tag:blogger.com,1999:blog-5303307482158922565.comments2015-08-24T20:14:09.863-07:00Math Mama Writes...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger2063125tag:blogger.com,1999:blog-5303307482158922565.post-31492773421540158582015-08-24T18:58:51.968-07:002015-08-24T18:58:51.968-07:00I value the whole discussion. I wish there was mor...I value the whole discussion. I wish there was more discussion of the modeling so that it didn't seem like our expert's numbers vs your expert's. Discussing the models would lend a lot more weight to the issue, plus raise the value of this kind of thinking.<br /><br />Here's the GeoGebra, if anyone wants to play: http://tube.geogebra.org/m/1509389<br /><br />Walt's reasoning looks solid to me.John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63460466309385238722015-08-23T16:34:48.682-07:002015-08-23T16:34:48.682-07:00Thank you for catching my error. That's two po...Thank you for catching my error. That's two posts in a row with silly errors. (Perhaps an indicator of my stress level, single parenting a 13-year-old.) <br /><br />Your answer is very close to John Golden's. I had thought the difference was because he integrated to look at continuous increase, but it's probably too big a difference for that to have made sense.<br /><br />I will work through the problem again myself. It's good I was vague when I posted on the blog where this was mentioned. 9% is still more than 3 times what the true increase is. So yeah, probably there probably very non-linear things happening. Unless that article included a typo.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-13171398985309347832015-08-23T12:20:33.504-07:002015-08-23T12:20:33.504-07:00Sue, you did drop the 'H' from your second...Sue, you did drop the 'H' from your second sum 'S' - you can't subtract the 16.6 and the 6.6 because they are in different "units".<br /><br />The proper equation is (sum if we reduce now) = (sum if we reduce after 5 years) + (sum of emissions over the next 5 years). Using N for current emissions rate and H for emissions in 5 years, this is <br />(N * 16.58) = (N * r^5 * 6.66) + (N * (r^5-1)/(r-1))<br />Solving this numerically for r I get a value of about 1.096, or an assumed 9.6% per year increase.<br /><br />Notes: I used 16.58 instead of 16.66 because (.94)^85 is still about ~.005, so it is more accurate. I used five years of increase instead of the six in your equation, thus H = N * r^5 and the 5-year sum is N * (r^5-1)/(r-1).<br /><br />While solving numerically by hand (Newton-Raphson) I noticed that the second derivative was large, so the exact solution may be very sensitive to the inputs - i.e. if the 15% was rounded from 14.5, or the 6% was really 6.2% you might get a full percent or more difference in the answer.<br /><br />I also note that the final term in each sum is the assumed emissions in the year 2100. The fact that they are so small brings the feasibility of a continuous decrease into question. For 6% reduction, the final term is about 1/200 of current emissions, whereas for 15% reduction it is barely more than a factor of 500,000 below 2020 emissions (which are 58% higher than current using 9.6% growth). These levels would represent a wholesale shift away from carbon emitting, rather than settling at a new, reduced, stable level.<br /><br />I suspect that the 6% and 15% numbers come not from a calculation of total carbon emitted into the air, but the results of a more complex model that represents how the atmosphere responds to total airborne carbon, and that such a model would be very non-linear - therefore the increase in needed reduction may not correspond to achieving a fixed value of the integral at all.Walthttp://www.blogger.com/profile/05235362518037728416noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-30002198474520789662015-08-22T10:52:10.306-07:002015-08-22T10:52:10.306-07:00They are row equivalent, but they are not the same...They are row equivalent, but they are not the same. I mistakenly thought they were in reduced echelon form. Silly me.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-4240654867991319912015-08-22T10:39:42.197-07:002015-08-22T10:39:42.197-07:00Oh! So, in an augmented matrix (last column repres...Oh! So, in an augmented matrix (last column represents the constant on the right side of the =), I still need to finish up, and I'll get 0 1 on the last column of both of these. Duh. (Since we always stop as soon as we know a system is inconsistent, I hadn't thought about including the last column in my process.)<br /><br />I was going to post in math stack exchange. Thank goodness I didn't. Feeling silly...