These materials have been produced by the Further Mathematics Support Programme and are designed to help teachers develop their students' problem solving abilities. Each problem comes with a set of suitable prompts for use with students and a full worked solution.
You can find the complete set of problems, prompts and solutions within the GCSE problem solving booklet.
Here are six activities that can be used with groups of 4 to improve problem solving skills.
The first three activities all use the same grid in which students have to create the correct design.
Grid with instructions without instructions 

Pattern 1 Card set Solution 
Pattern 2 Card set Solution 
Pattern 3 Card set Solution 
The next three use a variety of GCSE skills
Willis Tower Instructions Card set Solution 
Skills required: Angle of elevation Calculating an angle using inverse tan Pythagoras Theorem 

Building Bridges Instructions Card set Solution 
Skills required: Simple geometric recognition Simple arithmetic operations Scale drawing 

Epidemic Instructions Card set Solution 
Skills required: Expected numbers from probabilities Percentages and probability Interpretation of calculations 
Further problems suitable for GCSE mathematics students can also be found on the Integral Online Resources website. Some examples of these problems are below. Access to the complete set of problems is free when a school/college registers with the FMSP.
Circle Area Problem Solution 
Cube Slice Problem Solution 

Dodecagon and Hexagon Problem Solution 
Shaded Circle Problem Solution 
The FMSP has been superseded by the AMSP