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Plotting Graphs to Investigate the Intercept

Plotting Graphs to Investigate the Gradient

Interpreting Linear Graphs

Using Graphs to Solve Equations

Plotting Quadratic Graphs

Modelling Using Graphs

- 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

January 21, 2018

To add and subtract with numbers in standard form students apply a range of skills and knowledge of different topics. They need to be equally confident converting large numbers to standard form as they are with writing small numbers from standard to ordinary form. Column subtraction and addition may seem basic skills, but they become […]

January 14, 2018

Schemes of Work for Maths Teachers As a Head of Maths I understand the importance of a detailed, flexible and simple scheme of work. I designed the Key Stage 3 and GCSE schemes of work for maths teachers available at mr-mathematics.com to be just that. They are fully aligned with the current specifications and are […]

December 19, 2017

Solving Problems with Non-Right-Angled Triangles Solving problems with non-right-angled triangles involves multiple areas of mathematics ranging from complex formulae to angles in a triangle and on a straight line. As the GCSE mathematics curriculum increasingly challenges students to solve multiple step problems it is important for students to understand how to prove, apply and link […]