Describing patterns and sequences

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

Have a go at this 3D extension to the Pebbles problem.

Explore one of these five pictures.

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

It starts quite simple but great opportunities for number discoveries and patterns!