Rogo puzzles appeal to a wide range of ages. Here are some great ideas on how to use Rogo in the classroom. No doubt imaginative teachers will think up many more. You will need to be conversant with Rogo puzzles before some of the following ideas will resonate. If you would like to share your ideas, either add them as a comment to this blog, or email them to v...@rogopuzzle.co.nz.

## Exercises using Rogo puzzles as they are

- Reward activities for when pupils have completed their work.
- Laminate a set and include a whiteboard pen to use in the Maths activity box.
- Homework exercises, with or without the “best” score provided.
- Team competitions.
- Rogo installed on iPods or iPads for pupils to play on. (Note that there is an educational discount for the Rogo app.)

## Changes to Rogo puzzles:

- How many routes can students find that give a specific total (less than the Best!)
- What is the smallest score they can achieve with a legitimate route of the correct length?
- Give different length routes for pupils to try out on the same grid.
- Don’t give the “Best” or “Gold” and make it a competition to see who can get the highest score.
- Designate an additional forbidden square, and see if it alters the solution.
- Allow drawing over forbidden squares.
- Change the numbers to fractions, decimals or even algebraic expressions.

## Make your own Rogos

**Teachers **can easily make their own Rogo-type puzzles.

Note that finding the actual best route can be problematic, and making sure a Rogo puzzle has suitable distracters is also difficult. However for a quick exercise on the board, involving counting and adding, a made-up Rogo has great appeal. The class can help to devise the board at the start of the exercise.

**Students** make Rogo-type puzzles for each other.

Vote on which is the hardest, which is the most fun, which is the most attractive to look at…

- Students discover that it can be difficult to know when they have reached the optimal solution.
- Get students to make Rogo-type puzzles suitable for younger children, using pictures rather than numbers, and pictures on the forbidden squares. Use a theme of collecting flowers, coins, eggs, treasure or starfish, for instance.

(In time the Rogo website will have the facility for you to submit your devised Rogo puzzles for solving and evaluation.)

## Explorations and creative responses

*These more divergent ideas may be more suited for when pupils have had experience in solving Rogo puzzles and understand some of the structural elements.*

### Enumeration

Using a simple Rogo, get students to enumerate all possible routes.

Get students to write an algorithm that will make it possible to list every possible route.

See if students can generalise their enumeration method to a larger number of routes.

### Heuristics

What process do they use to solve a Rogo?

Come up with a set of steps which will help them to solve a new Rogo puzzle.

Could these be used to program a computer to solve a Rogo puzzle?

How do you know when to stop?

(There will be more about heuristics in a later blog.)

### Route shapes

For a certain route length, what shaped routes are possible? This leads to concepts of symmetry, reflection and rotation.

How could you classify each of the route shapes?

Is there a rule that can be used to generalise how many shapes there are?

### Forbidden squares

For a certain size grid, which patterns of black squares are of practical use? (For example a black square one away for the corner makes the corner square unattainable.)

Does this differ depending on the length of the route?

### Difficulty

- Explore what elements of a Rogo make it easier or more difficult to solve. A later blog will discuss the twelve elements we have identified and are exploring.
- Get a set of Rogo puzzles and get each student to time themselves solving them. Collect the data and use it for a statistical investigation. How would you present this data? Is the variation in time taken between people more or less than the variation among the different puzzles. This could be used to hypothesise what makes some Rogos more difficult than others.
- Get the class to postulate questions and then work out ways to explore them. For example, how dense should the numbers and squares be for a satisfactory Rogo? Does symmetry play a part in solving the puzzle. What is the relationship between difficulty and fun?

### Imaginative settings

Make up stories that would be solved by a Rogo puzzle. For example, shopping or holidaying among tourist attractions.

### Rogaining and the Travelling Salesperson Problem(TSP)

Rogo has its roots in a sport called Rogaining, which involves problem solving, strategy and navigation. A mini Rogaine could be devised in the school playground, perhaps formatted as a Rogo.

Students may like to explore the TSP and its historical background. Links are provided in this website. A previous blog explained the links between Rogo and the fascinating subject of Operations Research, which is becoming increasingly used in business in the area of Analytics.

## Potential for learning

Rogo has enormous potential to help students of all ages develop numeracy and problem-solving skills. Math teachers are encouraged to use games to liven up the classroom and enable learning.

Tell us your great ideas and successes and we will compile this for other teachers.