Explaining, convincing and proving

problem
Fibonacci factors

Age

16 to 18

Challenge level

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
problem
Flexi quad tan

Age

16 to 18

Challenge level

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.
problem
The bridges of Konigsberg

Age

11 to 18

Challenge level

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

Age

14 to 16

Challenge level

Can you find a rule which connects consecutive triangular numbers?
problem
Trig rules OK

Age

16 to 18

Challenge level

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
problem
Concrete wheel

Age

11 to 14

Challenge level

A huge wheel is rolling past your window. What do you see?
problem
Birthday party

Age

11 to 14

Challenge level

The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
problem
Old order

Age

11 to 14

Challenge level

Who is the youngest in this family?
problem
Honey bees

Age

14 to 16

Challenge level

How many bees could fly 1000 miles if they had 10 gallons of honey?
problem
9 weights

Age

11 to 14

Challenge level

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?