tag:blogger.com,1999:blog-4242439961617529545.post7265157427401059016..comments2023-06-01T15:50:15.447+01:00Comments on Resourceaholic: Factorising by InspectionJo Morganhttp://www.blogger.com/profile/11919801458664779971noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-4242439961617529545.post-44594780531512184142022-11-03T12:20:09.217+00:002022-11-03T12:20:09.217+00:00Thanks for this.
It got me thinking about the gro...Thanks for this.<br /><br />It got me thinking about the grouping method that I use, and how I show that the order of the two components doesnâ€™t change the final answer, so we can get them both without the full procedure.<br /><br />E.g. 12x^2+11x-15. Two numbers that add to 11 and multiply to -180 are 20 and -9.<br /><br />12x^2+20x. Factors to give 4x(3x+5)<br />12x^2-9x factors to give 3xAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-50892695159406883102020-09-11T12:54:36.361+01:002020-09-11T12:54:36.361+01:00I'd thought of doing it that way too - once yo...I'd thought of doing it that way too - once you have the first factor it's easy to factorise by inspection (even if it's a quartic or greater) - but it seems like overkill for just quadratics. I do show that it also works for quadratics when teaching factor theorem & factorising for cubics though.Lynnehttps://b28mathstutor.co.uknoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-46197864189249257802019-01-25T11:01:03.654+00:002019-01-25T11:01:03.654+00:00I feel what you say about inspection rings true, J...I feel what you say about inspection rings true, Jo. One thing I find really helps when I teach inspection as a method is to start by giving the students a ton of examples with a and c both prime numbers. They'll see the benefit of inspection straight away! Anonymoushttps://www.blogger.com/profile/01859436231945368531noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-14673593252779590762019-01-14T18:11:57.623+00:002019-01-14T18:11:57.623+00:00I'm thinking of this at GCSE where my students...I'm thinking of this at GCSE where my students do not have the Classwiz. You're right, if they have a Classwiz they can just use equation solver and this post isn't relevant to them. Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-61099690602192147082019-01-14T11:58:17.121+00:002019-01-14T11:58:17.121+00:00Even with 12x2 + 11x - 15? As someone who enjoyed ...Even with 12x2 + 11x - 15? As someone who enjoyed mental maths, I personally always liked inspection because of the Countdown-esque buzz of chasing down the numbers, but there are still plenty of A* grade pupils who struggle to plough through all the possibilities and dislike the trial and error element of inspection. <br /><br />For less number-crunchy students who take time to work through theJonathan Ratnasabapathynoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-49580069397457501342019-01-11T19:01:59.886+00:002019-01-11T19:01:59.886+00:00It just seems a rather convoluted method for somet...It just seems a rather convoluted method for something that can be done in seconds.Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-5400298249484831672019-01-10T23:00:32.074+00:002019-01-10T23:00:32.074+00:00Is there an argument against finding the roots of ...Is there an argument against finding the roots of the function first and factorising second? I go straight for the discriminant because it tells you immediately whether or not it is possible to factorise it, and once you know that, it's only a hop and a skip to the factors... Jonathan Ratnasabapathynoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-41383477079347599562019-01-01T10:11:37.148+00:002019-01-01T10:11:37.148+00:00I agree with you on that - insisting on full conce...I agree with you on that - insisting on full conceptual understanding before teaching procedures isn't always helpful. I'm more concerned with the fact that students are less likely to remember a string of steps with no logical connection. Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-81446606913819014922018-12-30T08:49:03.839+00:002018-12-30T08:49:03.839+00:00I agree that it's not a perfect method (Is the...I agree that it's not a perfect method (Is there a perfect method?) but I disagree that no explanation is a problem and that any damage is caused. As long as they can see the relationship between the question and the answer; understand what factorisation means i.e. breaking an expression/quantity into a product of two or more quantities and be able to factorise trinomials in different Vivienne Hhttps://www.blogger.com/profile/05370891191842279947noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-77341436029052235152018-12-29T11:55:26.479+00:002018-12-29T11:55:26.479+00:00I've seen that a few times before and I'm ...I've seen that a few times before and I'm not a fan tbh. I'm surprised you find it sticks in the long term - how have you assessed that? There are a number of steps to remember (and those steps have no logical connection) which would make it hard to remember. As you say, it seems like magic!Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-57037609513649237942018-12-29T11:51:45.430+00:002018-12-29T11:51:45.430+00:00Totally agree that the grouping method will stick ...Totally agree that the grouping method will stick better if you use the same method for monics. Nice post about that <a href="https://patternsinpractice.wordpress.com/2011/04/25/factoring/#respond" rel="nofollow">here </a>. Problem is, I find that using grouping for monics is unnecessarily inefficient - I don't want to teach a multi-step procedure for something that can just be written down.Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-81487573252460551042018-12-29T02:54:01.425+00:002018-12-29T02:54:01.425+00:00I'd argue that if you can't explain a tech...I'd argue that if you can't explain a technique well then its better to use an alternative that is comprehensible. And providing no explanation reinforces a view of math as an arbitrary set of "incantations" to be memorized rather than a logical system with structure. That actually causes a bit of damage.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-72223211830814156622018-12-28T13:28:45.487+00:002018-12-28T13:28:45.487+00:00After many years of teaching different methods of ...After many years of teaching different methods of factorising trinomials, I find this method below (which I call Slide and Divide and Bottoms up) the one that sticks best. However, it does seem like magic Maths. When I tried to explain why this method works, I completely lost the kids, so now I don't even bother.<br />SLIDE AND DIVIDE AND BOTTOMS UP METHOD<br /><br />Example: FactoriseVivienne Hhttps://www.blogger.com/profile/05370891191842279947noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-18799576084637435552018-12-27T19:32:37.538+00:002018-12-27T19:32:37.538+00:00Nice post Jo, thanks. Its got ke thinking about ho...Nice post Jo, thanks. Its got ke thinking about ho2 i t2ach and how i would do it.<br /><br />regarding stickability of the grouping method - i think it sticks much better if you use it for monic quadratics too. The issue with forgetting comes when you teach them to factorise by inspection for monic then bust an entirely different method for non-monic. It alsohelps is you teach full distributive Cavhttps://www.blogger.com/profile/08497166692282461180noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-15833639967110118522018-12-27T18:56:58.388+00:002018-12-27T18:56:58.388+00:00I just realized another strategy today: If you'...I just realized another strategy today: If you're trying to simplify an expression like: (x^4 + x^2 + 1)/(x^2+ x + 1) Rather than trying to factor the denominator just give polynomial division a try. <br />Benjamin Leishttps://www.blogger.com/profile/10974191081762367425noreply@blogger.com