tag:blogger.com,1999:blog-2256375873271579383.post2939149633817973331..comments2019-01-10T14:16:59.439-08:00Comments on Divisible by 3 [Andrew Stadel]: Thank You Math MistakesAndrew Stadelhttps://plus.google.com/116339709300820375507noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-2256375873271579383.post-9933081607910144062018-06-19T14:21:01.563-07:002018-06-19T14:21:01.563-07:00One idea that uses exponents that students might f...One idea that uses exponents that students might find interesting is the Richter magnitude scale for earthquakes. The scale numbers 1-9 are exponents on a base of 10 that compares amplitude magnitudes (sizes) of different earthquakes. So an earthquake of magnitude 5 is 100 times larger than an earthquake of magnitude 3. It's 10^5 versus 10^3. To compare them you subtract exponents to get 10^2. I don't have a prepared activity for this but think it could become one. If you use this, be ready to help the students work through the meaning of a magnitude with a decimal such as 3.5.Joylenenoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-34269089876148628882016-10-20T18:02:33.204-07:002016-10-20T18:02:33.204-07:00Right on. I'd love to hear how it goes!Right on. I'd love to hear how it goes!Andrew Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-78322267106180838042016-10-20T07:25:23.900-07:002016-10-20T07:25:23.900-07:00This is a fantastic post, and I will certainly use...This is a fantastic post, and I will certainly use this the next time I tackle the exponents unit! Thank you!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-67083243210284118452016-10-20T07:22:51.930-07:002016-10-20T07:22:51.930-07:00That is AMAZING! I will share this with my class t...That is AMAZING! I will share this with my class tomorrow! Thank you MaryAnn!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-27430307258837552412016-08-25T10:50:19.525-07:002016-08-25T10:50:19.525-07:00Thanks Mr. Clements. Exponents were a big thorn in...Thanks Mr. Clements. Exponents were a big thorn in my side. With your 26 years of teaching, I'm sure you have some gems to share too regarding error analysis. What wisdom would you be able to share with us all?Andrew Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-85565261377911198932016-08-25T08:47:02.461-07:002016-08-25T08:47:02.461-07:00This is coming a year or more late, also...but...w...This is coming a year or more late, also...but...who cares! I've been teaching for 26 years and a colleague sent out the link to this post. I LOVE IT. Error analysis is such a fantastic skill and shows depth of knowledge. Keep these great ideas coming!!! Thank you!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-52445198987683104342015-01-13T07:51:01.452-08:002015-01-13T07:51:01.452-08:00Welcome Sandra. I hope it goes well and I look for...Welcome Sandra. I hope it goes well and I look forward to your report.Andrew Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-341683474553573892015-01-13T04:50:09.039-08:002015-01-13T04:50:09.039-08:00LOVE this!!!LOVE this!!!Sandra Millerhttps://www.blogger.com/profile/04311786165141669898noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-78665404481061028362015-01-13T04:49:28.729-08:002015-01-13T04:49:28.729-08:00Hello! I know I am a year late to reading this bu...Hello! I know I am a year late to reading this but I just discovered your blog last night. Coincidentally I am starting the exponent unit today and guess what ... I am stepping way out of my comfort zone and doing THIS!!! I will let you know how it goes. Thank you!!!Sandra Millerhttps://www.blogger.com/profile/04311786165141669898noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-78729780345290354052014-02-22T22:14:10.699-08:002014-02-22T22:14:10.699-08:00Very cool. And timely. I'm going to be diving ...Very cool. And timely. I'm going to be diving in to dreaded exponents soon. Have you ever used a visual proof of power of zero=1? It's my favorite. Students fold their paper in half repeatedly. Because they are folding in half, the base is two. The number of folds is the exponent. To visually 'evaluate' the exponent expression, you unfold the paper and count the number of sections. We do this up to 2^3. Then I hold up a clean, unfolded sheet of paper and say, "So what if I fold it zero times?" and then I can see about 35 lightbulbs turn on. It's great. MaryAnnhttps://www.blogger.com/profile/03786890842875567416noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-49281699646356753712013-10-13T21:34:52.379-07:002013-10-13T21:34:52.379-07:00Thanks. I do enjoy "My Favorite No" and ...Thanks. I do enjoy "My Favorite No" and briefly mention it here:<br />http://mr-stadel.blogspot.com/2012/09/estimation-180.html<br />I morphed it into "My Favorite Yes/No" since there are times when I have a favorite "yes."Mr.Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-92229997572230422582013-10-12T21:49:08.886-07:002013-10-12T21:49:08.886-07:00This is a rock star post, Mr. Stadel. Kids need to...This is a rock star post, Mr. Stadel. Kids need to be given a chance to figure things out on their own, not just be told rules again and again. You might enjoy "My Favorite No" at http://www.youtube.com/watch?v=Rulmok_9HVs, which is similar to your idea above. Rock on!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-12578898927508987092013-09-29T20:45:42.387-07:002013-09-29T20:45:42.387-07:00I can relate! Been there! Please let me know how i...I can relate! Been there! Please let me know how it goes. Making connections and demonstrating the relevance of exponent rules to anyone, let alone middle schoolers, is a challenge.Mr.Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-15957607618558727742013-09-26T03:58:17.414-07:002013-09-26T03:58:17.414-07:00I'm at that point in Math 8 where we have spen...I'm at that point in Math 8 where we have spent a week on exponent rules and I loathe this unit. Something that makes sense mathematically to me... makes sense when we talk about it... but they can't keep it straight in their brains. I get depressed. I wonder what I'm doing wrong. And the cycle continues. Can't wait to try this out today! Thanks dood.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-31185867675345099372013-05-07T05:52:05.833-07:002013-05-07T05:52:05.833-07:00Hi Cathy,
