Writing with algebraic notation

Scheme of work: Key Stage 3: Year 7: Term 2: Writing with algebraic notation

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
  • Enumerate possibilities of combinations of two variables.

Key Concepts

  • An expression can be simplified by collecting like terms.  Like terms are those which contain the same letter symbol and equal powers.
  • As 2 + 2 + 2 can be written as 3 x 2, a + a + a can be written as 3 x a.  However, with algebraic notation, multiply and division symbols are not included.  3x a is written as 3a, and 3 divided a is written as a fraction 3/a.
  • An algebraic expression is a collection of mathematical terms with no stated value.
  • Multiplicative relationships such as xy = yx can be used to simplify some expressions.
  • The order of operations is used when substituting known values into expressions.

Working Mathematically

  • 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.

Subject Content

  • Algebra
    • use and interpret algebraic notation, including:
      • ab in place of a x b
      • 3y in place of y + y + y and 3 x y
      • a2 in place of a x a, a3 in place of a x a x a; a2b in place of a x a x b
      • a/b in place of a divided b
      • coefficients written as fractions rather than decimals
    • simplify and manipulate algebraic expressions to maintain equivalence by:
      • collecting like terms
      • taking out common factors

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