GCSE Problem Solving Materials

20 Problems for GCSE Mathematics

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.

Problem 1 Problem 2 Problem 3
Problem 4 Problem 5 Problem 6
Problem 7 Problem 8 Problem 9
Problem 10 Problem 11 Problem 12
Problem 13 Problem 14 Problem 15
Problem 16 Problem 17 Problem 18
Problem 19 Problem 20


You can find the complete set of problems, prompts and solutions within the GCSE problem solving booklet.

KS3/GCSE Groupwork Problems

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



Additional GCSE Problem Solving Materials

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