Annabella Wood29 June 2006

How many ways do you know to work this problem?
 1274 + 362

For most of us, this is how we would do it:
• 4 + 2 = 6. Write the 6 below the line in the ones column then move on to the tens.

• 7 + 6 = 13. Write the 3 below the line in the tens column and carry the 1 to the hundreds.

• 1 + 2 + 3 = 6 Write the 6 below the line in the hundreds column.

• Then bring the 1 in the thousands below the line in the thousands column.
Your finished problem would look like this:
 1 1274 +  362 1636

Though this method is good and is what most of us were taught, it is not the only way to work this problem. It is one of many. Let's explore some of the other ones, and then see why it matters that there are lots of ways to do it.

A different way to approach addition is to break the problem down into smaller calculations, and start on the left side of the problem instead of the right. What do I mean? Let's find out.

Any number bigger than 1 can be broken down into 2 or more smaller numbers. So for this problem, we can picture 362 as the combination of 300, 60 & 2. By looking at 362 as a combination of these three smaller numbers we can do the calculations in bite-sized bits.

Take the first number, 1274 and add 300 to it, then add 60 to that, then add 2 to that.

 Your calculations would go this way: 1274 1574 1634 +  300 +   60 +   2 1574 1634 1636

Here are some other problems to explore. See if you can solve them in two different ways, or maybe even more than two?

 1) 156 2) 578 3) 396 4) 274 5) 537 6) 1154 +   39 + 102 + 851 + 154 + 623 + 3296

If you'd like some help exploring, after you've done some exploring yourself, see the next page ...

 Playing with Arithmetic Index Page 1 Page 2 Page 3

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