Best for
Probability, experimental chance, decision-making, and culturally grounded maths discussions where students need help separating exact chance from contextual pattern judgement.
Pāngarau integration • Chance, patterns, and judgement • Years 7-10 • Ready to use tomorrow
Probability & Mātauranga Māori
Use this handout to help ākonga distinguish between formal probability and contextual decision-making. Mathematics helps when outcomes are clearly defined and measurable. Mātauranga Māori helps people read patterns, relationships, and signs in context. Strong reasoning knows when each lens is useful.
Free maths scaffold, premium adaptation path
This version is ready to print and teach. Te Wānanga can adapt it around a local event, sports context, maramataka-informed planning prompt, or differentiated numeracy sequence while keeping the conceptual distinction between exact chance and contextual judgement clear.
- Swap in age-appropriate event contexts or local weather-planning examples.
- Create junior support prompts or senior reasoning extensions.
- Save the adapted version and continue later in My Kete or Creation Studio.
Kaiako planning snapshot
- Use length: 35-50 minutes, depending on whether students complete the final scenario task in full.
- Grouping: Whole-class modelling first, then pairs for the tables and individual justification.
- Prep: Decide which concrete equipment or simulations students will use for the experimental chance task.
- Teaching move: Keep saying that not every real-life situation has equally likely outcomes, so formal probability and contextual judgement are related but not identical.
Resources already provided
- Probability comparison cards
- Chance-sort table
- Experimental probability table
- Context-based decision prompt
- Curriculum companion for teacher planning clarity
If the lesson mentions chance language, trials, or decision-making, those supports already exist here.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning when a situation suits formal probability and when it needs wider evidence.
- We are learning to compare theoretical and experimental probability.
- We are learning to make decisions using both numerical evidence and contextual knowledge.
Paearu Angitu / Success Criteria
- I can identify whether outcomes are equally likely or not.
- I can calculate or describe an experimental probability from trial results.
- I can explain what extra evidence matters in a real-life decision.
Curriculum integration / Te Marautanga alignment
Use the linked curriculum companion to make chance language, experimental probability, and contextualised reasoning explicit in your mathematics planning.
Important distinction
Formal probability is strongest when the possible outcomes are clear, like a fair die or coin. Reading patterns in weather, taiao, or local signs can inform decisions too, but it is not the same as assigning an exact fraction unless the event is structured that way.
Two useful reasoning lenses
Mathematical probability
- Works best with clearly defined outcomes
- Uses fractions, decimals, or percentages
- Can compare theoretical and experimental results
- Supports fair games and structured predictions
Contextual pattern judgement
- Uses observation, relationship, and accumulated experience
- Helps with decisions in complex real-world settings
- Needs careful interpretation, not false precision
- Benefits from local knowledge and multiple evidence sources
Quick formula and reminder
Probability formula
P(event) = favourable outcomes / total possible outcomes
This formula helps only when the event and its outcomes are clearly defined.
Task 1: Which events are equally likely?
| Event | Equally likely? | Why or why not? |
|---|---|---|
| Rolling a fair six-sided die | ||
| Landing on a colour on a balanced spinner | ||
| It rains tomorrow in your town | ||
| A school sports team wins its next game |
Task 2: Experimental chance
| Trial | Result | Experimental probability | How close to theoretical? |
|---|---|---|---|
| 10 trials | |||
| 25 trials | |||
| 50 trials |
Task 3: Real-life decision prompt
Scenario
Your class is deciding whether to run an outdoor event. You have a weather forecast, recent wind patterns, and local knowledge about how quickly the field becomes unsafe after rain. What evidence would you use, and why?
What numerical or forecast evidence matters most?
What contextual or local knowledge matters most?
Final decision and justification:
Support, core, and stretch pathway
Support
Use sentence starters and focus on two clearly structured events.
Core
Compare theoretical and experimental probability, then justify the scenario decision.
Stretch
Explain why an exact probability would be misleading in the real-life scenario.
Hononga Marautanga · Curriculum Alignment
Mathematics — Pāngarau
Level 3–4: Apply number operations, statistical analysis, and mathematical reasoning to solve real-world problems; represent data using appropriate tools; interpret and communicate mathematical findings clearly.
Social Sciences — Tikanga ā-Iwi
Level 3–4: Understand how mathematical data and statistics are used to describe and analyse social, economic, and environmental patterns; recognise how data can reveal or obscure inequality.
Aronga Mātauranga Māori
Mathematics has always been part of mātauranga Māori — in the navigation of Te Moana-nui-a-Kiwa, in the architectural precision of wharenui, in the sophisticated storage and accounting systems of rua kūmara, and in the patterns of kōwhaiwhai and tukutuku that encode mathematical relationships in visual form. When Māori students engage with mathematics, they are not encountering something foreign: they are meeting a domain of knowledge that their tīpuna practised with extraordinary sophistication. Framing mathematical learning through whakapapa — connecting concepts to real Māori contexts — is not "cultural add-on" but recognition of where much mathematical knowledge lives in this land.
Ngā Rauemi Tautoko · Resources already provided
- All referenced resources are provided alongside this handout in the Te Kete Ako collection.
- For related materials, use the search or browse by unit in Te Kete Ako.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will develop statistical investigation skills — tūhuratanga raraunga — through authentic data contexts drawn from Aotearoa New Zealand. Using real datasets about Māori communities, sport, environment, and society, students will learn to question, collect, analyse, and communicate statistical findings with cultural awareness and critical thinking.
Ngā Paearu Angitū — Success Criteria
- ✅ I can pose a statistical question, collect appropriate data, and display it using suitable graphs.
- ✅ I can calculate and interpret measures of centre (mean, median, mode) and spread.
- ✅ I can critically evaluate statistical claims and identify bias or misleading representations.
Differentiation & Inclusion
Scaffold support: Provide pre-structured investigation templates and graph frameworks for entry-level learners. Offer extension tasks requiring students to conduct an independent investigation on a topic of their choice, including a written analysis and critical evaluation of their own statistical process.
ELL / ESOL: Pre-teach statistics vocabulary (mean, median, mode, range, sample, population). Use visual data displays and real-world datasets students can connect to personally. Allow oral explanation of statistical reasoning before written tasks.
Inclusion: Offer calculator and digital tools access to all learners. Neurodiverse learners benefit from structured inquiry cycles, visual data displays, and real-world data that provides motivating authentic context. Ensure graph-reading activities include both visual and tabular formats.
Mātauranga Māori lens: Connect tūhuratanga (statistical inquiry) to traditional Māori practices of observation, pattern recognition, and knowledge-making through careful attention to the natural and social world. Use datasets about Māori communities, land, or environmental trends — with attention to the ethics of data sovereignty (who owns data about Māori communities and how should it be used). The maramataka itself is a sophisticated data system encoding centuries of ecological observation.
Prior knowledge: Best used after foundational number and measurement skills. Builds on Year 7 statistics exposure.
Curriculum alignment
- Mathematics — Statistics: Students investigate questions by using the statistical enquiry cycle, collecting, displaying, and analysing data to draw conclusions and communicate findings.