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

- 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

- 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.

- 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

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