tag:blogger.com,1999:blog-3071719252136968205.post8781276808300664313..comments2023-09-01T01:19:38.867-07:00Comments on Following Learning: A two-machine problemSimon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3071719252136968205.post-4783133887453000102019-03-18T01:34:02.230-07:002019-03-18T01:34:02.230-07:00Fascinating, Simon and definitely one I'll try...Fascinating, Simon and definitely one I'll try out. On the doubling 'wow!' I came across the pocket money question the other week: would you rather have 10 dollars a month for a year, or 10 cents in Jan, 20c in Feb, doubling each month until Dec? Haven't tried it in class yet (or on my kids!).Anonymoushttps://www.blogger.com/profile/02771357085251468135noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-23813188597671989722019-03-17T07:47:13.784-07:002019-03-17T07:47:13.784-07:00Thanks, John. They seemed engaged. It's hard f...Thanks, John. They seemed engaged. It's hard for me to say whether they would be more so with say a real-world context (and within that whether aspects of real world could be a distraction as well as other aspects introducing important questions and caveats). As you know, I do a lot of lessons with 'stuff', so it's not all numbers numbers numbers anyway.<br /><br />I had to resist the temptation to show my concentric grid (I think it was a temptation anyway!) although in hindsight a two-colour hundred square could have been good as the hundred square is a familiar representation.<br /><br />I thought of Collatz. But there are some simpler chains we might look at first.Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-45179719479517439832019-03-17T06:47:51.650-07:002019-03-17T06:47:51.650-07:00So fascinating! There's so much to notice and ...So fascinating! There's so much to notice and so many ways to represent what's happening. And it implies that problem of what other machines can we build... <br /><br />I was imagining a grid where to the right was x2 and down was -3. When I've had kids play with the Collatz conjecture, they get fascinated by how the network connects. "Oh, I got 17, and I know what happens from there." Of course, that's a specific rule, and here you have choices. What might a rule be for these machines?<br /><br />Did any challenges seem natural? Like which numbers can't you get starting from 0 or 1, or given a number what's the best path to some target?<br /><br />Also wondering how engaging this was for all the students with just the naked numbers. Of course, if anyone's classroom has kids interested in number for themselves, it's yours!John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.com