It’s time to put ideas about probability and uncertainty at the centre of learning about patterns and relationships in data. We’ll explore a range of activities where students create and explore chance situations. You will think about structuring randomness, stability in distributions, your modelling assumptions, fairness, “what if?” scenarios and good old proportional reasoning. We will use technology to aid our understanding about how random events behave and help us see the chance in data. We have the technology and it’s time to realise its full potential in the classroom.

The team for this session was: Anne Patel (al.blundell@auckland.ac.nz), Stephanie Budgett, Katalina Ma, Amy Renelle, Lorraine O’Carroll, Helen Teal, Aaron Webb, Liam Smyth, Emma Lehrke

There are four probability modelling activities in this session.

**The first activity** (CS1: Protecting your password) introduces learners to the CODAP technology, by building a model that explores random selecting three equally likely outcomes (with replacement), then altering the outcomes and number of outcomes in their model they can visualize and explore both uniform and non-uniform distributions.

The key points were to think about these observable teaching moments when visualizing randomness using a model:

- What does the chance distribution look like?
- How many possible outcomes are there?
- Explore the number of trials needed to be confident all possible outcomes (sample space) appear.
- Where, why/how much variation is there in chance distributions?
- After how many trials is it possible to visualise stabilised global features of the distribution?

**The second modelling activity** (CS2: Penalty shootout) investigates using an estimate of a realistic chance situation (event) to explore the likelihood of possible outcomes for a certain number of events. We can construct a chance model of a penalty shootout situation for a given number of shots at goal. Here both the probability (real-world estimate) and the number of goals can be varied to explore how the chance distributions change.

There is also assumptions about the model that need to be considered, e.g.:

- Will the probability of scoring a goal stay the same?
- Is each event independent?

**The third modelling activity** (CS3: Which team will win?) investigates possible combinations (sample space) of joint events that do not have equally likely outcomes. Learners will build models that explore multiple events with outcomes that are not equally likely. This results in chance distributions with interesting features, that can be examined and generalisations made about the likelihoods of joint events, e.g. *Do all possible outcomes occur in a limited number of trials?*

**The fourth modelling activity** (Ask Newton) involves a mini ePPDAC cycle, putting what we have learned today altogether, by translating a real world chance situation into a model to explore relative likelihoods in chance distributions.

The chance situation (one that was posed to Sir Isaac Newton) requires learners to build three or more models to investigate what happens when throwing different numbers of fair dice. This activity involves proportional reasoning and changing relative frequencies. It ends with learners summarising their understanding of the chance situation using appropriate probabilistic language.

The slides from the workshop can be downloaded here, and recordings for each activity are given below.

The static slides from the workshop can be . ## CS1: Protecting your password

- Link to CODAP with data generator plugin: https://codap.concord.org/releases/latest/static/dg/en/cert/index.html?di=https://annafergusson.online/data_generator/