Looking forward to the first London Maths event of the year, I was reminded of Colin Foster’s wonderful Mathematical Etudes site. To quote Colin Foster:
Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.
(The session charge of £10 covers you not only for this session but also for the 5 remaining sessions of the 18/19 academic year. The sessions are free for trainee teachers in their ITT year.)
Note the Etudes by topic at the foot of the page; Number, Algebra, Geometry, Probability & Statistics are available. Looking at Algebra for example, under Solving Equations we see Connected Quadratics. Intrigued by Lyszkowski’s method of factorising quadratics mentioned led me to another excellent lesson plan of Colin Foster’s on Quadratic Equations. I really like the starting activity in this lesson which should promote a deeper understanding of factorising quadratic expressions.
I have written before on the ‘Box Method‘ for factorising quadratic expressions where the coefficient of x2 is not 1 and note Quadratic Grids from Underground Mathematics will help students develop and understand the method.
Lyszkowski’s method seems even simpler, avoiding the manipulation required by conventional methods.
I think I’ll see what year 11 think of this!
Lyskowski’s method can be improved on using the square of the leading coefficient:
see an example:
5 * (x squared) – 8 x – 4
5 * 5 * (x squared) – 5 * 8 * x – 5 * 4 all div by 5
and do y = 5x
this lack of notation is driving me nuts !