Go for hybrids ! (How to spark off a Maths topic ? – Part 3)

This is the last part of our review of possible ways to spark off a Maths topic (preliminary note: it is recommended to read the 2 previous posts: How to spark off a Maths topic ? – Part 1: concept processors and How to spark off a Maths topic ? – Part 2: memory reinforcers).

Actually… the best sparks are often hybrids. It’s quite nice to have logic (conceptual processor) + emotional engagement in order to activate memory (memory reinforcer).

Let’s look at a few examples…

  • Card tricks:

Card tricks are among the most efficient ways to introduce algorithms. They are also essential to understand the difference between the world of probabilities (an event which is more or less likely to happen) and the world of algorithms and computer science (a process that NEVER fails). Card tricks are at the same time totally rational and spectacular, making them ideal hybrid sparks.


  • Pictures (again):

955-san-francisco-houseThis picture (from 101qs) is a good example of a hybrid spark for any lesson on angles or trigonometry. To start with, there is a striking and irrational element to it, which reinforces memory. Then reason takes over and concepts/skills provide the explanation.


  • Stories:

Stories provide an immense reservoir of hybrid sparks, particularly when the story seems totally mysterious to start with, but the lesson loops back on it and things appear absolutely logical and obvious in the end. More on that later…


  • Hoaxes:

An official-looking letter from the Minister of a fake African country usually works very well.


  • Students in space:

‘Conceptual’ does not necessarily mean ‘exclusively mental’. On the contrary, sparks were the body is involved can be very effective:

  • placing students in an x,y space, organising a transformation relay;
  • dividing the class into fractions, ratios, percentages.


  • Thunks:

Example: if you keep halving the distance between your fingers, will they eventually touch?


  • Quotes:

Example 1: There are 10 kinds of people in the world: those who understand binary numbers, and those who don’t.

Example 2 (to introduce vertical asymptotes): The right to swing my fist ends where the other man’s nose begins. (Oliver Wendell Holmes)


  • Manipulation:

Building 3D shapes from videos, nets, etc.


  • Games (and game deviations):

Games are not ideal sparks as such (they are actually ideal driving forces — more about that later…). However, they often prove efficient when embedded as a spark because there is a natural engagement when playing them and they provide opportunities for easy incrementing.

Let’s look at an example:  countdown. This is a common game in the classroom, but there are different ways to build on it:

  • Countdown is actually inverse Bidmas when you write out the solution in a single line
  • If you insert variables, then it becomes an algebraic countdown that can be used to expand multiple brackets, solve linear equations, etc.



One last point about sparks: from a great number of conversations with teachers, as well as observing lessons, I have often found that Maths teachers are not necessarily aware of the considerable variety of sparks that is available to them. And even then, they do not use this variety that much. Should they ? The answer is: yes if possible, they probably should. But why ?

Why is it important to vary the types of sparks from one lesson to the next ?

One of the best-kept secrets of using sparks to their full variety is that it enables Maths teachers to stabilize the structure of most of their lessons to a nice routine that students will feel comfortable with. In other words, the more varied the sparks, the more routine you can have otherwise, which will benefit the whole class.

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