Triangle numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you describe this route to infinity? Where will the arrows take you next?

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.