tag:blogger.com,1999:blog-1907702537884089718.post1761355935198296517..comments2023-10-07T09:26:02.868-07:00Comments on Exit 10A: My Continuing Battle With 3.MD.B.4Joe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-1907702537884089718.post-39980322466785145162015-05-30T18:48:00.378-07:002015-05-30T18:48:00.378-07:00You're welcome. Thanks for the comment!You're welcome. Thanks for the comment!Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-79388511951528050752015-05-30T18:47:31.272-07:002015-05-30T18:47:31.272-07:00Thanks Paula. Looking at your "Counting with...Thanks Paula. Looking at your "Counting with fractions on the number line" makes me think to use colored dot stickers for the same effect. The visual is striking.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-9204494501938640682015-05-30T18:42:55.118-07:002015-05-30T18:42:55.118-07:00Thanks for the comment. I think you've articu...Thanks for the comment. I think you've articulated what's troublesome about this standard, and why it has presented us with so many challenges. I'm intrigued with your observation about, "revisiting and rehashing concepts that should have been done with." Could you say more about that?Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-29189108059175971382015-05-29T07:59:03.783-07:002015-05-29T07:59:03.783-07:00Yep, 3.MD.4 is a beast. Maybe there's somethi...Yep, 3.MD.4 is a beast. Maybe there's something wrong with the standard, not the teaching. Or maybe continuing to require the use of rulers that have inches is the problem, as the rest of the world wisely uses the metric system, in which subdivisions are invariably powers of 10, and where fractions such as 5/10 more easily transition into...decimals.<br /><br />A more pointed grammatical ambiguity (read: weakness) in 3.MD.4 is why it states "halves AND fourths of an inch". If a ruler is marked off in fourths, then its halves are already marked, and the wording is redundant. If a ruler is only marked off in halves, then there are no fourths. Do the CC authors implicitly suggest that you start with halves rulers and then move on to fourths rulers? That would require keeping two sets of rulers, and if so, why don't they come out and say it? Or is the standard just sloppily written? That's the more likely option.<br /><br />The line plot portion of the standard, "whole numbers, halves, OR quarters" implies a teaching sequence, not a single version of a line plot. Changing from AND to OR suggests doing line plots first with just whole numbers, then doing line plots with halves, then finally doing line plots with fourths.<br /><br />How can Common Core suggest doing only one type of measurement but more than one type of line plot? Answer: you can't, unless you're standards authors with weak English skills unwittingly confusing both teachers and students.<br /><br />A class could easily spend weeks on this one standard by taking its wording literally, and not even reach closure, because, as you accurately point out, there are "more complex measurement and fraction standards awaiting them in the upper grades".<br /><br />This particular observation exposes the precise problem in American K-12 mathematics: the habit of revisiting and rehashing concepts that should have been done with.CCSSI Mathematicshttps://www.blogger.com/profile/12318317536740240935noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-34163474032514286342015-05-29T06:45:14.634-07:002015-05-29T06:45:14.634-07:00Love how your aggrandized the ruler. IT's like...Love how your aggrandized the ruler. IT's like you are wordlessly making an editorial comment about fractions. <br />Be sure to take a look at my equivalent fractions PDF https://bookzoompa.files.wordpress.com/2015/02/fractions-zero-to-one1.pdf<br />PaulaAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-66903164537482159852015-05-29T06:02:20.674-07:002015-05-29T06:02:20.674-07:00Love it! Thanks Joe. Love it! Thanks Joe. Mr. Kelleyhttps://www.blogger.com/profile/10530175457981150458noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-79888527794239649172015-05-29T04:01:35.053-07:002015-05-29T04:01:35.053-07:00Thanks! Knowing about the 1/2 but trying to maint...Thanks! Knowing about the 1/2 but trying to maintain the pattern by writing 2/4 is something I hadn't thought of. Now I need to revisit this class and see if, as they play, they are continuing with 2/4, or if some have switched to 1/2. That will generate an interesting conversation.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-31572511031845997002015-05-28T18:18:50.550-07:002015-05-28T18:18:50.550-07:00Awesome, Joe. Real evidence of student understand...Awesome, Joe. Real evidence of student understanding. I wonder if any of the students knew about the 1/2, but wanted to keep it fourths to maintain the beauty of the pattern.D. Gulickhttps://www.blogger.com/profile/05472010301756636544noreply@blogger.com