Reasoning, convincing and proving

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?

Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. Do you have any interesting findings to report?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

Can you find a rule which connects consecutive triangular numbers?