tag:blogger.com,1999:blog-2256375873271579383.post5477232912859599256..comments2024-03-27T23:55:01.532-07:00Comments on Divisible by 3 [Andrew Stadel]: ClotheslineAnonymoushttp://www.blogger.com/profile/06699410662148629132noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-2256375873271579383.post-54845716759228705992021-05-11T03:04:07.553-07:002021-05-11T03:04:07.553-07:00i will never ever in my life stop telling the whol...i will never ever in my life stop telling the whole entire world the great Job Dr. Abolo whose contact details is Abolospell@gmail.com did for me by making my relationship the best and the perfect one i wished for with his powerful love spell that works beyond human oh my goodness his spells is so effective and secondly there is know side effect and most importantly he is very legit what ever he says that is what he dose. now this was how meant with him that change my love life all of a sudden. I saw a comment here a few weeks ago about Dr Abolo and i decided to contact him as instructed, thanks to this man for bringing joy to me as wished for. i followed instructions which he gave in other to get my lover back who left me and the kids for 3years now, but thanks to Dr Abolo because they are back to me now for good and we are happy together. please do contact him for help too if in relationship problem via email at: ( Abolospell@gmail.com ) And testify for yourself. Great Abolohttps://www.blogger.com/profile/08070826399192422541noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-81619906421744850842019-02-25T02:03:29.090-08:002019-02-25T02:03:29.090-08:00AM SANDRA FROM CANADA, THANKS TO DR ONIHA WHO HELP...AM SANDRA FROM CANADA, THANKS TO DR ONIHA WHO HELP ME BRING MY HUSBAND BACK, MY HUSBAND LEFT ME WITH THREE KIDS, FOR ANOTHER YOUNG GIRL, FOR OVER TWO YEARS, I TRIED ALL I COULD TO SETTLED OUR DIFFRENCES, BUT IT YIELDED NO RESULT, I WAS THE ONE TAKING CARE OF THE CHILDREN ALONE, UNTIL ONE DAY, I CAME IN CONTACT WITH SOME ARTICLES ONLINE, CONTAINING HOW DR ONIHA HAS HELP SO MANY LOVERS AND FAMILY REUNION AND REUNIT AGAIN, AND I DECIDED TO CONTACT HIM, AND HE CAST HIS SPELL ON MY HUSBAND, WITHIN FIVE DAYS, MY HUSBAND RAN BACK HOME, AND WAS BEGGING ME AND THE KIDS FOR FORGIVENESS, IN CASE YOU ARE PASSING THROUGH SIMILAR PROBLEMS, AND YOU WANTS TO CONTACT DR ONIHA, YOU CAN REACH HIM VIA HIS CONTACT NUMBER, ON CALL OR WHATSAP +2347089275769 OR EMAIL DRONIHASPELL@YAHOO.COMgjhmhhttps://www.blogger.com/profile/02847497099430667579noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-68881151633030744802018-06-14T19:08:45.935-07:002018-06-14T19:08:45.935-07:00Spot on with this write-up, I really think this we...Spot on with this write-up, I really think this web site needs way more consideration. I’ll probably be again to learn much more, thanks for that info. <a href="https://onlinecasinoqe.com" rel="nofollow">online casino</a>yosabrams0918https://www.blogger.com/profile/11140186761749280113noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-48669005002415835272018-01-30T07:46:53.355-08:002018-01-30T07:46:53.355-08:00Sorry about the delayed reply.
I've found it h...Sorry about the delayed reply.<br />I've found it helpful to introduce students to the clothesline using carefully selected whole numbers and integers. For example, -8, -3, 0, 2, 8, 10<br />This way students can get familiar with placing and spacing the numbers while recognizing numerical relationships between the numbers. <br />Hope that helps.Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-83170859259143475682017-06-17T18:00:57.868-07:002017-06-17T18:00:57.868-07:00I am curious to know what is the first activity/le...I am curious to know what is the first activity/lesson you do with your students to introduce and understand what a clothesline is in class.<br /><br />I teach 8th grade where they will work often with real numbers and estimating square roots and cube roots and I can see this being a great understanding tool but am not sure how to introduce it. Anonymoushttps://www.blogger.com/profile/14972267571889318629noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-70640523071954599972017-01-19T12:22:21.325-08:002017-01-19T12:22:21.325-08:00Thanks for following up, Madelyne. I definitely ma...Thanks for following up, Madelyne. I definitely made a mistake and didn't check my thinking. I'd leave 0 and 3^0 (as 1) up and then start working on the negative exponents. <br /><br />I'm excited to see what you come up with.Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-1916361549903513242017-01-18T19:57:33.568-08:002017-01-18T19:57:33.568-08:00I get the two lines with 3^2 and 9 above, check.
