tag:blogger.com,1999:blog-355442528570693080.post4811622287710180250..comments2013-04-01T17:23:29.294-04:00Comments on crstn85: A Variety of Variablescrstn85http://www.blogger.com/profile/13549871309834864781noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-355442528570693080.post-27324409951507210202011-11-15T17:58:21.758-05:002011-11-15T17:58:21.758-05:00Oh excellent. I like this approach and I always l...Oh excellent. I like this approach and I always like simplifying the number of things we need to consider. My co-teacher actually did a lesson today on trying numbers in equations to see if they do or don't make the equation true, it's as if she read your mind! (Or your comment, but she doesn't know about this blog as far as I know.)crstn85http://www.blogger.com/profile/00549943329133396794noreply@blogger.comtag:blogger.com,1999:blog-355442528570693080.post-70274694143196099562011-11-14T18:36:23.915-05:002011-11-14T18:36:23.915-05:00Great post. Some really good ideas here.
In gene...Great post. Some really good ideas here.<br /><br />In general, I don't agree with #3. In the equation 5+3=A, A can still be any number. Depending on the choice for A, the equation is true or false. The language "solve for x" hides what is really happening: finding the value(s) that make the equation true.<br /><br />Going the other way with this ("a specific number we don't know") leads to big problems quickly, in equations with zero or multiple solutions, and especially in equations with an infinite number of solutions, such as 2x+3y=12 or x+1=1+x.<br /><br />This actually reduces the number of different ways to have to worry about, and eliminates the "unknowns" thing altogether.<br /><br />Thanks and keep up the great work!patternsinpracticehttp://patternsinpractice.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-355442528570693080.post-63950924728120003712011-11-13T13:07:15.716-05:002011-11-13T13:07:15.716-05:00I like the idea of using different words for unkno...I like the idea of using different words for unknowns and variables. There are so many details that we often gloss over. I look forward to seeing what you come up with when you get to this unit!crstn85http://www.blogger.com/profile/00549943329133396794noreply@blogger.comtag:blogger.com,1999:blog-355442528570693080.post-74027184449586164682011-11-13T11:59:26.247-05:002011-11-13T11:59:26.247-05:00I always find it somewhat funny, but most of all c...I always find it somewhat funny, but most of all cool, when someone post on an idea that I've been mulling over for the past few days/weeks/months. My math department (all three of us) had a conversation a few weeks ago about the difference between a variable and an unknown, and how and when we would teach this distinction. [FYI: the decision was 6th grade: unknown, 7th: variable]<br /><br />But it got me thinking about all the different ways we use letters to represent numbers. So far I've come up with four: 1. variables, 2. unknowns, 3. parameters (like m & b in y=mx+b), and 4. special numbers (like e, i & pi). I like your distinction between variables as quantities that change and as placeholders. <br /><br />One of my goals in sorting this out is to be very consistent in my language with students and only refer to the letter with its actual name and not just call everything a variable, as I often slip up and do. I'll probably wind up creating a "toolkit" note page about it at some point when I get around to our variable unit in 7th grade.betweenthenumbershttp://betweenthenumbers.wordpress.com/noreply@blogger.com