# Tricube Constructions B

### Task 90 ... Years 4 - 8

#### Summary

Students are shown an isometric view of a 'building' they know is made from all four Tricubes. From this they are asked to construct the buildings. They then become problem creators and are asked to construct their own 4 Tricube building, draw its isometric view and challenge a peer to reconstruct their building from the drawing.

Tricube Constructions B also appears on the Picture Puzzles Shape & Space A menu where the problem is presented using one screen, two learners, concrete materials and a challenge. In this context it is called Tricube Building B.

#### Content

• 3D spatial perception
• representing 3D objects in 2D
• isometric drawing
• plan (or aerial) view
• 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.

Answers are not necessary. Students will know when they have made the building. However to help them explore possibilities it could be useful to draw attention to these facts:

• One Tricube standing alone has a volume of 3 cubes, so four have a volume of 12 cubes. Does it appear from the drawing that the building you are working on has a volume of 12 cubes?
• One Tricube standing alone has a total surface area (including the base) of 14 squares, so four have a surface area of 56 squares. If you calculate the apparent surface area of the building in the drawing you are working on is it 56 squares?
• Is there more than one way to construct any of the buildings?
• Copy the isometric drawing of at least two buildings they solve and add dotted lines and/or colour to show how the Tricubes fit together.
• Draw the front, side and top views of at least two other buildings.
• Choose one building and invent a different way to make a drawing to explain to someone else how to construct it.
• Choose one building on the card and decide its purpose. Draw a floor plan for each level showing how the building is organised to achieve this purpose.
• Find examples of isometric, front, side and top views of buildings in the press or from other sources.

#### 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.

If you want the whole class to work on this investigation simultaneously, you will need a class set of Tricubes. These can be purchased (see Tasks, Kits & Resources) or making them in art or woodwork class could be a cross-faculty project. If you don't have a class set, you could use this task in a work station, probably with other spatial tasks, and rotate students through the station over a period of time. Keep a class scrap book at the work station in which each group records its new puzzle as suggested above.

At this stage, Tricube Constructions B 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.

Tricube Constructions B is not in any Maths With Attitude kit, however, it is included as a key component of the Mixed Media Unit titled Points of View: Representing 3D Objects in 2D.