Topic 3 Year 8 Mathematics
|No of lessons||12|
|When is it happening||Term 1 Year 8|
|What will students learn||
This unit is students’ first formal introduction to straight line graphs. The graphical representation of a sequence is used as a starting point for defining linear and non-linear functions.
This begins with the plotting of discrete points beginning with n = 1. The n-axis
is replaced by the ï¿½-axis and discrete points are replaced with a continuous line to represent all coordinate pairs. This is emphasised by looking at a range of examples of coordinate pairs along the line including fractional and negative values. The relationship within and between (x,y) coordinate pairs is explored and linked to the equation of the line where the equation is presented in the forms y =ax+b , ax + by = c and ax + by + c = 0
Students should be encouraged to see the connections between the different mathematical representations of a relationship e.g. the equation, the coordinates and the graphical representation. Functions derived from real life contexts are used to help give meaning to the features of a linear graph.
Students develop strategies for identifying and drawing graphs of linear functions. The concept of gradient is introduced as the rate of change of the y coordinates. Similar triangles are used to show the constant gradient of linear graphs and the gradient is linked the equation of the line in different forms.
Parallel lines are identified from the equation where the equation is given in different forms and this is linked to the graphical representations. Students work on coordinate geometry problems by finding the equation of a line through two points and finding the equation of a line through a point with a given gradient.
|Key Knowledge that students should know at the end of 'Topic'||This is the knowledge that students will meet for the first time in this topic||• Identify the equations of horizontal and vertical lines (from year 7) • Plot coordinates from a rule to generate a straight line • Develop a rule into an algebraic representation • Develop concept of gradient using graphs of the form y = mx before moving to equations of the form y = mx + c • Identify key features of a linear graph including the y- intercept and the gradient • Make links between the graphical and the algebraic representation of a linear graph • Recognise different algebraic representations of a linear graph • Identify parallel lines from algebraic representations|
|This is knowledge that students may have met before but will need to deepen their understanding||Graphical representation used to describe horizontal and vertical lines.|
|Key Skills that students should be able to demonstrate at the end of 'Topic'||This is the skills that students will meet for the first time in this topic||Plotting coordinates, a axis and y axis|
|This is skills that students may have met before but will need to develop||2x = 2 multiplied by x|
|Key vocabulary that students should know and understand||Equation, Intercept, Graph, linear, Table of values, Function.|
|The Big Question||Can you successfully find the equation of a linear line?|
Key questions that students should be able to answer at the end of the 'Topic'
|Are you able to identify which is the x co-ordinate and which is the y? Are you then able to plot them?|
|Can you identify the equations of horizontal and vertical lines on a graph? Can you plot them yourself?|
|Are you able to use your knowledge of horizontal and vertical lines to represent inequalities?|
|Are you able to describe the inequalities of lattice points and form shapes using inequalities on a graph?|
|Are you able to draw a line from a table of coordinates?|
|Can you identify linear and non linear graphs?|
|Can you use your journeys of one coordinate to another to spot a relationship of points on linear lines?|
|Are you able to remember the formulate for a equation of a line (y=mx+c) and understand what m and c represent?|
|Do you know what angle perpendicular lines cross at?|
|Are you able to successfully find the gradient of a linear line?|
|Do you know the gradient of a horizontal or vertical line?|
|Can you successfully find the equation of a linear line?|