# Collaborative Mathematics - February 2010, All Stages

This month we invite you to work on linked mathematical activities which naturally provide the insights which will enable you to tackle more significant challenges. This encourages a collaborative way of working on mathematics where the sharing of ideas and results leads to deeper insights for all.

## Problems

### Even and Odd

##### Stage: 1 Challenge Level:

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

### Jig Shapes

##### Stage: 1 Challenge Level:

Can you each work out what shape you have part of on your card? What will the rest of it look like?

### Sort Them Out (1)

##### Stage: 1 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

### How Do You Do It?

##### Stage: 2 Challenge Level:

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

### Sort Them Out (2)

##### Stage: 2 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

### Fingers and Hands

##### Stage: 2 Challenge Level:

How would you count the number of fingers in these pictures?

### Cinema Problem

##### Stage: 3 Challenge Level:

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

### Legs Eleven

##### Stage: 3 Challenge Level:

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

### Tower of Hanoi

##### Stage: 3 Challenge Level:

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

##### Stage: 3 and 4 Challenge Level:

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Why 24?

##### Stage: 4 Challenge Level:

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Areas and Ratios

##### Stage: 4 Challenge Level:

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### Prime Sequences

##### Stage: 5 Challenge Level:

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

### The Clue Is in the Question

##### Stage: 5 Challenge Level:

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .

### Transformations for 10

##### Stage: 5 Challenge Level:

Explore the properties of matrix transformations with these 10 stimulating questions.