Working the problems to the very end ~ will this be a problem for testing

[Ann.without.an.e]

Dd is my math girl. She has never needed an ounce of help and she scores 100% on almost every Alg. 1 test. Never less than a 95%. She works the problems out all.the.way though. She doesn't use a calculator so I have told her that she can save the time and leave pie. The answers rarely match my answer book because she works them out further than they intend. I simply check it with a calculator in hand. She seems to be happy with this, but then I wonder....what about testing. Would that produce an incorrect answer?

 

Any insight or thoughts from those more brilliant or more more experience than myself is appreciated :D

[regentrude]

What test are you thinking about?

 

ACT/SAT questions are either multiple choice, in which case she will see whether they leave pi or not, or grid-ins in which case she must get a numerical answer anyway.

[In The Great White North]

Have her do the SAT Questions of the Day and she will get a feel for how far she needs to work them out.

 

I think she'll be fine - its the kids who stop too soon who have a problem.

[kiana]

What do you mean by working them all the way to the end?

 

I just had to give many college students low marks in their math quiz, because when the answer should have been 'x + 2' they proceeded to do the problem, write down the correct answer in their work, then write 'x + 2 = 0' and then 'x = -2'. That's an issue.

 

If you mean 'she insists on getting a numerical approximation', that's less of an issue. It is, however, a minor issue in multi-step problems, because there is inevitably some rounding error involved. So if the answer to part a) is 14pi, and the student finds a decimal approximation (which involves some rounding), then uses that for part b, rounds again, uses that for part c, they sometimes get some weird answer when the answer should have been '5'.

 

It is also a bit of an issue because it wastes time during tests, which can become more of an issue during timed tests. We emphasize this at college all the time -- that if the problem says that you do not need to simplify your answer, and you do, you run a risk of not having enough time to finish the exam -- and many do.

 

I would much prefer to see the answer left as '14pi' unless otherwise specified, as that is most accurate, and anyone who needs to know the decimal can figure it out to the desired degree of accuracy.

[Ann.without.an.e]

What do you mean by working them all the way to the end?

 

If you mean 'she insists on getting a numerical approximation', that's less of an issue. It is, however, a minor issue in multi-step problems, because there is inevitably some rounding error involved. So if the answer to part a) is 14pi, and the student finds a decimal approximation (which involves some rounding), then uses that for part b, rounds again, uses that for part c, they sometimes get some weird answer when the answer should have been '5'.

 

It is also a bit of an issue because it wastes time during tests, which can become more of an issue during timed tests. We emphasize this at college all the time -- that if the problem says that you do not need to simplify your answer, and you do, you run a risk of not having enough time to finish the exam -- and many do.

 

I would much prefer to see the answer left as '14pi' unless otherwise specified, as that is most accurate, and anyone who needs to know the decimal can figure it out to the desired degree of accuracy.

 

This is what she is doing. She always works out pi to the very end and she ends up with a decimal.

 

For example

(14pi -2)3

 

My key would say 36pi

She gets 125.88

 

I also wondered if rounding the decimal slightly different would mess up her final answer too?

 

So, I should make her stop at pi, regardless of how upset it makes her to leave "loose ends".

[Ann.without.an.e]

That isn't a problem and the problem really is for her that she isn't sure what type of answer they want. My son encountered this and I would just show him the key and say they want the answer with just pie. And as was mentioned, the answers are provided so she would see the answer as 36pi But honestly, no big deal. He did VERY well on his ACT!!!

 

 

That is good to know. I have no doubt that she will do great on the math portion of the SAT/ACT. She just gets it without effort and she has this crazy ability to think through math she hasn't even learned yet. Her annual tester is always a little blown away.

Now the English portions, well....we'll see ;)

[Cosmos]

For example

(14pi -2)3

 

My key would say 36pi

She gets 125.88

 

If you have typed the problem correctly, then the book's answer is incorrect. (14pi - 2)3 does not equal 36pi. Your dd's numerical evaluation of 125.88, however, is correct (using 3.14 as an approximation for pi). So I'm a little confused by that example.

 

It really comes down to what the problem asks for. Is it asking the student to "evaluate" or "simplify" or "expand" an expression? Those all mean different things, and I do consider the distinctions important. If she wants to "evaluate" after she has done what the book asks for, that's fine, but she needs to know how to simplify as well.