| Title | Description |
|---|---|
| AZRS Probability Lab | An interactive probability simulation that compares theoretical and experimental probability. The two-dice option shows how experimental results get closer to theoretical probabilities as the number of rolls increases. |
| Two Dice Possibility Space | An interactive sample space for two dice. It shows the different combinations that can produce each sum and helps explain why some dice totals are more likely than others. |
| Expected Value | An interactive simulation that demonstrates expected value and the Law of Large Numbers. Users can change probabilities and observe how the expected value and running average change. |
| Which Spinners | An interactive simulation with two numbered spinners. It allows users to investigate the probability distribution of sums and see why some totals occur more often than others. |
| Rolling Dice | An interactive dice simulation that compares theoretical probabilities with experimental results. It shows how the experimental distribution becomes closer to the predicted distribution as more dice rolls are performed. |
| Title | Description |
|---|---|
| GeoGebra | A large collection of interactive mathematics activities covering topics such as algebra, geometry, probability, statistics, calculus, and other areas of mathematics. |
| Mathigon | A collection of interactive mathematics courses, activities, games, puzzles, and virtual manipulatives covering a variety of mathematical topics. |
| PhET Interactive Simulations | A collection of free interactive simulations for mathematics and science. The activities allow students to explore mathematical concepts through visual and interactive models. |
| NRICH Mathematics | A collection of mathematics problems, investigations, and interactive activities covering topics such as number, algebra, geometry, probability, statistics, and combinatorics. |
| Transum Mathematics | A collection of interactive mathematics activities, games, puzzles, investigations, and practice resources covering many different areas of mathematics. |
| Title | Type | Description |
|---|---|---|
| The Settlers of Catan: Using Settlement Placement Strategies in the Probability Classroom | Journal Article | An academic article that uses settlement placement in Catan to explore probability and expected value. It shows how mathematics can be used to compare different settlement locations and strategies. |
| I Analysed 47,000 Games of Catan | Video | A video that uses data from thousands of Catan games to investigate mathematical ideas related to probability, resources, settlement placement, and game strategy. |
| CATAN Game Rules | Official Game Rules | The official rules of Catan. This resource explains the dice, resource production, settlements, cities, the robber, and other game mechanics needed to understand how probability affects the game. |
| Introducing Probability Using Settlers | Educational Blog | An educational article about using Settlers of Catan to introduce probability. It connects the game's dice and resource system with mathematical ideas about probability. |
| Catan Dice Probability & Resource Yield Calculator | Interactive Calculator | An interactive calculator for exploring Catan dice probabilities and expected resource production. It can be used to compare the mathematical value of different numbers and settlement locations. |