Functions, Graphs and Equations

Students learn how to plot linear graphs and use them to estimate the solutions to equations.  As learning progresses students begin to plot and identify the properties of quadratic graphs.  Later, they estimate the solution to quadratic equations using graphical methods.

This unit takes place in Term 3 of Year 8 and follows Expressions, Equations and Formulae.

Functions, Graphs and Equations Lessons

Prerequisite Knowledge
  • 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

Key Concepts
  • 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.

Working mathematically

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.

Functions, Graphs and Equations Subject Content


  • 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

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Teaching Reciprocals of Numbers and Terms

To introduce teaching reciprocals of numbers and terms I begin the lesson explaining that everything has an opposite.  The opposite of shutting a door is to open it.  The opposite of saying hello is to say goodbye.  Numbers have opposites too we call them reciprocals. Teaching Reciprocals of Numbers and Terms To start the lesson […]

Surface Area of Cylinders

When I teach how to find the surface area of cylinders I like to add a constant level of challenge and enjoyment to the lesson.  Rather than repetitively calculating the surface area of a cylinder I introduce more complex cylindrical shapes. How to find the Surface Area of Cylinders To find the surface area of […]

Teaching Mathematics for a Growth Mindset

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach.  The feeling of success is addictive.  The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it.  Teaching […]