Can you make sense of these three proofs of Pythagoras' Theorem?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Can you find the hidden factors which multiply together to produce each quadratic expression?
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Which armies can be arranged in hollow square fighting formations?
Surprising numerical patterns can be explained using algebra and diagrams...
