# Making Solids

### Task 67 ... Years 2 - 10

#### Summary

Colourful, tactile materials encourage students to become involved in this set of spatial puzzles in three dimensions. The challenges are sometimes harder than they look and to solve some of them students have to realise that the procedure for isometric drawing might mean that some parts of the object can't be 'seen'. This is a consequence of representing three dimensional objects in two dimensions. Students are also encouraged to count cubes to calculate the volume of each object, but in some cases counting from the picture, rather than the construction, may lead to an incorrect calculation.

#### Content

• 3D spatial perception
• isometric drawing
• volume as counting cubes
• 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.

This series of 3D spatial challenges is presented as isometric drawings. Students are expected to recreate how they were made from the given pieces and to create their own isometric drawing of how the pieces join. Any of the six blocks can be used for any of the puzzles. For example, one way to solve the last puzzle on the card is:

Single cubes are not used in this construction.

Challenges need not be tackled in a particular order and students can come and go from the task and experience success each time.

The task also touches on the concept of volume as measured in unit cubes. Reading across the card, the volumes are:

9, 8, 9
12, 6, 10
12, 16
Extension questions include:
• Can any of the objects be made in more than one way?
• Can you create your own object from these blocks and record it as a new puzzle for the class?

#### 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 solids. These can be purchased, 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 so each group has a turn to record at least one solution, or make up a new puzzle.

At this stage, Making Solids 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 Making Solids task is an integral part of:

• MWA Space & Logic Years 3 & 4
This task is also included in the Mixed Media Unit titled Points of View: Representing 3D Objects in 2D.