School mathematics moves up a gear between KS2 and KS4.  KS3 constitutes the (widely neglected) link between these phases.  At KS4 the content is more abstract, more complex, and apparently new ideas arise with greater frequency.  This is only digestible if the connections with KS2 are understood, the links between apparently separate topics are clear, and concrete foundations are laid at KS3 for the abstractions of KS4 (and beyond).  We explore this neglected phase in conjunction with the (free) resource Teaching mathematics at secondary level.


  • Insights into the bigger Mathematical conceptual picture
  • In depth exploration of key topics and how to teach them
  • A joined up coherent understanding of perspective of how topics link together
  • Clear understanding of the KS2 curriculum and prior experiences of where students are coming from
  • Strategies to raise understanding and success in your classroom
  • A set of resources and key text to build on after the course
COURSE DATE London | Friday 22 January 2021
  • Heads of Mathematics
  • KS3 maths teachers
  • LA and Academy chain advisers
IN-SCHOOL You can also book this as an In-School Course
  • A specially prepared folder of detailed notes, practical advice and guidance
  • Notes prepared by the educational experts leading the course
  • Expert produced PowerPoint presentations
  • CPD Certificate of attendance


10.00 – 11.00: Identifying the challenge. Indicating the solution.

  • Teaching mathematics at secondary level: Introducing the (free) core resource
  • Why KS3? The vital (but neglected) link (between KS2 and KS4 – and beyond)
  • Laying foundation for KS3. The evidence: what is needed (with examples)
  • Integrating the curriculum

11.00-11.15: Break

11.15 – 12.45: Multiplicative reasoning (= fractions) concepts and teaching ideas

  • Units and measures (multiples)
  • Changing units: easy proportion
  • Multiplication: beyond repeated addition
  • Fractions – as operators (percentages), and as numbers (submultiples): arithmetic
  • Ratio and proportion
  • Fractions and decimals

12.45 – 13.45: Lunch  

13.45 – 15.00 Roots into Algebra and its links and use across the other core topics

  • KS2 revisited: Area of a rectangle (or triangle); “I’m Thinking Of A Number”; structural arithmetic
  • From arithmetic to formulas, equations, and expressions
  • Arithmetic: how operations work; changing notation; brackets; MBA
  • The ingredients: “Collecting up” (place value, measures, fractions, surds); Negatives and fractions; Powers and index laws (place value)
  • Red herrings

15.00 – 15.45: How to embed and make problem solving a natural part of your lessons

  • The difference between an exercise and a problem
  • Variation (from simple exercises towards more challenging problems)
  • Integrating problem solving in regular instruction
  • Improving problem solving

15.45 / 16.00pm: Depart

Tony Gardiner

Tony is a mathematician, married to a teacher, who has worked with students and teachers for 50+ years.  He was part of the SMP 11-16 curriculum development project; started the national pyramid of Challenges, Olympiads, and summer schools for interested secondary students; published the Problem Solving Journal for secondary students; ran the National Mathematics Teachers’ Summer School; and has published around 30 books of materials for students and teachers.  He received the 1995 Paul Erdös Award, and the 2016 International Award for Excellence in Mathematics Education.

Tony will be co-leading this course with a current practitioner tbc