# Recognising standard graphs

This list of resources contains activities which are designed to support students to learn to recognise, sketch and interpret graphs of:

- linear functions,
- quadratic functions,
- simple cubic functions,
- the reciprocal function y =
^{1}/_{x}, y = kx with x ≠ 0, - the exponential function for positive values of k,
- the trigonometric functions for angles of any size

Visit the secondary mathematics webpage to access all lists.

### Factorising Cubics A11

Factorising Cubics A11

In this resource from the DfE Standards Unit students learn to:

associate x-intercepts with finding values of x such that f (x) = 0,

sketch graphs of cubic functions,

find linear factors of cubic functions

develop efficient strategies when factorising cubic functions.

Students should have some familiarity with quadratic graphs and factorising quadratic functions. This activity uses card sorts and a true/false plenary to consolidate learning.

These materials exemplify the ideas and approaches adopted in the Standards Unit pilot. To get best value from them use them in association with the guidance and other materials in Improving Learning in Mathematics: Challenges and Strategies.

### Interpreting Functions, Graphs and Tables A7

This DfE Standards Unit resource, contains activities designed to support students when learning to

understand the relationship between graphical, algebraic and tabular representations of functions,

the nature of proportional, linear, quadratic and inverse functions

doubling and squaring.

Students should already be familiar with algebraic symbols such as those representing squares, square roots and fractions, which are revised during the introduction. Most students will already be familiar with making tabular representations of functions and drawing graphs, but they may not have considered the relations between different representations of functions.

Card sorts, group work and discussion are used to extend pupils exiting knowledge with links to a number of other objectives

These materials exemplify the ideas and approaches adopted in the Standards Unit pilot. To get best value from them use them in association with the guidance and other materials in Improving Learning in Mathematics: Challenges and Strategies.

### Graphs, Equations and Inequalities

This MEP resource from CIMT is taken from text book 9B.

Chapter 13 explores **Cubic and Reciprocal functions**. Alongside the pupils' material there are lesson plans which outline the content of the unit, these are differentiated into three levels, ST, A and E as well as suggested routes through them.

### Functions and Graphs

Mathcentre provide these resources which cover aspects of functions and graphs often used in the field of engineering. They include descriptions of the graphs of the trigonometric functions.

Comprehensive notes, with clear descriptions are provided, together with relevant diagrams and examples.

This leaflet would be useful for students wishing to review, and consolidate, their knowledge and understanding of surds and the leaflet also includes a selection of questions to be completed, for which answers are provided. The leaflet could also be used to support “flip learning” where students are introduced to content independently and practice working through examples collaboratively.

### Graph Detectives

AnchorIn this group activity, students are given a list of functions contained in the matching cards file. Students are given time to work out what the graph of each function will look like. Some graphs will need to be plotted, others can be sketched. The functions are a mix of quadratics, cubics and reciprocals.

The posters file contains diagrams showing the graphs of the functions. Students are required to match each function to its graph. The instruction PowerPoint suggests how the lesson could be structured. This is a good activity to consolidate and assess students understanding of a range of standard graphs suggested under this objective. Examples of trigonometric and exponential functions could be added to challenge students further.

### Reciprocal Function

This interactive file from The Virtual Textbook displays the graphs of functions as well as the graph of the corresponding reciprocal function.

It begins with the graph of a linear function where the gradient and intercept can be changed. The reciprocal is plotted on the same diagram.

The next two sheets show graphs of quadratic and cubic functions whose coefficients can be altered. The graph is plotted and the graph of the reciprocal function shown.

In the same way the graphs of trigonometric and exponential functions and their reciprocals can also be explored.