### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

# Journeying in Numberland

##### Stage: 2 Challenge Level:

Tom and Ben are in Numberland in the district called Addition.
They have a map which looks like this:

They are at point B and they begin 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 add two for every square, and if they go South (down on the map), they take away two for every square.

First they make these journeys:

The blue line shows Tom's journey and the green line shows Ben's.
How many points do they have each when they reach 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 explore here too. Each time they start at B with $10$ points and make their way to E. Try lots of journeys yourself.