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Students continue to develop their algebraic reasoning skills by expanding a pair or brackets, factorising expressions, solving equations and formulae and changing the subject of a formula.

This unit takes place in Term 4 of Year 8 and follows on from setting up and solving equations.

- 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)

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]