Serenade Posted November 4, 2014 Share Posted November 4, 2014 In Lesson 41, problem 17, it appears that one needs to know how to approximate square roots or use a calculator to get the final answer. Now, my understanding is that one is not to use a calculator with Saxon, at least until somewhere at the end of Saxon Algebra 2, so my son hasn't been, and so far he's been able to solve all the problems without one. However, he got stuck on this problem, and so I turned to the solutions manual. Except the solutions skips some of the last steps and went straight to the answer, not showing how those last steps were done. So then I turned to the Saxon Teacher DVD, and on that video, they solved the problem by approximating the square root. Except I don't believe that this has already been taught, which is frustrating. Causing further frustration was the fact that Saxon Teacher solved the problem using a decimal, and the Solutions manual solved the problem using a fraction. Generally, the Solutions manual seems to use fractions, I guess because often you can pull a square root out of the numerator or denominator further simplifying the problem. At any rate, I'm wondering how others are solving this sort of problem. Do you use a calculator? Did the book somewhere teach approximation of square roots and we missed it? Did you turn to another source for instructions on how to approximate a square root? I ended up going to Kahn Academy, where they had an easy-to-understand video on the topic, but it is time consuming, and a calculator would certainly be simpler. Quote Link to comment Share on other sites More sharing options...
kiana Posted November 4, 2014 Share Posted November 4, 2014 What are you trying to take the square root of? Is it irrational? I would absolutely use a calculator at the final step for approximating irrational square roots. A student should understand, for example, that the square root of 27.4 is "five and a bit", but there is no need to get more precise than that by hand. However, if there are factors that can be extracted from the square root (for example, sqrt 12 = 2 sqrt 3) I would do that first. Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 4, 2014 Author Share Posted November 4, 2014 What are you trying to take the square root of? Is it irrational? I would absolutely use a calculator at the final step for approximating irrational square roots. A student should understand, for example, that the square root of 27.4 is "five and a bit", but there is no need to get more precise than that by hand. The problem involved finding the area of a figure that included a semi circle and a triangle. The area of the triangle, solved using the Pythagorean theorem, included the square root of 55 as part of the answer, and then this area had to be added to the area of the semicircle. The Solutions Manual showed the answer to two decimal places. From what you wrote above, it sounds like in this case it would be OK to use the calculator. I do think I will also show my son the Kahn Academy video, just so he understands how the square root could be manually approximated. It just kind of bugged me that this problem was thrown into the book without an explanation, and I feel kind of badly because I gave my son a hard time for not figuring it out after several attempts. However, if there are factors that can be extracted from the square root (for example, sqrt 12 = 2 sqrt 3) I would do that first. Most of the problems (all?) have been like this in the past, where the student just had to extract a number, and it was OK to leave a final answer as 2 times the square root of 13 over 5, for example. This particular problem seemed to come out of the blue, where a decimal was given as the answer instead. Anyhow, thank you for you input . That was helpful, and I appreciate it! Quote Link to comment Share on other sites More sharing options...
Arcadia Posted November 4, 2014 Share Posted November 4, 2014 Was PI given as 3.14? If PI was given as 3.14, I'll let my kids punch the calculator for the final answer and leave the answer as 2 decimal places. Quote Link to comment Share on other sites More sharing options...
bethben Posted November 4, 2014 Share Posted November 4, 2014 In Algebra 2, I let my son use the calculator. I feel like having to do all the extra computations just slows the child up from learning higher level concepts. They should know how to compute by now. Beth Quote Link to comment Share on other sites More sharing options...
KarenNC Posted November 4, 2014 Share Posted November 4, 2014 My daughter uses a calculator for algebra 2. In fact, I have started requiring her to use the graphing calculator all the time just so she gets used to it. Here, the schools require a graphing calculator starting in pre-algebra and when she sat for a practice PSAT this year, the school provided graphing calculators for all students rather than letting them bring their own. Quote Link to comment Share on other sites More sharing options...
LinRTX Posted November 4, 2014 Share Posted November 4, 2014 I let my child use a calculator in Saxon Algebra 2. This is the first year I allow it. But I also don't make them solve the square root or multiply by 3.14 for pi. She leaves the answer with the square root sign and with pi. The other answers are approximations. Quote Link to comment Share on other sites More sharing options...
