Triangle numbers

problem
Triangles within pentagons

Age

14 to 16

Challenge level

Show that all pentagonal numbers are one third of a triangular number.
problem
Alphabet blocks

Age

5 to 11

Challenge level

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
problem
Satisfying four statements

Age

7 to 11

Challenge level

Can you find any two-digit numbers that satisfy all of these statements?
problem
Swimming pool tiles

Age

7 to 11

Challenge level

This activity creates an opportunity to explore all kinds of number-related patterns.
problem
Cat food

Age

7 to 11

Challenge level

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?
problem
Graphing number patterns

Age

7 to 11

Challenge level

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?
problem
A square deal

Age

7 to 11

Challenge level

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
problem
Light the lights again

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?
problem
Human food

Age

7 to 14

Challenge level

Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?
problem
Satisfying statements

Age

11 to 14

Challenge level

Can you find any two-digit numbers that satisfy all of these statements?