Animal FarmTask 229 ... Years 2  7SummaryIn essence, Animal Farm is a more visual form of Arithmagons (Tasks 188 & 194) which has also been embedded in a simple story shell. This allows younger or less experienced students to enter the family of problems. As one teacher commented, I love this task. It helps them to understand what's going on.. The problems are based around three known numbers, three unknown numbers and addition relationships between them. In the first part of the task students create problems where all the numbers are known. Then come the questions with missing information where the unknown numbers have to be found. It is not necessary to use algebra to find them, even though this will probably be the tool of choice for many teachers. Instead working like a mathematician to play with the problems, collect and organise data, look for patterns or connections and make and check hypotheses is the first principles approach structured into the task. 
Materials
Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
Questions 1 and 2 are intended to get students playing with the problem and collecting data about how they are constructed. Once a problem is successfully created on the board it is best if it is transcribed into the students' journals, or onto this Recording Sheet. The numbers involved in each creation become the data for the missing number problems which begin with Question 3. If a permanent record isn't kept this data isn't accessible. In preparation for the next part of the task, the double line on the card is the signal to discuss the work so far with the teacher. You might ask questions like:
Beginning with the smaller of the left and right circle numbers...So now finding T (and hence the numbers in the other two fields) only involves an organised substitution of every possible value of T into the equation. Or, for the mad keen algebraists, solving: (10  T) + (9  T) = 13 <=> 19  2T = 13 <=> T must be 3 because 19  6 = 13. Other observations of the data from Questions 1 & 2 that can be lead to other methods of solution are:
ChallengeThe challenge asks What happens if the farmer's map is missing one circle number?. The short answer is you get multiple solutions.Using the example on the card, suppose the 13 is missing. To show that let's call the missing number X. The equations above then become:
Extensions

Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. 
To convert this task to a whole class investigation you need lots of objects to be animals and an A4 size Animal Farm for each pair. The farm is fairly easy. Sketch on the board as you say:
The lesson will develop along the lines of the iceberg above and you will have the opportunity to (a) pause to share individual insights with the class and (b) highlight the various elements of working like a mathematician. At this stage, Animal Farm does not have a matching lesson on Maths300. However Lesson 63, Arithmagons, extends the problem for older, or more experienced, students. Heads & Legs, a related problem, is explored in Maths300 Lesson 41, which also includes software. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
Animal Farms is not in any MWA kit. However it can be used to enrich the Pattern & Algebra kit at Years 3/4. 