tag:blogger.com,1999:blog-2256375873271579383.post2238275702561090325..comments2024-03-27T23:55:01.532-07:00Comments on Divisible by 3 [Andrew Stadel]: Integers [temperatures]Anonymoushttp://www.blogger.com/profile/06699410662148629132noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-2256375873271579383.post-25033608391461782302019-01-10T14:16:59.439-08:002019-01-10T14:16:59.439-08:00Just something to point out: the screenshots share...Just something to point out: the screenshots shared in the folder are over 3 days. I had the kids plot points from 4 different screen shots, thinking that they were over one day. I wanted them to see the trend of the whole day. This didn't work. So next time, I'll just give them screenshots from the SAME day. If that makes sense. Anonymoushttps://www.blogger.com/profile/05332084708951629432noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-22891978260873205352016-01-18T07:03:37.314-08:002016-01-18T07:03:37.314-08:00Hi Kent,
Thanks for sharing your thoughts. I comp...Hi Kent,<br /><br />Thanks for sharing your thoughts. I completely agree with temperature being a poor context to model integer relationships. Shame on me if I didn't make the learning objectives of this activity clear. The learning objectives were to place integers on a vertical number line and discuss the change in temperature between two temperatures.<br /><br />I would not use temperature (as a false context) to model -3+5 with a student. If any connection with temperatures could be made, it might be the average temperature over a span of time, but even then I'm not sure I'd go there with students.<br /><br />Yes, vertical number lines for the win regarding integers. <br />Thanks for the input. Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-21427413425655386772016-01-18T06:44:14.404-08:002016-01-18T06:44:14.404-08:00I forgot one thing: Vertical Number Lines FTW!
I ...I forgot one thing: Vertical Number Lines FTW!<br /><br />I think that the vertical number line is the best model for integers. It's much more intuitive for students than the horizontal number line, where left is up and right is down. Or is it the other way around? If only there were some model where up was up and down was down!Kenthttps://www.blogger.com/profile/17251777011355228189noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-17137020769547484632016-01-18T06:42:13.877-08:002016-01-18T06:42:13.877-08:00I've been talking a lot with Michael Pershan, ...I've been talking a lot with Michael Pershan, Andrew Gael, and Aran Glancy about integers this year. We've been discussing the benefits and drawbacks of various models or contexts for integers, among other things.<br /><br />Temperature is a good context in some ways because a lot of kids (at least in the North) have some experience with negative temperatures, but there are drawbacks as well.<br /><br />For example, positive and negative temperatures are not distinct objects, and they don't "cancel" to zero. If you think of a problem like 5+(-3), it's hard to model that specific problem with temperature. It's much easier to model -3 +5 by saying the temperature was at -3 and then rose by 5 degrees. But if you have two distinct objects like anchors and floats, balloons and sandbags, or assets and debts, then -3+5 and 5+(-3) are equally easy to model. The anchors and floats cancel with each other, so you can evaluate the remaining objects. Also, 0 degrees Fahrenheit is an arbitrary point, which is kind of annoying. Celsius would be much better, as Martin mentions above.<br /><br />I wrote a post about integer contexts a while back, but I've learned a TON since then. I might write it up again.<br /><br />But to your more general point about student intuition, I totally agree. The more we can get kids to keep the rest of their brains on when they enter "Math World" the better.Kenthttps://www.blogger.com/profile/17251777011355228189noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-32242958503875060882016-01-16T08:45:02.546-08:002016-01-16T08:45:02.546-08:00Thanks Debbie!Thanks Debbie!Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-46246736537806335552016-01-16T08:44:50.264-08:002016-01-16T08:44:50.264-08:00I hear ya, brother.
Personally, I think we (in Am...I hear ya, brother. <br />Personally, I think we (in America and even in warmer states) can totally introduce children to negative temperature before 6th grade. If my 5-year old can tell me that -6 degrees is below zero, then I think it's most beneficial we tap into this intuition more in 6th grade math.Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-8946914074068532852016-01-16T08:40:58.275-08:002016-01-16T08:40:58.275-08:00Thanks amigo!Thanks amigo!Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-66057303676110607842016-01-15T10:18:06.854-08:002016-01-15T10:18:06.854-08:00Great Job Andrew!!!!!!Great Job Andrew!!!!!!Anonymoushttps://www.blogger.com/profile/18342366268871521998noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-38601070457363232612016-01-15T02:59:57.791-08:002016-01-15T02:59:57.791-08:00This is great Andrew and thanks for curating all t...This is great Andrew and thanks for curating all these pieces into a lessons page. What a great opportunity for students to building automaticity with integers in context. Cheers!Anonymoushttps://www.blogger.com/profile/08525114028095675402noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-84804528070731441832016-01-13T20:24:19.116-08:002016-01-13T20:24:19.116-08:00Great work. I will forward this on to my 6th and 7...Great work. I will forward this on to my 6th and 7th grade colleagues.<br /><br />I was having a conversation with my 8th grade teaching colleague who was born in France and thought that European students / people have less trouble with negatives because they are in celcius and since zero is freezing they are used to seeing negative numbers more and also they use a vertical number line much more often.<br /><br />And don't get me started about how if we, as Americans, used the metric system as our standard and how students would adapt and be more fluent with the base 10 number system.Anonymousnoreply@blogger.com