Year 9 studies probability weeks 1,2,3 & 4; Year 10 studies probability in weeks 4 &5.

Vocab List: Certain, Likely, Unlikely, Impossible, Even, Chance, Probability, Distribution, Random, Variation, Odds, Strategy, Systematic Problem Solving, Theoretical, Experimental, Expected Outcome, Event, Outcome, Trial.

Wishball Observations:

• I notice the median number of turns reduced from game 1 to game 4 (11, 10, 8, 6).
  • I assume people got better at the game as they understood it more by playing it.
• Interesting: The mean does not show the improvement in scores as clearly. (10, 10.2, 9.4, 7.9).
• During period 5 on Tuesday, 9x played 92 games. The median number of turns was 8, the mean number was 9.4 turns.
  • I think the median is more reliable as it is less effected by extreme values.

Curriculum Level Probability Skills:

Level 3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.

Level 4: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. Use simple fractions and percentages to describe probabilities.

Level 5: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. Calculate probabilities, using fractions, percentages, and ratios.

Level 6: Investigate situations that involve elements of chance: comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size; calculating probabilities in discrete situations.

NZ Maths:

Students are learning about the three different types of model which can arise in chance situations.

1. Good model: An example of this is the standard theoretical model for a fair coin toss where heads and tails are equally likely with probability 1/2 each. Repeated tosses of a fair coin can be used to estimate the probabilities of heads and tails. For a fair coin we would expect these estimates to be close to the theoretical model probabilities.
2. No model: In this situation there is no obvious theoretical model, for example, a drawing pin toss. Here we can only estimate the probabilities and probability distributions via experiment. (These estimates can be used as a basis for building a theoretical model.)
3. Poor model: In some situations, however, such as spinning a coin, we might think that the obvious theoretical model was equally likely outcomes for heads and tails but estimates of the outcome probabilities from sufficiently large experiments will show that this is a surprisingly poor model. (Another example is rolling a hexagonal pencil.) There is now a need to find a better model using the estimates from the experiments.