# Algebraic Expressions

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

#### Prerequisite Knowledge

• 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

#### Success Criteria

• use and interpret algebraic notation, including:
• ab in place of a x b
• 3y in place of 3 x y
• a2 in place of a x a, a3 in place of a x a x a and a2b 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 x2 + bx + c, including the difference of two squares
• simplifying expressions involving sums, products and powers including the laws of indices

#### Key Concepts

• 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 (x2) and cube terms (x3)cannot be collected together.
• Understanding quadratics in the general form (x2 + bx + c) helps to factorise and expand expressions.

#### Common Misconceptions

• 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.

## Algebraic Expressions Resources

### Mr Mathematics Blog

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