What do you notice about the sum of two identical triangular numbers?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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?
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?
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.
