UKMT (teacher’s notes) – JMC 2015

This is the first post presenting my teacher’s notes of past UKMT papers, starting with JMC 2015.

The objective of these teacher’s notes is not to provide solutions — UKMT already provides an excellent Pdf of solutions and further investigations, which you can download here — but to provide insights to teachers as to how UKMT questions can be used in the classroom.

In other words, these teacher’s notes are about making the best of the educational value of UKMT questions. Which, by the way, extends the scope of UKMT questions beyond their target age group. For example, some JMC questions, although intended for Year 7-8 students, can be used for educational purposes up to GCSE, sometimes even with A level students with the addition of relevant extensions and investigations.

In order to help teachers, I have indexed each UKMT question by Maths skills and problem-solving skills.

With the Maths skills index (which will ultimately be laid out in an Excel file when more of these teacher’s notes have been published), a teacher can access all questions related to a particular topic (fractions, for example, or simultaneous equations, etc.).

With the problem-solving skills index, it is possible to select questions according to which specific key drivers you want students to learn in order to solve problems more efficiently, such as:

  • Complete the grid
  • Deduction
  • Easy way out
  • Economy
  • Elimination
  • Alternative strategies
  • Name / Label
  • Systematic list
  • Tree
  • Bar modelling

(NB: these problem-solving skills will be fully explained in my next post: Introducing some problem-solving skills)

The JMC 2015 paper can be downloaded here. We all have favourite questions. For me, the prize for JMC 2015 is Question 24, a highly educational problem on palindromic numbers.

Here is a recap table of JMC 2015 questions indexed by Maths skills and problem-solving skills, please click here to download the full PDF UKMT JMC 2015 (teacher’s notes).

JMC 2015 Teacher’s notes – Recap table

Competition Year Question Skills Problem-solving
JMC 2015 1 ·      Number / Adding and subtracting integers

·      Number / Negative numbers

·      Elimination

·      Deduction

·      Alternative strategies

JMC 2015 2 ·      Measuring / Time units
JMC 2015 3 ·      Number / Estimating

·      Number / Properties of number

·      Elimination

·      Alternative strategies

JMC 2015 4 ·      Number / Adding and subtracting integers

·      Algebra / Forming and solving linear equations

·      Deduction

·      Economy

JMC 2015 5 ·      Fractions / Adding and subtracting fractions

·      Algebra / Forming and solving linear equations

·      Name / Label

·      Bar modelling

 

JMC 2015 6 ·      Geometry / Angles in a triangle ·      Deduction
JMC 2015 7 ·      Numbers / Factors and multiples ·      Economy

·      Deduction

·      Alternative strategies

JMC 2015 8 ·      Numbers / Factors and multiples ·      Elimination

·      Deduction

·      Alternative strategies

·      Easy way out

JMC 2015 9 ·      Number / Estimating ·      Bar modelling
JMC 2015 10 ·      Number / 4 operations on integers
JMC 2015 11 ·      Number / Properties of numbers ·      Systematic list
JMC 2015 12 ·      Fractions / Adding and subtracting fractions

·      Algebra / Forming and solving linear equations

·      Name / Label

·      Bar modelling

JMC 2015 13 ·      Number / Adding and subtracting integers

·      Number / Factors and multiples

·      Systematic list
JMC 2015 14 ·      Number / Properties of numbers ·      Elimination
JMC 2015 15 ·      Number / Factors and multiples ·      Elimination

·      Alternative strategies

 

Competition Year Question Skills Problem-solving
JMC 2015 16 ·      Geometry / Polygons / Angles in a triangle

·      Algebra / simultaneous equations

·      Algebra / Rearranging formulae

·      Name / Label

·      Alternative strategies

JMC 2015 17 ·       Binary logic ·      Tree

·      Economy

JMC 2015 18 ·      Fractions / Equivalent fractions ·      Easy way out
JMC 2015 19 ·      Number / Properties of numbers ·      Systematic list

·      Elimination

JMC 2015 20 ·      Measuring / Area and Volume

·      Algebra / Sequences

JMC 2015 21 ·      Geometry / 2D shapes

·      Algebra / Forming and solving linear equations

·      Name / Label

 

JMC 2015 22 ·      Geometry / 2D shapes

·      Geometry / Symmetry

·      Fractions / Introducing fractions

·      Complete the grid

·      Economy

 

JMC 2015 23 ·      Measuring / Area ·      Deduction

 

JMC 2015 24 ·      Number / Place value

·      Number / Factors and multiples

·      Deduction

 

JMC 2015 25 ·      Geometry / Angles in a triangle

·      Algebra / Forming equations

·      Algebra / Rearranging formulae

·      Deduction

 

 

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