From the University of Cambridge comes Underground Mathematics which started in 2012 as the Cambridge Mathematics Education Project (CMEP). The site provides a library of rich resources for age 16+ students with the aim of “Enabling all students to explore the connections that underpin mathematics”. Underground Mathematics is being developed by the University of Cambridge, funded by a grant from the UK Department for Education. The resources are free for all users.
From the home page and you will find the very clear ‘How-to guide‘; use the sections and/or watch the video. Resources are helpfully classified by type and you can browse in many ways.
Note that you can also select individual elements on the map. Try Quadratics for example and check the station guide for information. Looking at the guide led me to Name that graph; as with all the resources on the site more than just the problem is provided, we also have printable resources, solutions and teachers notes.
I thought I’d have a look at Review Questions on Algebra – so much to choose from! How about an A Level question from 1975?! As you can see, not only do we have the question, but a suggestion, then a solution. And if that’s not enough let’s take it further and generalise, exploring on GeoGebra as we do!
I’m tempted to try that one with my very able Year 10 set studying for the new Mathematics GCSE qualification. In fact I suspect we can find other useful questions here for our most able GCSE students.
Prepare to lose yourself for some hours / days in this treasure trove! This resource is frankly incredible and I applaud the team behind this. The site I know will be on my own go to list of places where I know I will always find high quality resources to make my students think and more than that has suggestions for exploring further on a given area and of course explore connected areas.
I predict rich and happy travels around these lines for students and teachers!
See the Underground Maths series of pages for further information.
thanks for sharing this information. I didn’t know about this and I find it very useful 🙂
Nice resources which I didn’t know about, even though I did Mathematical Education at Cambridge. I like the fact that it links to Geogebra, the delights of which I continue to discover, and the mysteries of which still get me every time.
A good idea as you say to extend with GeoGebra, particularly as that is now available for mobile devices. I’d use Desmos as well where appropriate.
I checked out this example, and didn’t think much of the solution statement:
“Substitution works well as a method here. Elimination won’t work, as subtracting (a multiple of) one equation from the other will not cancel any terms.”
“Don’t think, just find a method that works.” This is hardly mathematical. The real reason that “elimination” won’t work is that the second equation is not linear. I was also under the impression that “cancel” was a dirty word nowadays!
I was not aware that cancel is a dirty word! 🙂 I do think some of the things the students do when they think they are canceling belongs in the big book of Illegal Algebra!
Remember that GCSE students have been used to adding and subtracting, so pointing out that this does not achieve a lot seems reasonable. I would also make the comment re non linear as well as discussing the methods.
The anti-cancelling thing is a USA thing. Personally I like the word !
I had another look and didn’t see any suggestion of testing the solution by substitution of the results into the second equation. Students are regularly asked to “check their work”, so they go through it again, not seeing the errors in the algebra. Testing the results is seriously overlooked over here (USA). What about the UK ?
It’s certainly something my colleagues and I all tell them to do! I tell my students there is no excuse for getting solutions to equations wrong because you can check!
Hello Howard, and thanks for your comments.
You may notice that there is a “Discuss” button at the top of the page – this is a great place to leave feedback about issues you have found in a resource, so that the Underground Mathematics team is guaranteed to see them.
I have edited the solution (hopefully improving it!) to take account of your comments. I have not removed the word “cancel”; it is still in common use in the UK, and describes the elimination process well.
Julian, from the Underground Mathematics team
Julian thanks so much for the response.
Did you notice the twitter chat yesterday evening (#mathsTLP)? Lots of recommendations for the site from various people.
(I set the question for my Year 10s at the end of the lesson today!)