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

problem icon

Finding Factors

Stage: 4 Challenge Level: Challenge Level:1

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

problem icon

Multiplication Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

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

problem icon

Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

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?

problem icon

Poison, Antidote, Water

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

problem icon

Weekly Challenge 25: Trig Trig Trig

Stage: 5 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Irrational Arithmagons

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

What's a Group?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Sheep in Wolf's Clothing

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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