In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Think of a number... follow the machine's instructions. I know what
your number is! Can you explain how I know?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Weekly Problem 37 - 2011
Rotating a pencil twice about two different points gives surprising results...
Solutions from Mathew, Ben, Catherine and Yi Jean all show clearly explained reasoning.
Go to last month's problems to see more solutions.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Exchange the positions of the two sets of counters in the least possible number of moves