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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)

April 12, 2017

Many problems involve three-dimensional objects or spaces. Pythagoras Theorem in 3D Shapes can be used as much with these problems as those in plane shapes. Knowing when to use Pythagoras Theorem The starter recaps applying Pythagoras Theorem as part of a larger problem involving the perimeter of a trapezium and square. The aim of this […]

March 27, 2017

Drawing frequency trees for GCSE maths is a new topic and appears on both the higher and foundation curriculum. I’ve taught this lesson a couple of times, once to Year 10 and once to Year 11 and I have to say the kids really enjoy it. What is a frequency tree? Frequency trees can be […]

February 17, 2017

Whenever I teach how to calculate speed as a measure of distance and time I either use the formula or the triangle method. In my experience most students are know about the triangle method from their science lessons. For this reason I would have expected speed to appear either within the algebra or shape and measures strands of […]