<br /><br />So now my question becomes whether we can consider the three cases (one, many, or no solutions), and build a simpler proof than Lay's. I'll keep thinking about that.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-43972713028721644252015-08-22T10:30:12.054-07:002015-08-22T10:30:12.054-07:00Are those matrices not row equivalent to each othe...Are those matrices not row equivalent to each other? You can multiply the second row by any arbitrary value (so 0, 0, -3 can be changed into 0, 0, 2.5) and you can then add that to the first row to change the 3rd column value to any arbitrary value.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-7773583358412999312015-08-22T10:19:00.284-07:002015-08-22T10:19:00.284-07:00You've got that right, John.You've got that right, John. Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-65371347590869812662015-08-22T10:16:04.432-07:002015-08-22T10:16:04.432-07:00I think echelon implies leading ones and zeroes ab...I think echelon implies leading ones and zeroes above leading 1s, but I don't have Lay handy. John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-92155566005943361702015-08-08T08:51:19.183-07:002015-08-08T08:51:19.183-07:00Six wonderful reviews up now. Whenever I want a bo...Six wonderful reviews up now. Whenever I want a boost, I can go to those reviews to make me happy. We are always eager for more reviews...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-82355087501493532112015-08-01T18:31:15.031-07:002015-08-01T18:31:15.031-07:00I don't feel like I'm teaching him much. J...I don't feel like I'm teaching him much. Just supporting him as he works through the curricula I've chosen for him. He has not made as much progress as I had hoped this summer. He will definitely be behind in math. I still think he's good at mathematical reasoning. But he will be faced with knowing much less than his classmates (in just a few weeks). <br /><br />Once school starts, I hope he'll ask me questions about anything in math class that confuses him. But he may not. I'll definitely blog about anything interesting that comes up.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-72405674349177333652015-07-30T02:13:28.569-07:002015-07-30T02:13:28.569-07:00Really looking forward to hearing more about your ...Really looking forward to hearing more about your journey with maths and your son. It is a curious process as a teacher, teaching your own kids, isn't it?Unknownhttp://www.blogger.com/profile/16614718846168142640noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-9673317913789690182015-07-21T17:56:44.556-07:002015-07-21T17:56:44.556-07:00I'll edit the post to show a diagram...I'll edit the post to show a diagram...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-11209982290342141192015-07-21T15:02:07.518-07:002015-07-21T15:02:07.518-07:00I don't get the 13. Help!I don't get the 13. Help!MariaDhttp://www.blogger.com/profile/00769513929584082597noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-6063817949548939042015-07-16T12:37:00.285-07:002015-07-16T12:37:00.285-07:00I love what you got from that photo!I love what you got from that photo!Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-9094819604649007752015-07-16T12:35:12.195-07:002015-07-16T12:35:12.195-07:00Well, he still claims to hate math, but I think he...Well, he still claims to hate math, but I think he is seeing that it's not beyond him. We are now working from Key to Fractions. (The Key to series is pretty straightforward, and I use it with adult students who are having trouble thinking about fractions.) I also bought Art of Problem Solving's Pre-Algebra book, so he could see some math at "his level". He hasn't done anything from that yet, but it's available to glance at.<br /><br />"Making him" do schoolwork has been very stressful. He fights it (even though he does want me to make him do it). We're doing ok this week...<br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-69224838954576019882015-07-16T09:12:39.207-07:002015-07-16T09:12:39.207-07:00FWIW, I see that top picture as a 7x8 grid with a ...FWIW, I see that top picture as a 7x8 grid with a 6x7 grid inside, so 7x8+6x7 = 7x(6+8) = 7^2 *2 = 98<br /><br />It reminds me of a 13 configuration I really like: 2x2 array inside a 3x3 array. I am not sure why I like it so much, but I somehow feel it shows me a feature of 13 that I hadn't otherwise seen to be part of the number's "personality."Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-46995695152773629602015-07-16T09:08:10.424-07:002015-07-16T09:08:10.424-07:00As a kid, I remember the constant feeling of being...As a kid, I remember the constant feeling of being behind. The fact of modern life is that, in any particular area or skill, there is almost certainly going to be someone somewhere who is ahead in that facet. Looking back, I can now see how much one can accomplish with a moderate, but consistent effort applied over time (including time spent practicing the skills). I hope your son is able to appreciate this and will have an opportunity to impress himself about how far he can get.<br /><br />Also, I hope he can savor the things he is learning through the process and not just the end result.<br /><br /><br />Good luck! Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-50275722837831525082015-07-13T08:36:15.889-07:002015-07-13T08:36:15.889-07:00One other direction of line vs circle is the compa...One other direction of line vs circle is the comparison between compass+straight edge constructions and origami. I'm not an expert, so take the following with a little caution:<br /><br />To a modern way of thinking, origami is more powerful because the set of constructible points is larger. Not larger cardinality, since both are still countable but larger because all C+SE constructible points are origami constructible, but not vice versa. For example, generic angle trisection is possible with origami, but not C+SE.<br /><br />On the other hand, origami can't construct a circle. If you consider geometric shapes to be the fundamental objects of study (like the ancient Greek mathematicians seemed to) then origami is less powerful.Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-52483552542383887752015-07-13T07:26:18.962-07:002015-07-13T07:26:18.962-07:00Thank you, Joshua! This is why I blog - I love con...Thank you, Joshua! This is why I blog - I love connecting people with good ideas. Your post makes me realize that this has a different sort of solution than the puzzle it reminds me of. You might like that one too. It's #7 in this <a href="http://mathmamawrites.blogspot.com/2013/03/pi-day-puzzle-party-join-in-bit-late.html" rel="nofollow">Pi Day Puzzle Party</a> post.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-88267943941976292412015-07-13T07:18:55.742-07:002015-07-13T07:18:55.742-07:00Jason, I never did write any of these up. Which on...Jason, I never did write any of these up. Which one would you like me to write up?Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-32313383559742755142015-07-13T07:03:41.372-07:002015-07-13T07:03:41.372-07:00The coin flipping puzzle was great. Listening to m...The coin flipping puzzle was great. Listening to my kids discuss it gave me the idea to identify possible states, the different moves, and the potential outcomes of applying each move to each state.<br /><br />Also, try the puzzle with only 3 coins!<br /><br />Here are some other <a href="http://goo.gl/3nepvW" rel="nofollow">ideas for extensions.</a><br /><br />Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-6995315150573466022015-07-03T05:29:05.079-07:002015-07-03T05:29:05.079-07:00I think the more common interpretation is what you...I think the more common interpretation is what you intended. I'm happy to leave it the way it is in the book.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-46621993143973364362015-07-03T03:36:51.546-07:002015-07-03T03:36:51.546-07:00She understood the words differently than I'd ...She understood the words differently than I'd intended - though the wording really could support either interpretation.<br /><br />I could reword the question in the future to remove the ambiguity.<br /><br />I guess this is something that happens when a problem is shared with a wider audience! Cool. Thank you.jd2718.orghttp://jd2718.org/noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-17428832948716539012015-06-26T07:33:38.860-07:002015-06-26T07:33:38.860-07:00Thank you, Anthony! I should have pointed that out...Thank you, Anthony! I should have pointed that out long ago. My main interest is math, so I wasn't thinking in that direction. But your reply is an important one for people who want to use it for vocabulary.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-10294466221791048672015-06-26T05:25:37.295-07:002015-06-26T05:25:37.295-07:00Very late response here. Just thought I'd let ...Very late response here. Just thought I'd let you know that its easy to make your own Spot It cards without any maths at all. <br />All you need to do is choose 1 new item or word and pair it to an existing spot it symbol. Then it'simply a matter of going through each card (from Spot It) and directly substituting the Spot It word for your own word. I am an ESL teacher. That's what I did.anthony. s-phttp://www.blogger.com/profile/14081757458215501875noreply@blogger.com