We started with a green cube and then built a square of orange cubes around it. Then we made another square of green cubes and so on...

maths investigation

We decided to count the number of cubes in each square.
The first square of orange was made using 8 cubes.
The next square of green had 16 cubes.
We tried to guess how many cubes the next square would need. Here are some of the numbers we thought: 14, 20, 90, 26, 27, 19, 18, 30...
So we counted very carefully; we found out that...
The next orange square had 24 cubes.

We wondered if we might be able to find a pattern...

We put 8 in our heads and counted until we got to 16; we found that the difference was 8
We put 16 in our heads and counted until we got to 24; we found that the difference was 8 (again!)
The next green square had 32 cubes
We put 24 in our heads and counted until we got to 32; we found that the difference was 8 (again!)
The next orange square had 40 cubes
We put 32 in our heads and counted until we got to 40; we found that the difference was 8 (again!)
The last green square had 48 cubes
We put 40 in our heads and counted until we got to 48; we found that the difference was 8 (again!)

How many orange cubes do you think will we need to make the next square? How could you find out? Does your answer follow the pattern we found?

What are some things you could say about this pattern?