### Who's Who?

Can you solve the clues to find out who's who on the friendship graph?

### Can You Traverse It?

How can you decide if a graph is traversable?

### Euler Meets Schlegel

Discover how networks can be used to prove Euler's Polyhedron formula.

# Waste and Recycling

### Why do this problem?

This problem challenges students to make sense of a lot of random information and to apply their knowledge of percentages and proportionality to answer the questions.

It is based on a problem from the book Teaching Mathematics as if the Planet Matters

This problem is one of a collection designed to develop students' carbon numeracy; we hope it will encourage students to think about the issues surrounding climate change.  You can find the complete collection here.

### Possible approach

This is an activity for small groups of students (about four is probably ideal) to work on together that will offer opportunities for collaborative working.  The set of statements refer to waste and recycling habits of a "typical" family in the UK.

The statements can be printed out and cut up, and then shared between the members of the group.  The task is to answer the two questions using the information given to them.  This should be done by talking about the information that each student has rather than "pooling" the cards, so that everyone in the group stays involved and has useful information to contribute.

Each group could be asked to set out their working/justifications on a large sheet of flipchart paper before being asked to talk to the whole class. How did they group the information to make it more manageable? How did they decide that some of the information was unnecessary?

### Key questions

• Which cards would it be helpful to group together?
• Which cards do you need to answer question 1?
• Did you need to use all the cards?

### Possible extension

Students could be challenged to think of another question that could be asked.  What extra information woud they need to answer their question?  Can they think of a question that uses one of the "unused" cards?

Students might like to investigate carbon footprints with the problem Comparing Carbon Footprints

### Possible support

A possible way to simplify the problem could involve offering students the information in an organised form.