Thanks for checking in and sharing your ...Hi Cathy,<br />Thanks for checking in and sharing your "Find 'n Fix" activity. I'll have to try that some time. Mr.Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-17253519052508487962013-05-05T05:25:36.480-07:002013-05-05T05:25:36.480-07:00Love the strategy of presenting mistakes. To add ...Love the strategy of presenting mistakes. To add to the middle-school drama, I created a "Find 'n Fix" template where I do 4 hand-written problems, claiming the work has been done by "other students". They always want to know whose work they're analyzing. Sometimes all 4 problems are wrong, and sometimes there's a mix of correct and incorrect problems. Students actually "grade" the paper, providing comments and advice, as well as corrected work for the problems that are wrong (in red ink, of course). They love owning the role of the teacher who gets to grade the paper. It's always fascinating when they're convinced a problem that is actually wrong is correct, and vice-versa. Activities like this truly give the teacher a direct peek inside the brain!Cathy Yencahttp://mathycathy.com/blognoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-92091773126694068572013-04-17T15:48:19.630-07:002013-04-17T15:48:19.630-07:00Yes, those student conversations were wonderful. I...Yes, those student conversations were wonderful. I agree, we need more of those.Mr.Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-75245779349201621372013-04-17T15:47:19.905-07:002013-04-17T15:47:19.905-07:00I'd go former as well. I can't describe th...I'd go former as well. I can't describe the level of engagement my students had when tasked with finding and correcting the mistakes. The entry point is so low. They aren't intimidated with expressions that they have to simplify. Here, they know that if they get the "wrong" answer they can try another theory in solving.<br />The engagement level was head and shoulders above any previous year where I too "burned" through the properties and kids get practice exercises in front of them, immediately saying, "Mr. Stadel, I forget what to do. I don't get this. Do you add or multiply?" <br />Exponent properties aren't necessarily perplexing. That's fine. My goal was to increase the level of engagement and encourage students to have a better understanding through exploration instead of direct instruction. We're getting there.Mr.Stadelhttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-29379380290805892282013-04-17T06:34:37.766-07:002013-04-17T06:34:37.766-07:00Love this post, and the idea of having students ex...Love this post, and the idea of having students explain the minor math errors they see around them. I think the 37^0 problem opens up nice discussions about concepts in math we need to establish via rule or definition, vs concepts we can understand through tangible means. Sometimes we need to have a toolbox of established rules, which then provide a framework for everything which follows. It feels like Euclid's postulates: ideas which "seem" correct, would be logically impossible to prove, yet are critical for everything that comes after. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-34930942632322665912013-04-16T17:03:21.179-07:002013-04-16T17:03:21.179-07:00I'm so glad you've posted this. I am in a...I'm so glad you've posted this. I am in a weird situation with exponent props right now. Starting 2.5 weeks ago:<br /><br />1. We burned through the properties in a few days.<br /><br />2. Spring break hit us - prior to Spring Break I assigned a project on the properties. Here's an example of what I've received: http://mrwardteaches.wordpress.com/2013/04/10/exponent-properties-as-explained-by-star-wars-characters/<br /><br />3. The entire week after Spring Break, I had less than half of my class (the class is 8th and 9th grade, 8th graders were on class trip to D.C.), so we've been in a holding pattern and I let the 9's finish up their projects.<br /><br />4. Tomorrow is the first day with the entire class back together. I've set aside the 65 minute period to review the props.<br /><br />I was going to do a practice and share activity where students work through examples individually and then each student has to volunteer to "present" one of the problems - they'll kind of self-differentiate with me pushing the more advanced kids to volunteer to do the tougher problems.<br /><br />However, now I'm wondering. I might swipe your mistakes worksheet and start with that, then move onto the practice problems. Or do I start with the practice and then attack the mistakes. I'm leaning towards the former, but it's an interesting dilemma.Anonymousnoreply@blogger.com