# Actions on objects - March 2011, Stage 4&5

In preparation for this month we worked with Professor John Mason exploring 'actions on mathematical objects'. All the tasks involve appreciating mathematical structure, whether this is through recognising relationships or perceiving properties.

## Problems

### Finding Factors

##### Stage: 4 Challenge Level:

Can you find the hidden factors which multiply together to produce each quadratic expression?

### Multiplication Arithmagons

##### Stage: 4 Challenge Level:

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

### Arithmagons

##### Stage: 4 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

### Vector Journeys

##### Stage: 4 Challenge Level:

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

### Poison, Antidote, Water

##### Stage: 4 and 5 Challenge Level:

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.

### Weekly Challenge 25: Trig Trig Trig

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

### Irrational Arithmagons

##### Stage: 5 Challenge Level:

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

### What's a Group?

##### Stage: 5 Challenge Level:

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

### Sheep in Wolf's Clothing

##### Stage: 5 Challenge Level:

Can you work out what simple structures have been dressed up in these advanced mathematical representations?