TES Maths: Inspect the spec - brackets

Craig Barton
17th November 2016
TES Maths, inspect the spec, GCSE, new specification, brackets, expanding, factorising, single brackets, double brackets, triple brackets, completing the square, quadratics, polynomials, secondary, KS4, Year 10, Year 11

Advice and resources to demystify the requirements for teaching brackets as part of the new GCSE specification

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.

What does the specification say?

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

A4: Simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:

  • collecting like terms
  • multiplying a single term over a bracket
  • taking out common factors
  • expanding products of two or more binomials
  • factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares
  • factorising quadratic expressions of the form ax2 + bx + c
  • simplifying expressions involving sums, products and powers, including the laws of indices

What's the same?

Brackets fans will be pleased to know that they continue to feature in the new specification. After all, it wouldn't be a GCSE exam without them! Students across both tiers will still need to be able to expand and factorise expressions involving single brackets. But when it comes to double brackets, a few things have changed...

What has changed?

There has been an increase in the number and difficulty of bracket-related questions for both higher and foundation students.

Firstly, foundation students will not only be required to expand double brackets, but also factorise quadratic expressions for the first time. If the examiners are feeling particularly nasty, this could include factorising the difference of two squares, and be combined with deducing the roots of a quadratic graph (as outlined in this previous post).

Students taking the higher paper are once again in for a treat. What do you give the person for whom expanding two brackets is just not enough? Three brackets, of course! Yes, higher students will now be expected to expand triple brackets. Importantly, there is no requirement to go the other way and use something like the factor theorem to factorise cubic expressions, but using the factorised form of a cubic expression to deduce facts about the shape and the roots of a cubic graph may well be called upon.

Finally, it is worth pointing out that higher students may be expected to complete the square for expressions in the form ax2 + bx + c, where the coefficient of x2 is greater than 1. Another fine example of AS-level work creeping its way into GCSE.

How can TES Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

  1. Pixi_17's collection
    Once again, Pixi_17 offers a series of differentiated lessons on many of the key teaching points for brackets. All tailored to the new GCSE, these include expanding single bracketsfactorising single bracketsexpanding double brackets and sketching quadratics and completing the square.

  2. Dr Frost's collection
    Not to be outdone, Dr Frost has his own well-structured collection of bracket-related lessons on expanding single brackets, expanding multiple brackets, factorising quadratic expressions and brackets for further maths.

  3. Defuse the bomb worksheets
    Only your students’ skills of expanding and factorising brackets can save the world from imminent disaster in these engaging tasks... Who says maths isn't useful?

  4. Magic box activity
    Previously selected as a Resource of the Week, this versatile activity gets students expanding double brackets, as well as helping to develop independence.

  5. Factorising quadratics codebreaker
    Help students to consolidate the skills involved in factorising quadratic expressions with this pair of worksheets.

  6. Triple brackets lesson*
    This well-structured lesson comes complete with a full plan, accompanying resources and suggested support and extension activities.

  7. Expanding polynomials
    Develop students' understanding of the expansion of triple brackets with this well-presented task, which is sure to offer a challenge.

  8. Completing the square visualisation
    These simple presentations are ideal for introducing and demonstrating the steps involved in completing the square. 

  9. Completing the square cards
    Differentiated by colour, these well-designed cards require students to complete the square to sketch quadratic graphs, including those where the coefficient on x2 is greater than 1.


Craig Barton, TES Maths adviser

Craig is a secondary maths teacher in the North of England.
 

*This resource is being sold by the author

Find more resources to support the changes to the GCSE maths specification by taking a look at the rest of the series.

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