Bingo chips
Here's an idea I got from a website which was very helpful to me when explaining regrouping across zeros. I'm going to quote just a bit and give the link.
"We have these three different color poker chips, white ones, blue ones, and red ones. Whenever you have ten white ones, you can exchange them for one blue one; or any time you want to exchange a blue one for ten white ones you can do that. And any time you have ten BLUE ones, you can trade them in for one red one, or vice versa." Then you can show them how to count ten blue ones (representing ten's), saying "10, 20, 30,...,90, 100" so they can see, if they don't already, that a red one is worth 100. Then you do some demonstrations, such as putting down eleven white ones and saying something like "if we exchange 10 of these white ones for a blue one, what will we have?" And the children will usually say something like "one blue one and one white one". And you can reinforce that they still make (i.e., represent) the same quantity "And that then is still eleven, right? [Pointing at the blue one] Ten [then pointing at the white one] and one is eleven." Do this until they catch on and can readily and easily represent numbers in poker chips, using mixtures of red, blue, and white ones. In this way, they come to understand group representation by means of colored poker chips, though you do not use the word representation, since they are unlikely to understand it.
Let the students get used to making (i.e., representing) numbers with their poker chips, and you can go around and quickly check to see who needs help and who does not, as you go. Ask them, for example, to show you how to make various numbers in (the fewest possible) poker chips -- say 30, 60, etc. then move into 12, 15, 31, 34, 39, ... 103, 135, etc. Keep checking each child's facility and comfort levels doing this.
Then, when they are readily able to do this, get into some simple poker chip addition or subtraction, starting with sums and differences that don't require regrouping, e.g., 2+3, 9-6, 4+5, etc. Then, when they are ready, get into some easy poker chip regroupings. "If you have seven white ones and add five white ones to them, how many do you have?" "Now let's exchange ten of them for a blue one, and what do you get?(18)" Add larger and larger numbers and also show them some easy subtractions -- like with the number 12 they just got before, with the blue one and the two white ones, "If we wanted to take 3 away from this 12, how could we do it?" [Someone will usually say, or the teacher could say the first time or two] "We need to change the blue one into 10 white ones, then we could take away 3 white ones from the 12 white ones we have." ETC. Keep practicing and changing the numbers so they sometimes need regrouping and sometimes don't; but so they get better and better at doing it. (They are now using the colors both representationally and quantitatively -- trading quantities for chips that represent them, and vice versa.) Then introduce double digit additions and subtractions that don't require regrouping the poker chips, e.g., 23 + 46, 32 + 43, 42 - 21, 56 - 35, etc. (The first of these, for example is adding 4 blues and 6 whites to 2 blues and 3 whites to end up with 6 blues and 9 whites, 69; the last takes 3 blues and 5 whites away from 5 blues and 6 whites to leave 2 blues and 1 white, 21.) When they are comfortable with these, introduce double digit addition and subtraction that requires regrouping poker chips, e.g., 25 + 25, 25 + 28, 23 - 5, 33 - 15, 82 - 57, etc.
http://www.garlikov.com/PlaceValue.html
The whole website is really useful.
