Multiple Representations of Quadratics

Quadratics is a big topic for our pupils to learn.  So many interlinked ideas.  There are many representations of the same idea.  This task is designed to help learners come develop an understanding of the equivalences of the representations.  

A potential use of the task is to present the first poster as it is, fully complete.  Then ask pupils to complete the first of the blank grids where only the expanded form of the quadratic is given.   There is much potential for collaborative work here.  The follow up tasks ask pupils to complete the grids based upon a different starting point.  It might be better to use A3 paper to print this task. 

Follow up tasks could be to give pupils one of the other representations and to work form there to complete the grid. 

Further follow up might be to use this as a means of introducing cubic functions – why this can’t be expressed in completed square form is an interesting conversation.  

A PDF of the full task is available here:

Credit:  @chrismcgrane84



  1. […] This fantastic task comes from Andy Creighton. It’s a great way of making the connections between the tiles, grid model and the algebra. Moreover, it’s also lets pupils observe how the same quadratic can have the factorised, expanded and completed square forms. Andy said the idea for the task is similar to mine: […]


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