In this feature, we offer a selection of rich problems on quadratics, which yield some surprising results. We hope to stimulate students' curiosity and challenge the view that algebra is dull. We invite them to explain and justify their conjectures using algebraic and diagrammatic representations.
problem
Quadratic patterns
Age
14 to 16
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
problem
Hollow squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Difference of two squares
Age
14 to 16
Challenge level
What is special about the difference between squares of numbers adjacent to multiples of three?
problem
Pythagoras perimeters
Age
14 to 16
Challenge level
If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Mega quadratic equations
Age
14 to 18
Challenge level
What do you get when you raise a quadratic to the power of a quadratic?
problem
System speak
Age
16 to 18
Challenge level
Five equations... five unknowns... can you solve the system?