**This resource is no longer actively suported.**

**The Bright Sparks applets were developed 10 years ago using Java. Recent security updates have meant that the Bright Sparks no longer work using default settings. While it is possible to run the applets by adding them to the Exception list for Java's security settings, we are unable to support users in doing so.**

**Six Circles and Frogs have been redeveloped as part of e-ako maths, which is freely available to learners in New Zealand.**

This section of the website provides information to help understand the Bright Sparks problems and to assist teachers in guiding students use of them. The Bright Sparks problems have been set up for able students to attempt by themselves on a computer either at home or at school. We hope that you will assist and encourage them to get as far into the problem as they can.

The Teachers' notes have been written to provide a theoretical background to each problem and some of the ideas that need to be understood to solve it.

The Students' notes provide hints as to what to try at various stages of the problem investigation. These might be useful for you to read to ensure that you have a sound understanding of the processes students are likely to follow to solve the problem.

Click on the links in the table below to access the Bright Sparks activities or their notes.

To detect which version of Java you have installed click here (WindowsXP users, click here). To run the Bright Sparks from your desktop go to the webstart page.

There are four basic phases that we expect the students will go through in exploring these problems:

- understanding and solving specific problems
- generalising these cases to conjectures
- proving or justifying their conjectures
- extending the problems in other ways.

For practical reasons it is best to have no more than three students working on the same computer together. There just isn’t enough room to gather round the screen. However, it is often better to have more than one student working on the problem as this allows for interactions and such interactions can often be very profitable.

While each activity is set up so that students can work on it independently, you should perhaps have some reporting back arrangements so that you can keep track of their progress. This may mean that you just pop in on them if they are working in the classroom. It might mean that they report to you after they have worked at home or in a computer lab. But the scaffolding that you give them should be similar to what you would give with a normal class. Keep it open so that they have a chance to think for themselves. Remember “The one who does the thinking does the learning.”

Students might be encouraged to write up a summary of what they did while working on each problem.

## Background Knowledge

Students can make a great deal of progress in many of these problems without knowing too much material that is specific to any particular part of the curriculum. For instance, Diamonds and Sole Survivor rely on little more than logic, some basic spatial ‘feel’ and knowing how to tackle a problem.

In other problems knowing how to express a pattern in algebraic terms will be enough to get the student a long way. This is the case with Frogs, Round Table and Six Circles.

It is only in Nice Dice, where some basic probability is required, and Toni’s Tiara, which assumes a knowledge of the properties of small polygons, that much specific content knowledge is required.

But all of the problems require the following:

Attitudes:

- the ability to think and not be put off by the thought of thinking

Mathematics involved:

- logical thinking

Problem solving:

- get more information from a step than appears to be there
- try small cases
- be systematic
- make a conjecture (guess a pattern)
- test a conjecture
- justify steps
- generalise and extend

It is probably in the area of problem solving that most learning will need to take place.