### 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?

# Sitting Round the Party Tables

##### Stage: 1 and 2 Challenge Level:

We had some really good ideas sent in, some that were illustrated well using the computer. From Kent College we had Primrose and Charlotte, Sophie and Nia, Stephanie, Nandini and Hazel.

Well here we have a superb piece of work, sent in by Abi and Charlotte from the same school, that I would advise people to look at for working investigatively on this activity.

When we first looked at the problem we decided to test the difference between the amount of sweets each table needed, and we came up with these results.

We looked at the results to see if there was a pattern in the difference between the amounts of sweets. Despite the fact there wasn't a pattern there we were determined to find a pattern. So we looked further into the problem and saw a pattern between the differences.

From that we could guess the next two amount of sweets needed.

When we saw this we thought of why it could have happened. Then we realised that a square has four sides and four squared is $16$ so to get proof we checked with a triangle.

There is a pattern. So the difference between the difference between the difference is always nought.