Exploring Long Addition

We take a lot for granted in our number system. Place value is one example. It’s difficult to see how revolutionary it is. It’s like the fish who doesn’t know what water is. We take it for granted.

It’s funny to think that at one point, Europe used Roman numerals to record numbers and do calculations. It is likely due to this extremely inefficient number system that Rome had no mathematicians of any historical importance and why there are not many to speak of in Europe until Europeans started using the decimal system. In fact, Fibonacci (whose actual name was Leonardo Pisano Bigollo) is commonly known as the greatest mathematician of the middle ages and he was also one of the first to argue for the adoption of the Hindu-Arabic number system we use today, a couple of hundred years before the rest of Europe.

So today’s challenge gets us to explore how place value works for us. The first place we really need to make use of place value is when learning the technique of long addition.

How does long addition work? We organise the numbers we are adding into columns according to the place value of each digit. Here’s an example:

The technique involves:

  • adding up the digits in the right most column
  • placing extra digits from the answer into the next column

We can also rearrange digits in a column and keep the same result:

Try this challenge and see how close to 1000 you can get this sum to be. Can you get exactly 1000? Is it possible just using each digit once?

Once you’ve tried this, try the challenge with different digits. You could use zero for example of even negative digits (how would that work?)

Download the example grids to get started

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