# Communicating and reflecting - September 2009, Stage 2&3

This month NRICH gets involved in the conversational side of mathematics, with problems which naturally lead to discussion and sharing of ideas and methods. Which forms of communication and presentation of the mathematics will prove to be the most effective? Through discussion and explanation you will refine your thinking and perhaps make connections with other areas of mathematics.

## Problems

### Tricky Track

##### Age 7 to 11 Challenge Level:

In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?

### A Square of Numbers

##### Age 7 to 11 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

### Coded Hundred Square

##### Age 7 to 11 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

### Sets of Numbers

##### Age 7 to 11 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

### Buckets of Thinking

##### Age 7 to 11 Challenge Level:

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

### How Much Can We Spend?

##### Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

### Sticky Numbers

##### Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

### Where Can We Visit?

##### Age 11 to 14 Challenge Level:

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?