# Actions on objects - March 2011, All Stages

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

### The Add and Take-away Path

##### Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

### Count the Digits

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

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

### The Numbers Give the Design

##### Stage: 2 Challenge Level:

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

### Journeys in Numberland

##### Stage: 2 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

### Area and Perimeter

##### Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### Missing Multipliers

##### Stage: 3 Challenge Level:

What is the smallest number of answers you need to reveal in order to work out the missing headers?

### Arithmagons

##### Stage: 3 Challenge Level:

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

### Opposite Vertices

##### Stage: 3 Challenge Level:

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

### 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?

### 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?