http://dailycaller.com/2014/02/12/another-impossibly-stupid-common-core-worksheet-sure-to-make-your-kid-a-moron/
Don't tell me that you've never estimated the answer to an addition problem before. I do it all the time. When I'm in the grocery store and I need to keep a running total of what the stuff in my cart costs, including the sales tax, I don't meticulously add the full price to my running total, and then 8.375% of the price to account for the sales tax - while trying to keep straight in my head what things are subject to tax and what not - I round, usually to either the closest whole dollar, or the half-dollar if the price is very close to that (e.g., $6.58 gets rounded to $6.50, not $7), I then take 10% of that rounded running total, knock a dollar or so off it (the amount gets bigger as the running total gets bigger), and use that figure as the tax. That is much easier to keep in my head without bogging down my trip through the store, and it usually gives me a tolerably - i.e., reasonably - good estimate of my ultimate cost.
All this exercise is trying to do is teach the kids the ins and outs of estimating, and as I can testify to from personal experience, kids have a lot of trouble with rounding and estimating when they first get introduced to it.
The funny thing is, the example you've shown doesn't even demonstrate a "close enough" attitude in the first place. Why? Because the first thing the kids are required to do is to find the actual answer: right up there at the top, on the second line, the kid has to give the exact answer to the question 354 + 291.
However, what no one seems to have picked up on is that this example - like too many examples I've seen under the old non-CC standards - contains a mistake: the second estimated number should be 300, not 200, because in
front-end estimation one rounds to the left-most digit, so that all other places contain a zero when you're done. In this case the example correctly rounds 345 down to 300 - because 345 is less than 350 - but incorrectly rounds 291 down to 200; since 291 is greater than 250, that number should have been rounded up to 300. When done correctly the example results in the front-end estimation of the sum being 600, which is reasonably close to the actual answer of 645.
Now, here's the little twist this problem puts on things, and it really only makes sense when looked at from a child's point of view. The reason the question asks if the front-end estimation makes the actual answer reasonable is because kids have a much harder time learning to do column addition with multiple digit numbers than they do with adding numbers where all digits but the most significant are zero. So, given that rounding - once mastered - is easy to do and since the kids have already been taught that this sort of rounding can give you a good estimate of the actual answer, what this example is illustrating is that you can double-check your answer to the actual problem - which is difficult, particularly for a kid who's just learning math - by doing the much easier front-end estimation and then seeing how closely your answer to the actual problem comes to that estimation.
In this case, since the (correct) front end estimate is 600, and since 645 rounds down to 600 using the same rounding method as is used for front-end estimation, we know that our actual answer is probably the correct answer because it comes reasonably close to the estimate.
This isn't about replacing an exact answer with an estimate, it's about learning all sorts of different techniques for checking yourself and your work when you're not sure what the answer really is.
And this is a very time-honored technique by the way. In fact, estimation basically forms the basis for calculus. Calculus largely springs from the realization that the area of something like a curve (i.e., the area under the curve), which isn't directly computable, can be approximated using geometric shapes for which the area is directly computable by finding which shapes take up as much room under the curve as possible, along with the realization that the smaller each shape is in the direction that is parallel to the x-axis, the more closely the sum of the areas of those shapes approximates the area under the curve. The "trick" in calculus is that this process is taken to its ultimate limit so that the x-axis length of each geometric shape approaches, but never reaches, zero.
So in a way, this very simple problem has a fundamental connection to the complicated problems of calculus. Now I don't harbor any illusions that the teacher realizes this connection, nor that the teacher is going to point the connection out to his (or her) students. All I am pointing out is that a facility with using estimates to arrive at reasonably good approximations to the actual answer is not only useful and efficient, it gives you one of the basic tools for understanding how, and why, calculus works.
