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Rearranging formulae

- Use and interpret algebraic notation, including:
- ab in place of a × b
- 3y in place of y + y + y and 3 × y
- a
^{2}in place of a × a, a^{3}in place of a × a × a; a^{2}b in place of a × a × b - a/b in place of a ÷ b

- coefficients written as fractions rather than decimals
- simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms

- Expanding brackets means to take out of brackets. Factorising an expression is put in brackets.
- When expanding brackets by a negative students often forget to multiply every term inside the bracket by the negative.
- When factorising expressions the highest common factor of each term. A common misconception is to only partially factorise. For example 9a + 12a
^{2}is fully factorised as 3a(3 + 4a) not a(9 + 12a). - When solving equations involving brackets it is not always necessary to expand the bracket first. It is often possible to divide both sides by the number outside the bracket.
- To solve an equation you have to get the letter on its own on one side of the equation. Begin by collecting like terms so all the letters are together.
- When substituting known values into a formula remember to use the correct order of operations. Students often make mistakes when substituting in negative and fractional numbers.
- Formulae have an unknown on its own. This is the subject of the formula. Use the balance method and order of operations to change the subject of the formula.

Develop fluency

- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
- Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

- Identify variables and express relations between variables algebraically and graphically

Solve problems

- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Algebra

- Substitute numerical values into formulae and expressions, including scientific formulae;
- Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors;
- Simplify and manipulate algebraic expressions to maintain equivalence by:
- Collecting like terms
- Multiplying a single term over a bracket
- Taking out common factors
- Expanding products of two or more binomials

- Understand and use standard mathematical formulae; rearrange formulae to change the subject
- Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

August 14, 2017

While I was teaching a higher GCSE class about Reflections, Rotations and Translations I wanted to explore extending transformations beyond shapes on a grid to include transforming straight line graphs. About forty minutes into the lesson on reflections the majority of the students were quietly working their way through the activities. The class were well […]

June 4, 2017

Here is a list of what I consider to be the best secondary school maths websites that I use every week. Best secondary school maths websites are ... UK Maths Challenge Geogebra http://prethomework.weebly.com/ This website has a good range of homework tasks for key stage 3 classes. Every worksheet includes a skill, challenge, literacy, research […]

May 20, 2017

As we approach the start of a new school year I thought I would share some tips on behaviour management in a mathematics lesson. These are things that I have picked up over the years and have worked well for me. I am sure there are opposing viewpoints and you may find some of these […]