### Area and Perimeter

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### Polygonals

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

# Journeys in Numberland

##### Stage: 2 Challenge Level:

Tom and Ben were in Numberland in the county of Addition.
They had a map which looked like this:

They were at point B and they began their journey with ten points.
For every square they walk to the right on the map, they add five.
For every square they walk to the left on the map, they take away five.
If they go North (up on the map), they added two for every square, and if they go South (down on the map), they take away two for each square.

The blue line shows Tom's journey and the green line shows Ben's.
How many points did they have each when they reached E?
Do you notice anything?

Here is a different grid for you to make up some journeys of your own, beginning at B and ending at E.
You can download and print off this sheet which has two copies of the grid map.
They explored here too. Each time they started at B with $10$ points and made their way to E. Try lots of journeys yourself.