That's why I mentioned math illiteracy. Common core has the kiddies going through umpteen unnecessary steps to solve simple math problems. It's the* how * that is the problem.

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With all due respect,

I use all sorts of similar "tricks" when I'm trying to explain a new math concept to my daughter and I can see she's struggling with the "normal" or "usual" way of doing things.

The fact of the matter is, adding 10 to a number is very easy - it's in the nature of a base-10 number system, and it's a lot easier for a kid to pick up that part. It's also pretty easy to get 7 from 10 - you just subtract 3 - so, one way to count by 7s is to add 10, and then subtract 3. Those two operations are each a lot easier to do than say, adding 7 to 46, when you're new to math.

In point of fact, I do something similar for multiplication - always have and always will. For example, when I go to the grocery store I frequently see a price of $1.99 for a certain item. If I'm trying to juggle a budget for some reason and I need to know how much 17 of these items is going to cost, I can either multiply 1.99 by 17, or I can multiply $2 by 17 and then subtract 17 cents. Which do

you suppose is easier?

There's another alternative they've introduced in the schools since I was in elementary school to help kids figure out how to do two-digit multiplication: it's called chunking, or grouping (I've heard both). Basically, you break each number down into its 10s component and its 1s component, put them on the sides of a 2x2 grid, do the multiplication for each grid box, then add the rows up first, and finally add the sums of each row together to get your final answer.

So, if one has to multiply 21 by 45, you would decompose (yes, that word applies to this situation - for example when it comes up in modern algebra, a college level math course) those numbers into the sums 20 + 1 and 40 + 5. You would then arrange them around a 2x2 grid like so:

20 1

---------------

40 | | |

---------------

5 | | |

----------------

You would then multiply each grid, add up the rows, and finally add the sums of each row, like so:

20 1

---------------

40 | 800 | 40 | = 840

---------------

5 | 100 | 5 | = 105

---------------- ------

945

(btw, that is, in fact, the correct answer).

What makes this a lot easier to do is that in each case you are basically just multiplying two single digit numbers together and then adding the correct number of zeroes to the right-hand side of the product. For example, 40 x 20 is basically just 4 x 2, with two 0s tacked onto the back. Kids can get this much more readily than, say, traditional long multiplication in columns. Using this method in conjunction with demonstrating long multiplication to the kids helps them to "get it" much more readily than if they were just being drilled on multiplication by columns alone.

Another, more subtle, thing to point out is that this is, in fact, helping to get them more comfortable with concepts they will soon enough see when they get to algebra. Why? Because that grid method is analytically equal to finding the product of (20 + 1) x (40 + 5), which is a specific instance of the more general algabraic equation (a + b) x (c + d). It's even a good way to visualize the narrower algebraic equation of (a + b)^2 = c, which is equal to (a + b) x (a + b) = c, which in turn is equal to the quadratic equation a^2 + 2ab + b^2 = c.

Another technique my daughter's teacher showed her, which actually irked me until I finally realized what was going on, was approaching long division - with answers expressed in terms of a quotient and a remainder - by having the kids subtract out "chunks" of numbers - determined by picking some simple number, such as 20, 30, or 50, and multiplying it by the divisor, to have them get as close as possible to the dividend to the point where they cannot subtract any more multiples of the divisor. Does my description make a lot of sense? Probably not, which is why I was puzzled at first, too. Here's an illustration that should make it clearer:

Suppose you want to divide 195 by 7. To do it by chunks, you could do the following: first, try multiplying 7 by 20; that is 140, which is less than 195, so we know our eventual answer will be bigger than 20. To get closer to that answer we then subtract 140 from 195 and keep track of that 20. We now have 55 left, which is bigger than 7 so we know we can subtract more multiples of 7. This time we try 10; but 7 times 10 is 70, which is bigger than 55, so we know that 10 is too big; however, we also know that we're getting close and that the next number we have to pick will be a single-digit number. And that's good because kids find single-digit multiplication a lot easier to deal with. So, since 10 doesn't work, we try 9 - too big - 8 - too big - and 7, not too big, so we go with 7. 7 times 7 is 49. 55 minus 49 is 6. And now we know that we've gone as far as we can because 6 is less than 7. So, we add up the multiples we subtracted out - 20 plus 7 - and we get the result of 27. So now we know that the answer to 195 divided by 7 is 27, remainder 6. And that is the correct answer.

Here's something else that doing long division that way helps to reinforce - the relationship between multiplication and division, and the fact that they are inverse operations; that is, what multiplication does, division undoes. That's a pretty big concept for elementary school kids to start chewing on.

And the best thing? By showing kids a number of different ways to analyse - and thus solve - a given problem, one makes it more likely that more of the kdis will actually "get it" because kids learn in different ways and each has his or her own set of strengths and weaknesses, so each kid will find one way easier to grasp than another.

Are there some really dumb things in the new curricula that are being invented to meet the new standards? Yup, and when I find 'em I write a note to the teacher on the homework pointing that out (typically it'll be an ambiguity in the way the question is asked that leads to two different answers).

So, whether or no there are serious flaws with common core, this is not one of them.