Being curious

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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

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?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Follow the clues to find the mystery number.

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Watch this animation. What do you see? Can you explain why this happens?