# Which View?

### Task 78 ... Years 2 - 8

#### Summary

Students are shown the front, side and top views of a 'building' and are asked to build it from wooden cubes. There may be more than one answer. The task also invites the students to work backwards, create their own 'building', then record its various views.

#### Content

• 3D spatial perception
• plan and elevation views
• problem solving

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

When students are examining their buildings to check them against the views, encourage them to get down to table top level - in direct line with the building - and cover one eye with their hand. There may be some debate over which side is represented by the side view. Traditionally it is the left side, with respect to the front of the building, but you could also explore what difference if would make to the 3D object if side view was interpreted as the right side.

The next problem is how to record the object the students think is correct. A digital camera may be useful, or students could record in storeys, as below, where there is at least one cube in each position.

Question 1

Question 2

A further development is to ask students to represent the object as an isometric drawing - in fact, as four isometric drawings representing the four sides.

#### Whole Class Investigation

Tasks 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.

A set of wooden cubes is a multi-useful mathematics aid. In this case, to fulfil the whole class lesson life of this task, that is what you need. If you have lots of cube dice, they can work at a pinch, but they tend to be more slippery than the wooden cubes. Click together cubes are less satisfactory because they make it difficult to add or remove cubes without disturbing the rest of the building. You may find that it is possible to arrange with the craft teacher that the students cut their own cubes from square section timber. This can be a worthwhile cross-discipline activity because the mathematics developed with the cubes in this task will help to prepare the students to read design drawings. If you want to purchase wooden cubes as in the task, they are listed in Mathematics Centre Resources & Ordering.

Which View? as such does not have a matching Maths300 lesson, but its partner Building Views has. For more ideas and discussion about Building Views, open a new browser tab (or page) and visit Maths300 Lesson 163, Building Views, which also includes an Investigation Guide.

Building Views is also included in the Pictures Puzzles Shape & Space A menu. If you are creating a unit of work on representing 3D objects in 2D, then Which View and this Picture Puzzle menu would be excellent inclusions,

#### 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 Which View? task is an integral part of:

• MWA Space & Logic Years 5 & 6
This task is also included in the Task Centre Kit for Aboriginal Students.