TravelingChris Posted June 22, 2009 Share Posted June 22, 2009 I don't understand what her problem is. She is saying she doens't understand it and doesn't want to use it unless she does. I tried to read the wikipedia answer to her and she got very angry. She is a perfectionist. Please give me a good web site to explain this. Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted June 22, 2009 Share Posted June 22, 2009 http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html http://mathforum.org/library/drmath/view/52589.html I simply googled archimedes deriving pi. Pages of references came up. Quote Link to comment Share on other sites More sharing options...
WishboneDawn Posted June 22, 2009 Share Posted June 22, 2009 (edited) I know just how your daughter feels. I never used to be able to remember a concept and put it to use if I couldn't understand why it was so. It may help to express Pi as a fraction while you explain it. In fraction form its 22/7 and that represents circumference/diameter on any circle. Any circle at all! So it's a ratio. If the diameter is 7 inches the distance around that circle will be 22 inches. If the diameter was one the circumference would be, ta da, 3.14. Why not spend a lesson testing this? Use some string to get a rough idea of the circumference of various circles then measure the diameters and see if they do indeed demonstrate a ratio of 22:7. I'd also scour the internet for lesson plans, activities, poems, and crafts related to Pi and spend awhile with it. She needs to get it right down to her toes so make it as familiar to her as you can. I'd even make a running joke about it and anytime you ate out or went shopping for deserts I'd be talking about cherry 3.14s or apple 22/7s. Here are a bunch of activities for Pi day that you could use. Personally, understanding Pi in fraction form made all the difference for me. 3.14 is a number, irrational but still a number while 22/7 (okay I know that's a number too but you know what I mean) contains more hints about the origins and how c and d relate to each other. Edited June 22, 2009 by WishboneDawn Quote Link to comment Share on other sites More sharing options...
Highereducation Posted June 22, 2009 Share Posted June 22, 2009 I know just how your daughter feels. I never used to be able to remember a concept and put it to use if I couldn't understand why it was so. It may help to express Pi as a fraction while you explain it. In fraction form its 22/7 and that represents circumference/diameter on any circle. Any circle at all! So it's a ratio. If the diameter is 7 inches the distance around that circle will be 22 inches. If the diameter was one the circumference would be, ta da, 3.14. Why not spend a lesson testing this? Use some string to get a rough idea of the circumference of various circles then measure the diameters and see if they do indeed demonstrate a ratio of 22:7. I'd also scour the internet for lesson plans, activities, poems, and crafts related to Pi and spend awhile with it. She needs to get it right down to her toes so make it as familiar to her as you can. I'd even make a running joke about it and anytime you ate out or went shopping for deserts I'd be talking about cherry 3.14s or apple 22/7s. Here are a bunch of activities for Pi day that you could use. Personally, understanding Pi in fraction form made all the difference for me. 3.14 is a number, irrational but still a number while 22/7 (okay I know that's a number too but you know what I mean) contains more hints about the origins and how c and d relate to each other. Dawn, Thank you for this! I'm not at the point I need to teach this yet, but I'm going to keep a copy of your post for when I do need it - I can see already that it will make perfect sense to dd! Kris Quote Link to comment Share on other sites More sharing options...
WishboneDawn Posted June 22, 2009 Share Posted June 22, 2009 Dawn, Thank you for this! I'm not at the point I need to teach this yet, but I'm going to keep a copy of your post for when I do need it - I can see already that it will make perfect sense to dd! Kris You're welcome. :) I didn't get any of this in school myself - no one was willing to humour a kid who needed to understand everything completely so I spent a lot of time failing math. Quote Link to comment Share on other sites More sharing options...
Dana Posted June 22, 2009 Share Posted June 22, 2009 It may help to express Pi as a fraction while you explain it. In fraction form its 22/7 and that represents circumference/diameter on any circle. Any circle at all! So it's a ratio. .... Personally, understanding Pi in fraction form made all the difference for me. 3.14 is a number, irrational but still a number while 22/7 (okay I know that's a number too but you know what I mean) contains more hints about the origins and how c and d relate to each other. Just a warning... Pi is generally the first irrational number a student encounters. Pi is the ratio of a circle's circumference to diameter and the idea of measuring a bunch of different circles with string and doing the division is great. This concept is actually discussed in the first few pages of Contact by Carl Sagan, so that could be fun to look at too (from the point of a girl learning about pi for the first time). I had some real confusion because I was told pi was 22/7 and I thought that was the exact value of pi instead of another approximation (like 3.14 is an approximation). This misunderstanding caused trouble for me for a while when talking about irrational numbers (real numbers that cannot be written as a ratio of two integers... like pi... decimal representation goes on forever and never repeats and never ends). Be careful not to make the connection that pi is 22/7 or 3.14. These numbers are simply approximations that get us generally "close enough" for computation, but neither is pi. Quote Link to comment Share on other sites More sharing options...
chai Posted June 22, 2009 Share Posted June 22, 2009 ... I had some real confusion because I was told pi was 22/7 and I thought that was the exact value of pi instead of another approximation (like 3.14 is an approximation). This misunderstanding caused trouble for me for a while when talking about irrational numbers (real numbers that cannot be written as a ratio of two integers... like pi... decimal representation goes on forever and never repeats and never ends). Be careful not to make the connection that pi is 22/7 or 3.14. These numbers are simply approximations that get us generally "close enough" for computation, but neither is pi. This drove my dd crazy too. She also is a perfectionist. Irrational numbers are messy and imperfect. (Or perhaps they are too perfect?) Quote Link to comment Share on other sites More sharing options...
WishboneDawn Posted June 23, 2009 Share Posted June 23, 2009 Just a warning...Pi is generally the first irrational number a student encounters. Pi is the ratio of a circle's circumference to diameter and the idea of measuring a bunch of different circles with string and doing the division is great. This concept is actually discussed in the first few pages of Contact by Carl Sagan, so that could be fun to look at too (from the point of a girl learning about pi for the first time). I had some real confusion because I was told pi was 22/7 and I thought that was the exact value of pi instead of another approximation (like 3.14 is an approximation). This misunderstanding caused trouble for me for a while when talking about irrational numbers (real numbers that cannot be written as a ratio of two integers... like pi... decimal representation goes on forever and never repeats and never ends). Be careful not to make the connection that pi is 22/7 or 3.14. These numbers are simply approximations that get us generally "close enough" for computation, but neither is pi. True enough. To drive that home something that might also be helpful is some information and reading on the history of pi and an article or two on current efforts to find the next digit in the sequence. I probably was less concerned with your point because personally, the problem was always how they got pi, not that it was irrational. The idea of it being an approximation I never had trouble with so I sort of sailed over that in my post. Thanks for pointing that out! Quote Link to comment Share on other sites More sharing options...
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