FriedClams Posted November 4, 2014 Share Posted November 4, 2014 We use calculators in alg 2. But, if I see my kids using one when a brain is sufficient, I take it away. I want her to be able to think without it. It's her first year being able to use one. Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 7, 2014 Author Share Posted November 7, 2014 Was PI given as 3.14? If PI was given as 3.14, I'll let my kids punch the calculator for the final answer and leave the answer as 2 decimal places. In Algebra 2, I let my son use the calculator. I feel like having to do all the extra computations just slows the child up from learning higher level concepts. They should know how to compute by now. Beth My daughter uses a calculator for algebra 2. In fact, I have started requiring her to use the graphing calculator all the time just so she gets used to it. Here, the schools require a graphing calculator starting in pre-algebra and when she sat for a practice PSAT this year, the school provided graphing calculators for all students rather than letting them bring their own. I let my child use a calculator in Saxon Algebra 2. This is the first year I allow it. But I also don't make them solve the square root or multiply by 3.14 for pi. She leaves the answer with the square root sign and with pi. The other answers are approximations. We use calculators in alg 2. But, if I see my kids using one when a brain is sufficient, I take it away. I want her to be able to think without it. It's her first year being able to use one. Thanks, all, for your input! I think I'll loosen up a bit on the calculator usage. Although the thought of a graphing calculator scares me... Quote Link to comment Share on other sites More sharing options...
MarkT Posted November 7, 2014 Share Posted November 7, 2014 (lots of good answers but this topic normally should be on the high school forum since Algebra 2 is typically taught in HS) Quote Link to comment Share on other sites More sharing options...
Erin Posted November 7, 2014 Share Posted November 7, 2014 Just to the calculator issue-- I had no problems letting Buck move to a calculator-based math day in Algebra 1. By the time a kid is to this level, either he knows his facts or he doesn't. And some kids never do. The processes, OTOH, are going to be the same whether on paper or via calculator (but the calculator is less likely to make those dreaded "stupid mistakes.") Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 7, 2014 Author Share Posted November 7, 2014 (lots of good answers but this topic normally should be on the high school forum since Algebra 2 is typically taught in HS) I was wondering about that... Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 7, 2014 Author Share Posted November 7, 2014 Just to the calculator issue-- I had no problems letting Buck move to a calculator-based math day in Algebra 1. By the time a kid is to this level, either he knows his facts or he doesn't. And some kids never do. The processes, OTOH, are going to be the same whether on paper or via calculator (but the calculator is less likely to make those dreaded "stupid mistakes.") See, I have this fear of the calculator, I guess mostly because I grew up without using one (yes, I'm that old), and I'm so afraid to make my son dependent on the calculator. I don't mind him using the calculator for specific problems like the one above, but I'm not yet sure about just allowing free use for the entire lesson. However, I probably need to rethink that, because he simply can't accomplish as much math when he has to work everything out himself. So my next question is, if you allow your students to use a calculator, what kind of work are they required to show on paper? Quote Link to comment Share on other sites More sharing options...
Arcadia Posted November 7, 2014 Share Posted November 7, 2014 So my next question is, if you allow your students to use a calculator, what kind of work are they required to show on paper?For the problem example you gave, I would expect something like Area = area of triangle + area of semicircle Area of triangle = 1/2bh = calculated ans. (1) Area of semicircle = 1/2pi(r^2) = calculated ans. (2) Area = calculated ans. (1) + calculated ans. (2) It's easier to spot careless errors like using the wrong height for the triangle's area or the wrong value for radius. ETA: They use the scientific calculator app for the phone/tablets and I do have a scientific calculator Casio FX-115ES. They aren't allow to use a graphing calculator for math but they play with the graphing calculator apps for entertainment. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 7, 2014 Share Posted November 7, 2014 Just to the calculator issue-- I had no problems letting Buck move to a calculator-based math day in Algebra 1. By the time a kid is to this level, either he knows his facts or he doesn't. And some kids never do. The processes, OTOH, are going to be the same whether on paper or via calculator (but the calculator is less likely to make those dreaded "stupid mistakes.") No, that is not entirely true. And it has nothing to do with "knowing the facts". The problem with allowing a calculator is that sometimes the calculator completely eliminates the learning objective of a problem. If, for example, the student has to work out some complicated logarithms, using the calculator will mean that the student misses the opportunity to learn how to manipulate the expression using laws of logarithms. Ditto for evaluating the values of trig functions: the student who uses the calculator to find, say, the sin (105 degrees) learns absolutely nothing - whereas the student who uses trig identities and his knowledge of trig function values for special angles learns a ton. With a well designed curriculum, calculator use should not be necessary through calculus. A curriculum that requires students to use calculators is poorly designed and misses learning opportunities. But writing problems that require number crunching is, of course, much easier than thoughtfully designing problems that simplify without the help of a calculator. (but the calculator is less likely to make those dreaded "stupid mistakes.") LOL. I have made the opposite observation. Students will use the calculator and take the calculator result as the absolute truth - even if it is clearly nonsensical. There are some nice example in a current thread (ps vent) on the Highschool board. Whenever I give a problem with numerical values (I do in my easy" physics course, not in the one for STEM majors), a significant portion of the answers are incorrect and students never realize that, for example, 1.8kg can not possibly be the mass of the planet Jupiter. because, after all, the calculator said it was. Quote Link to comment Share on other sites More sharing options...
