tag:blogger.com,1999:blog-4242439961617529545.post8435692534940385234..comments2023-05-26T13:04:17.896+01:00Comments on Resourceaholic: Teaching TrigonometryJo Morganhttp://www.blogger.com/profile/11919801458664779971noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-4242439961617529545.post-7314053587755721272022-02-06T16:45:44.321+00:002022-02-06T16:45:44.321+00:00Have you considered using a physics approach? In ...Have you considered using a physics approach? In physics--I'm thinking of vectors primarily, but the word vector doesn't have to be used--a vector quantity is split into two orthogonal components because the two components are completely independent of each other. So the quantity is a %age of one and %age of the other. Whatever amount a vector is in one direction is shown by the John teaches Mathhttps://www.blogger.com/profile/11724625940335707813noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-21179896043182923132022-02-06T16:10:10.306+00:002022-02-06T16:10:10.306+00:00Have you considered using a physics approach? In ...Have you considered using a physics approach? In physics--I'm thinking of vectors primarily, but the word vector doesn't have to be used--a vector quantity is split into two orthogonal components because the two components are completely independent of each other. So the quantity is a %age of one and %age of the other. Whatever amount a vector is in one direction is shown by the John teaches Mathhttps://www.blogger.com/profile/11724625940335707813noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-24835545583765993572021-05-12T20:34:01.380+01:002021-05-12T20:34:01.380+01:00I am so excited to try this new angle for teaching...I am so excited to try this new angle for teaching trig (geddit). My brighter students definitely demanded a fuller understanding rather than just a method, so very excited to try out the similar triangle approach. Thank you so much!!!Bananabananahttps://www.blogger.com/profile/11838698637160127965noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-20645810129253849062021-02-16T10:09:12.698+00:002021-02-16T10:09:12.698+00:00Hi. Sorry for the slow reply. Did you get the answ...Hi. Sorry for the slow reply. Did you get the answer from Twitter in the end?Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-43750064628215908822021-02-07T20:43:12.318+00:002021-02-07T20:43:12.318+00:00Hi Jo,
As always, a really useful post. Do you kn...Hi Jo, <br />As always, a really useful post. Do you know when trig tables stopped being used in schools and calculators took over?<br />Thanks youAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-43559450273351395802019-02-04T23:09:45.636+00:002019-02-04T23:09:45.636+00:00Hi. I can’t remember because this post is very old...Hi. I can’t remember because this post is very old but I probably used CIMT images and edited them in Paint! Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-28726454261926964782019-02-03T14:42:47.716+00:002019-02-03T14:42:47.716+00:00Hey Jo, great post!
It's helping with my plan...Hey Jo, great post!<br /><br />It's helping with my planning for my top set year 9 who will be meeting Trigonometry for the very first time and I would love for them to appreciate the patterns and the mathematics behind it all rather than the good old 'here's SOHCAHTOA, now label the sides and find x' approach. I wondered where your triangle example images are from? You said you Anonymoushttps://www.blogger.com/profile/01621405718961080749noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-2122075620679646902018-11-25T07:44:53.123+00:002018-11-25T07:44:53.123+00:00It sounds like you’ve done a great job! What wordi...It sounds like you’ve done a great job! What wording do you think will confuse them? Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-49897484393471859342018-11-20T09:56:29.639+00:002018-11-20T09:56:29.639+00:00Hi Jo
I have taught quite a low attaining set of ...Hi Jo<br /><br />I have taught quite a low attaining set of y11 pupils trigonometry through ratio. It followed on nicely from our previous unit of work in which they asked "what's the point of writing a ratio in the form m:1?" What I am worried about now is that we didn't quite make the leap to using the formula algebraically. They currently feel confident in trigonometry which Niamh Geehttps://www.blogger.com/profile/17655478557787525548noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-50951061938903805742017-10-27T19:43:44.097+01:002017-10-27T19:43:44.097+01:00Sorry, I've not been clear. It's not a stu...Sorry, I've not been clear. It's not a student's work, it's *my* example of what a student's work would look like if they used this approach. And the degrees symbol is a mistake - a 'typo' by me! I have corrected now (kind of, without rewriting it all), thank you for pointing it out! <br /><br />When I wrote this post a couple of years ago I was thinking of new Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-15160635231948185572017-10-27T18:28:24.023+01:002017-10-27T18:28:24.023+01:00Looking at the example student working using the s...Looking at the example student working using the similar triangles method, I was initially impressed with her apparent understanding of trig functions as ratios - this is not always evident to students when the ratios are presented as decimals, rather than fractions. But looking at her final answer made me wonder if she really understood what she was doing - her final answer should be a length!