Maths Lessons

Lesson Plans

I have brought both academic and business experience into the design of my Lesson Plans. For GCSE there are 80, one for each Maths topic covering full syllabus sections of Numbers, Algebra, Graphs, Ratios, Geometry, Trigonometry and Statistics. They each follow a consistent template, built around the following key sections of a 1 hour lesson, which we go through in discussion and by touch screening to reveal the next stage. I often send these materials at the end of each lesson and also they are now published and available through Times Education Supplement in this link: in which you can see a video which describes the content below. Note that I have built up a similar set of materials for A Level Maths but I will focus on GCSE : 

  • Context
    The lesson begins with a review of the previous week’s homework. Following this there are descriptions of where this week’s topic sits in the course (Numbers, Algebra, Graphs, Ratios, Geometry, Trigonometry, Statistics), what topic came before and what is next. The grade band for the topic’s questions is also shown (1-3, 4-6,7-9)  There is sometimes a light hearted reference to break the ice (for example a record, Blondie’s Parallel Lines: what actually is the definition of parallel lines?). The choice of topic is often determined by the pupil themselves – what they are doing at school, what they are being tested upon. I am very flexible because I can immediately find my materials on my well ordered data base of files.  
  • One-page coaching card – high level summary.
    This is a description of the lesson in terms of key formulae or definitions, methodologies, golden rules, resources such as BBC Bitesize and CGP guidebook, typical numerical question, typical tricky problem am finally tips and hints
  • One page coaching card – detail
    Definitions, formulae, methodologies and golden rules to solve the full range of specific types of questions likely to crop up at GCSE are examined in more depth. This involves both ensuring the basics are embedded, and discussion of the topic with the student.
  • Guided solutions
    I use interactive technology to reveal step by step on screen the methods leading to the solutions for at least 4 numeric and applied problems per topic. These questions follow the syllabus religiously, but will often adapt them in a light-hearted way (for example, “express 1 million in standard form” becomes “express Brad and Angelina’s retweets” or “Wayne and Christiano’s Facebook Like numbers” in standard form).. I also use material from the 1000 questions interactive quiz I’ve created which is also available on TES in this link.
  • Fast and Furious 7 round up
    Finally there are 7 quick-fire questions to check understanding, starting with the pupil talking me through the definitions and important tips in their own words, then answering some easy problems in their head.  To finish the pupil will attempt a few problems on their own in writing, often from my huge bank of topic specific past paper questions. 
  • Homework
    I will set/email homework after each lesson on the topic we have covered – a combination of written past paper questions, with worked solutions next page, in powerpoint and on-line quiz links generally from a website such as the BBC Bitesize or CGP Maths Buster site (my course is fully compatible with CGP, the most popular set of GCSE guidebooks).  I will provide extracts of real GCSE or KS3 test papers so I can check methodologies for a few questions per week. The coaching cards described above can be printed double sided onto one sheet, so the pupil can build up a non-cluttered set of consistent one-page “crib sheets” to keep for revision. Ideally the lessons are run one a week over the 2 year programme, in line broadly with the pace at school, but a course of lessons can be tailored to cover specific priorities. I have also published a fast Maths mock interactive quiz which generates an approximate grade a revision list.

    • Exam management and Problem Solving
      Finally, I have developed a specific set of lessons on “exam management” covering golden rules for revision.  These rules cover the weeks leading up to the exam, the period just before the exam, and even in the exam hall itself. An example of a tip could be: if you are asked to solve a quadratic equation in the non-calculator exam, you generally use the factorisation method, whereas in the calculator exam, you should use the formula method if specifc decimal places are requested.  Many of these tips will be covered at school, but perhaps the pupil might miss some

      I have also studied many past papers in particular the mark schemas and examiners comments and will present a list of “twenty things the examiners do and don’t want to see”.

      A couple of golf analogies are apt, First, as Gary Player said, “the more I practice the luckier I seem to get”. So revision and tutoring has to be active for the pupil not passive, though a degree of concentrated absorption is still needed!. Second, even the great golfers use “course management” to supplement their talents, for instance using their caddies for on-course advice on distances and terrains, and still use coaches and putting practice, and driving ranges for pre-tournament warmup. Think of the tutor as coach and caddie! I also have a Problem Solving short course which describes  up to 6 quick mental steps to go through when faced with tricky problems which GCSE increasingly throws at you, These could be problems shrouded in wordy description or where two or even three separate methods are required in one question.

      I am a big believer in the importance of end of topic or end of half term tests so if a pupil is going to be tested on a particular set of topics I take the trouble to prepare “mini-mocks” – a couple of questions with worked solutions for each topic to help revision.