GCSE Extension Materials
Aims
The aims of the materials are:- To introduce students to new ideas so as to stimulate their interest in the subject.
- To reinforce some of the concepts in GCSE so as to improve students’ understanding of them.
- To highlight how some areas of GCSE are developed at A level so as to encourage students to continue their studies.
Format of the materials
All of the materials have the following format:- Starts from a topic or idea that is in GCSE Mathematics and features a ‘What you should know’ section.
- A ‘New idea’ that is an extension to GCSE Mathematics.
- A task for students to attempt so they can investigate the idea.
- Ideas for further investigation suggested in a ‘Take it further section’.
- A brief explanation of how this topic is developed at A level.
- All the materials are based on a single sheet of A4 (except for NA 11, SSM 4 and SSM 6) which can be copied and given to students.
- Teachers’ notes, including solutions, are available to all schools who subscribe to the online resources or register with the Further Mathematics Support Programme. Registration with the Further Mathematics Support Programme is free and will also give you access to information about local events which could be useful for your students. See: www.furthermaths.org.uk/register.php
Ways to use the materials
Some suggestions for ways to use the materials:- As a whole-class activity when students have finished studying the topic.
- As extra materials to stretch and challenge some of the more able students within a class.
- As a regular, possibly optional, homework task.
- As a basis for study in lunchtime or after-school maths club.
Notes
- The tasks are not intended to be linear. Students will benefit from the investigations even if they do not ‘complete’ them.
- In each of the three sections the resources are ordered by accessibility; however, it is inevitable that some students will progress further with some tasks than with others.
- The materials are based on interesting mathematical ideas and are not designed to provide extension to every aspect of the GSCE specifications.
Do you have any feedback on these resources?
FMSP Support Manager, Kevin Lord, is reviewing these GCSE extension materials in order to help teachers use them more effectively with their students.
If you have used the resources with students and have feedback or suggestions as to how to make the resources more useful, then he would like to hear from you. You can contact him at kevinlord@furthermaths.org.uk. Any feedback you have, positive or negative, would be gratefully received.
Materials
Number/Algebra
| GCSE topic | |
|---|---|
| NA 1 | Graphs of quadratic equations |
| NA 2 | Surds |
| NA 3 | Interpreting graphs |
| NA 4 | Trial and improvement |
| NA 5 | Functions |
| NA 6 | Indices |
| NA 7 | Simultaneous equations |
| NA 8 | Solving quadratic equations |
| NA 9 | Adding fractions |
| NA 10 | Inequalities |
| NA 11* | Plotting curves |
* NA 11 features a separate extension sheet
Shape, Space and Measure
| GCSE topic | |
|---|---|
| SSM 1 | Trigonometry 1 |
| SSM 2 | Trigonometry 2 |
| SSM 3 | Circles |
| SSM 4† | Pythagoras’ theorem |
| SSM 5 | Loci |
| SSM 6† | Vectors |
Handling Data
| GCSE topic | |
|---|---|
| HD1 | The mean from a frequency table |
| HD2 | Interquartile range |
| HD3 | Tree diagrams |
Accessing the Teachers' Notes
Teachers’ notes, including solutions, are available to all schools who register with the Further Mathematics Support Programme. Registration with the FMSP is free and will also give you access to information about local events which could be useful for your students. Register with the FMSP
