Math Background

Two-Digit Addition With Regrouping: Overview

In learning two-digit addition with regrouping, children need a solid conceptual foundation. They begin by using mental math and basic facts to add tens, as well as using a hundred chart to add tens to other numbers without regrouping.

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Children are introduced to the concept of regrouping by using tens and ones blocks to show how to regroup 10 ones as 1 ten. This helps children think of numbers in terms of ones and tens instead of just ones.

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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 adding two-digit numbers, children will be looking at the ones and deciding if they can regroup them for a ten. You might want to equate regrouping with trading, a term that they will understand immediately.

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Children begin to add two-digit numbers by using tens and ones blocks. They make the transition from using models to add two-digit numbers to using the addition algorithm once they understand the concept of regrouping. To ease the transition, children begin by regrouping values from 10 to 12, which includes many opportunities for them to add and get a zero in the sum, often a difficult concept for children to grasp. As children become proficient in regrouping 10 to 12, they are introduced to regrouping values from 13 to 18. In these lessons, the emphasis is on recording the regrouped ones in the tens column, something children often forget to do.

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While working on regrouping, children also learn to estimate sums by using a number line to round addends to the nearest ten and then add tens. Children learn that an estimate is appropriate when the exact answer is not necessary. Some children may discover that estimating is a quick way to check to see whether an answer is reasonable.

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To further practice the skills they have learned, children apply two-digit addition to adding money and adding three addends. Children learn that there are different methods for adding: They can choose to use mental math, a hundred chart, tens and ones blocks, or paper and pencil.

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Houghton Mifflin Math Grade 2