Erin Posted November 7, 2014 Share Posted November 7, 2014 You're obviously using a MUCH nicer calculator than we are. ;) Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 8, 2014 Author Share Posted November 8, 2014 For the problem example you gave, I would expect something like Area = area of triangle + area of semicircle Area of triangle = 1/2bh = calculated ans. (1) Area of semicircle = 1/2pi(r^2) = calculated ans. (2) Area = calculated ans. (1) + calculated ans. (2) It's easier to spot careless errors like using the wrong height for the triangle's area or the wrong value for radius. ETA: They use the scientific calculator app for the phone/tablets and I do have a scientific calculator Casio FX-115ES. They aren't allow to use a graphing calculator for math but they play with the graphing calculator apps for entertainment. Thank you. This is helpful. Quote Link to comment Share on other sites More sharing options...
Serenade Posted November 8, 2014 Author Share Posted November 8, 2014 No, that is not entirely true. And it has nothing to do with "knowing the facts". The problem with allowing a calculator is that sometimes the calculator completely eliminates the learning objective of a problem. If, for example, the student has to work out some complicated logarithms, using the calculator will mean that the student misses the opportunity to learn how to manipulate the expression using laws of logarithms. Ditto for evaluating the values of trig functions: the student who uses the calculator to find, say, the sin (105 degrees) learns absolutely nothing - whereas the student who uses trig identities and his knowledge of trig function values for special angles learns a ton. With a well designed curriculum, calculator use should not be necessary through calculus. A curriculum that requires students to use calculators is poorly designed and misses learning opportunities. But writing problems that require number crunching is, of course, much easier than thoughtfully designing problems that simplify without the help of a calculator. LOL. I have made the opposite observation. Students will use the calculator and take the calculator result as the absolute truth - even if it is clearly nonsensical. There are some nice example in a current thread (ps vent) on the Highschool board. Whenever I give a problem with numerical values (I do in my easy" physics course, not in the one for STEM majors), a significant portion of the answers are incorrect and students never realize that, for example, 1.8kg can not possibly be the mass of the planet Jupiter. because, after all, the calculator said it was. Thanks for your input, Regentrude. I *think* Saxon is mostly designed to be used without a calculator, but today my son had some problems where the book specifically requested that students use the calculator. I asked him to only use the calculator for those specific problems, though. The above-mentioned square root problem was an exception to the norm -- most of the problems can be worked out and simplified by extracting or otherwise reducing, but for some reason this problem was worked out in decimals. Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 8, 2014 Share Posted November 8, 2014 I vaguely recall somewhere along the way we learned how to estimate square roots. It wasn't in Saxon though. I would have allowed a calculator for that problem and then maybe spend a bit of time showing how it could be done without a calculator. Once in a blue moon DS asks to use the calculator for a really gnarly problem and I usually say yes. For the most part he doesn't use one though. I remember encountering something like this in Saxon algebra 1 and thinking wait a minute I don't recall them going over how to solve these kinds of square roots. So I looked up how those things are done and then I though oh ok..now I know why. LOL It's a pain in the neck. I'd challenge my kid to come up with a good guestimate. I bet he/she could do it if he understands square roots. Quote Link to comment Share on other sites More sharing options...
MarkT Posted November 8, 2014 Share Posted November 8, 2014 For the problem example you gave, I would expect something like Area = area of triangle + area of semicircle Area of triangle = 1/2bh = calculated ans. (1) Area of semicircle = 1/2pi(r^2) = calculated ans. (2) Area = calculated ans. (1) + calculated ans. (2) It's easier to spot careless errors like using the wrong height for the triangle's area or the wrong value for radius. I agree it is Algebra 2 - let them use a calculator but show all the thought process steps to the solution including any diagrams (especially for word problems). If the answer should be expressed in terms of Pi, then maybe the problem should ask for that. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 9, 2014 Share Posted November 9, 2014 If the answer should be expressed in terms of Pi, then maybe the problem should ask for that. I think leaving an accurate answer in terms of pi should be the default. If the answer should be approximated as a decimal, the problem should ask for that. :001_smile: Quote Link to comment Share on other sites More sharing options...
kiana Posted November 10, 2014 Share Posted November 10, 2014 LOL. I have made the opposite observation. Students will use the calculator and take the calculator result as the absolute truth - even if it is clearly nonsensical. There are some nice example in a current thread (ps vent) on the Highschool board. Whenever I give a problem with numerical values (I do in my easy" physics course, not in the one for STEM majors), a significant portion of the answers are incorrect and students never realize that, for example, 1.8kg can not possibly be the mass of the planet Jupiter. because, after all, the calculator said it was. I see the same issue. Quote Link to comment Share on other sites More sharing options...
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