## Thinking Outside the Algorithm

Above and beyond the traditional algorithmic approaches to subtracting is the development of subtraction strategies that allow children to *explore* subtraction rather than be subject to a grueling procedure that, if they don’t fully understand, comes to haunt them when they want to find the answer to a subtraction problem.

Too often I come across kids who, when faced with a subtraction problem, don’t know how to set up their columns, cancel, borrow and successfully subtract. They typically sit stone-faced wondering what they could ever possibly do to solve the problem. If they had been taught from the beginning they may not necessarily have to *subtract* to solve the problem then perhaps a new confidence would intercede.

There are a number of ways children can calculate math without algorithms. These methods are far more efficient and elegant than the messy algorithmic approach. Math teachers across the nation have to start teaching with these progressive and constructivist ideas.

In this article, “adding up” to solve a subtraction problem is the idea. Other subtraction strategies are presented in the series links at the bottom of this article

Teachers generally teach children to use adding up to check their answers to a problem in subtraction, but why not use this method to actually *solve* the problem?

## Adding Up to Subtract: Example Problem

Let’s take the problem of 1, 278 – 580.

Now, let’s say we have children start with their base number of 580. What can we add to 580 to get us closer to 1,278?

It should be a number that can mentally calculated. Perhaps some children will suggest 100. If so, a teacher can guide them to build from there.

A more saavy student might suggest 500. Great! **500** + 580 is 1080. Now what else can we add to 1080 to get us closer to 1,278?

Perhaps **100 **will come up. This will give us 1180. Then someone else might suggest to add another **100**. Great.

However, this will take us 2 past 1,278 to 1,280. No problem, because this extra 2 can be subtracted from the final answer in the end.

The final step would be to add up all the smaller numbers that were used in building toward 1,278. In doing so we would get the answer of 700. Of course, we would need to subtract out the 2 in the end for a total of 698…the answer.

See….by adding up we avoided the algorithm, the messy cancelling and borrowing procedures, and the likely chance that this procedure would be performed incorrectly. On top of it, the children learn that there is a relationship between addition and subtraction that is not only ever-present, but can help them calculate. What traditional math text teaches this?

In the next article, we’ll take a look at “breaking it down” as another subtraction strategy.

## This post is part of the series: Teaching Young Elementary Students Subtraction

- Elementary Math Simplified: How Addition Becomes Subtraction
- 'Breaking it Down' Strategy for Teaching Subtraction
- Using Context to Help Students Subtract Whole Numbers