The Romsey School Mathematics Faculty - Year 8
Objectives graphs in the form x + y = 6
All pupils should be able to:
> use co-ordinates to identify lines such as x=3, y=-1, y=x etc.
> use 'function machines' (forwards and backwards) to generate input and output data for simple functions
> generate and plot pairs of co-ordinates that satisfy a simple linear relationship e.g. y = x + 1 http://www.mymaths.co.uk/gold/graphs/plottingGraphs.swf
> begin to consider the features of graphs of simple linear functions and recognise that equations in the form y = mx correspond to straight line graphs through the origin
6 sets of axes on one page
Most pupils should be able to:
> generate co-ordinate pairs and plot graphs of simple linear functions in all 4 quadrants
> plot the graphs of linear functions in the form y = mx + c on paper and using ICT
> recognise that equations of the form y = mx + c correpond to straight line graphs planet hop
Some pupils should be able to:
Possible
Starters:
Possible
Misconceptions
> plot the graphs of linear functions in the form ay + bx + c = 0 on paper and using ICT
> given values of m and c find the gradient of lines given by equations of the form y = mx + c
> calculate the equation of the straight line passing through any two given points
> Recognise that the graphical solution of two equations is their intersection (sim. eq.)
> Recognise reciprocal and exponential graphs
> Input/Output machines (robots). Encourage pupils to work forwards and backwards and also to identify the function. Extend with two step fns etc.
> Matching exercises with functions and their graphs
> Human Graphs - use two walls as axes and stand in 'y=x' etc.
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Some pupils may think that a sketch is a very rough drawing. It should still identify key features, and look neat, but will not be drawn to scale
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Some pupils may confuse the x and y direction when calculating gradients.
Probing
Questions
Assumed knowledge
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Show me a point on this line (e.g. y = 2x + 1). And another, and another …
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Always / Sometimes / Never: The line x = a is parallel to the x-axis
> Plotting C0-ordinates
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Basic algebraic substitution
Ma1 opportunities
ICT opportunites
> Investigate the graphs of different functions
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What happens to the vertices of a shape when it is reflected in y=x? etc.
> ICT TASK GRAPHS
> Project Omnigraph or GSP onto the board and get pupils to predict the line
> Graphs are saved on Omnigraph - pupils must deduce the equations