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Trade First Subtraction

In Everyday Mathematics (EDM) students are introduced to many different methods for subtraction. As they get older, they are introduced to subtraction algorithms. Some are easier to learn, but not as efficient as others. EDM picks one algorithm as its focus algorithm. Focus algorithms are powerful, relatively efficient and easy to learn and understand. The focus algorithm for subtraction is trade first subtraction. Students are taught this method and expected to show that they know how to use it, starting in second grade. In problem solving, however, students may use any algorithm they chose. The aim of this approach is to promote flexibility while ensuring students know at least one reliable method for each operation.

The trade first subtraction algorithm resembles the traditional U.S. subtraction algorithm, except all the trading is done before all the subtraction, allowing the user to concentrate on one thing at a time. The steps involved are below.

1. Examine all columns and trade as necessary so that the top number in each place is as large or larger than the bottom number. The trades can be done in any order. Working left to right is perhaps more natural, as with partial sums addition, but working right to left is a bit more effective. (When students first learn this process it is modeled with base-10 blocks.)

2. Check that the top number in each place is at least as large as the bottom number. If necessary, make more trades.


3. Subtract column by column in any order.


Trade first subtraction is highly efficient, similar to the traditional algorithm, and relatively easy to learn. It is an effective algorithm for paper and pencil calculation.

Many teachers find that drawing vertical lines between the places is helpful for students when first learning this algorithm. The vertical lines allow for students to focus on one column at a time. They also help students avoid mistakes if unnecessary trades have been made.


Examples of all of the algorithms are available online. If you go to the PES website ( find the “Curriculum” dropdown menu, and chose “Everyday Mathematics”. This will bring you to a page with many useful links. The first link will bring you to a page that demonstrates the different algorithms taught to students.