## 1. Happy homes

##### Our farmers all want to buy some animals, but they each have different kinds of food available. Can they each buy an animal which they'll be able to feed?
 Time required: 20-40 min Equipment: Printouts, scissors (for the extension blue-tack or similar may be useful) Mathematical themes: Matchings Comments: This activity has a very open-ended extension, so is quite flexible in terms of timing.

Detailed instructions

Happy homes - scenario descriptions

Happy homes - scenario cards

Happy homes - card game

## 2. Planting time

##### It's time for our farmers to plant their crops. To reduce problems with pests, they want to avoid planting the same kind of crop in adjacent fields. Can they do this with the crops they usually grow, or will somebody have to start planting cabbages?
 Time required: 15-30 min Equipment: Blank paper and pens or pencils; it will be useful to have five different colours of pen/pencil or sticky post-it notes. Mathematical themes: Graph colouring, Four Colour Theorem Comments: If you plan to run "Inspecting the Fences" afterwards, everyone should keep hold of their farm design.

Detailed instructions

## 3. Inspecting the fences

##### It's important to make sure all the fences are in good repair - otherwise rabbits might get in and eat all the crops. So our farmers need to inspect all their fences regularly. But how far will they have to walk each time they do this?
 Time required: 15 min for the basic activity; 30-40 minutes for each of the extensions. Equipment: For the basic activity - pens and paper; for Extension 1 - a large space and objects to represent islands (e.g. gym mats, hoops) and bridges (e.g. small mats, skipping ropes); for Extension 2 - each pair needs a printout of the two files "Inspecting the Fences - game board" and "Inspecting the Fences - bridges" as well as a small token (e.g. counter or coin). Mathematical themes: Euler tours Comments: This works well as a follow-on activity to Planting time as the same drawings of fields can be used in the first part of the activity. Each of the extension activities can be run without running the basic activity first.

Detailed instructions

Inspecting the fences - game board

Inspecting the fences - bridges

## 1. Which cow coughed first?

##### Some of our animals are sick. We want to work out who was sick first and passed on their germs to the other animals.
 Time required: 30 min for the basic activity; 15-20 minutes for each extension. Equipment: Paper and pens, plus a coin or die for each member of the group in Extension 1. This activity is best run in either a large empty space or a room with furniture that is easily moved. Mathematical themes: Connectivity, epidemiology, cellular automata, probability

Detailed instructions

## 2. Vet vs Mosquito

##### An evil mosquito is flying around all our friends' farms, making the animals sick. Luckily, a friendly vet is on the case and is going to visit all the farms with a vaccine. But can he get to all the farms before the mosquito does?
 Time required: 45 min Equipment: Pens/pencils and a reasonably large space (5m square should be plenty) where the group can walk around; also for each of the four senarios you will need various printouts (see instructions for full details). Mathematical themes: Traveling Salesman Problem Comments: The activity can be made shorter by omitting one or more of the scenarios, or longer by re-running some of the scenarios with roles reversed, but it is recommended to try at least three of the scenarios to provide enough material for discussion.

Detailed instructions

Vet vs Mosquito - Record Sheet

Vet vs Mosquito - Farmers - Scenario 1

Vet vs Mosquito - Farmers - Scenario 2

Vet vs Mosquito - Farmers - Scenario 3

Vet vs Mosquito - Farmers - Scenario 4

Vet vs Mosquito - Vets - Scenario 1

Vet vs Mosquito - Vets - Scenario 2

Vet vs Mosquito - Vets - Scenario 3

Vet vs Mosquito - Vets - Scenario 4

## 3. Market day

##### It's time to take the animals to market. But we have to make sure there's enough food to keep them happy along the way - how many cows can we take to the market? And what if a rival farmer is trying to stop you getting there?
 Time required: 15-20 minutes for the basic activity; another 20 minutes for the extension. Equipment: A printout of the file "Market Day - Scenarios" for each member of the group; for the extension, you need another printout of this file for each pair in the group, and some blu-tack or similar. Mathematical themes: Network flows and cuts Comments: The extension to this activity is particularly beneficial, if time permits.

Detailed instructions

Market Day - Scenarios