Four and Twenty BlackbirdsTask 62 ... Years 2  10SummaryTwentyfour birds land on eight feeding tables that are mounted around the edge of the Royal Garden. The garden is a rectangle and the feeding tables are at the four corners and the four midpoints of the sides. The birds arrange themselves so that nine can be counted along each side of the rectangular garden. How many are on each feeding table?

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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
As the task card suggests, there are many ways to arrange the 24 birds so there are 9 on each side of the rectangle. For younger students it will be a joy to find only some, but the big challenge for older, or more experienced, students is to find them all. To do this the students have to find sufficient solutions to be able to discover clues such as:
One way to approach finding all the solutions is to focus on one corner, say the top left, and break the problem into parts by trying each number in turn in this corner. For example, if 9 is in the top left...
then we automatically know the top row and the left column...
Carefully continuing this reasoning for 8, 7, 6, ... in the top left corner will lead to finding all solutions. The card also suggests the What happens if..? questions:
Could the 24 blackbirds be placed with 9 along each side of the triangle? 
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. 
As a whole class investigation, there are three parts. Firstly a class 'floorboard' where the story can be told and each of the students can contribute a large blackbird to an attempted class solution. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 62, 4 & 20 Blackbirds, which includes and Investigation Guide. Visit 4 & 20 Blackbirds in Menu Maths Pack D (where it is called 4 & 20 Red Birds). 
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. 
The Four and Twenty Blackbirds task is an integral part of:
The Four & Twenty Blackbirds lesson is an integral part of:
