Multiple Representations
This activity is based on a set of three spreadsheets with lesson notes which allow you to quickly display and make links between equations, their resultant tables and graphs. There are spreadsheets for linear, quadratic and simultaneous equations.

Year 7 Objectives covered:
  • Generate coordinate pairs that satisfy a simple linear rule
  • Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT
  • recognise straight-line graphs parallel to the x-axis or y-axis
Year 8 Objectives:
  • Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT
  • Recognise that equations of the form y = mx + c correspond to straight-line graphs
Year 9 Objectives:
  • Find the gradient of lines given by equations of the form y = mx + c, given values for m and c
Year 10 Objectives:
  • Investigate the gradients of parallel lines and lines perpendicular to these lines
  • Use ICT to explore the graphical representation of algebraic equations and interpret how properties of the graph are related to features of the equation, e.g. parallel and perpendicular lines
  • Understand that the point of intersection of two different lines in the same two variables that simultaneously describe a real situation is the solution to the simultaneous equations represented by the lines
  • Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or a pair of equations to the algebraic solution; consider cases that have no solution or an infinite number of solutions
  • Explore simple properties of quadratic functions; plot graphs of simple quadratic and cubic functions, e.g. y = x2 , y = 3x2 + 4, y = x3
You can use the spreadsheets to encourage pupils to predict the shape of a graph from its equation or table. The ‘hide and reveal’ feature gives the option of concealing the coefficient of x or the constant in the resulting table. The ability of the spreadsheet to speed up the drawing of the graphs and tables removes potential arithmetic errors and allows examination of the underlying ideas.

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