Functions, Graphs and Equations

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

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.

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.