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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)

October 22, 2017

When factorising algebraic expressions with powers students often struggle to identify the highest common factor when it involves an algebraic term. For example, factorising 3h + 12 as 3(h + 4) is attempted correctly much more often than factorising 3h2 + 12h as 3h(h + 4). In this lesson students learn how to identify the […]

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 […]