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Regrouping With Money
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.
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Now, work through the problems on the board with the students. When the students have to regroup, have them trade in their ten pennies for dimes. Students will see that the amount of pennies they have left will be the same as the number they will write in the ones column for the answer to the problem. Students will also see that the amount of dimes they have is the amount they will "carry over" to the tens column.
Activities like these can produce that "click" in your student's mind that lets you know they understand the concept you are trying to explain to them! This makes learning fun and painless for you and your students!