Double-digit addition is just one of the many mathematical concepts that students are expected to master in first and second grade, and it comes in many shapes and sizes. Many adults are probably comfortable performing double digit addition with regrouping, also called borrowing or carrying.

The word "regrouping" describes what happens when numbers are shifted into the appropriate place value. This means shifting numbers into a higher place value if, after adding digits together, they no longer fit where they started. For example, 10 ones should become one 10 and 10 tens needs to become one 100. The value of the numbers do not change, you just adjust place values. When performing double digit addition with regrouping, students use their knowledge of base ten to simplify their numbers before finding a final sum.

## Double Digit Addition Without Regrouping

Students will also encounter double digit addition without regrouping, or double-digit addition that does not require them to make changes to the place value of any digits in order to calculate a sum. This simpler version of double-digit addition is an essential building block to learning more advanced mathematical concepts. Two-digit addition without regrouping is just one of the many steps that students must take to become more skilled mathematicians.

Without first understanding how to add without regrouping, students will find it extremely difficult to add when regrouping is required. That is why it is important for teachers to provide constant practice with addition and only introduce more sophisticated addition once students are comfortable adding when carrying is not involved.