Pattern

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

How many possible symmetrical necklaces can you find? How do you know you've found them all?