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.