Math Background

Two-Digit Subtraction With Regrouping: Overview

In learning two-digit subtraction with regrouping, children make the transition from thinking of numbers as ones to thinking of numbers as tens and ones. They use mental math and basic facts to subtract tens, as well as using a hundred chart to subtract tens by counting back from other numbers without regrouping. Children are introduced to subtracting in both the horizontal and vertical format.

Using a hundred chart to subtract tens

Children are introduced to the concept of regrouping by using tens and ones blocks to show how to regroup 1 ten as 10 ones. This helps to prepare children for regrouping tens when subtracting two-digit numbers.

Regroup 1 ten as 10 ones

The focus of instruction is on the use of place-value concepts as well as the knowledge of the facts and the strategies for learning the facts. See Addition and Subtraction Facts to 20. When subtracting two-digit numbers, children will discover that they may need to regroup, or exchange, to continue the subtraction process.

Regroup 1 ten as 10 ones to subtract nine

Children begin to subtract two-digit numbers using tens and ones blocks. Once children understand the concept of regrouping, they make the transition from using models to using the subtraction algorithm. To ease the transition, children begin by regrouping to make 10 and 11 in the ones place, which gives children the opportunity to focus on subtracting from zero in the ones place. This is often a difficult concept for children to grasp. Children then continue to develop proficiency subtracting with two-digit numbers by regrouping ten to make 12 to 18 in the ones place. They make the transition from working with the place-value chart to using the algorithm.

stacked equations

While learning to regroup, children review different ways they have learned to subtract and apply those strategies to subtracting two-digit numbers. They choose to use mental math, a hundred chart, tens and ones blocks, or paper and pencil. They also learn to estimate differences using a number line to round the subtrahend and minuend to the nearest ten.

number line and stacked equation

To further practice the skills they have learned, children apply two-digit subtraction to adding and subtracting money. Finally, children use addition to check subtraction.

using addition to check subtraction

Houghton Mifflin Math Grade 2