Best for
Week 5 when students are moving from raw data into likelihood statements and need help speaking carefully about chance, risk, and uncertainty.
Mathematics • Years 7-10 • Unit 9 Week 5 uncertainty reasoning
Unit 9 Week 5 Probability Modeling
Use this worksheet to turn environmental uncertainty into reasoned probability statements. Students use evidence, assumptions, and careful language to judge how likely an event or impact is and what action should follow.
Free probability task, premium local-risk version
This version is ready to teach immediately. Te Wānanga becomes useful when you want local flood, pest, drought, or biodiversity scenarios tailored to your region or class reading level.
- Generate a simpler support version with fewer scenarios.
- Swap in local evidence or a current class monitoring dataset.
- Save an adapted Unit 9 risk-and-probability pack in My Kete.
Kaiako planning snapshot
- Use length: 30-40 minutes.
- Grouping: Pairs for estimating, individual justification writing.
- Prep: Choose environmental scenarios your class already has evidence for.
- Teaching move: Keep asking “What evidence supports that probability?” rather than accepting a number without reasoning.
- Support / stretch: Offer a vocabulary bank for support; ask students to compare two models with different assumptions for stretch.
Resources already provided
- Likelihood-estimate table
- Assumption and uncertainty prompts
- Decision-planning cards
- Kaitiakitanga reflection prompt
- Teacher-only curriculum companion
This rebuild turns the old generic maths worksheet into an environmental probability task with real judgement and context.
Ngā Whāinga Ako / Learning Intentions
- We are learning to estimate how likely an environmental event or impact is.
- We are learning to justify probability statements using evidence and assumptions.
- We are learning to make careful decisions when certainty is incomplete.
Paearu Angitu / Success Criteria
- I can estimate a probability or likelihood for more than one scenario.
- I can explain what evidence and assumptions shaped my estimate.
- I can describe what action makes sense when uncertainty remains.
Curriculum integration / Te Mātaiaho alignment
The companion page makes the mathematics fit explicit around probability estimates, uncertainty, and using evidence to communicate claims in context.
Probability helps people act before certainty arrives
Environmental decisions often happen before people have perfect information. Probability modeling helps students explain how likely something seems and what action is justified by that level of risk.
Through a mātauranga Māori lens, probability is not permission to be careless. Kaitiakitanga asks what responsible action looks like when uncertainty could still affect whenua, wai, and community wellbeing.
1. Estimate the likelihood
Use evidence from your learning to estimate how likely each scenario is.
| Environmental event or impact | Evidence you have | Likelihood word or estimate | Why did you choose that? |
|---|---|---|---|
| Heavy rain or flooding event | |||
| Drought or water shortage period | |||
| Ecosystem stress or species decline |
2. Build your model
Assumptions
What are you assuming about weather, place, timing, or data quality?
What could change the estimate?
Which missing factor could make the event more or less likely?
Best-case and worst-case
What is the safest range of possible outcomes?
Check your language
Does your wording match the evidence: possible, likely, unlikely, or almost certain?
3. Decide what action fits the risk
Action now
What should happen immediately if the risk is moderate or high?
Wait for more evidence
What would you monitor before making a bigger decision?
Kaitiakitanga check
How does care for taiao shape the decision when uncertainty remains?
Final probability statement
Write one clear sentence: how likely is the event, and what should people do about it?
Ngā Whāinga Akoranga · Learning Intentions
- We are learning to use evidence from multiple sources to understand environmental change.
- We are learning to connect scientific data with mātauranga Māori observations of the taiao.
- We are learning to make informed, evidence-based decisions about environmental care.
Hononga Marautanga · Curriculum Alignment
Science — Planet Earth and Beyond
Level 3–4: investigate how the Earth's climate has changed over time; understand how human activity affects ecosystems and atmospheric systems; use evidence to evaluate claims about climate impacts on local environments and communities.
Social Sciences — Ecological Sustainability
Level 3–4: understand that environmental changes have consequences for communities and future generations; develop the ability to evaluate responses to environmental challenges and propose informed, responsible action.
Aronga Mātauranga Māori
Probability and uncertainty have always been part of traditional Māori environmental decision-making, even if they were not expressed in mathematical terms. When elders assessed whether conditions were right for fishing, they were making probabilistic judgements based on accumulated evidence — 'these signs usually mean good kahawai conditions; occasionally they are wrong; we proceed with care.' The rāhui system was itself a risk-management protocol: when uncertainty about resource health was high, the cautious action (prohibition) was taken to protect future wellbeing.
Probability modelling formalises this reasoning. You are learning to assign likelihoods to outcomes, quantify uncertainty, and use that uncertainty to inform decisions. The mātauranga Māori parallel is important: both systems recognise that we cannot know the future with certainty, and that the response to uncertainty should be guided by values — in particular, the value of protecting the taiao for future generations. Kaitiakitanga is, in this sense, a precautionary principle.
Ngā Rauemi Tautoko · Support Materials
Resources already provided:
- This handout — complete during Weeks 4–5 of the climate inquiry
- Traditional Climate Indicators (unit-9-week4-traditional-climate-indicators.html) — mātauranga Māori lens on environmental change signals
- Local Climate Impacts Worksheet (unit-9-week4-local-climate-impacts-worksheet.html) — evidence-based local impact analysis
- Integrated Forecasting (unit-9-week5-integrated-forecasting.html) — synthesis task combining scientific and mātauranga knowledge
- Probability Modeling (unit-9-week5-probability-modeling.html) — quantitative forecasting methods
- Prediction Accuracy Analysis (unit-9-week5-prediction-accuracy-analysis.html) — evaluate how accurate environmental forecasts were