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Pupils should be taught to recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y =  with x not equal to 0, {the exponential function y = k^x for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

• Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
• Straight Line Graphs Video After drawing a straight line graph learn about its equation in the form y = mx + c.
• Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.
• Graph Patterns Find the equations which will produce the given patterns of graphs.
• Straight Line Graphs 10 straight line graph challenges for use with computer graph plotting software or a graphical display calculator.
• Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.
• Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.
• Human Graphs Students should be encouraged to stand up and make the shapes of the graphs with their arms.

Here are some exam-style questions on this statement:

• "Sketch the graph of \(y=0.5^x +1\) for \(0 \le x \le 5\) labeling the y intercept." ... more
• "(a) Use the red graphs to solve the simultaneous equations:" ... more
• "The images below show a graphic display calculator screen with different functions displayed as graphs." ... more
• "Match the equation with the letter of its graph" ... more
• "The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).

  \(x\)	-3	-2	-1	-0.5	0.5	1	2	3	4
  \(y\)	3.2	2.5		8.5	7.5	1.0		-2.8

  (a) Complete the table of values." ... more

• "(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis." ... more

See all these questions

Here is an Advanced Starter on this statement:

• Venn Graphs
  Type the equation of a graph into each section of the Venn diagram. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.