Writing with algebraic notation

Students learn how to form and simplify algebraic expressions involving multiplication, addition, division and subtraction.  They use this knowledge to begin solving equations using the balance method.

This unit takes place in Year 7 Term 2 and is followed by Expressions, Equations and Formulae


Writing with algebraic notation Lessons


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.
  • Just as 2 + 2 + 2 can be written as 3 × 2, a + a + a can be written as 3 × a.  However, with algebraic notation × and ÷ symbols are not included.  3 × a is written as 3a and 3 ÷ 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 × b
    • 3y in place of y + y + y and 3 × y
    • a2 in place of a × a, a3 in place of a × a × a; a2b 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
    • taking out common factors

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