🤔 Will It Happen?
Probability is the study of how likely something is to happen. From weather forecasts to games, probability helps us understand and predict the world around us.
📏 The Probability Scale
Probability ranges from 0 to 1
0 (Impossible)
0.5 (Even chance)
1 (Certain)
❌
Impossible (0)
Rolling a 7 on a normal dice
🤷
Unlikely
Rolling a 6
⚖️
Even (0.5)
Flipping heads
👍
Likely
Not rolling a 1
✅
Certain (1)
Sun rising tomorrow
🧮 Calculating Probability
The Formula
P(event) = Favourable outcomes / Total possible outcomes
Example: Rolling a 3
On a normal dice:
- Favourable outcomes = 1 (just the 3)
- Total outcomes = 6 (1, 2, 3, 4, 5, 6)
- P(3) = 1/6 ≈ 0.17 or about 17%
📖 Probability Language
Words We Use
- Impossible — cannot happen (0%)
- Unlikely — probably won't happen
- Even chance — 50/50
- Likely — probably will happen
- Certain — will definitely happen (100%)
📊 Types of Probability
Theoretical vs Experimental
- Theoretical — what SHOULD happen mathematically
- Experimental — what ACTUALLY happens when you try it
The more trials you do, the closer experimental gets to theoretical!
✏️ Activities
Activity: Coin Flip Experiment
- Flip a coin 20 times
- Record heads: _____ Tails: _____
- What is your experimental probability of heads?
- How does it compare to the theoretical (0.5)?
Calculate These
A bag has 3 red, 2 blue, and 5 green marbles:
- P(red) = ___
- P(blue) = ___
- P(not green) = ___
My calculations:
👩🏫 Teacher Notes
Curriculum Links
- Mathematics: Statistics — probability
Curriculum alignment
- Statistics — Knowledge: - complements / complementary event - experimental or theoretical probability - estimated probability.
- Geometry — Practices: - A map’s scale is the ratio between a distance on the map and the corresponding distance in the physical world.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop statistical investigation skills — planning inquiries, collecting and analysing data, interpreting distributions, and communicating findings. Tūhuratanga (investigation) is framed as a tool for understanding our communities and environment in Aotearoa New Zealand.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify an investigative question, collect relevant data, and display it clearly.
- ✅ Students can interpret statistical findings and discuss what they might mean for a real-world community or environmental context.
Differentiation & Inclusion
Scaffold support: Provide structured investigation frameworks (PPDAC cycle templates) for entry-level access. Offer partially completed data tables for students who need additional support. Extend capable learners by asking them to critique a statistical claim from a news article, or to design their own community data investigation.
ELL / ESOL: Pre-teach statistical vocabulary (median, mode, range, distribution, sample, population). Pair visual representations (graphs, tables) with plain-language explanations. Allow students to discuss statistical ideas orally before writing. Encourage use of home language for initial sensemaking.
Inclusion: Statistical investigation offers natural differentiation — all students can engage with the same real-world question at different levels of mathematical complexity. Neurodiverse learners benefit from structured, step-by-step investigation processes. Use collaborative group investigation formats that distribute roles (data collector, recorder, analyst, presenter).
Mātauranga Māori lens: Tūhuratanga — the practice of careful investigation — resonates deeply with mātauranga Māori. The maramataka is a sophisticated data system: tracking environmental patterns, seasonal cycles, and ecological indicators over generations. Iwi environmental monitoring — counting kaimoana populations, tracking water quality, observing bird migrations — is applied statistical thinking. Framing statistics within community and environmental inquiry connects data to mana whenua responsibilities.
Prior knowledge: Students should have basic familiarity with data displays (bar graphs, dot plots). No prior statistical investigation experience required — the PPDAC inquiry cycle provides accessible scaffolding for first-time investigators.
Curriculum alignment
- Statistics — Statistical Investigation: Plan and conduct investigations using the statistical enquiry cycle — determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate display.
- Statistics — Probability: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging uncertainty.