# AoPS -- Calculator Use

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I'm rather curious, how does the AoPS series address the use of calculators? Specifically in Algebra, Pre Calc and Calculus.

You can't search through their text books and I haven't seen anything about calculators at all in their excerpts though I could be over looking the mention...

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I haven't seen anything in Intro to Algebra or Intermediate Algebra except for a couple mentions on tedious arithmetic problems that the calculator can be used (like 2^(200), that sort of thing).

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No calculator use in AoPS Intro to Algebra, Intro to Geometry and Intermediate Algebra (we are through ch. 11). The series is about problem solving, not about cranking out numbers.

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I haven't seen anything in Intro to Algebra or Intermediate Algebra except for a couple mentions on tedious arithmetic problems that the calculator can be used (like 2^(200), that sort of thing).

A calculator isn't going to help you on 2^200 -- it's going to give you a rough approximation, but not (for instance) the last digit.

Most often, in AoPS, if there's something ridiculous to work out, there's another way to do it. So 2^200 might be in a fraction that can be simplified, or the question might be what the last digit is (and not the whole number). DS did Counting & Probability and Number Theory mostly without a calculator, although once he had simplified a C&P problem sometimes I'd let him use the calculator at that point.

My rule is always (always!) to set up and simplify the problem before deciding whether a calculator is needed. More often than not you can do it by hand once you know what you're doing.

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A calculator isn't going to help you on 2^200 -- it's going to give you a rough approximation, but not (for instance) the last digit.

Most often, in AoPS, if there's something ridiculous to work out, there's another way to do it. So 2^200 might be in a fraction that can be simplified, or the question might be what the last digit is (and not the whole number). DS did Counting & Probability and Number Theory mostly without a calculator, although once he had simplified a C&P problem sometimes I'd let him use the calculator at that point.

My rule is always (always!) to set up and simplify the problem before deciding whether a calculator is needed. More often than not you can do it by hand once you know what you're doing.

That wasn't the exact example, just saying I have seen it a couple of times in the Intermediate Algebra. I think one time was graphing and asymptotes and an approximation was what was wanted.

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That wasn't the exact example, just saying I have seen it a couple of times in the Intermediate Algebra. I think one time was graphing and asymptotes and an approximation was what was wanted.

My point, though, is that most of the time when AoPS is asking for something you think you can't do by hand, what they really want is something else that you can.... and grabbing the calculator isn't going to do it.

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just saying I have seen it a couple of times in the Intermediate Algebra. I think one time was graphing and asymptotes and an approximation was what was wanted.

One extremely useful skill that few students possess nowadays is the ability to sketch the basic behavior of a function without a calculator. This can often be done by thinking about the asymptotic behavior for very small and very large values, comparing the behavior of different terms, knowing how many roots can be expected; often one can draw conclusions about the existence of local extrema solely from this, without even resorting to calculus.

This kind of analysis familiarizes a person with functions to a much higher degree than simply putting it into a graphing calculator. I am appalled to see how few of my students can sketch the trig functions, exponentials, logarithms or even something as simple as 1/x. Forget functions like 1/x^6- 1/x^12. If I discuss this in class, they stare at me blankly and seem to have never encountered these techniques.

So, when problems like this are posed, I would encourage the student to first think about the expected behavior by investigating asymptotic values and trying to draw conclusions about the shape in between. The calculator is good for verifying the prediction, but it does not constitute a substitute.

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Just as an aside, I'm always shocked at how expensive graph paper seems to be these days. I guess they are only selling it as an esoteric niche item anymore.

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I got the little notebooks of graph paper (like the old black composition books) for around a dollar at Staples back to school sales. We use graph paper for all the math.

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Just as an aside, I'm always shocked at how expensive graph paper seems to be these days. I guess they are only selling it as an esoteric niche item anymore.

At back to school sales in August, graph paper filler packages are reasonable. I think I paid \$1 or so for an 80 sheet package. Staples sometimes has good back-to-school offers too.

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Graph paper is used for all math work here - even for scrap paper work. What I've liked about Saxon is that they do teach how to graph, but in the 2nd edition, they also teach how to use the graphing calculator. Personally, I think it's good to know both ways and very handy when it comes to standardized tests.

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We bought the graph composition book from Staples too during back to school sale.

I also make an Excel graph sheet so that I can print out one when I don't have a graph paper on hand.

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Did someone say graph paper? I use this all the time - http://incompetech.com/graphpaper/plain/

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Did someone say graph paper? I use this all the time - http://incompetech.com/graphpaper/plain/

But isn't it a LOT more expensive to print your own compared to buying a pack?

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But isn't it a LOT more expensive to print your own compared to buying a pack?

Well, probably depends on your printer and how much graph paper is in your area -I've got a laser printer that makes printing VERY cheap for me, I can print for about 3 cents a page, graph paper is generally about 5 cents a page in my area.

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