# Button Sort

### Task 74 ... Years 2 - 6

#### Summary

Sorting and classifying on the basis of properties is a vital skill for a mathematician. Consider for example how numbers can be sorted into odd and even, square, triangular, prime and so on, or shapes into triangles, quadrilaterals, pentagons and so on. This task offers the opportunity to develop those skills using a 'feel good' material.

#### Materials

• A collection of buttons

#### Content

• sorting and classifying
• use of terms such as 'and', 'or' and 'not' which are key concepts in mathematical logic

#### Iceberg

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

There are no specific solutions to this task. The answers students offer will depend on the collection of buttons they have to work with and the button they choose to start the puzzle. The task is not so much about the answer, as it is about justifying the chosen answer in a manner appropriate to age and ability.

Unlike educational materials such as attribute blocks which are designed for the purpose, the set of available buttons may not provide the button required for a certain space. In that case it is great if a student can describe the attributes of the button they need; sometimes even placing a scrap of paper in the box to record those attributes. You could extend the possibilities by asking students to bring unwanted buttons from home.

The task assumes that the set of buttons displays a range of sizes, shapes and colours. To assist with the task it can be useful to sort on just one of these criteria at a time and come to an agreement about what the criterion means. For example will size mean diameter in millimetres or two or three groups such as large/small or large/medium/small. Colour is another characteristic to be discussed, for example, does 'same colour' mean exactly the same brown (for instance), or a button with a brownish look?

When mathematicians organise the data related to a problem they are trying to solve, they have to make similar decisions about what goes with what. In doing so, they realise that choosing a different set of organising criteria could change the solution of the problem.

Students might also want to add sorting criteria, such as the number of holes in the button. Overall, although the task card simply gives instructions for the challenge, you can encourage them to begin by sorting all the buttons and refining the criteria they will use. Venn diagrams could help here too.

This task is a partner to Task 228, Koala Karts, which uses a closed set of koalas with various attributes to sort based on a logic track.

#### 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.

To turn this task into a whole class investigation with the intention of all students working on it simultaneously would require a massive number of buttons. Better to use it a work station situation and grow your class collection of buttons to a reasonable size. You, or the students, can also design your own sorting trails.

At this stage, Button Sort 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.

Button Sort is not in any MWA kit. However it can be used to enrich the Space & Logic kit at Years 5/6.