The Farmer's Puzzles
Task 29 ... Years 2 - 7
SummaryA spatial task with a hint of algebra and a reminder of the properties of regular shapes. The farmer puts animals into pens according to certain rules. How does she do it?
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
Students will soon discover that making square pens won't work. The diagonal of square is longer than its side, so the sticks can't be placed end to end within the square to make triangular pens. However, triangular pens turns out to be the solution when they are arranged like this:
The solution suggests a way of making pens that leads to a pattern. Generalising the pattern leads to algebra.
One unfriendly horse:
Two unfriendly horses:
Three unfriendly horses:
Four unfriendly horses:
An answer to Question 2 on the card is suggested by the solution of Question 1. Two of the trapeziums make a hexagon like this:
which uses just 12 lengths the six animals can now wallow in equal areas.
Extensions suggested by this solution include:
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.
This is an easy task to convert to a whole class lesson. All you need is lots of pop sticks or short straws to be fences and counters to be pretend animals.
At this stage, The Farmer's Puzzles does not have a matching lesson on Maths300. However, there is a totally different lesson titled The Farmer's Puzzle, which models a Poster Problem Clinic.
Is it in Maths With Attitude?Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The Farmer's Puzzles task is an integral part of: