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**Scheme of work: GCSE Foundation: Year 9: Term 2: Algebraic Expressions**

- Use simple formulae
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of numbers that satisfy an equation with two unknowns

- use and interpret algebraic notation, including:
- ab in place of a x b
- 3y in place of 3 x y
- a
^{2}in place of a x a, a^{3}in place of a x a x a and a^{2}b in place of a x a x b - a/b in place of a / b
- coefficients written as fractions rather than decimals
- brackets
- simplify and manipulate algebraic expressions 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 x
^{2}+ bx + c, including the difference of two squares - simplifying expressions involving sums, products and powers including the laws of indices

- Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers, which are represented as letters.
- It is important to define the difference between an expression, equation and formula.
- The multiplication symbol is omitted when using algebraic notation to avoid confusion and divisions are written as using simplified fractions.
- Linear (x), quadratic (x
^{2}) and cube terms (x^{3})cannot be collected together. - Understanding quadratics in the general form (x
^{2}+ bx + c) helps to factorise and expand expressions.

- When collecting like terms, students often forget ab = ba = a x b and b + a = + b.
- When multiplying out brackets students incorrectly forget to multiply the second term, especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x – 10
- When factorising expressions, a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
- When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown.

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