It's even more important in multiplication when one mistake can get an answer an order of magnitude away from the real answer.
Agreed. Mentally check all calculations. Do not depend on electronics. You might make an entry error.
Yeah, I would round both of those up. 400 + 300 = 700
Yep, when you throw the numbers into a calculator and slip a digit you should have some idea when the number is wildly off.
Estimation has its places, but it seems to be given way too much emphasis.
agreed that the estimation is terrible....especially for addition. 291 is much close to 300. all they are accomplishing here is validating that the 1st digit is close; so for addition, this estimation exercise is not of much value...
I agree with you. They are attempting, in math at least, to teach a wise check on ones calculations.
IMO, 354 should also be rounded up instead of down. (I thought 50 and under round down, and 51 and up round up.)
My immediate estimate of that would be 350 plus 300, just as quick and much more accurate than 500!
Why not just teach kids to do addition so they get the right answer. Then they don’t have to worry about estimating the number, they know what it actually is.
Both numbers were incorrectly rounded down. Perhaps this means students can no longer learn, “Round down from 49 or lower; round up from 50 or higher.”
“But estimation is a valid technique for making sure that the real answer is just horribly wrong and for real life when you need to do something like estimate how much fertilizer you need (since you can’t buy 6.47839 bags, 7 is a good enough answer).”
I agree, knowing how to estimate should be taught.
You are correct. The problem here is not the concept of estimating, but the fact that they are teaching kids to estimate improperly. The proper technique is to pick the degree of accuracy and then round to the nearest zero. In this case, the most accurate estimate is achieved by rounding up or down to the nearest zero: 354+291=645 becomes 350+290=640.
Estimation is a great tool, but only viable when you’ve done enough arithmetic for the concept to dawn on you. If you haven’t figured out estimation on your own, you’re not ready to learn it.
Interesting that they always estimate down, e.g., 291 -> 200.
The next time I am charged $2.91 I’ll tell the clerk I’ll give her $2. I like this idea of estimating down.
Yes estimation is a legitimate technique. It also assumes that you know how to round correctly.
The best method is have these children learn their tables and then there is no issue.
"Front end estimation" is bad stuff that they're using. It uses the "front" number of hundreds instead of rounding off to the nearest 100.
Thus, the "front end estimate" is 300 + 200 or 500. It shouldn't be called a front end estimate, it should be called a lower bound. If you have a lower bound, you should have an upper bound which is 400 + 300 or 700.
Thus, it would be not hideous to say the solution is between 500 and 700.
This is a lousy idea in teaching. The estimate is a guess. One should only venture a guess on something about which they've experienced certainty. Thus they should learn to add correctly, and then be asked to notice things about the answers.
In my adventures in substitute teaching, I encountered some classes that were totally confused from this nonsense. I was very bad. I taught them how to add the old fashioned way with regrouping, so they knew the answer. And I had them develop their estimates after they solved the problem, using the "between" estimate.
The kids hugged me after my old fashioned math classes, no kidding.
I agree. It’s valid lesson for a 1st or 2nd grader. Estimation is a transient skill that through more education gets improved and added upon.
Here is another good technique. I called it ‘Stand Up’ math. no chairs or tables, pencils, paper, calculators. — Toss them two numbers to add or subtract, have them guess as close as possible and as fast as possible without going over, then have them calculate the real answer.
Pair off the students and run them through drills. Sit down pencil and paper math learning at the early age cripples some students down the line. Just take an informal survey and start asking your friends a random math problem like adding two 1423 + 8534, See how many “hummmms” you get as many of them have to divert their minds and enter a quasi meditative state. Give them more complex problems and watch them search for pen/pencil, paper and a flat space. They are inhibitors — they learned at an early age to sit down, be quiet and concentrate to do math.
However, if I used this method of estimation, I'd end up with 5 bags of fertilizer when I needed 7. Interestingly, if I rounded the two numbers correctly, I'd have exactly the right number of bags to buy.
I don't get this "front-end estimation." If all you do is round down to the nearest 100, then your answers might be up to 200 off. I wouldn't call that "reasonable" by any stretch, for any sum under, say, 1000. Especially when the students have obviously been taught to add. I'd take 645 as a reasonable answer, because it's right.