KS3
 

These problems have been used with Key Stage 3 pupils although many of them have also been used with Gifted Pupils in Years 6 and 7.

The mathematical ability needed ranges from Level 5 to Level 7

Problem 1   Number Based Problems
Problem 2 Coloring Problems 
Problem 3 Number Based Problems
Problem 4 Isaac Newton Research
Problem 5 Buying Flowers costing £100
Problem 6 Champion Dice
Problem 7 Pond Borders Investigation  
Problem 8 Max Box - PowerPoint Presentation
Problem 9 Soma Cube - Puzzle - Nets
Problem 10 Several short slightly harder problems 
Pentominoes 
30 Problems Teacher

Pupil Problems
Pentominoes 1 pdf
Pentominoes 2 pdf
A range of problems all using the 12 shapes that can be formed from 5 squares, commonly known as pentominoes
Shape Investigation A series of problems involving arrangements and counting numbers of shapes or outcomes
Dominoes Various number problems using a set of dominoes
Nrich  The NRICH site allows you to explore problems by selecting a topic and level of difficulty.
www.nzmaths.co.uk Graded topic related problems with guidance
www.mathforum.com/pow/ Mixture of problems
Galileo Educational Problems suitable for a Maths Fair

This set of 8 booklets comprise short questions which I have nominally assigned a National Curriculum Level, not in terms of pure content but in terms of problem solving skills.

Booklet 1 - Level 5- Booklet 2 - Level 5 Booklet 3 - Level 6 Booklet 4 - Level 6
Booklet 5 - Level 7 Booklet 6 - Level 8 Booklet 7 - Level 9 Booklet 8 - Level 10