What biological growth processes can you fit to these graphs?

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

These resources are suitable for teaching about graphs in Core Maths

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross

Working on these problems will help students develop a better understanding of functions and graphs.

Working on these problems will help students develop a better understanding of functions and graphs.

A collection of short problems on straight line graphs.

Working on these problems will help you develop a better understanding of functions and graphs.

Working on these problems will help you develop a better understanding of functions and graphs.

Working on these problems will help you develop a better understanding of functions and graphs.

Can you find the area between this graph and the x-axis, between x=3 and x=7?

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

What is the area of the triangle formed by these three lines?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Be playful with graphs and networks, and see what theorems you can discover!

Graphs are a crucial tool in dealing with the data that science generates.

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

How can you work out the equation of a parabola just by looking at key features of its graph?

If you know some information about a parabola, can you work out its equation?

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

You can get a great feel for functions by sketching their graphs or using graph plotting software...

An introduction to the ideas of public key cryptography using small numbers to explain the process. In practice the numbers used are too large to factorise in a reasonable time.

Look for the common features in these graphs. Which graphs belong together?

If you can sketch y=f(x), there are several related functions you can also sketch...

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

These problems will require you to consider the gradients, intercepts and equations of straight line graphs.

Can you work out the equations of the trig graphs I used to make my pattern?

An example of a simple Public Key code, called the Knapsack Code is described in this article, alongside some information on its origins. A knowledge of modular arithmetic is useful.

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has. . . .

These problems will require you to consider practical contexts in which graphs can be used.

Can you work out which processes are represented by the graphs?

Which line graph, equations and physical processes go together?