Posted on 02/13/2014 8:05:41 AM PST by rktman
Significant figures. There is no decimal point in either number so have to assume that both were measured to 3 significant figures. A “ball park” estimate is not the same thing.
They are confusing apples and oranges.
I rounded both numbers up to the nearest thousand and got 2,000. Just as valid in this instance.
I just got a twinge from a semiconductor physics class where the professor gave us a "simple" problem (only about five pages of calculations) which resulted in an electron going twice the speed of light. Each of the students independently was asking the professor bizarre questions about how relativity works in a semiconductor lattice or what effects the increase in mass of an electron because of its speed would have without ever admitting the problem - the professor broke the primary law of the universe. The next class the professor said "I don't know why you thought this problem was hard," cranked out two blackboards of math and came up with twice the speed of light. Oops. He admitted to just changing a couple of input numbers from the problem he gave the class a couple of years before without solving it himself.
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.
LOL! Reasonable answer.
“Reasonable”? Not accurate?
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.
1. Many real life problems don't require exact answers.
2. Most people (even students now, unfortunately) will use calculators for the exact answer. Estimates are good to check for fat fingering the inputs so you know the answer is way off and needs to be redone.
3. Long multiplication and division require many steps where it is very easy to screw up and put the numbers in the wrong columns. Estimation gives you a quick check to make sure you haven't really screwed up.
4. In long division to get each individual digit of the quotient you make an estimate of the current division. For example 63496/874 will be estimated to be 70 (63000 / 900), which will give 7 as the first digit of the quotient.
I think estimation comes naturally over time.
I suck at math but I’ve found my own means of estimating to close and measuring to accurate.
I had a job where I had to cut a hole in the center of truck lids for a key/latch assembly. Rather than measuring the whole distance and calculating the center, I measured to a round number near center and then measured the same distance from the other side and gave myself a nice short 2 to 4 inches distance to measure the center accurately. The boss shook his head at it but couldn’t complain because I was finding center.
Maybe that’s what happened to poor Loretta Fuddy’s plane.
Close enough is good enough for government work. And since all the products of Common Core will be working for the government, why give them more than enough?
Please check the problem in the main article once again. The problem was correctly solved at the top. Then as a check on the answer simple 100’s and tens were used. I was trained in this method 60 years ago. Scientists use it, engineers use such a check, businessmen use it. IT IS A METHOD USED TO CHECK ONES INITIAL COMPUTATION. IT IS NOT THE COMPUTATION ITSELF. IT IS NOT INTENDED TO REPLACE TRUE AND ACCURATE COMPUTATION BUT TO CHECK.
I would be interested in seeing more of this work book. Are they teaching truncation as the only method, or is this the first day and then the next day they will show that rounding is more accurate than truncating?
Some of my complaints with some of the newer math techniques are that they get stuck on more explanatory but less efficient methods (like lattice multiplication, if I have the term right) rather than just using that as a stepping stone to the best methods.
I have a BS degree in Business Administration and a MBA.
My senior year in college, my landlord and also an accounting professor gave me some great advice re checking accts.
His advice was to forget about the pennies. If the cents were under 33 cents on a check, round down to the nearest $. If over 33 cents round up to the nearest $.
We have used that advice for over 50+ years with our personal checking accts., and we have never had a problem.
A friend, with a Masters in Accting and years as a CFO for big and small companies uses that rounding system with his non profits. He never has a problem.
I have used the rounding up or down in most aspects of my life with no problems. I have never run out of gasoline on a trip or just driving around town. I know when/where to stop to eat on a long road trip.
Many fly fishers with the one or two handed rods carry and/or use a small electronic scale to weigh their lines, leaders and even flies. I use a simple SWAG system, and it works. I know with a couple of practice casts if the fly line and terminal system is too light, too long, too short, too heavy or too light or just right.
However, the rounding up or down could be a disaster if one is in medicine, heavy duty construction, flying an airplane, payroll accounting, and other services where accurate math is a must.
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.
Excellent point.
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.
I was gonna say......if they just teach them basic arithmetic they don’t have to estimate. lol
I observed an entire family in a restaurant trying to puzzle through just such a worksheet with their child. There was a grandmother, grandfather, mother, and a 9 year old boy. The book they were using was called “California Math”, which was offensive right there.
I couldn’t see what they were doing, but the grandfather worked on the problem for about an hour, muttering things like, “What is this estimate thing?” and “You cannot round up 229 to 300. That’s just not right!”
Sheer abuse by the educators.
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