Author: tombennison

I’ve produced another revision clock activity for the new specification A-Level, this one is focussed solely on mechanics.

Download the file here.

At some point I hope to get round to writing up worked solutions, but at the moment I am focussed on getting resources out there for students to use.

I’ve recently shared an A-Level Further Maths vectors relay and thought I would make one for my AQA Level 2 Further Maths students.

There are 16 questions in total, so 8 per person in a pair. The idea of these is like the UKMT Team Challenge relays. One person works on the even numbered questions and their partner works on the odd numbered questions. They have to pass values between them to enable them to complete all questions.

As ever, the file is available to download here – let me know if you spot any errors please 🙂

One of the topics requested by my current Year 13 Further Mathematicians in their revision lessons has been the geometric interpretation of the solution of simultaneous equations.

I hadn’t taught this at A-Level until the new specification so it was interesting to teach. I would always have done this using augmented matrices, performing row operations and then looking at the difference in rank between the matrix and the augmented matrix so the approach at A-Level was new to me.

The idea of the activity is to sort the 12 given situations into the five geometric possibilities.

File for use available here.

I’ve recently been listening to the latest episode of Craig Barton’s (@mrbartonmaths) always excellent podcast series. In it he discusses various things with Michael Pershan (@mpershan) but something that caught my ear in the first 15 minutes or so was a short discussion of “two column proofs”.

We don’t seem to have this formalism (actually “structure” is probably a better word here) much in the UK.

This post is to share a resource that I thought I had shared a couple of years ago (apologies if I did and I just can’t find my own post anymore….)

When I started teaching the new specification Mathematics A-Level; with its increased emphasis on proof, I decided to formalise some of the GCSE style number proofs and use these as an introduction to the topic at A-Level. To do this I used what I called “know-why” tables which seem very like this “two column” method Michael describes, so I suspect I originally saw the idea in an American textbook at some point.

If you want to take a look at the whole worksheet – which includes definitions, examples and exercises – download it here.

I’d love to know what you think…

This is a post mainly for me…. and a resource I wrote probably 5 years ago now.

I routinely want to use this resource and always have trouble finding it in my files so I hope that once it is up on here Google will be able to help me locate it in future!

As we all know when faced with a quadratic \(y = x^2+bx+c \) that has integer roots we can find the factors by looking for two numbers that multiply to give the value of \(c\) and add to give the value of \(b\). I often start this topic with getting students to complete a few of these kind of puzzles:

I’m not sure where I saw this idea originally  – possibly Jo Morgan (@mathsjem) or Don Steward maybe.

Anyway if you fancy using my sheet with a lot of them download it here

Back in March I saw the tweet shown below from Mike Lawler (@mikeandallie).

I think I would default to substituting \( u = \mathrm{e}^x \) here but in the thread were a range of different approaches. Tim Gower’s (@wtgowers) was particularly inventive.

I’ve always enjoyed asking students to integrate things in different ways and then asking them to show their solutions are equivalent. A favourite one of mine is \(\int \sin(x) \cos(x) \ \mathrm{d}x \). Because of this I have made a sheet asking students to explore a few of the possible methods.

The sheet for printing to A3 can be downloaded here.

For preparation for Year 12 Mocks I made my class an AS Further Revision clock activity. My Year 13s have also done it.

The file can be found here.

A fair while ago I wrote an FP1 Revision Relay for the old specification.

I have recently written one that targets the Vectors content of (predominantly) AS-Level Further Maths. 

The intention is that it is used like the UKMT Senior Team Challenge relays, in fact that is how I used it last week with my Year 13 Further Mathematicians. Students work in pairs – one of them answering the odd numbered questions and one of them answering the even questions and passing the solutions between them.

If you would like to give it a go download the file to use here.

Short post as I need to go to bed!!

I have made my first Revision Clock activity for the new syllabus.

Please let me know if you use the file located here with your classes, I would love some feedback.

So this was meant to be posted on Monday evening and time has got away with me. Hence an early Tuesday morning post.

Something a bit different as im sharing a revision sheet I made for my Year 11 Level2 Further Maths students last week’s. It covers matrix transformations and has some brief notes plus a few exercises. I guess it could be used to revise the basics of transformations for Year 12.

File Here.

Solutions here.