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.

I Hate Top 10 Lists!

This morning I enjoyed reading Ross Morrison McGill’s thoughtful “Top 10 UK Education Blogs Or Not?”. It was the or not part of his title that caught my eye. Ross is quite rightly talking about the validity of the ranking but Top Ten lists have interested me for some time.

Top 10I have often been wary of so called Top (insert number) lists particularly when said list is simply a blog post and there may be little validity behind the choices. You will see that I always preface my own favourite lists with a reminder that the choices are personal to me – I am not claiming any authority.

Others have written well on this subject. So I present in no particular order and with no authority whatsoever some of my favourite articles on hating top 10 lists!

Returning to the list of Top 10 UK Education Blogs mentioned at the beginning of this post, regular readers will be aware I look regularly at Ross’s site – I’m a fan of the 5 Minute Series, particularly when it comes to Lesson Planning. On that list is a real personal favourite – David Didau’s The Learning Spy, a favourite because David constantly challenges my thinking. I am currently feeling guilty at the number of times I must have written about students being engaged when it comes to lesson observation! I try to be so aware of Robert Coe’s Poor Proxies for Learning. What I really mean by engaged is that students are indeed getting on with the task they have been set. I’ll only know more about their learning by
Poor Proxies for Learning

looking at other evidence. I recently noticed some of my own Year 11 students in a general revision session for the Year group successfully answering a GCSE question on Direct Proportion. I taught that topic to them some months ago and recall being pleased with the lesson at the time but it is so much more convincing seeing them answering problems some time later! (We have also picked it up again using resources such as Mr Corbett’s 5-a-day). I’ll be even more convinced of course when I look at the exam board question by question analysis later this year.

I read many Maths blogs of course, but think it is important to look at some of the more general education blogs too.

Happy Reading!

Final Revision

That quote from Robert Collier seems so appropriate when it comes to revision. This academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

Once again we are in the final run up to examinations, so I checked the various revision resources I have highlighted on this blog earlier this year and created a series of revision pages which I hope makes resources easier to find. I have recently updated these again. Before mentioning the resources though we should think about how best to use them.

The first page ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. Earlier this academic year when I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to the report the two learning strategies with the highest utility are distributed study sessions (last minute cramming is not effective) and practice testing.

Interestingly, interleaved practice: though rated as just moderate utility gets a special mention for students’ learning and retention of mathematical skills. William Emeny has written on this see this post and a follow up on Great Maths Teaching Ideas.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

There have been recent updates, in particular to the examination questions page. I will certainly be using all the resources I have mentioned on that page. Resources in the collection allow for a mix it up approach but also provide examination questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources.

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Wishing teachers and students everywhere a successful final revision period.

Easter 2017

It’s Easter time again, so time for some Mathematical Easter treats, including an updated version of the best Easter eggs – those from WolframAlpha!

Also a post for students – a puzzle which is just an excuse to solve some simultaneous equations (and how to do it on Excel with the neat MINVERSE function!)

Google - easter

Google graph – click on the image.

A reminder that you can just type a function into Google and its graph will be returned!

Darth Vader curve

Darth Vader on WolframAlpha – click on the image

WolframAlpha of course can show you some graphs of Easter eggs!
I have noticed whilst using WolframAlpha random suggestions of queries popping up that somebody out there thought I might enjoy (very worrying how right they are!); this popped up – typing for example Darth Vader curve into WolframAlpha gives you just that! And my favourite Dilbert and associates are all there too!

On the subject of Easter eggs I must return to this definition. An updated edition of…
WolframAlpha – a little fun! 

Happy Easter to educators and their students everywhere!