tag:blogger.com,1999:blog-30226356.post2188343934601609986..comments2024-02-16T23:32:12.073-08:00Comments on The Exponential Curve: What's the percentage of "adders-across" in Numeracy?Dan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-30226356.post-56998246859987726532008-02-25T06:20:00.000-08:002008-02-25T06:20:00.000-08:00This is one thing my students learned well this ye...This is one thing my students learned well this year. (The fact that i'd scheduled 3 months just for fractions might have something to do with it.)<BR/><BR/>We used fraction strip manipulatives to start. They had a lot of experience with these, so not a lot of prep work was needed. We started off just adding fractions with like denominators - they worked in pairs, each one finding their part of the sum and putting them together.<BR/><BR/>They quickly realized (during the recording part - making them write what they see is important) that they just added the numerators, and the denominators stayed the same. I asked them often enough that they soon had a mantra of "during adding, the denominator stays the same". Note that I didn't give them this as a mnemonic - they figured it out and I just asked them enough to cement it for the next step.<BR/><BR/>That was asking them to try the fraction strips with different denominators. Confusion! They couldn't figure out which denominator to use! Some tried adding the two numbers together, but quickly realized on their own that meant a new strip which obviously wasn't the sum of the two.<BR/><BR/>Fortunately, they had equivalent fractions down cold at this point, so when i rewrote one of them with a new denominator, they quickly got it, and were able to rewrite the second one. Everyone got the having to rewrite part after only a couple of tries - as long as I was providing them with the common denominator. They referred to this as "making the pieces the same size", since that's how it looked on their fraction strips.<BR/><BR/>It was at *this* point that I let them teach each other. Some were stuck with just multiplying the two denominators together, and having to simplify later. Others got the idea of using the least common multiple (why introduce a new term for something they already knew how to do?) and happily used that as their new denominator.<BR/><BR/>I had numbers like your 6th period for adders across, and now have 90% of my kids not only doing it right, but understanding why it has to work that way. None of them will use the phrase "lowest common denominator", but they can all do it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-55245539477852471682008-02-24T14:27:00.000-08:002008-02-24T14:27:00.000-08:00jd - That's cool - I never thought about that befo...jd - That's cool - I never thought about that before. But you're right, I think it would just confuse the issue for the students more than anything right now. Maybe I can go back to this toward the end of the unit and see if they can explain why it works.<BR/><BR/>Continuities - my Numeracy sections are at 20 students each (we keep the remedial classes as small as possible). So not all students can be paired up with someone who already has the adding skill. It will be interesting, because I don't want to make simple high-low pairs.. I want students who can effectively collaborate, which can be hard to predict sometimes. My 6th period has my weakest students in it - only 1 already can add fractions. But, since the start of the new semester, there have been a few kids added to that class, and they have been a breath of fresh air. They don't have the skills, but they have the motivation, and they are helping bring some of the others up. I love that feeling when you have a class that you used to dread going to, and now becomes one you look forward to. It's amazing what an impact switching a few students out of/into a room can have on the culture of a class.Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-49585456493679197492008-02-24T12:20:00.000-08:002008-02-24T12:20:00.000-08:00Looking at the number of NAA's in each section, pa...Looking at the number of NAA's in each section, pairing will be interesting. Unless of course you have some really small sections. Good Luck!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-77460568619735391612008-02-23T21:38:00.000-08:002008-02-23T21:38:00.000-08:00So adding across, in its own way, is pretty cool. ...So adding across, in its own way, is pretty cool. It doesn't give a sum, but it is a quick way of getting a number in between two numbers.<BR/><BR/>1/2 and 2/3 ? 3/5 is in between them.<BR/><BR/>2 and 3? That's 2/1 and 3/1. 5/2 is between them. <BR/><BR/>I don't know if that helps your kids at all (I kind of doubt it), but it's still pretty cool.<BR/><BR/>Good luckAnonymousnoreply@blogger.com