Ship Odyssey Teacher Resource
We can use noisy data to make estimates of unknown but specific values. The summary measure we use depends on the shape of the distribution; the size of the sample depends on both the variability of the process and also the level of accuracy we require.
Levels and Possible Activity Routes
There are six levels in the game, and four activities we've developed around them. Generally, it will take about one hour-long class period to complete an activity. To do all of the activities requires at least 4 hours. Recognizing that many teachers will not be able to devote this much time, we recommend two shorter routes:
1. Hundred O' Rats —> Sea Walls —> Treasure or Not ( 2-3 days)
2. Hundred O' Rats —> Rat Shortage —> Small Hook —> Deep Water (2-3 days)
The document linked below — Activities Overview — provides descriptions of the levels, the possible routes above, and their objectives.
Activity: Hundreds o' Rats
In this level, students can only send down 100 rats at a time. Initially, most of them use either the apparent mode of the distribution or the center of the modal clump to decide where to drop their hook. Using these methods, they generally can get no more than 4 treasures before the game ends (after they miss twice with the hook).
After testing various methods, students observe that they can get higher scores of 7 or 8 using the mean or median. This may be the first time that many of the students have ever found the mean or median actually useful. In future missions, students learn that the mean or median of samples are not always reliable indicators of the treasure location, that their usefulness depends on the size of the sample and the shape of the distribution.
Activity: Sea Walls — Treasure or Not
Students play Sea Walls and then Treasure or Not. They learn that the mean even of large samples is not necessarily a good estimate of the treasure location. In Sea Walls, this is because the mean is unduly influenced by values in the long tail of the distribution. In this context, the median works better than the mean. In Treasure or Not, it is because when there is no treasure, the mean or median tells you nothing; when there are two treasures, you get a bimodal distribution and so the overall mean or median again is useless.
Activity: Rat Shortage
Given the opportunity to control the number of rats they send down, most students initially send down too few and thus do poorly. After several minutes of play, they discover that they need larger sample sizes to reliably capture the treasure. This sets the stage for an exploration of how the mean (and median) stabilize as a sample gets larger, one of the main ideas of the Law of Large Numbers.
Teacher Facilitation Guideline  pdf | Word
Handout: Pre and Post-Assessment  pdf | Word
TinkerPlots file: Mean movement.tp
Movie : Movement of the Mean
Movie : Stabilization of the Mean
TinkerPlots file: Stabilization of mean.tp
Activity: Small Hook — Deep Water
These levels build on what students have learned in the Hundred's o' Rats activity. Students come to understand that the size of the sample you need to accurately predict the treasure location is dependent on both the amount of variability in the rat readings and on the size of the hook. Student first play Small Hook where the hook is half the size as it is in other levels. In this case, most students intuit that they need a larger sample than before. But they need to send down a lot more rats then they initially think. They then play the level Deep Water where the rats have further to swim. The result is that their surface locations are more spread out than in previous levels.