 In this lesson, students learn how to add numbers when one of the numbers is between 11 and 20 and the other is a single digit, and no regrouping is required. The addition process is illustrated by decomposing the two digit number into 10 and some number of ones. These ones are then added to the single-digit number. Finally, the result of that addition is added to 10 to get the sum of the original two numbers.

There are two important prerequisites to this lesson that are covered in prior lessons: 1) students know the addition facts that have sums of 10, and can supply a missing factor when one of these numbers is given, and 2) students know the numbers that result when a single digit is added to ten.

In this lesson, the “sum” is defined as the result of adding two numbers. The vertical format for adding numbers is introduced, and the relationship to the horizontal format is illustrated.

The addition of single-digit numbers with a sum greater than 10 is taught using a “tens complement” approach. This strategy has three steps:

1. The tens complement of the larger number is subtracted from the smaller number.
2. This number, the tens complement, is then added to the larger number, to “make a ten.”
3. The difference from the subtraction is added to ten to get the final result.

This “make a ten” strategy is important for two reasons. One is that it makes explicit the place value concept that underlies all regrouping in addition with larger numbers. The second is that it provides a meaningful thinking strategy that eliminates the need for memorizing the basic addition facts with sums from 11 through 20.

### Three Numbers

In this lesson, students learn how to find a sum that requires adding three numbers. To add three numbers, first find the sum of the first two numbers. That number is then added to the third number to find the sum, which represents the sum of all three numbers.

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