Up and Down Staircases
First, we started off by trying to solve how many blocks would be needed to build an up and down staircase problem, that has five steps up and five steps down. We drew it out on a whiteboard and counted the number of blocks. The total number of blocks was twenty-five.
To try and see if we could spot a pattern, we tried again, but this time we tried seven steps up and seven steps down. The total number of blocks was forty-nine.
Then, we realized that twenty-five and forty-nine are square numbers, so we knew that we had to times the number of steps up and steps down by itself.
Example
You have to work out how many blocks would be needed to build an up and down staircase with three steps up and three steps down. You do three times three (because there are three steps up and three steps down) which equals nine, so there are nine blocks.