Expanding and factorising quadratics

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Can you find the hidden factors which multiply together to produce each quadratic expression?

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...

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?