cannon ball counting

if you wanted to count your cannon balls and calculators weren't invented, what could you do?

what Sir Walter Raleigh is supposed to have done is summon his chief calculator, Thomas Harriot

who, also supposedly, devised a formula



the intention of this task is that students
(a) guess the number in the pile and then
(b) substitute into a formula to check their answer(s)

if you know the formula for summing the squares and for a triangular number, the formula for a rectangular based pile can be derived