Reasoning, convincing and proving

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?

Show that it is rare for a ratio of ratios to be rational.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Have a go at being mathematically negative, by negating these statements.

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?