Teach children about regrouping by explaining the concept of place-value and demonstrating how to use math manipulatives to group ones into a group of 10. Practice basic addition and subtraction up to 10 with children, and explain how to use regrouping with vertical addition and subtraction questions.
Begin by explaining that a group of 10 objects is not just a single group of 10, but also 10 separate objects. Help children grasp this concept by working with base ten blocks and confirm that the value of 10 ones and one group of 10 is the same.
After this concept is clear, explain to children that some addition and subtraction questions require regrouping 10s and ones to make them solvable. Show the children a question in which the ones of the first number is smaller than the ones of the second number, and explain how to regroup the 10s of the first number to create enough ones to make subtraction possible. This should first be demonstrated with base ten blocks to allow the children to see what is happening physically, as it is easier to understand with visual representation.
After children can solve regrouping equations with base ten blocks, have them practice with vertical addition and subtraction on paper. Rather than regrouping objects, explain that a group of 10s is "borrowed" by crossing out the original number of 10s, reducing the number by one, and moving the borrowed group of 10s to the ones column.