tag:blogger.com,1999:blog-5303307482158922565.post1796564502009444059..comments2024-07-23T09:12:20.588-07:00Comments on Math Mama Writes...: FractionsSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-5303307482158922565.post-56364584664742088492011-11-15T19:29:21.956-08:002011-11-15T19:29:21.956-08:00Sue, JUMP has a fractions unit that they recommend...Sue, JUMP has a fractions unit that they recommend as an intro-unit for all their courses:<br />http://jumpmath1.org/introductory_unit<br />Now, this is aimed at elementary school kids, but you may be able to extract some useful stuff from it.<br />-- Dandan.mackinnonhttps://www.blogger.com/profile/13603404133431327842noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-40134587027597219932011-10-28T13:14:54.890-07:002011-10-28T13:14:54.890-07:00I love both of those, but neither is fractions, of...I love both of those, but neither is fractions, of course.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-89210309416546930442011-10-28T11:38:07.460-07:002011-10-28T11:38:07.460-07:00MM
Another deep and approachable problem that alw...MM<br /><br />Another deep and approachable problem that always works for my students is the 'Locker Problem' (a nice explanation of it is at (http://connectedmath.msu.edu/CD/Grade6/Locker/index.html ) I always follow up with a great factoring conversation about why the open doors are the ones that they are. The handshake problem (http://mason.gmu.edu/~jsuh4/impact/Handshake_Problem%20teaching.pdf) is another rich onemrdardyhttps://www.blogger.com/profile/00226520636242484791noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-28780188285016362532011-10-28T08:42:42.792-07:002011-10-28T08:42:42.792-07:00Thanks, Mr. Dardy! If your honors students worked ...Thanks, Mr. Dardy! If your honors students worked on this for an hour, you're making me realize that there are many hours worth of work for students with less skills and confidence in math.<br /><br />I haven't yet worked with the problem much, so your reply made me think about how deep it can be.<br /><br />I'm still hoping I can collect other really deep and approachable problems.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-3204384136232518932011-10-28T05:48:39.043-07:002011-10-28T05:48:39.043-07:00Mathmama
Thanks for presenting this problem. In m...Mathmama<br /><br />Thanks for presenting this problem. In my Alg II Honors class this week I posed this as a class opener thinking we might talk for about ten minutes. Forty minutes later we, they did all the heavy lifting, decided that 1/n is always equal to the sum of 1/(2n) , 1/(3n), and 1/(6n) They saw great patterns along the way. I presented the following three follow ups to 1/2 = 1/3 + 1/6<br /><br />I asked them to decompose 1/10, 1/20, and 1/17<br /><br />They saw that for the evens you could write the first fraction as 1.5n and the second denominator as 3n. This did not work for the odd denominator and we stumbled on to the pattern I identified above. <br /><br />It was a fantastic conversation!mrdardyhttps://www.blogger.com/profile/00226520636242484791noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-64012441539272409112011-10-25T09:56:19.816-07:002011-10-25T09:56:19.816-07:00One easier (I think) way of hooking students is pr...One easier (I think) way of hooking students is providing problems they can relate to. There are a lot of fractions in their world that they find challenging or make incorrect assumptions about.<br /><br />One example brings geometry into the mix by using 22/7 as an approximation for pi. Pizza places often sell circular pizzas in small, medium, and large. If the small is a 6 in. pizza and the large is a 12 in. pizza, is the large double the size of the medium? <br /><br />Stores often do some crazy things with sales. 25% off one item plus 20% the entire purchase. The percents can be converted to fractions and students can consider what these discounts do to the original price.Ashleysheahttps://www.blogger.com/profile/10402840649286278563noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-43334834822357814612011-10-24T08:23:12.747-07:002011-10-24T08:23:12.747-07:00Thanks for mentioning that, mathmom. I had thought...Thanks for mentioning that, mathmom. I had thought about it, but wrote this post in a hurry. <br /><br />Many of my students are African-American, and working with sophisticated mathematical ideas from ancient Egypt will be a plus for them, and perhaps for all students of color.<br /><br />James Tanton has a bit about Egyptian Fractions in his book Arithmetic: Gateway to All. If you google 'james tanton egyptian fractions', you can get a free download of his fraction chapter.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-51523917829667289022011-10-24T04:14:22.784-07:002011-10-24T04:14:22.784-07:00For the unit fractions, it is very interesting (at...For the unit fractions, it is very interesting (at least to me!) that these are what the ancient Egyptians worked with. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html<br /><br />Maybe for some students, knowing the history might give it even more interest? It is fun...mathmomhttps://www.blogger.com/profile/07887205622583099966noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-33869320718547596172011-10-23T20:38:15.808-07:002011-10-23T20:38:15.808-07:00What about (1/2)/2 + (1/2)?
A student might simp...What about (1/2)/2 + (1/2)? <br /><br />A student might simplify the first fraction, or might use 2(1/2)/2 = (1/2). This seems like a cool problem. They could check answers on their calculators.Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-60041540697558215712011-10-23T20:27:19.229-07:002011-10-23T20:27:19.229-07:00I was really just trying to play around with the n...I was really just trying to play around with the notation and stretch it in interesting ways. I was imagining ((((1/2)/2)/2)/2).<br /><br />One of the things that seems to work, sometimes with my students, is pushing notation to its limits. What I think is happening is that, sometimes, when you push notation into strange, absurd looking forms, one is forced to confront what the notation really signifies.Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-13213150565689565812011-10-23T17:59:41.021-07:002011-10-23T17:59:41.021-07:00@Raymond, those might be a good start.
Since I&#...@Raymond, those might be a good start. <br /><br />Since I'm working with adults, I'm concerned they might not be hooked into feeling like they're doing something new, and not just more review.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-19280377497583084112011-10-23T17:57:08.010-07:002011-10-23T17:57:08.010-07:00Are you suggesting that they should decide how man...Are you suggesting that they should decide how many ways there are to interpret that?Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-92209220487139759282011-10-23T17:36:39.348-07:002011-10-23T17:36:39.348-07:00How about something like evaluating 1/2/2/2/2?How about something like evaluating 1/2/2/2/2?Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-56261433069146519282011-10-19T17:40:11.052-07:002011-10-19T17:40:11.052-07:00One of my favorites is on the 6th slide of this pr...One of my favorites is on the 6th slide of this presentation:<br /><br /><a href="http://www.fi.uu.nl/en/fius/rmeconference/handouts/shepard/Realisticmath2009Shepard.pdf" rel="nofollow">http://www.fi.uu.nl/en/fius/rmeconference/handouts/shepard/Realisticmath2009Shepard.pdf</a><br /><br />Part (a) is certainly for newbies, but beyond that you have to be able to stretch your understanding of fractions and see the unit change size.Raymond Johnsonhttps://www.blogger.com/profile/14213559862857292867noreply@blogger.com