I...I get the two lines with 3^2 and 9 above, check.<br />I lost you a little bit after that... But If I leave 3^2 on the line, have a student add 3^1 and then enquire about 3^0 and get it placed, we could still explore the patterning in the integers (* or / by 3).<br />But what were you doing by placing 3^0 and 3^1 on the line? The only thing in between those are roots...Anonymoushttps://www.blogger.com/profile/00279039340807527502noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-32746999833079442512017-01-18T11:02:13.406-08:002017-01-18T11:02:13.406-08:00Great question: off the top of my head, I would us...Great question: off the top of my head, I would use one clothesline to hold the expressions (ex. 3^2) and another clothesline to contain the value (9).<br />I might JUST do 3^0, ^1,2,3 and then remove ^2 and ^3 so that we can expand the range of the number line so it's between 3^0 and 3^1. Now I would start using that space for the negative exponents. <br />Does that make sense?Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-84695308786087468632017-01-18T10:48:53.999-08:002017-01-18T10:48:53.999-08:00I love that idea! I teach Algebra I. I didn't ...I love that idea! I teach Algebra I. I didn't think about using it to introduce negative exponents but your illustration makes perfect sense.<br />So without knowing everything about how the clothesline works, would I hang more than one and use the top for base 3 and then use one of the other "lines" for base x???Anonymoushttps://www.blogger.com/profile/00279039340807527502noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-86805787016295704932017-01-18T10:42:05.514-08:002017-01-18T10:42:05.514-08:00Great question. Not knowing what grade level you t...Great question. Not knowing what grade level you teach, I'm wondering if it would benefit to students to start with a more concrete and conceptual way of thinking in conjunction with identifying patterns.<br />For example, where would we place 3^1, 3^2, 3^3, 3^4 and then ask where 3^0, 3^-1, 3^-2, 3^-3, 3^-4 would go...<br />Maybe once you have formalized some "rules" from a base of 3, maybe introduce x^2 and x^-4.<br />What do you think?Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-90419457810444346362017-01-18T10:15:53.446-08:002017-01-18T10:15:53.446-08:00Thinking of using this when we introduce exponent ...Thinking of using this when we introduce exponent rules... asking Ss where would you place (x^2)^2 versus x^-4, etc...to see if ,in one variable, students understand, what the rules "do"...<br />any thoughts on that?Anonymoushttps://www.blogger.com/profile/00279039340807527502noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-77409049309806464422016-01-21T20:17:52.003-08:002016-01-21T20:17:52.003-08:00Thanks for the comment. I appreciate the request a...Thanks for the comment. I appreciate the request and think the TMC scholarship is an awesome idea!<br />Yes, I grant you permission to include the Clothesline post in your collection.<br />Let me know if you have any further questions.Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-70455515225870036872016-01-21T17:55:29.944-08:002016-01-21T17:55:29.944-08:00Hello! This post was recommended for MTBoS 2015: a...Hello! This post was recommended for MTBoS 2015: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts and use the money raised toward a scholarship for TMC. Please let us know by responding via email to tina.cardone1@gmail.com whether or not you grant us permission to include your post. Thank you, Tina and Lani.Tina Cardonehttps://www.blogger.com/profile/00549943329133396794noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-6209482048115439372015-12-16T09:26:27.969-08:002015-12-16T09:26:27.969-08:00I might need some clarification just to be sure we...I might need some clarification just to be sure we're talking about the same thing. When you say "system" I think something like y=5x-7 and y=3x+9 and I would think there is some overlap with solving the equation 5x-7-3x+9.<br />With the system, it's been established there are two different variables and we typically use the coordinate plane where the two axis represent x and y.<br />However, with the equation with variables on both sides, the focus can be just the unknown value of x. So how does this work with a double number line?<br />I use the top number line as the placement of concrete numbers. The bottom number line is used for the algebraic expressions and how they relate with their location in regards to the concrete numbers above them.<br />I'll post some examples soon.Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-54115580719468851072015-12-14T11:29:29.384-08:002015-12-14T11:29:29.384-08:00I was curious how well thing would pan out if we d...I was curious how well thing would pan out if we did a system of equations (other than equal values) with the clotheslines... I'm still not able to wrap by brain around it. Thoughts?kquezhttps://www.blogger.com/profile/12413753203795297404noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-60943432834928413072015-10-08T14:26:32.461-07:002015-10-08T14:26:32.461-07:00Right on. Let me know how it goes!Right on. Let me know how it goes!Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-44787037865772672822015-10-08T13:14:34.963-07:002015-10-08T13:14:34.963-07:00Love this! I've used my smart board to have st...Love this! I've used my smart board to have students move numbers around on a number line, but I think I like this better. <br /><br />Also, love the idea of raffling off a clothesline after introducing the idea at teacher PD. Totally stealing that idea! ;)Annie Foresthttps://www.blogger.com/profile/16589957773353987984noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-64111320804790560572015-09-11T12:00:54.092-07:002015-09-11T12:00:54.092-07:00It's really just practice. We leave the string...It's really just practice. We leave the string up all the time and that makes it easy to ask them to "put a fraction between 0 and 2 up" or something like that on the fly and then have that discussion around relative vs absolute position often. The fact that the kids don't have names attached to the numbers means we can point out errors without calling out the students individually. David Petrohttps://www.blogger.com/profile/16551690042242217798noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-22887739054593955992015-09-10T22:02:12.614-07:002015-09-10T22:02:12.614-07:00Right on! Thanks for sharing. Have any strategies ...Right on! Thanks for sharing. Have any strategies to share with helping students space the numbers correctly?Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-48207225908880329982015-09-04T07:49:16.684-07:002015-09-04T07:49:16.684-07:00We have been using this idea for a few years now. ...We have been using this idea for a few years now. I love the idea of using it with functions (place x on the line and then ask where 2x or x/3 is). We have a set of tent cards that we re use by just putting post-it notes on them (you've probably got a few of those). You can see an image of this on the banner of my blog here http://engaging-math.blogspot.ca/David Petrohttps://www.blogger.com/profile/16551690042242217798noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-45418573706340879432015-08-25T20:35:13.674-07:002015-08-25T20:35:13.674-07:00Right on! Thanks Tammy! Right on! Thanks Tammy! Anonymoushttps://www.blogger.com/profile/06699410662148629132noreply@blogger.comtag:blogger.com,1999:blog-2256375873271579383.post-38542829567852177262015-08-25T17:34:23.006-07:002015-08-25T17:34:23.006-07:00Wow. I love the number sense we can talk about thr...Wow. I love the number sense we can talk about through this post. Teachers and students will all benefit.Tammynoreply@blogger.com