Addition to 100 via compensation method

General

Students learn to add to 100 using the compensation method. They learn that compensation means that they round one of the addends to the nearest tens number.

Common core standard(s)

2.NBT.B.5
2.OA.A.1

Relevance

It is useful to be able to use the compensation method because it makes adding numbers to 100 easier and faster.

Introduction

Explain that a tens number is a group of 10 and, they always end in a zero, and that they are round numbers. Ask students if they can name any other tens. Next students practice rounding to a tens number. The interactive whiteboard shows a selection of balls with a selection of numbers. Have a ball ready to toss into the classroom. Call a student by name and throw them the ball. They must make a round number of the number shown on the interactive whiteboard. 18 becomes 20, 27 becomes 30, etc.

Development

Explain that the compensation method is a way to make addition to 100 easier. Take the addition problem 38+5 as an example. Using the compensation method you round one of the addends to the nearest tens to simplify calculation. The 38 becomes 40 by adding 2. You solve 40+5 =45. You now need to take away the 2 that you added to compensate. You get 45-2=43. The total is the same regardless of if you solve 38+5 or 405-2. Solve a few more addition problems using these steps and explain that sometimes it is the first addend which is rounded, and other times it is the second addend that is rounded. Always take the addend that is closest to the tens number. Check that students know which compensation step they need to create by asking them to match compensation steps to addition problems. Erase the grey boxes to show the answers. Using a number line, show that they need to select the addend that is closest to the tens for the compensation method. Ask students to calculate on their own and say that they should use a compensation step to solve. Have them do this in their heads.

Check that students are able to use the compensation method in adding to 100 by asking the following questions:
- Round the following numbers to their nearest tens: 38, 69, 88, 49, 78
- How can you solve 69+6 using the compensation method?
- What is the most important step of the compensation method? (That which you have added, you must take away)

Guided practice

Students first practice determining which addend should be rounded to create the compensation step. They are then asked to calculate the addition problems after rounding an addend. They are then asked to round in their heads and solve the addition problems.

Closing

Show the statements on the interactive whiteboard and ask students which one is correct. The statements are about which compensation step (or rounding of addend) is useful for a given addition problem. Ask students why they think their given answer is correct. Discuss when it is useful to use the compensation method and repeat how it works. Be sure to emphasize that what they add via rounding in the compensation method, they must be sure to take away, otherwise the total will not be correct.

Teaching tips

Students who have difficulty with the compensation method can make use of manipulatives to help visualize the process. They can then see what is being added to round to the nearest tens and they also can see exactly what they need to take away again. Writing out the problem in steps can also be helpful. Srudents who are ready for more challenge can calculate these addition problems in their heads. they do not need to write out the problems if they are comfortable compensating in their heads.