Reasoning, convincing and proving
problem
Concrete wheel
Age
11 to 14
Challenge level
A huge wheel is rolling past your window. What do you see?
problem
Harmonic Triangle
Age
14 to 16
Challenge level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
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
More Total Totality
Age
11 to 14
Challenge level
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
problem
Total Totality
Age
11 to 14
Challenge level
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
problem
Day of the Triffids
Age
14 to 16
Challenge level
Jasmine buys three different types of plant. How many triffids did she buy?
problem
Multiplication square
Age
14 to 16
Challenge level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
problem
Plus or Minus
Age
16 to 18
Challenge level
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.