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-28242244645826104822017-09-28T09:34:59.730+01:002017-09-28T09:34:59.730+01:00This comment has been removed by the author.reginald suricthttps://www.blogger.com/profile/02865395258495641241noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-88538668392185181232016-03-02T21:11:50.607+00:002016-03-02T21:11:50.607+00:00Hi. Thanks for the comment. I'm afraid I can&#...Hi. Thanks for the comment. I'm afraid I can't help with this - I'd love the answers too. I'd suggest sending a quick email to manager@cleavebooks.co.uk to request the answers, and if you hear nothing back try the affiliated feedback@cimt.org.uk. No harm in trying! Do let me know if you have any luck, and sorry again that I don't have the answers!Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-10863306810375594442016-03-02T16:40:28.529+00:002016-03-02T16:40:28.529+00:00Thank you for this excellent breakdown, and lovely...Thank you for this excellent breakdown, and lovely wealth of resources.<br /><br />I have just been looking through the TROL booklet, which is great, however I am unable to find a link to where I might find the answers. I could of course sit down and work them all out, but it would save me a lot of time if anyone is able to let me know where I need to look. There is a description as to where Anonymoushttps://www.blogger.com/profile/05340627084368613003noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-45788491835687429292016-01-17T10:53:04.950+00:002016-01-17T10:53:04.950+00:00I agree that it is our job to help students unders...I agree that it is our job to help students understand mathematics and teaching just a method is wrong. I'm not sure that I agree that solving a quadratic by the method Hannah does not encourage understanding. It shows how the quadratic is split and can then be used in a grid method or other method, it is particularly useful when factorising quadratic where a > 1 ( whilst it is clunky it Anonymoushttps://www.blogger.com/profile/00467302177692913021noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-55636059116397812712015-11-26T19:21:15.288+00:002015-11-26T19:21:15.288+00:00Thank you for this comment. This sounds like an am...Thank you for this comment. This sounds like an amazing lesson - I'm so pleased to hear that my post gave you some ideas. Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-65586568970981500542015-11-26T18:55:08.940+00:002015-11-26T18:55:08.940+00:00I introduced trig in this way to my top set year 1...I introduced trig in this way to my top set year 10s today. They've all met it in year 9 and are familiar with SOHCAHTOA, but they engaged really well with developing the concepts from ratios. Students felt they had a better understanding of why we use the ratios at the end of the lesson and what the random decimals the calculators produce meant. They were fascinated by the tables and the Unknownhttps://www.blogger.com/profile/15065445779281059436noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-55649093832384667292015-07-04T19:57:06.289+01:002015-07-04T19:57:06.289+01:00Thanks for your comment Paula, lots of very good p...Thanks for your comment Paula, lots of very good points made and things for me to look into.Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-82561063323947737922015-07-01T22:56:16.368+01:002015-07-01T22:56:16.368+01:00Great post! I think that Hannah's and my brain...Great post! I think that Hannah's and my brain might have been made from the same mold: I followed all the rules and got high marks in trig but it took revisiting trig as an adult for the light to go on that sine referred to a fraction, which, or course, is a ratio. The fact that, in high school, all my "answers "were in the form of decimals made the whole ratio thing so opaque.In Anonymoushttps://www.blogger.com/profile/04092889700238975792noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-51515196235739748872015-05-25T03:32:12.415+01:002015-05-25T03:32:12.415+01:00Very useful resources. Thank you.
I also have a us...Very useful resources. Thank you.<br />I also have a useful book related to this topic.<br /><br />Trigonometry For Dummies (2014).pdf - 7.2 MB<br />http://www.anafile.com/hxsuffw53wx2.htmlAnonymoushttps://www.blogger.com/profile/13649451028474587142noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-68673978394987095222014-10-16T13:30:36.313+01:002014-10-16T13:30:36.313+01:00Thanks to @letsgetmathing for sharing this excelle...Thanks to @letsgetmathing for sharing this excellent blog post which contains similar ideas, though a slightly different approach: <br /><br />http://danpearcymaths.wordpress.com/2013/04/17/introducing-trigonometry-taking-a-digital-leaf-out-of-fawn-nyugens-book/<br /><br />I've tried the triangle-measuring approach before but I find that as soon as a calculator method is introduced, the Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-14095350328169596542014-10-15T09:17:38.563+01:002014-10-15T09:17:38.563+01:00Brilliant, thank you.
I just assumed that the ta...Brilliant, thank you. <br /><br />I just assumed that the tables were stored in the memory, didn't realise the calculator was computing them. I've learnt something new! Thanks.Jo Morganhttps://www.blogger.com/profile/11919801458664779971noreply@blogger.comtag:blogger.com,1999:blog-4242439961617529545.post-44719429974538656962014-10-15T08:57:00.004+01:002014-10-15T08:57:00.004+01:00I like that similar triangle idea.
Among other th...I like that similar triangle idea.<br /><br />Among other things I use this http://burymathstutor.co.uk/UnitCircle.html <br /><br />By the way, I wouldn't tell them:<br /><br />"...that all the numbers from these tables are saved in the memory of a scientific calculator..."<br /><br />I've read that calculators use Taylor series or the CORDIC algorithm. Anonymoushttps://www.blogger.com/profile/11246289123353125013noreply@blogger.com