You may also like

problem icon

Area and Perimeter

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

problem icon

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: Challenge Level:1

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

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.


First they made these journeys:
 map

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.
map
You can download and print off this sheet which has two copies of the grid map.
What do you notice about your different journeys?
Can you explain your observations?


After they had explored in the county of Addition in Numberland, Tom and Ben went on to the county of Multiply.
Here they had a new map which looked like this (here are two copies of the map):
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.

What do you notice about the journeys this time?
Can you explain why this happens?