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

problem icon

Tricky Track

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Coded Hundred Square

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Sets of Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Buckets of Thinking

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

How Much Can We Spend?

Stage: 3 Challenge Level: Challenge Level:1

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?

problem icon

Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?