tag:blogger.com,1999:blog-18322056.post406051352805995437..comments2024-03-22T06:46:20.694-04:00Comments on Homeschool Math Blog: Word problems in Russia and in AmericaUnknownnoreply@blogger.comBlogger8125tag:blogger.com,1999:blog-18322056.post-35608309047011623882010-06-07T10:47:38.977-04:002010-06-07T10:47:38.977-04:00I think that the fact that the problem of finding ...I think that the fact that the problem of finding two consecutive numbers admits a solution (taking the integer part of the square root) need not diminish the value of the problem, even if it was not the intended solution. This is just a perfect opportunity to illustrate the idea that most problems do not have a canonical solution, and even if they do, the canonical solution need not be the best or the shortest or the most intuitive. It's up to the teacher to exploit (or miss) such an opportunity. <br /><br />I <a href="http://www.mathteacherctk.com/blog/?p=188" rel="nofollow">have written</a> in a similar vein concerning a different word problem.Alexander Bogomolnyhttp://www.cut-the-knot.orgnoreply@blogger.comtag:blogger.com,1999:blog-18322056.post-51571078958129657502009-01-28T11:49:00.000-04:002009-01-28T11:49:00.000-04:00hey that is so cool what you did!!!hey that is so cool what you did!!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-18322056.post-79728047153125710072008-07-24T18:57:00.000-04:002008-07-24T18:57:00.000-04:00Maria,Thanks to you, mathmom and others I have con...Maria,<BR/>Thanks to you, mathmom and others I have confidence that our students will one day return to "real" problem-solving as opposed to "real-world" problem solving! Keep up the great work and thanks for the link. <BR/><BR/>Encouraging elementary students to use their innate insight complemented by visual and physical representations is crucial for developing number and algebra sense long before the formalism of algebra is needed. I strongly agree with all of hte comments expressed in this post. Children need to be challenged with more sophisticated problems that develop insight (yes, one can develop it!) and computational fluency. IMO,"number sense" without numerical skill is analogous to a conceptual understanding of how to shoot a basketball without being able to put the ball in the basket... <BR/><BR/>Dave Marain<BR/>MathNotationsDave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-18322056.post-40157459942773480352008-01-06T17:49:00.000-04:002008-01-06T17:49:00.000-04:00We have just begun an Algebra Verbal Problem of th...We have just begun an Algebra Verbal Problem of the Week for students in grades 3 and up. The first problem posted is noted below:<BR/><BR/>"Theresa could purchase four small gifts and a $3 doll for the same price as three of the same small gifts and one $5 doll. What was the price of each of the small gifts?"<BR/><BR/>This problem is designed for students already using Hands-On Equations. Otherwise, it would require a creative child with algebraic reasoning skills to solve the problem.<BR/><BR/>The posting of the problem can be found on:<BR/>http://hands-on-equations.blogspot.Henry Borenson, Ed.D.https://www.blogger.com/profile/08802274549861879287noreply@blogger.comtag:blogger.com,1999:blog-18322056.post-65811307530184171622008-01-03T14:39:00.000-04:002008-01-03T14:39:00.000-04:00This comment has been removed by the author.Maria Millerhttps://www.blogger.com/profile/00230743954246449727noreply@blogger.comtag:blogger.com,1999:blog-18322056.post-64666958630496895042008-01-03T10:38:00.000-04:002008-01-03T10:38:00.000-04:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-18322056.post-72546524223566957102008-01-01T08:56:00.000-04:002008-01-01T08:56:00.000-04:00A boy and a girl collected 24 nuts. The boy collec...A boy and a girl collected 24 nuts. The boy collected two times more nuts than the girl. How many did each collect?<BR/><BR/>Regarding the above problem, since the boy collected two times MORE nuts than the girl, he actually collected three times AS MUCH as her. Hence, the boy collected 18 nuts and the girl 6.<BR/><BR/>Many verbal problems (including coin, age and distance problems) can be found in the Hands-On Equations Verbal Problems Book, which is used with the Hands-On Equations program. The Making Algebra Child's Play workshop for teachers shows them how they can introduce significant algebraic concepts at the grade school level, including solving equations such as 4x + 3 = 3x + 9, and applying these skills to solving verbal problems.<BR/><BR/>Here is one example taken from the book: <BR/><BR/>Tom buys 2 packs of football cards to add to the 5 cards a friend gave him. His mother then gives him 3 packs as a present. Now he has as many cards as Billy who owns 2 packs and 20 loose cards. If all the packs have the same number of cards, how many cards are in each pack?<BR/><BR/>The solution to problems such as this one using the game pieces (pawns and numbered cubes) may be found at the website www.borenson.com.<BR/><BR/>Thanks for referencing the book, Word Problems in Russia and America.<BR/><BR/>Henry Borenson, Ed.D.Henry Borenson, Ed.D.https://www.blogger.com/profile/08802274549861879287noreply@blogger.comtag:blogger.com,1999:blog-18322056.post-77056894213540246432007-12-31T00:32:00.000-04:002007-12-31T00:32:00.000-04:00Just wanted to say, "Great Post!" (Also, the joke...Just wanted to say, "Great Post!" <BR/><BR/>(Also, the joke formatting is wonky in my browser, so I can't see all the words on the right)mathmomhttps://www.blogger.com/profile/05869925405540832241noreply@blogger.com