### A Method of Defining Coefficients in the Equations of Chemical Reactions

A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.

### Tournament Scheduling

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

### Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

# Carbon Footprints

### Why do this problem?

This problem offers a good opportunity to discuss some of the maths behind the issue of carbon emissions. It is a chance for students to use some maths to support their viewpoint, and to equip themselves with the skills needed to analyse critically what they see in the media about climate change. There is real scope for making cross-curricular links through this problem. It is almost certain to raise surprising realisations about the sheer volume of carbon produced by everyday activities.

### Possible approach

One way of approaching this problem with a class is to divide them into groups and provide each group with a copy of the data given in the problem, which can be found here. Allocate one of the questions for consideration to each group, and give them plenty of time to discuss which pieces of information are useful to them in answering the question. Each group could prepare a presentation or poster to present to the rest of the class explaining their answer to the question and stating any assumptions they have made. Students could also consider questions of their own, and could use some of the links provided at the bottom of the problem to find other useful information needed in order to answer the questions.

### Key questions

Which pieces of information are useful in answering each question?
What assumptions need to be made in order to answer the questions?

### Possible extension

Students could be encouraged to think about what extra information would help them better to answer these questions, and could seek out this extra information.

### Possible support

Suggest starting with common-sense reasoning and then look for the numbers to back up what their common sense suggests.