Task 121 ... Years 2 - 8
SummaryA wonderful beginner's task for exploring the same set of objects from looked at from different points of views. This task contributes to the development of spatial perception and includes a challenge to prove the result. The students are encouraged to look at a 2D representation of a farm paddock and imagine themselves in a 3D environment created from it. This skill is similar to that required when interpreting many text book illustrations.
This cameo includes an Investigation Guide.
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
A solution to Question 1 is:
Question 2 asks if there is another solution, but first, the students should be asked to record what would be seen in this case from Sides 3 and 4 (still looking from left to right).
There is only one solution to the given problem, but how can students convince someone of that? Perhaps they will use an argument that breaks the problem into smaller parts such as:
Further, the reasoning above begins with all the objects in the top row, as a solution to the first condition. But there are other ways to arrange the objects to satisfy the first condition, so there is still more to check before it can be concluded with certainty that there is only one solution.
Other iceberg challenges related to this task are:
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 prepare this task as a whole class investigation you only need to prepare a grid and clip art pictures to match the size of the grid. Or, since the task indicates the value of 'home-made' clip art, use an Investigation Guide that encourages students to create their own drawings. Ownership of materials is one of the features that captivates students as they learn to work like a mathematician.
From here an appropriate start is for each pair to place their pictures anywhere on the grid. Then ask them to imagine a 'walk' around the sides of their paddock from Side 1 and record what can be seen from each side. Teams discuss and check each other's recording. Continue the lesson with the problem on the card and the iceberg aspects appropriate to your year level.
At this stage, Farmyard Views does not have a matching lesson on Maths300.
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 Farmyard Views task is an integral part of: