Base-10 blocks are essential for teaching regrouping. These are blocks that model our number system. There are very small cubes that equal a one. If 10 of those cubes were placed together into a long row, they would be the same length as a rod, otherwise known as a 10's rod. There are also flats that are equal to 100, and very large cubes, which are equal to 1000. Some base-10 blocks interlock, so students can see even better how they model 10, 100, or 1000. Whether students are adding and regrouping, or subtracting with regrouping, using base-10 blocks helps make it more concrete. Students can actually trade in their ones pieces for a 10's rod. If you are teaching younger children, they can practice adding numbers that go over 10 and realize that 7 + 7 is equal to one 10 and four ones. If you are teaching older children, you can help them to see that 35 + 28 is equal to 6 10's and 3 ones. Using base-10 blocks regularly when first teaching this concept will help students to become proficient.
Using dimes and pennies to teach regrouping is very similar to using base-10 blocks, but it gives students a slightly different perspective, and it reinforces money skills as well. Dimes and pennies can be used for teaching regrouping with either addition or subtraction. If doing it with subtraction, students can be taught to turn in a dime, get 10 pennies, then continue with their subtracting.
This game allows students to practice their regrouping skills. In order to play this game you need base-10 blocks or something to equal ones, 10's and a 100. Each student rolls one dice. They collect the number of ones blocks (or pennies or whatever is representing a one) that they roll. If they roll a 5, they collect five blocks. As they continue to roll, they trade in their ones blocks for 10's rods (or whatever is representing a ten). If the next roll is a six, then the student collects six more ones. Now the student has 11 ones, so they can trade 10 of the ones in for one 10 rod. At the end of that turn they still have 11, but it is in the form of one 10 rod and a one block. They continue taking turns and trading in their ones for 10's. The first person to collect 10 of the 10's rods, and trade them in for a 100 flat, is the winner.
A T chart is a chart that looks like a capital T, creating two columns. Using a T chart when adding is the first step between regrouping with manipulatives and regrouping with the algorithm. Instruct students to make a T chart and to label the ones on the right side of the chart the ones and the 10's on the left side of the chart. Instruct students to rewrite their problem into the chart, placing the numbers from the ones place onto the ones side and the numbers from the 10's place onto the 10's side. Have students add the ones side first and write the answer under the ones side. If adding 5 + 7 in the ones column, students would write 12. Then explain to students that each side of the chart can only hold one number. Lead them to the conclusion that the 1 in the twelve is really a 10, and that they should erase it and add it to the 10's column. Then they add the 10's column to get their final answer. Help students to equate this with activities that were done previously with base-10 blocks. Students should practice this way until they don't have to write and erase the number from the ones column, but instead realize they should put the 10's number into the 10's column automatically.