Objectives:


Support:

  • Simplify linear algebraic expressions by collecting like terms.
  • Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations).
  • Generate coordinate pairs that satisfy a simple linear rule; recognise straight-line graphs parallel to the x-axis or y-axis.
  • Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.

Core:

  • Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
  • Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in the same way).
  • Begin to use graphs and set up equations to solve simple problems involving direct proportion.
  • Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT.
  • Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations.
  • Solve more demanding problems and investigate in a range of contexts: algebra.
  • Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for algebraic manipulation.

Extension:

  • Simplify or transform algebraic expressions by taking out single term common factors.
  • Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution), using an appropriate method.
  • Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20.
  • Solve problems involving direct proportion using algebraic methods, relating algebraic solutions to graphical representations of the equations; use ICT as appropriate.
  • Plot graphs of linear functions (y given implicitly in terms of x), e.g. ay + bx = 0,
    y + bx + c = 0, on paper and using ICT.
  • Use trial and improvement methods where a more efficient method is not obvious.

Key Vocabulary:


  • algebra, symbol, expression, linear equation, term, coefficient, solution, brackets, verify, prove, therefore.
  • symbol, expression, algebra, function, mapping, linear, coordinates, term, equation, straight-line graph, quadrant, axis, axes, origin, gradient, intercept, origin.

Suggested Lesson Outcomes:


SUPPORT CORE

Framework:















Teaching & Learning Resources:


Brackets Resources
Simplifying Resources
Substitution Resources
Equations Resources
Function Machine Resources
Coordinates Resources
Graphs Resources
y=mx c Resources
Solving Equations Resources
Trial & Improvement Resources