What is subtraction anyway? Difference or...?

We will be starting our investigations in the area of number sense tomorrow, and our unit starts with a look at subtraction. You know, where you find the difference between two numbers.

What if I changed that to read "find the distance between two numbers"? Does that sound any easier?

Here's my point: If I ask a kid to subtract 95 from 100, I hate to see the kids that are driven by traditional thinking as they line up their numbers in columns and subtract to find the distance. Wouldn't it be easier to just think about how far it is from 95 to 100? You can use an open number line if you wish as well, for all of you visual learners out there. Hopefully, you'll just think about the distance and know that the distance is five.

Many teachers that I talk to say "That's great for easy small numbers, but I don't want my kids to rely on that for bigger numbers!" I think that you might want to rethink that stance if you've taken it already.

Using an open number line or "counting up" works well with any numbers, and it prepares kids to make estimates far better than traditional thinking. We all know that "in the real world" folks will use calculators to deal with big numbers anyway. So why not build some audacious number sense now.

$1,000,000 - $257, 665 can be solved as follows:

257,665 +35 = 257,700 +300 =258,000 +2,000 = 260,000 +40,000 = 300,000 +700,000=

Bingo 1,000,000

So, if I add the numbers in bold that I "added on" I get a sum of $742,335 which is the distance between the two numbers. The beauty is that I did it in my head for the most part:-} Another beautiful thing is that there are an infinite number of ways to "add on". Kids choose the number combinations that they like. I would, of course, make sure to lead them into using landmark numbers (usually numbers that end in 0, 00, 000...) as targets to add up to.

Peace, and try it...

T-Cubed P.S. Do you know the man in the picture?

Subtraction by Addition?

Ask somebody to think of subtraction as the distance between two numbers. Then ask them to find the distance between 464 and 782 by adding up (you may want guide them into using landmark numbers...usually numbers that end in 0 or 00 or 000...). 782 - 464 becomes: 464 + 6= 470 470 + 30 = 500 500 + 282 = 782 In summation, we found the distance to be 6 + 30 + 282. Adding from left to right gives place value sums of 200 (2 is the only hundreds place value digit)+ 110 (the sum of 30 +80) + 8 (6 + 2) or 318. This may look complicated, but all can be done as simple mental math, and the concept works well with all number combinations.

Please remember that you can start thinking this way using really small numbers to help understand. We all know that 10-4 = 6, but if you think about the distance between 4 and 10, it becomes easy to see how we can add-on to 4 until we get to 10 (4 + 6 =10)

Peace,

T-Cubed