tag:blogger.com,1999:blog-8268773079578019071.post5590768587291860474..comments2019-01-23T07:08:01.906-06:00Comments on Mrs. E Teaches Math: How I Teach Factoring QuadraticsMrs. E Teaches Mathnoreply@blogger.comBlogger14125tag:blogger.com,1999:blog-8268773079578019071.post-72326107988632556412018-11-14T08:43:17.458-06:002018-11-14T08:43:17.458-06:00I'm curious as to *why* we teach factoring qua...I'm curious as to *why* we teach factoring quadratics of the form ax^2 + bx + c<br />The proof grouping works is *NOT ACCESSIBLE* to high school students: http://www.onemathematicalcat.org/algebra_book/online_problems/facByGrpPf.htm<br /><br />Presumably then, we need factoring by grouping for *what it does*, not *why it works*. Factored representation reveals x-intercepts (and thus, vertex). However, completing the square directly reveals vertex and is how we can derive the quadratic "formula" - which is accessible to grade 11 students<br />https://mindyourdecisions.com/blog/2015/10/02/the-quadratic-formula-an-intuitive-explanation/<br /><br />Can someone comment on why we labor to teach this algorithm? I'm at a loss to know why.Unknownhttps://www.blogger.com/profile/05172893982322187065noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-2361421149265170322018-09-02T16:02:05.919-05:002018-09-02T16:02:05.919-05:00So glad to find someone else who skips a=1 at firs...So glad to find someone else who skips a=1 at first. It helps students immensely!Suzy Qhttps://www.blogger.com/profile/16744065172460051023noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-8045414008793584302018-03-13T14:09:12.989-05:002018-03-13T14:09:12.989-05:00I don't teach the shortcut. Many of them figu...I don't teach the shortcut. Many of them figure it out for themselves, and that's fine. However, the students that don't figure it out on their own are typically the students that need a little more practice anyway. Mrs. E Teaches Mathhttps://www.blogger.com/profile/14333418485408024108noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-84793796355716491292018-03-13T13:11:09.103-05:002018-03-13T13:11:09.103-05:00I use the phrase...we are looking for TWO KEY NUMB...I use the phrase...we are looking for TWO KEY NUMBERS that multiply to "ac" and add to b.<br />BUT my question is, when a=1, do you still have the students break bx into 2 separate terms and using grouping method or do you teach them a shortcut and go right to the factors (x___)(x___) ? In the past, I have not shown my students this little shortcut until a few of them discover it on their own. Harv Ebbenhttps://www.blogger.com/profile/03025322281516690592noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-37121669378644498442018-03-05T12:59:23.740-06:002018-03-05T12:59:23.740-06:00Add a zero placeholder; it still works (for simpli...Add a zero placeholder; it still works (for simplicity/clarity I used "x" instead of "b").<br />4x^2 + 0x -25<br />Multiply "a" term times "c" term:<br />4 * -25 = -100<br />Factors that multiply to -100, and add up to 0: 10 and -10<br />So the above becomes:<br />4x^2 + 10x -10x -25<br />Group factor the first two terms:<br />4x^2 + 10x = 2x(2x + 5)<br />Group factor the second two terms:<br />-10x - 25 = -5(2x + 5)<br />Put them together, and you have:<br />(2x - 5)(2x + 5)<br />Unknownhttps://www.blogger.com/profile/16112023140931239458noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-53471758851652049442018-03-04T15:55:21.425-06:002018-03-04T15:55:21.425-06:00I'm a bit confused though. How you would you g...I'm a bit confused though. How you would you go about it if it was 4b^2-25?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-8286799545238039142018-02-15T05:08:42.287-06:002018-02-15T05:08:42.287-06:00Thats exactly how I teach factoring too. I ask the...Thats exactly how I teach factoring too. I ask the students to make a list of all factors that multiply to ac using rainbow method and then add them to see which one gets to b!!! Always good to know that there are other good teachers who have same thoughts/ methods as you. I love your resources and your facebook page. Keep them coming Vasudha Uddavanhttps://www.vsonlinemathtutoring.com/noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-64865050657702768902018-02-06T08:55:31.696-06:002018-02-06T08:55:31.696-06:00Genius! Thank you!Genius! Thank you!Daynahttps://www.blogger.com/profile/11194335295679801885noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-5561193199286060472017-08-10T19:05:32.459-05:002017-08-10T19:05:32.459-05:00Over (too many) years of teaching, I have seen and...Over (too many) years of teaching, I have seen and used numerous techniques to factor quadratics (from guess-and-check to box-method) .... this is my favorite and the most easily understood. <br />sandyhttps://www.blogger.com/profile/02193454733831390620noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-79407848225113764172017-03-20T11:01:14.247-05:002017-03-20T11:01:14.247-05:00I've been doing this for a few years - it also...I've been doing this for a few years - it also makes it easier when you have to go into factoring four or more terms because they already know how to factor by groupingEmilynoreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-17563452137312660612017-03-08T06:43:00.290-06:002017-03-08T06:43:00.290-06:00I teach special education students and use this sa...I teach special education students and use this same method, in the same order. Your'e right. It works every time. I find I rarely have to teach a=1 because they don't see it as any different. When you multiply a*c, it doesn't matter if a=7 or a=1. Lisa McLeodhttps://www.blogger.com/profile/01834212637096602115noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-45551977536388733102017-02-26T11:17:38.486-06:002017-02-26T11:17:38.486-06:00Great strategy. I enjoy the hands on method of te...Great strategy. I enjoy the hands on method of teaching quadratics using Mortenson math blocks. I had some of my own personal "ah, ha" moments playing around with quadratics. Lacy Cokerhttps://www.blogger.com/profile/03263922018766478257noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-37963246203367971922017-02-03T11:43:39.295-06:002017-02-03T11:43:39.295-06:00I do this in a similar manner, but when I have the...I do this in a similar manner, but when I have them do the factor by grouping I have them put it into an area model. The graphic organizer helps them to see where the common factors are. It works for solving quadratics where a is not 1 as well as cubic expressions that can be factored by grouping. It's also a method I teach to multiply polynomials for those who need their work to be more organized than just distributing.Amy and Bryanhttps://www.blogger.com/profile/02108206089675671888noreply@blogger.comtag:blogger.com,1999:blog-8268773079578019071.post-74609948808521946592017-01-30T08:24:51.144-06:002017-01-30T08:24:51.144-06:00I use the same method when teaching factoring, alt...I use the same method when teaching factoring, although I LOVE that you teach the a=1 case after because I always have a student or two who get confused between the two strategies. I think that would help a lot. Thanks!Amanda Nixhttps://www.blogger.com/profile/06376739116359741785noreply@blogger.com