KS4 Problems

AQA 90 Problems
A superb document listing 90 problems which have been categorised by difficulty, approach and topic, which has the aim of providing a resource that enables tachers to prepare students for open, less structured problems
For access to the 90 problems - Click here
For access to a commentary on 30 of the problems - Click here

The following files are a collection of problem solving questions designed to promote thought, some are taken from an American Website www.learnnc.org/index.nsf/doc/problems0402a
Area, Surface Area and Volume A set of 6 problems involving manipulation of sides of squares, rectangles, and rectangular solids and explaining resulting changes in area, surface area, and volume.
Fencing Problems A set of 8 related problems involving building of fences around various sizes of garden plots.  Solutions provided.
Garden Problems A set of 3 related problems involving manipulation of sizes of garden plots and construction of boxes from sheets of given sizes. Illustrations provided.
Volumes Comparison of volumes of containers of various shapes.
Circles and Regular Polygons Using a spreadsheet to explore relationships between sizes of inscribed and circumscribed circles.
Opposite Faces of a Cube Show students three views of the same cube and have them identify opposite faces.
PE Storage Box A set of 7 related problems involving the visualization and manipulation of boxes of different sizes and their contents.
Manipulating Pyramids Finding surface area and volume of a pyramid from given dimensions; understanding the relationship between changes in various dimensions of the pyramid.
Pythagorean Problems A set of 5 real-life problems requiring use of the Pythagorean Theorem.
Explaining the Area of a Triangle From a triangle with given dimensions, explain three different ways of computing the area.
Overlapping Triangles Comparison of areas of various triangles in a complex diagram.
What’s my rule? A game to help students understand the concept of adding squares and their square roots.  This makes a good way to begin a lesson on the Pythagorean Theorem.
Visualizing Halves Students examine diagrams to determine whether exactly half is shaded. Could be used as a warm up exercise.
www2.edc.org/makingmath/mathproj.asp#rsskil Mixture of accessible but harder problems [Level 7+ ]
www.nzmaths.co.uk New Zealand website with graded topic related problems with guidance
www.nrich.maths.org.uk/public/leg.php  The NRICH site allows you to explore problems by selecting a particular topic and level of difficulty.