Factorisation – The Box Method!

Responding to a Twitter chat we were discussing the splitting the middle term method (which some students have difficulty with); if one must have a recipe to follow – try the box method. I always encourage students to check coefficients first, if the coefficients of x2 and the constant are prime they clearly do not need elaborate methods.

Working on Quadratic Grids from Underground Mathematics will help students develop and understand the method.


For instructions on the method:

Quadratic Factorisation Box method (pdf file)

An introductory post on Underground Mathematics is here and you can view all posts in the category Underground Mathematics.

Last Revision Lessons

Study leave is approaching fast for our examination classes so it’s time to think about those last lessons. I will be using a few mental tests with all my examination students as I find these work very well indeed. Last week with Year 13 we had a C3 (an A Level module – OCR MEI) mental test; at the end of the lesson they said that was really useful and requested a C4 mental test for this week. I think my favourite kind of lesson feedback is when students make requests like this!

Note that the ideas here can be used all year round – not just for last revision lessons.

These tests are simply short questions that test recall of the basic skills needed for the module; so for example some standard derivatives and integrals, graph sketches, changing the subject of the formula for expressions involving exponential functions and so on. Note that another possibility is to ask students to write down the expressions / calculations needed for a question (they can always come back and complete it later).

Basically, sit down with the syllabus in front of you and cover as much as possible. Although informal this is making the students individually recall material they will need – see Highlighting is a Waste of Time.

CIMT Teacher Resources

CIMT Teacher Resources

For some inspiration for mental tests have a look at the Centre for Innovation in Mathematics Teaching resources for GCSE (and for younger students note that mental tests are supplied for all the Key Stage 3 (UK age 11-14) units). In fact the GCSE resource shown above would also apply to AS level.

For the Teacher Resources scroll down to the end of the GCSE Resources page and you will find resources for each unit.

CIMT Mental Test

CIMT Mental Test – Using Graphs

For A Level students, questions such as Mohammed Ladak’s Essential Skills pack for Core AS or Corbett Maths A Level 5-a-day could be used / adapted. Questions do need to be short, recall type questions where just a short time is needed for any working out. I do find that because I use this idea regularly, I can just ask questions by looking at the specification and using my experience of what I know students forget!

Looking at the CIMT resources I noticed some more valuable revision resources; note the GCSE Revision pack; this has quick checks at Foundation, Intermediate and Higher Level and example papers with answers and mark schemes.

CIMT GCSE Quick Checks

CIMT GCSE Quick Checks

CIMT Higher Paper example

CIMT Higher Paper example

For revision tests by topic, each unit of the GCSE course has a revision test with answers. Whilst the vast majority of the material on the CIMT site is freely accessible, a few documents such as these revision tests are password protected. The password can be obtained if you send a request using your educational institution email address; CIMT also give the password to home educators.

I have added the CIMT GCSE Revision pack to the examination resources page which is part of the Revision Activities series of pages.