When you say "carry the one," there is a good chance your students eyes will glaze over and you will know that comprehension is lost, so using something they are familiar with will engage them as well as feeling more accessible to them.
To begin with, you will need to have explained the value of coins to your students. Hopefully, you have read my lesson plan on teaching the value of money, which means that you already have the play coins that you bought for that activity. If not, go to the dollar store and get some inexpensive packs of pretend money which include pretend coins that look very much like real U.S. currency. Pass out the pennies and the dimes to your students.
Write a couple of problems on the board that will use regrouping. As you write them, write "ones" over the ones column. Write "tens" over the tens column. Have students take out their coins for each problem. Have students count out the correct amount of pennies for the "ones" column. Have the students count out the correct amount of dimes for the "tens" column. Explain as you go along why pennies work for ones and dimes work for tens.