# Playing With Objects

### Task 226 ... Years 2 - 8

#### Summary

A mathematician's work begins by playing around with a problem they are interested in. Everything about this task - the objects, the funny name cards, the rice - invites the students to play. Through the play they encouraged to find relationships between the volumes of the objects. The task opens up the areas of solid geometry, mathematical nomenclature, volume and possibly other measurements.

#### Materials

• At least 7 objects
(The card says 7, but often an extra has been packed.)
• 20 name cards
(They may not all be needed.)

#### Content

• 2D representation of 3D objects
• equations, creating
• language of space, position and order
• measurement, area
• measurement, length
• measurement, mass / weight
• measurement, perimeter
• measurement, volume
• sorting, classifying, ordering
• spatial perception, 2D or 3D

#### Iceberg

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

Too often 3D geometry and is learnt from the pages of a book and appeal to experiences the learners might have had and the visual image that might remain in their brain. This task provides relevant, real experience with a wide range of objects.

The first part of the task is about developing the names a mathematician uses for the objects and their parts. However it starts from names students might conversational give to the objects and encourages them to find out the mathematical name, rather than from a sticker on the object or a 2D page drawing that says 'This is a ...'. The device for achieving this is simple.

• Collect a set of objects.
• Make set of cards that name them with words a student might use.
• Make a second set of cards that name them with words a mathematician would use.
• Give the students some of the objects and all of the cards.
Whichever objects they have there will be two name cards for each one. If it happens that is not the case and a student name is missing, they invent one. If a card is missing and it's a mathematical one, then they have to find out that name. Mathematical names are not negotiable. All mathematicians agree on them so the challenge becomes finding out what the names are and what extra information the name might give. For example:
• What distinguishes a pyramid from a prism?
• What feature distinguishes one pyramid or prism from another?
• Which mathematical names are the same in daily language?
The task also encourages recording and although it doesn't specifically ask for drawing within the recording expecting that makes the children realise the problems involved in trying to represent three dimensional objects in two dimensions.

The challenge uses the rice to encourage comparison of volumes. Encourage recording predictions or hypotheses, for example:

• It will take two cubes to fill the cuboid.
• Three square pyramids will fit into the cube.
before testing by pouring. The relationships the students find will depend on the objects in their set, and even if they don't find any, the experience of actually 'measuring' the capacity of such a variety of objects will be worthwhile.

An extra activity could be to be to tell the story of the mathematician Leonard Euler who discovered an equation linking the number of faces, edges and vertices in any object that has all polygon faces. Challenge the students to use the objects to rediscover this connection?

#### 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 your school happened to have a class set of a wide range of objects you could recreate the essence of this task. However, that's not very likely, nor is it very likely that you will be able to collect enough which have a volume relationship to each other.

So in a whole class situation we suggest that this task is probably best used at task work station in a unit of work on measurement. Related tasks could be Task 20, Pack The Box, Task 193, Surface Area With Tricubes, Task 227, Volume Line Up. Other volume and capacity activities can be found in most curriculum documents. These could be the basis of other work stations. You could also consider the whole class investigation section of Task 63, Fried Rice, which begins with a classic volume problem used in a Die Hard film and develops into an investigation in prime numbers.

At this stage, Playing With Objects does not have a matching lesson on Maths300, but Lesson 80, Cylinder Volumes, and Lesson 81, Biggest Volume, are related. Together with the tasks they could form the basis of a Mixed Media Unit.

#### 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 Playing With Objects task is an integral part of:

• MWA Chance & Measurement Years 7 & 8