The Crawl Years 3 - 8

### Summary

This is a probability-based game for two who begin with the boards set up as shown using two columns of nine spaces. Players have a team of three plugs of one colour and compete to be first to move a team member out the front door to win. However, the first to move a team member out the back door loses.

Beyond just playing the game, the investigation question is How likely is a front door win?. Working as a class children collect and analyse data, then compare their results with the theoretical analysis of dice totals.

### Materials

• 2 Poly Plug sets between 2 players
• 2 dice per pair
FRONT DOOR THIS END

BACK DOOR THIS END

### Procedure

The game has similarities to physical education activities such as tunnel ball, so consider introducing it through physical play in a hall or outside. A large plastic mat works well for this purpose if you have one.

#### Rules

1. Players take turns to roll 2 dice and add the result.
2. If the sum of the dice is 6, 7, or 8, the player moves their first plug (the one closest to the front door) to become the last plug in the team.
NB: In effect this is the same as the whole team moving backward one space.
3. If the sum of the dice is any other number, the player moves their last plug (the one closest to the back door) to become the first plug.
NB: In effect this is the same as the whole team moving forward one space.
4. The winner is the first player to move a plug out the front door.
But, if you move a plug out the back door, you lose.

### Content

• data: collecting, recording, displaying
• data: describing & comparing with statistics
• data: interpretation
• estimating number
• likely, less likely and unlikely events
• mathematical conversation
• tallying

The game is called The Crawl because the rules cause the plug teams to crawl forwards and backwards along their path.

### Investigation

1. As children play the game for fun begin a class record of whether the game ended with a front door win or a back door loss (and consequent win for the opponent). This data will indicate that a front door win is more likely and invite the question of how much more likely.
Suppose we played 100 games. Estimate the number you would expect to be front door wins?
Record children's predictions, then arrange to gather data for 100 games. This need not all happen in one session, and it can include the data already collected. Compare the collected data to the predictions.

2. Begin a discussion about the unusual back and forward nature of the game (it is also similar to Snakes & Ladders in this sense). Examine what it is in the rules that is causing this to and fro. Lead into an examination of the chances of rolling a 6, 7, or 8 and compare with the chances of rolling the other numbers.
So, in theory, if we played 36 games you would expect 20 front door wins. What would you expect if we played 360 games? Why?
How could we check this hypothesis?
The obvious answer is to play that many games and, if there is sufficient interest, that could be done over time. However, this could also be the time to suggest that if a mathematician wanted to check this prediction they might program a computer to play the game.

Whether or not the class goes on to collect data about the extra games, you can round off here by reminding children that the overall purpose is to learn to work like a mathematician. Check the Working Mathematically process to see how the children have indeed been working like mathematicians.

3. Another avenue for investigation is the average number of rolls to get a decision in the game, be it front door win or back door loss.
4. Suppose the game used ten-sided dice that were numbered from 0 to 9? What would be the rules of the game now?

Calculating Changes ... is a division of ... Mathematics Centre