Writing with algebraic notation

Diagrams with Algebra

Collecting like terms

Multiplying and dividing with algebra

Writing expressions with algebra

Substituting numbers into expressions

Finding the unknown

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