Functions, Graphs and Equations

Scheme of work: Key Stage 3: Year 8: Term 3: Functions, Graphs and Equations

Prerequisite Knowledge

  • Use coordinates in all four quadrants.
  • Substitute positive and negative numbers into formulae
  • Solve a two-step linear equation
  • Simplify an expression by collecting like terms.
  • Expand and factorise algebraic expressions

Key Concepts

  • Graphs are used to show a relatioship between x and y values.  This relationship can be written as an equation.
  • A straight line graph is made up of a gradient, denoted as M which determines the steepness and an intercept, denoted as C, which determines where the line crosses the y axis.
  • A graph is a visual representation of a continuous function.  Students often mistakenly draw line segments at the two extreme x values.
  • It can be helpful to record x and y values in a table when calculating the coordinates for any graph.
  • Quadratic graphs are in the shape of a parabola and symmetrical about the turning point.
  • When using a graph to solve an equation the solution can be taken as an estimate due to the inaccuracies of measurements and drawings.
  • Graphs can be used to model situations as the line represents a continuous set of results.

Working Mathematically

  • Develop fluency
    • Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
    • Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions
  • Reason mathematically
    • Identify variables and express relations between variables algebraically and graphically.
  • Solve problems
    • Begin to model situations mathematically and express the results using a range of formal mathematical representations
    • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

  • Algebra
    • Work with coordinates in all four quadrants
    • Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
    • Interpret mathematical relationships both algebraically and graphically
    • Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
    • Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
    • Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

Functions, Graphs and Equations Resources

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