more smoothly. I also, aside from all of the manipulative/pictoral teaching, do teach a straight up algorithm - I use a modified Knockin' On Heaven's Door, "Knock, knock, knockin' on my neighbor's door, to borrow 10," to remind them of procedure and make it fun. There are some kids, in my experience, who get the concept but not the procedure until they are explicitly taught the algorithm. I have no idea what would or would not apply to SPED in this case, so your mileage may vary here.

Thanks for all the suggestions! Lots of good ideas here. We spent about a month at the beginning of the year with place value, and most have a basic to good understanding of it. We've been going over some of the most difficult things IMO to teach all in the name of a test: place value to hundred millions, rounding to nearest million, subtraction with renaming, and estimating sums and differences (through millions)... I have at least 5 different ability levels at the same time. I really don't like teaching math much this year

I love using graph paper to help kids line things up- it makes things so much easier. I know it's not a way to teach, but it's a little thing that helps me.

Probably the most difficult concept teaching math to students with autism I faced was regrouping. The problem I encountered was that so many could not tell me which number had the greater value. Typically if the bottom number had a greater value, they would subtract in reverse. I started to teach that if the larger number was on top, then subtract. Larger number on bottom, borrow. They learned which number was larger through a chart where 0 was literally smallest and the nine was the largest. Showed very good success, yet the concept did not sink in.

Just please, please, please be careful with the "rules" you teach students... If you heard a big explosion coming from the midwest about 9:00 this morning, it was just my head, which combusted while trying to teach 3 special ed 6th grade students how to regroup mixed numbers and subtract. Somewhere in their past, they have been taught hard and fast "RULES" about ALWAYS crossing out a number, ALWAYS writing one less than the number that you crossed out, and ALWAYS making a little one next to the other number. Um, not always, as in 4 5/9 - 2 8/9. What drives me batty is teaching, drilling, and killing an algorithm without thought to the purpose for said algorithm. I'm not saying they don't need to know the algorithm, and how to use it, but it is necessary to spend time on why 42-19 becomes thirty-twelve take away 19.

Thanks for that tip! I think it will really help a couple of my students. I'm not too sure they understand which is more either. I will design one ASAP to try!

Great...I hope it works out. We taught the kids the rules that there is a B (Big) on the top line, then borrow. S (small #) then subtract. One exercise was to label the top line with a B or S. Unconventional but rarely we had students who understood place value.